The paradox of omniscience
According to modal logic, that p is true does not entail that p is necessarily true.
1. p ? ?p
It then follows that even if knowledge that p entails that p is true it does not prima facie entail that p is necessarily true.
2. Kp ? ?p
The implication of this is that if p is not necessarily true then I can know that p is true even if it is possible that p is not true.
3. Kp (premise)
4. ¬?p (premise)
5. Kp ? ?¬p (from 3 and 4)
Given that knowledge that p entails belief that p it then follows that I could be wrong:
6. Kp ? Bp (premise)
7. Bp ? ?¬p (from 5 and 6)
We then conclude that I could be wrong even if I know everything (and assuming that some p is not necessarily true):
8. ?p: p ? Kp (premise)
9. ?p: p ? ¬?p (premise)
10. ?p: p ? Bp ? ?¬p (from 6, 8, and 9)
This strikes me as a somewhat counterintuitive conclusion.
1. p ? ?p
It then follows that even if knowledge that p entails that p is true it does not prima facie entail that p is necessarily true.
2. Kp ? ?p
The implication of this is that if p is not necessarily true then I can know that p is true even if it is possible that p is not true.
3. Kp (premise)
4. ¬?p (premise)
5. Kp ? ?¬p (from 3 and 4)
Given that knowledge that p entails belief that p it then follows that I could be wrong:
6. Kp ? Bp (premise)
7. Bp ? ?¬p (from 5 and 6)
We then conclude that I could be wrong even if I know everything (and assuming that some p is not necessarily true):
8. ?p: p ? Kp (premise)
9. ?p: p ? ¬?p (premise)
10. ?p: p ? Bp ? ?¬p (from 6, 8, and 9)
This strikes me as a somewhat counterintuitive conclusion.
Comments (326)
I'm a bit lost, which is not unusual when we get into more formal logic. I can see two possible meanings for "it ain't necessarily so," 1) it is not logically required that it must be true and 2) there is some doubt about whether it is true. I would have thought that 1 is the proper meaning. If so, then there is not contradiction between "it is true" and "it is not necessarily true."
I'm not saying that it's a contradiction? I'm just explaining that p ? ?p is not a valid inference.
Agreed. Here is where I get confused:
Quoting Michael
I assume we are operating under Justified True Belief rules. Given that, I don't think your statement is true. A true statement would be "p is true, even though it could have been otherwise."
How is the symbolic different to what I used?
Kp ? ?¬p
Sorry. I'm not very good with logical symbols. I guess I misunderstood. We can leave it at that.
Couldn't we be "wrong" about this conclusion?
Doesn't knowledge presuppose the fallibility of knowing?
Wouldn't "omniscience" consist in (1) knowing the entire set of non-truths and (2) knowing that truths belong to a subset of the set of non-truths (corollary: knowing what we do not know (contra not knowing what we do not know))?
That's what I'm suggesting. The conclusion is counterintuitive, so something is probably wrong somewhere but I can't see where.
1. ?p: Kp (premise)
2. ?p: ¬?p (premise)
3. ?p: Bp ? ?¬p (from 1 and 2)
It could be that this is a reductio ad absurdum against 1: it is logically impossible to know everything. Or it could be that all truths are necessary. Or it could be that "Bp ? ?¬p" is not the definition of "I could be wrong".
Or maybe it really is the case that its possible to be wrong even if you know everything.
It is possible that I know everything and am wrong about something
I know everything and it is possible that I am wrong about something
The former is false but the latter seems possible as the argument above shows.
I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know everything even if I am not certain about anything. In this case I have fallible omniscience.
And I think certainty is only possible if the truth is necessary, so infallible omniscience requires that all truths are necessary.
Yeah, in other words, 'knowing everything' that is true, not-true & unknowable.
Quoting Michael
I don't think knowledge entails "certainty" (Peirce-Dewey, Popper-Taleb); only logic & mathematics (i.e. tautologous syntactic transformation systems) produce "necessary truths" (Spinoza, Hume, Witty).
Is that the right parsing? If you know that p then p is true, after all, and you could not be wrong about p being true, even if p, in some other possible world, might have not been true...
That is, that p might have been false does not imply that you are wrong that p is, as things turned out, true.
The cat is indeed on the mat, you know the cat is on the mat, it is true that the cat is on the mat, you believe that the cat is on the mat, but the cat might have been elsewhere.
Exactly my thoughts. This seems to be an epistemic version of a modal scope fallacy where the possibility that not-p entails some possibility of not-p as a conjunction with knowing-that-p. But this is impossible: while p is possibly false, there are simply no worlds where p is both known and false (these worlds are contradictory, i.e. impossible).
So in virtue of knowing that p, we know that p is actually true, which is perfectly consistent with the fact that the truth of p could've been otherwise.
:up: :100:
Well, there's a difference between these two:
1. I believe p but I am wrong
2. I believe p but I could be wrong
How do we formulate these in symbolic logic? This is my attempt:
1. Bp ? ¬p
2. Bp ? ?¬p
It makes sense to me. "I believe p but I could be wrong" means "I believe p and it's possible that not p".
If not these then what?
Again, from the OP:
1. Kp (premise)
2. ¬?p (premise)
3. Kp ? ?¬p (from 1 and 2)
This is a valid argument. To deny the conclusion you must deny one of the premises.
Note that I'm not saying:
?(Kp ? ¬p)
From here:
1. It is possible that I know everything and am wrong about something
2. I know everything and it is possible that I am wrong about something
The former is false but the latter seems possible as the argument above shows.
@Rocco Rosano quoted a phrase in his first post which says: An omniscient being needs no logic and no mathematics,
It is so interesting, indeed. Trying to answer your question I guess omniscience doesn't suggest knowledge of all possible errors because it is not a logical entity. When we debate about errors inside logic we have to start with the premise that the thing is logical itself, so we conclude it makes "errors" because it doesn't fit what we consider as "logic" or "success", etc...
But omniscience cannot fit those parameters because it isn't logical since the beginning.
I agree, but I think the inevitable landing zone for all omni posits is called paradox.
I mean paradox as a purely logical proposal (or of propositional logic). Therefore we end up in the zone of neither true or false. To me this is like the measurement problem in quantum mechanics. Only when you make the measurement and the 'wave collapses,' will you get an outcome which is 'true' or 'false' this is what we call reality as far as I can project what that word refers to.
Logic comes from Plato's logos, yes? and that reference has serious religious connotations as do the omni references but to me, they just don't hold up to any definition I can hold as part of 'reality', not now, not in the past and not in the future. You can poke too many holes in the omni posits, especially when they refer to deities. If one is omniscient then how can its creation be flawed? Unless it was deliberate and therefore Christopher Hitchen's claim would be true. You were made sick and commanded to heal yourself on the threat of eternal punishment if you don't. What kind of omniscient monster would create rules like that?
Omnipotent must follow from omniscience if knowledge is power. But you land on paradox straight away with omnipotent. Can an omnipotent create something more powerful that it?
Can an omniscient create new knowledge it never knew before?
Can an omnipresence expand?
Can an omnibenevolent do evil?
They all end in paradox!
So all that can then be claimed is as you and Rocco suggests all omnis cannot be approached via logic or propositional logic to be more precise but then the omnis must be metaphysical or metalogical, 'after logic' or 'beyond logic' so does that mean we must employ a label like omnimetaphysical or omnimetascience or omnimetascient or omnisupernatural? How about omniwoowoo!
Quoting universeness
A selfish one. Or at least someone or something who makes us remember that it is over of all criteria and goes beyond to all the limitations of possibilities. Writing this answer I am acknowledging that this has no sense. I guess this is what a omnipotent looks like in the infinite universe of metaphysics or quantum mechanics.
"We", thus, their "creation" are flawed because the omnipotent entity would not create something clever and mightier than itself. But we end up in a paradox again as you perfectly explain previously.
I see a paradox here because his perfection is senseless is he pretends to elaborate just flawed creations.
Quoting universeness
:eyes: :sparkle: This one goes beyond to any category of reason!
Well, in that case, I hope I am correct. :up:
Quoting javi2541997
Its been a long time theistic claim that humans cannot approach god or understand god using human intellect or inquiry. Only belief is required and obedience. The epitome of a nefarious sociopolitical tenet, if ever there was one. I remain a fan of the Greek 'cosmos,' the universe is knowable and I refute and reject the omnis (perhaps, apart from omniwoowoo or maybe just omniwoo) and their supernatural connotations, its nothing but omniwoo!
Kp ? x knows p
Bp ? x believes p
1. Kp ? Bp (premise)
2. ?p: Kp (premise)
3. ?p: ¬?p (premise)
4. ?p: Bp ? ?¬p (from 1, 2, and 3)
I am not saying that there is anything that satisfies the second premise, I'm just looking at what would follow were there to be something that knows everything.
I would appreciate it if you could keep on topic and not discuss unrelated issues.
Ok, but could we have more lay terms please.
So does 1. translate into:
1. For all values of p, Kp (does his mean K is a function or process performed on values of p? Are you using the colon to indicate a ratio?)
2. 3p (3 multiplied by p) :(ratio?) ¬(not) ? (what does this symbol indicate?) p
3. I got bored looking up maths symbols at this stage. I know ^ means to the power of but what does B represent and what are you using the small rhombus shape for?
I taught maths to higher grade level at secondary schools before going full computing and I studied maths pure and applied up to 2nd year uni but I will be rusty to say the least. Perhaps you need someone like @jgill to answer. You would have to explain the maths symbology you use a little more for me to make any useful contribution.
I don't want to turn this discussion into a lesson on symbolic logic so I'll just refer you to these:
List of logic symbols
Modal logic
As I mentioned in the previous post (as an edit, so you may need to refresh to see it), Kp means "x knows p" and Bp means "x believes p" ("x" being some hypothetical person and "p" being some state of affairs).
Ok I see I am better to keep my Computing hat on as you are using ^ as the logical AND operator etc.
I will do my own translation and perhaps comment later if I come up with any points I have not already touched on in what I have already typed.
EDIT: Ok, thanks for the edits you made above it makes things a little clearer.
Defending my own typings, I thought I was on topic. Your title is 'The paradox of omniscience,' which I quite clearly responded to. The term omniscience strongly relates to theism and the symbology in your OP is cryptic to say the least. Are there many people on TPF with quite advanced mathematical knowledge? Do you not want to open your OP up to as many members as possible? I assume you do, based on your attempt to provide further explanation in your edits.
It really isn't. It's very basic modal logic.
Once you explain it or a person, understands it based on their own research then sure, it becomes basic, but not until then. A good teacher does not make inaccurate assumptions regarding the previous knowledge of those they are attempting to teach or even create a discussion with. Best to explain as clearly and fully as you can.
'all physical theories, their mathematical expressions apart ought to lend themselves to so simple a description 'that even a child could understand them.'
Albert Einstein.
I would apply this to your descriptions of 'basic modal logic,' if you want to encourage as wide a variety of responses as possible.
I'm not here to teach. In fact I specifically posted this to get answers from people more knowledgeable than me because, as I said, the conclusion seems counterintuitive.
That's the point of symbolic logic. Ordinary language is often vague and ambiguous and open to misunderstanding. Symbolic logic allows us to clarify our terms and better make sense of inferences.
I typed Quoting universeness
Quoting Michael
I agree, once all who can or want to contribute, understand the symbology used in the logic you are presenting. My complaint towards you is a minor one.
Tell me if I am getting anywhere with:
Kp ? x knows p
Bp ? x believes p
1. Kp ? Bp (premise)
2. ?p: Kp (premise)
3. ?p: ¬?p (premise)
Ignoring 4 for now.
1. Knowing and believing become synonymous in the case of omniscience.
2. If all knowledge is accessible then something (person/transhuman/computer) could become omniscient
3. There exists at least 1 example of omniscience that does not logically contradict itself or its own existence.
1. Knowledge entails belief. In other words, if I know p then I believe p.
2. For everything that is the case, this hypothetical person knows that it is the case. In other words, our hypothetical person is omniscient.
3. At least one thing that is the case is not necessarily the case. In other words, it is possibly not the case.
4. For at least one thing that is the case, this hypothetical person believes that it is the case and it is possibly not the case. In other words, he could be wrong.
The counterintuitive conclusion is that an omniscient being could be wrong about something.
Why would it be wrong in modal logic to state knowledge subsumes belief?
Quoting Michael
So, in general, line 2 is just a modal logic premise that it's possible for an omniscient to exist which is why you stated earlier Quoting Michael yes?
Quoting Michael
Is this not equivalent to stating that the exception does not prove the rule? Yet in the case of an omniscient it would, to me it would be like demonstrating one system only that has mass but could still travel at light speed in normal space (ie not using a worm hole of some currently sci-fi warp tech etc). You only need to climb Everest once to show it is possible.
Quoting Michael
Ok, I agree this last one is much tougher but you describe it very well. I can see the underlying paradoxical logic in play. As you say if 1, 2 and 3 are true then 4 'An omniscient can,' exist can be true.
but if your modal logic ends up in paradox then that is not good logical evidence for the existence of the omniscient, or am I missing something? Do we not end up in the same place as stating that a logical approach to omniscience is an unsuccessful one and you are left with nothing but appeals to esoteric ideas such as the supernatural?
Are you hoping that others will offer an argument that provides stronger evidence for or against the existence of omniscience based on a modal logic approach?
I thought I might try to explain my thinking on the 'exception' issue.
I was thinking about stuff like 'all snow is white,' except for some bits of snow that are not white but in general the rule holds. Some system might seem omniscient but if it's impossible to ask all possible questions then how can omniscience ever be proved?
This might be an interesting description for those who can follow this kind of symbolic logic. I can't.
However, I have something to say about the subject of this topic.
This kind of paradoxes --"The paradox of omniscience", "The paradox of omnipotence", etc.-- are well known and have been and are being discussed quite a lot in here and elsewhere.
What they all have in common is that they are not actual paradoxes because they are based on arbitrary and inexistent elements and/or facts. First we assume that there is some entity, a being, e.g. "God" --not done in this topic, but it is implied, since "omniscience" has a meaning only if it is an attribute of some entity-- then we attribute imaginary features to it --"omnipotent", "omniscient", etc.-- and then we try to prove, and we actually do, that these are impossible to exist or happen and even maybe the entity itself. In this way we create a "pseudo-paradox", a paradox with unsound foundations. From the moment that we assume the existence of an "omniscient" being, or of a concept of "omniscience", which have no foundation whatsoever, and start "building" on them, what should we expect other than a construct that will fall apart on the first blow of air?
Again, it may be a good "exercise" in modal logic to prove that there's no such a thing as omniscience, but the same process can be described using plain logic: If I say "I know everything", it means that I know every thing, i.e. "all things". But "all things" cannot be defined. They indicate a quantity and this quantity is undefinable. They also indicate a quality, which is also undefinable. What are these things? What do these things consist of? Therefore, my statement "I know everything" is empty, just air. It's just nonsense.
I am mostly with you here. Certainly, the only system that could prove a system was omniscient would have to be itself, omniscient. As only an omniscient would know all possible questions.
I am now positing a multiplicity of omniscients! What would be the point of two omniscients communicating? This is as bad as 1/0=infinity, your calculator just reports ERROR.
Yes
Quoting Michael
Prima facie, this seems ridiculous. I know Crowley's religion , Thelema, but I do not believe it. I must be missing the subtlety. I haven't read the entire thread; the symbolism seems alien which demonstrates the fact that mathematicians don't have to be logicians. We operate at a much more humble level.
Sorry, I wasnt precise. If I know that p is true then I believe that p is true.
But, is it not the same for the liars paradox or the barbers paradox? Why are they 'actual paradoxes?
I mean 'This statement is false,' is not well defined, is it? I would call this arbitrary, a self-referential statement that states it is false, but based on what?
If the barber only shaves those who do not shave themselves then who shaves the barber?
Also very arbitrary and inexistent as any real barber can shave themselves regardless of what propositional logic demands.
Kp ? x knows that p is true
Bp ? x believes that p is true
1. Kp ? Bp (premise)
2. Kp (premise)
3. ¬?p (premise)
4. Bp ? ?¬p (from 1, 2, and 3)
In ordinary language:
1. Knowing that something is true entails believing that this thing is true (premise)
2. I know that something is true (premise)
3. This thing is not necessarily true (premise)
4. I believe that this thing is true and it is possible that this thing is not true (from 1, 2, and 3)
The counterintuitive conclusion is that I could be wrong in believing that something is true even though I know that this thing is true.
I get that so if applied to omniscience this shows we land in paradox, does it not?
If it does then does this not suggest omniscience cannot be evidenced by this method so we are left with appeals to metalogic are we not?
I know that my name is Michael but it's possible that I'm wrong.
Well does that not bring us back to the other thread about absolute truths and the proposal that there are no universal absolute truths but we can get pretty close with values we might declare 'constants' such as the mass of an electron but any declared constant will not be absolutely accurate. So we might get close to omniscience or the speed of light in a vacuum but we will never reach it.
2. Kp ? ?p
Kp is knowledge that p is true. It is not knowledge of whether p is metaphysically contingent or necessary.
4. ¬?p (premise)
...this entails p is metaphysically contingent. (but does not imply you know this to be the case)
7. Bp ? ?¬p
By this stage: a) you believe p; b) p is true; and c) p is metaphysically contingent. d) you don't have a belief (or knowledge) about whether p is metaphysically necessary or contingent.
8. ?p: Kp (premise)
OK, then you now are stating that you know the truth of all propositions, this includes the proposition "p is metaphysically contingent"
9. ?p: ¬?p (premise)
Which means some propositions are metaphysically contingent.
10. ?p: Bp ? ?¬p (from 6, 8, and 9)
Which means you believe some propositions that are true, but are metaphysically contingent. Not really a problem.
So what does your analysis tell you about whether omniscience or/and absolute truths has/have existed, can exist or will exist?
My analysis of what? Of the argument? Premise 8 asserts someone is omniscient, and this contradicts no other premise.
Aside from the argument, I'd say that it seems logically possible (but not physically possible) for something to have knowledge of everything that is knowable. However, the outcome of a future metaphysically indeterminate outcome (like quantum indeterminacy) is unknowable. So it depends on how you define "omniscience".
I only value that which is physically possible. I also would not connect metaphysical indeterminacy (whatever that might mean) with quantum indeterminacy. As I suggested, omniscience belongs to musings on the supernatural but it remains true that through scientific endeavor, we will learn more in the future, than we know now.
I'm probably being slow as usual, but can all p be known? I'd have thought only the true ones could.
Do you not think this means I believe p but its possible that Im wrong?
Or consider the simplified argument here.
Edit: Ive edited that in.
Quoting Michael
The difference can be made explicit using possible worlds - but also more complex...
It's the difference between Moore's paradox and the simple admission that things may have been otherwise than they actually are.
1. I believe p but I am wrong
Suppose that in this possible world - the actual world, I believe p but I am wrong - hence ?~p.
This is of course Moore's paradox, since the speaker has contradicted themselves.
2. I believe p but I could be wrong
But suppose also that in the actual world, p, but in other possible worlds, ~p; then we have
2. (In the actual world, p and Bp) ^ (in other possible worlds, ~p)
Now I hope this parsing makes the difference clear to you , but doubtless from others there will be ensuing posts taking up irrelevant or trivial issues.
So in summary,
Quoting Michael
Might be read as "I believe p is true in the actual world, but in other possible worlds it is false" without contradiction.
I dont think thats right because when I say I believe shes 30 years old but I might be wrong Im not saying that in some alternate world she might not be 30 years old, Im saying that she might not be 30 years old in the actual world.
If it helps, think of it in the third person instead. John believes that p is true and it is possible that p is not true.
Kp is read as "x knows p", where p is a proposition or a statement. So implicitly Kp is "x knows that the statement p is true". .
When you say you know Crowley's religion, you are presumably saying that you know Crowley made certain claims, but not that you know those claims to be true.
That to know something is to believe it follows from the Theaetetus portrayal of knowledge as true belief with an account. It would be hard to justify going against this without demonstrating much misunderstanding.
Quoting Michael
Well, yes, you are saying that in some possible world here age might not be 30. The congenital problem with possible worlds is that folk over interpret them. A possible world is exactly a situation that might have been otherwise; it's just a way of talking about modality.
Note the change from "possible world" to "alternate world" in your text. Possible worlds are perhaps not alternate worlds... but thereby hang more than a few Doctoral dissertations...
Quoting Michael
Makes no difference. There is no paradox here.
Well, you can. You know that her age is 30 even if it might have been that she was 29. There's no paradox here.
A priori underlying the arguments in the thread then.
No. That's because Premise 8 states: ?p: Kp
Which means there is knowledge of p (knowledge = a belief that is true).
Consider Schroedinger's cat. You open the box, and observe the cat is alive. You KNOW the cat is alive. Therefore you BELIEVE the cat is alive.
But it could have turned out differently: the cat could have been dead. So the fact that the cat is alive is a contingent fact. This isn't a case of ignorance, it's a case of metaphysical possibility.
When I see a philosophical thread with the words Omniscient or God, I wonder what a philosopher thinks when he sees a mathematical one with the word, infinity. :chin:
When I see a philosophical thread with the words Omniscient or God, I think "that's not philosophy".
What we have here is a failure to parse stuff well. It's not too unlike those proofs that 0.9999... is not equal to 1.
The problem of scope is within your English phrasing (the worlds which we read the word 'possibly' to quantify over), not the trivial inference (Kp ? ¬?p) ? (Kp ? ?¬p), which really is just an instance of a replacement rule.
We could not be wrong about p given that we know that p when we already restricted 'could've been' on the condition of whatever is accessible from our epistemic modality (meaning that Kp is true in all accessible worlds). Kp entails p in all worlds where Kp, so p is true in all epistemically possible worlds. Had we not known that p, it could've been that ¬p, which is a trivial and uninteresting result.
If 'could've been' is just our broadest alethic modality, then Kp does not entail ?p for all contingent truths. This just means that we could've not known that p (where not-p could've been the case), not that we could've known p and been wrong about p
As you yourself suspect,
Quoting Michael
(1) and (2) are both false when the modality of 'possible' is epistemic, (2) is only true when the modality of 'possible' is alethic, or if we know that p fallibly. There's really not much more to it.
I'm not just saying that. I'm saying that she might not be 30 in the actual world. When we admit to the possibility of being wrong we're not saying "I'm actually right, but in some possible world I'm wrong". We're saying "I might actually be wrong." That's fallibilism.
Yes, that's what I said here:
Quoting Michael
Omniscience aside, if we're fallibilists then we could be wrong even if we have knowledge.
But the actual world is a possible world...
So when you say that she might be 30 in the actual world, you are saying she might be 30 in some possible world...
In any case, it's clear this line of thought is not going to help.
That's why I said "I'm not just saying that."
The point is that when I say "I believe p but I could be wrong" I'm not saying "I believe p and in the actual world I'm right and in some other possible world I'm wrong". I'm saying "I believe p and in the actual world I could be wrong".
I regret using that term now. Too many can't seem to get past it. That's why I offered this as an alternative.
Quoting Michael
That's not a good rendering of 4.
A better would be something like "I believe that in the actual worlds, p, although in other possible worlds, ~p"
And note that since your premise is now that that you know the woman is 30, you cannot conclude that you might be wrong.
The literal translation of 4 is "I believe that this thing is true and it is possible that this thing is not true" which is just what I understand "I could be wrong" means.
Because, as above, when I say "I believe p but I could be wrong" I'm not saying "I believe p and in the actual world I'm right and in some other possible world I'm wrong". I'm saying "I believe p and in the actual world I could be wrong".
It is possible that I am wrong about what is the case in the actual world. That seems to me to be the ordinary meaning of "I could be wrong".
Who you calling a neophyte? Ya neophyte!
Not about things you know - they are true.
She cant be 30 and not 30 at the same time. That's the paradox and if she is 29 then she's not 30 so how can you know she is 30 if she is 29? REAL world.
Some of the things I believe but don't know are true as well. When I say "I believe p but I could be wrong" I'm not saying "I believe p but I am wrong". And when I say "I know p but I could be wrong" I'm not saying "I know p but I am wrong".
"I could be wrong" can be true even if I'm not wrong. So that I'm not wrong if I know isn't that I can't be wrong if I know.
Can you give a real-life example or does this have to firmly stay in propositional logic?
Say about your own attributes for example. I know I am male, could I be wrong? I know I am caucasian, could I be wrong? etc.
It's better understood with belief.
1. I believe that you are a mathematician, but I could be wrong.
Even if my belief is true it is still the case that it could be false. There is a difference between "I am wrong" and "I could be wrong". I could be wrong even if I'm not wrong.
If 1 is true of a true belief then it's also true of knowledge because knowledge just is true belief (with sufficient justification).
I think the reason that this conclusion seems counterintuitive is that even if we claim to be fallibilists there is this intuitive sense that knowledge entails certainty.
I like your introduction of 'fallibility' into the discussion. Fallible, described as 'capable of making mistakes or being wrong.' Fallibility could imo be a candidate for an absolute or objective truth about humans.
I believe @jgill is a mathematician but is he the best mathematician that has ever existed in human history? I think this is the direction of play with concepts such as the omnis. I am currently convinced that we can only ever display an asymptotic approach to the omnis. If jgill was the best ever then would that mean he is not fallible in the subject of maths, he cannot make a mistake. It seems intuitive to me that for him to be omnimathematical, he must demonstrate infallibility in maths, do you agree?
Based on the discussion so far, has your opinion altered in anyway?
Your statement in the OP was:
Quoting Michael
I assumed this meant that you were undecided whether or not there was a modal logic pathway to strong/good/respectable evidence to support or refute the possibility of an existent omniscient, past, present or future. Is this accurate? and has your position altered any based on the discussion so far?
Exactly. Good point!
So, we have a closed, self-referential system, about and from which no knowledge can be obtained. As far as we are concrened, it represents an absolute "unknown". Yet, we are giving it a name it and even we define it. How can we do that, if we don't know what's in it? Well, I guess, in order to be able then to refute it! :smile: It's one of these games/tests that we create --knowingly or not-- so that we can challenge our logic. This is good. We must test and challenge our logic on a constant base!
I agree.
I like your Quoting Alkis Piskas
Do you have any philosophical musings about why we are compelled to do this, without going off thread!
You don't want to invoke the wrath of the mighty titans, labeled 'mods,' and their terrifying siren call!
We arra mods, We arra mods, We are, We are, We arra mods! :scream:
If you don't feel you can comment without going off thread then you could PM me a response if you want.
I just don't see how you're getting here.
Here's Oxford Reference...
The point is all about tense. The definition given here is in the past tense (modal) 'could have been'. Not 'still could be'.
So if p is not a necessary truth it still only means that p could have been otherwise, not that p still could be otherwise. As such one's belief that p is true, p not being a necessary truth doesn't seem to imply that p could be false, only that it could have been.
When I say "I believe that you are American but I could be wrong" I'm not saying "I believe that you are American but I am wrong" and I'm not just saying "I believe that you are American but in some other possible world I am wrong".
"I believe that you are American but I could be wrong" is true even if you are in fact an American.
There seems to be this assumption made by some that if I'm not wrong then I can't be wrong, but then via modus tollens it then follows that if I can be wrong then I am wrong. This obviously isn't right.
Yes. We all agree that beliefs could be wrong.
Quoting Michael
Again, it's just not clear how you're getting here. The "...I could be wrong" cannot be true if the proposition is it's referring to is true.
Quoting Michael
Draw that out for me...?
p ? I am wrong
q ? I can be wrong
¬p ? ¬q
? q ? p
If I'm not wrong then I can't be wrong
Therefore, if I can be wrong then I am wrong
I think the conclusion is false, therefore I think the premise is false.
Quoting Isaac
Are you saying that "I believe this but I could be wrong" is only true if I am wrong (as per the above conclusion)? Then what's the difference between "I am wrong" and "I could be wrong"?
I just wonder ... If you know that 'p' is true, why do you have also to believe it is true? What does "belief" add to it? Anyway, knowledge is stronger than belief. Beliefs are not knowledge. A belief may be an opinion, a certainly and at most a conviction. But all these are relative. They lie on a scale of of certainty: from very low to very high. Knlowledge on the other hand is not relative. It refers to something absolute or definite. "I know that this is true." That's all. (If it is true or not for you or most people, it's another story.) On the other hand, saying "I believe this is true" is quite different. I leave a window of uncertainly open, however small.
In fact, I could say that belief precedes knowledge, rather than follows it. I say, "I believe he is innocent. There's some good evidence about this." Then, when if the person is proved indeed innocent, I will know that he is.
What do you think?
(I had to look up "musings". :smile:) I don't think we can discuss this without going off thread! :grin:
Anyway, I don't know if we are compelled to do that or just "fall" into that, like in a trap. And our mind can set up a lot of traps. Esp. if we let it do that. A fallacy, a self-contradition and all kinds of mistakes of logic, occur when we give our logic a "break". When, e.g. we are too cool, or inattentive or not interested enough, etc. Not a big deal, though. As long, of course, as we are able to detect and correct these mistakes ...
Well, all these are offhand thoughts ... I was never asked such a question! :grin:
Quoting universeness
"Mods" ... It seems it's my vocabulary day ... But I wan't so lucky with this one! :smile:
Quoting universeness
I think this is a wise idea. Well, it was, because I already replied in here! :grin:)
I will PM you.
If I'm not a cat then I can't be a cat
Therefore, if I can be a cat then I am a cat.
It doesn't work no matter what.
So either you've broken modus tollens, or you've rendered it wrong. It doesn't seem to say anything specific about knowledge.
I think there's something wrong with using 'can be' as proposition to be negated...?
I understand "I can be wrong" as "it is possible that I am wrong". So:
p ? I am wrong
¬p ? ¬?p
? ?p ? p
If I am not wrong then it is not possible that I am wrong
Therefore, if it is possible that I am wrong then I am wrong
I think the conclusion is false, therefore I think the premise is false.
Which part do you disagree with? Do you think that the conclusion is true or do you think that the premise is true even though the conclusion is false?
I think the logical entailment is wrong. As per my reply...
Quoting Isaac
It doesn't seem to matter what we put into that syllogism (right term?), it seems to come out wrong.
After all...
If I'm not {right about this} then I can't be {right about this}
Therefore, if I can be {right about this} then I am {right about this}.
Because premises of that form are almost always false. You cannot go from "not p" to "not possibly p".
The only time the premise is true is when p is necessarily true.
Consider the conclusion.
?p ? p
If it is possible that I am wrong then I am wrong
Do you believe that this is false?
If I'm not a cat, I can't possibly be a cat. I could have been, but I cannot actually be at the same time as I'm not.
You conflate "it is possible that I am wrong" and "I am wrong". These two mean different things:
1. ?p (it is possible that I am wrong)
2. p (I am wrong)
And so the two similar, but different, claims are:
3. ¬p ? ?p (I am not wrong and it is possible that I am wrong)
4. ¬p ? p (I am not wrong and I am wrong)
When you say "but I cannot actually be at the same time" you are referring to 4 being false, not 3. 3 is true if ¬p is not necessarily true.
Are you saying it's possible to be x at the same time as not being x?
These are two different claims:
1. ?(¬p ? p)
2. ¬p ? ?p
Translated:
3. It it is possible that I am both not wrong and wrong
4. I am not wrong and it is possible that I am wrong
1 and 3 are false, 2 and 4 are true.
Returning back to this to explain it:
5. ?p ? p
6. If it is possible that I am wrong then I am wrong
You seem to disagree with 5 and 6. If you disagree with 5 and 6 then you accept that there is some situation where ?p is true and p is false. In other words, you accept that there is some situation where 2 and 4 are true.
I disagree. 2 and 4 are false at any given time. It is not true that something can not be the case at the same time as it is possible that it's the case. The very fact that it's not the case completely prevents it from also being the case. Since we've just established that something is categorically preventing x from being the case (the fact that it's not the case), we can't at the same time say it's possible x is the case.
Then you agree with this:
1. ?p ? p
2. If it is possible that I am wrong then I am wrong
I don't see how. Your argument for which that was the conclusion was wrong. One clearly cannot use such an argument in such cases. The example of the cat shows that.
Because you say that ?p ? ¬p can never be true. If you say that ?p ? ¬p can never be true then you say that ?p ? p is always true. If ?p ? p is always true then ?p ? p.
No. I said that ?p ? ¬p cannot be true at the same time. Your implication ?p ? p is for all times.
You don't seem to understand what "possibly" means.
Because of the law of excluded middle, this is true:
1. ?p ? (¬p ? p)
It's possible that I'm wrong and I'm either right or wrong.
This then means that for any given p, one of these is true:
2. ?p ? p
It's possible that I'm wrong and I'm wrong
3. ?p ? ¬p
It's possible that I'm wrong and I'm right
If you say that 3 is false for all p then you are saying that 2 is true for all p. If 2 is true for all p then:
4. ?p ? p
The problem here is with using modal logic terms together with knowledge. The 'possibility' of something is a measure of our uncertainty about it, so once we know x is the case, the possibility P(x)=1 which is the same as just x.
I'm not even talking about knowledge at this point.
I'm just talking about claims like "I believe that you are American but it's possible that I'm wrong". My claim is true if my belief is right and my claim is true if my belief is wrong.
I don't have any knowledge of your nationality whatsoever.
So you reject fallibilism and claim that knowledge requires certainty?
I think it is "could have been wrong" not "could be wrong" the latter is a contradiction.
It's not a contradiction.
p ? ?p
¬?p
? p ? ?¬p
p being true does not entail that p is necessarily true
p is not necessarily true
Therefore, if p is true then p is possibly false
This is a valid argument.
Necessity and possibility are defined by each other:
?p (necessarily p) is equivalent to ¬?¬p ("not possible that not-p")
?p (possibly p) is equivalent to ¬?¬p ("not necessarily not-p")
Then just look to the ordinary understanding of the words "possibly" and "necessarily" to inject some actual substance into the meaning.
I did. That it is necessary that p is true is that it is not possible that p is false.
If p is necessarily true it is not possible that p could have been false. If p is contingently true is it is not possible that p is false, but it is possible that p could have been false.
I think you should read up on modal logic. Here is how possibility and necessity are actually defined:
?p ? ¬?¬p
?p ? ¬?¬p
I thought the very basis of modal logic is that contingent truths, which cannot be false (obviously) could have been false (which means could be false in other possible worlds).
No, it's just saying something like "aliens exist" is not necessarily true and not necessarily false, therefore it's possibly true and possibly false.
But that's not different from what I'm saying. So, "aliens may or may not exist" is an epistemological, not an ontological, statement; ontologically speaking aliens either exist or they don't, and if "aliens exist" is true, then "aliens exist" cannot be false (unless conditions changed such as they became extinct), not in this world at least.
If "aliens exists" is true then "aliens exist" is not false.
"is not" does not mean "is not possibly". ¬p does not mean ¬?p.
Again, see the valid modal logic:
p ? ?p
¬?p
? p ? ?¬p
Both of these are true:
1. "aliens exist" is possible true
2. "aliens exist" is possibly false
One of these is true:
3. "aliens exist" is true
4. "aliens exist" is false
Therefore, either these three are true:
1. "aliens exist" is possible true
2. "aliens exist" is possibly false
3. "aliens exist" is true
Or these three are true:
1. "aliens exist" is possible true
2. "aliens exist" is possibly false
4. "aliens exist" is false
Again, seems as the modals are being muddled. What we can conclude is that omniscience can know everything and yet things might have been other than they are; not that the omniscience might be wrong.
There's nothing more here.
:rofl:
Right, if "aliens exist" is true then "aliens exist" is not false, and it could not possibly be false without negating "aliens exist" being true. So. as long as "aliens exist" is true then, "aliens exist" could not possibly be false.
But, in any case "aliens exist" could have been false. I think it's easier to parse this stuff in plain English, and in accordance with common usage. If modal logic yields something contrary to common usage, then there must be something wrong with the modal logic.
Possible-worlds semantics makes this all clearer:
Therefore
If you like, you can say, "There exists at least one possible world -- not this one, obviously -- in which aliens don't exist."
It is emphatically not the case that aliens existing makes it impossible that they don't exist. That would mean everything that exists exists necessarily, and every proposition that is true is true necessarily. If you want to claim specifically that, go ahead, but don't get there just by misinterpreting the now generally agreed understanding of the modal operators.
"Necessarily" always includes our world because it always includes all possible worlds. "Possibly" is explicitly non-committal on whether our world is the one described. If aliens are known to exist here, they are known to be possible; they may even be necessary, who's to say? But if you claim their existence is contingent, you're explicitly not claiming that in addition to existing here they don't exist here; you are claiming there is a possible world (maybe nearby, maybe accessible, whatever) in which they do not. Again: in that world, they do not; in this one, they still do. "Possibly not" just isn't about the facts here being different here. That rather misses the whole point.
Quoting Janus
Almost everything you say there makes sense to me, so I am not sure if you were thinking it contradicts anything I had said. I thought I had already covered the "possible world" caveat with the above.
Quoting Srap Tasmaner
That's the way I understood "necessarily" also. When you say "they (aliens) may even be necessary", though, I encounter a difficulty: I assume you can't mean logically necessary, so are you signalling that you are allowing that there may be a physical necessity that must obtain across all possible worlds, just some possible worlds or just this world?
That is about knowledge, since using 'believe' instead of 'know' is all about making it clear your level of uncertainty is greater than 0. Saying "I believe that you are American but it's possible that I'm wrong" is just a tautology. The expression "I believe..." already means (in most cases) "I could be wrong but..."
Quoting Michael
I'm trying to use your terminology here so as not to get into six discussions at once about truth, belief, and knowledge. It has been your claim that if you know something, that something is true. If you merely claim to know something, then you're saying nothing different to "I believe..." with a greater degree of confidence. In that case your conclusion is not at all counterintuitive...
Quoting Michael
It's counterintuitive only if you assume that to know something is to have certainty that that something is the case. Something cannot possibly be the both the case and not the case. therefore, it follows that once we've established that something is the case, it is not possible that it it's not the case (our uncertainty about it is 0).
Quoting Srap Tasmaner
Clarity it may have, but accuracy...?
"It is possible that..." clearly does not mean only that "There is at least one possible world in which..." otherwise we end up with silliness like my saying "It is possible that I can jump to the moon" being perfectly right.
"It is possible that..." simply reflects (in most cases) our uncertainty. We're saying that although we believe one thing, we cannot be sure it's opposite is not the case.
Which means that once we can be sure what is the case, we can eliminate the uncertainty about it. Once we are sure aliens exists, claiming it is possible that aliens don't exist is just a contradiction, we've only just established that our uncertainty about their existence is zero.
As @Janus, @Banno and I have all been arguing (I think) the matter is about what could have been, and the temporal aspect makes a difference. Here we are saying that our uncertainty about the present is low, but our uncertainty about hard determinism is higher. We know what is the case, but we're not so sure that it was pre-determined and so could never have been otherwise.
:up:
When I say that I believe that you are Australian but that it's possible that I'm wrong I'm not just saying that there is some possible world where you're not Australian and I'm wrong. I'm saying that it's possible that you're not actually Australian and I am actually wrong.
And what I say is true even if I am not wrong.
Their point is that the truth of a proposition can vary from one possible world to another while maintaining consistency.
You've had the error of your account explained several times, but you reply "Nuh, that's not it!'. You haven't understood the explanation.
But you will get it, sometime.
I don't think temporality has much to do with it.
Here it is again.
If you know the cat is on the mat in reality, then it is not possible in reality for the car to not be on the mat.
Nevertheless, one can picture a different reality in which the cat is not on the mat.
I know that the cat is on the mat, but it might have been otherwise.
There, I replaced "possible world" with "reality". Does that help?
So I am entertaining possible worlds. I'm simply explaining that this is the incorrect translation of our claims.
If you were wrong, you didn't know it.
My claim that I might actually be wrong is true even if I'm not wrong. If it's true of a true belief then, if we're fallibilists, it's also true of knowledge.
I think I was on the mark here:
Quoting Michael
And the way to make this consistent is to observer that if you know something to be the case in reality, you cannot be wrong in reality; but there might be an alternate state of affairs in which you thought you knew, but you were wrong.
If it's true of a true belief then, if we're fallibilists, it's also true of knowledge.
What?
I believe that aliens exist but I don't know that aliens exist. I claim that I might actually be wrong. My claim that I might actually be wrong is true even if aliens exist and I'm not wrong.
If you know aliens exist, then aliens exist. (if they do not, then you didn't know...)
Hence, if you know aliens exist, you cannot be wrong. Nor can you actually be wrong.
Quoting Michael
What?
What's the problem? I can't explain that any simpler than I already did.
Quoting Michael
If you actually know, you cannot actually be wrong.
(If you know in this possible world, then in this possible world you cannot be wrong)
I'm not talking about knowledge at this point. I explicitly said that I don't know that aliens exist:
I believe that aliens exist but I don't know that aliens exist.
I claim that I might actually be wrong.
My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.
I have a true belief and yet "I might actually be wrong" is true.
IF your belief is true in reality, it cannot be false, and so you could not in reality be wrong.
But even if it is true in reality, it may be wrong in some other reality, and in that reality you would be wrong.
See how introducing possible worlds keeps things coherent?
Perhaps not.
If my belief is true in reality, it isn't false, and so I am not wrong.
You're making the same mistake as others. "it isn't" doesn't mean the same thing as "it cannot". "I am not" doesn't mean the same thing as "I could not be".
Again, these three claims are true:
I believe that aliens exist but I don't know that aliens exist.
I claim that I might actually be wrong.
My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.
No, because the second is modal.
Quoting Michael
So what?
Exactly what I said above. I have a true belief and yet "I might actually be wrong" is true.
Not if it is a true belief.
Quoting Michael
See the word "actually"? It sneaks in a misplaced modal quantifier.
1. I believe that aliens exist but I don't know that aliens exist.
2. I claim that I might actually be wrong.
3. My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.
Are you now saying that the third claim is false?
Quoting Banno
I am using that word to account for what I explained here:
Incidentally your reasoning entails that everyone lies when they admit that they might be wrong. If theyre not wrong then they cant be wrong (according to your reasoning). They believe that theyre not wrong. Therefore they believe that they cant be wrong (if they accept your reasoning). When they admit that they might be wrong theyre saying something they believe to be false.
:up:
Do you think there is credence in the proposal that there WILL BE a time in the future when a human, a transhuman or a non-human system will be declared as omnimathematical and have some accompanying proof from first principles based on modal logic?
What about
Isn't that unintuitive enough?
I mean, do you want it to be true, even if you're not wrong that p?
Quoting Michael
Green zone is p ? ?¬p. Imagine the complement-donuts on the left are un-wound to make their own circles on the right.
Quoting Michael
Quoting Michael
Is it relevant that your K is an ordinary predicate not a modal operator? Sending the modal operator (or rather a corresponding extension) on the same adventure of enlargement would push back the territory of ?¬p
Try this: there are possible worlds in which she is 30, and possible worlds in which she is not; if you do not know whether she's 30, you do not know which bucket this world goes in.
To say, I know she's 30, is to say, I know this is one of the worlds in which she's 30. You can happily say I think she's 30 but maybe I'm wrong, because that's just saying, I think this is one of the worlds in which she's 30 but it might be one of the others.
But if you want to say, I know she's 30 but I might be wrong, then you're trying to say, I know this is one of the worlds in which she's 30 but I don't know if this is one of the worlds in which she's 30. That's a tough sell.
1. I believe that aliens exist but I don't know that aliens exist.
2. I claim that I might actually be wrong.
3. My claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.
This just seems to confirm that belief does not require irrefutable evidence but knowledge does.
There are possible worlds in which aliens exist and possible worlds in which they don't.
I believe this world is one in which they do, but I don't know it for a fact.
This world might be one of the ones in which aliens don't exist.
This world might, for all I know, be one of the ones in which aliens don't exist, even if it is one of the ones in which aliens exist.
The problem here is that we still have subjunctives, because we're layering the epistemic issue on top of the, let's say, metaphysical one. What we want is all indicatives, so we can quantify properly:
That looks fine. Can we also say this?
Of course. What about this?
Yes.
If the sorts of available possible worlds are clear enough, but the problem is knowing which sort this one is, then you can still analyze it as sets of possible worlds in which you're right about which sort of possible world this one is, and possible worlds in which you're wrong.
Yes, and do you accept that this is true?
To make it simpler to understand, if necessary:
1. This world might be one of the ones in which aliens don't exist
Is this true? If yes then does it entail that aliens don't exist? If no then it is true even if aliens exist
Quoting Srap Tasmaner
I'm not sure what's problematic about the sentence above. It seems straightforward to me?
If aliens don't exist in this world, then this is one of the worlds in which they don't exist, whether you know it or not. If aliens are possible, then they are possible whether you happen to be in a world where they are actual or not, and whether you know they're possible or not.
I think you're trying to ask if this world could conceivably be a different world, but that's already baked in. All the possible worlds are already there; the question for you, the epistemic question, is which one you're in.
Sure, so is the below true?
This world might be one of the ones in which aliens don't exist
If that's a way of saying, I don't know which sort of world I'm in, sure.
But if you know aliens are actual, then they are actual, and you know this is not a world where they're not.
So returning to my original wording, my claim that I might actually be wrong is true even if aliens happen to exist and I'm not wrong.
So I might actually be wrong even if I have a true belief.
Are you trying to equivocate? Why not distinguish the issue of what sort of world you happen to be in from the issue of what sort of world you think you're in?
Except you seem also to want to say that your true belief "might be" false.
The words "omniscience" and "God" are not in my vocabulary normally. Initially I would have thought that modal logic had no place in the mathematics I have known, but I see according to page views on Wiki it is popular and there is something called "multiverse set theory", so I guess I was wrong. There are now so many mathematical topics I can no longer even pretend to define what "mathematics" is.
Yes.
1. I believe that aliens exist
2. I might be wrong
These are both true.
Can I derive aliens dont exist from 2? No, because aliens can still exist even though 2 is true. It then follows that if aliens exist then I have a true belief and I might be wrong.
To deny the conclusion you must argue that you can derive aliens dont exist from the truth of 2. You must argue that if I might be wrong then I am wrong.
If aliens exist, then it follows that you are not wrong to think they do.
Not being wrong won't stop you from thinking you might be, but it quite definitely stops you from actually being wrong.
If aliens exist, neither you nor anyone else can be mistaken in thinking they exist. That possibility is blocked by them existing.
You can still think they might not all you like. You'll always be wrong, though.
I'm not saying that if aliens exist then I have a true belief and am wrong. I'm saying that if aliens exist then I have a true belief and I might be wrong.
Again, these two are true:
1. I believe that aliens exist
2. I might be wrong
One of these is true:
3. Aliens exist
4. Aliens do not exist
Therefore, either these 3 are true:
1. I believe that aliens exist
2. I might be wrong
3. Aliens exist
Or these 3 are true:
1. I believe that aliens exist
2. I might be wrong
4. Aliens do not exist
If the first set is true then I have a true belief that might be wrong.
These two are true:
1. I believe with justification that aliens exist
2. I might be wrong
One of these is true:
3. Aliens exist
4. Aliens do not exist
Therefore, either these 3 are true:
1. I believe with justification that aliens exist
2. I might be wrong
3. Aliens exist
Or these 3 are true:
1. I believe with justification that aliens exist
2. I might be wrong
4. Aliens do not exist
If the first set is true then I have knowledge that might be wrong.
To avoid the conclusion you must be an infallibilist and claim that knowledge requires certainty. In which case if I am certain that aliens exist then "I might be wrong" is false, and so I can't have knowledge that might be wrong.
I think a mistake that some fallibilists here are making is that they switch to infallibilism. They say that we don't require certainty to have knowledge but then imply that if we have knowledge then we're certain.
:smile: I know what you mean. It's hard to keep up with developments in computing science as well, which is my field of expertise.
But projecting my knowledge of computing science I cannot conceive of any system, human, transhuman or machine based that could be omniscient, regardless of any mathematical system that suggests it may be or is possible.
So if, a mathematician like you who achieved the title of professor does not think there is any mathematical pathway to omniscience, based on:
Quoting jgill
Then this adds to my skepticism regarding a modal logic path towards it.
These premises are not independent. The truth-value of (2) depends on which of (3) and (4) is true. If aliens exist, you cannot be wrong to think they do; if they don't, you cannot be wrong to think they don't.
The actual world cannot "possibly" be a different one. It simply is whichever one it is, just as all the others are. It is not a matter of which name goes on which world, because "actual" is not a name but an indexical.
Quoting Srap Tasmaner
So if I might be wrong then I am wrong?
"Possibly" in current math would be a conjecture. It would go nowhere logically by itself. "Believe" really would be nonsense in mathematics.
I think that's the converse of what I was at least trying to say.
Let's suppose aliens might not exist. Then there is at least one possible world in which they don't.
Can the possible world in which aliens do not exist be a world in which aliens exist? No.
Can it be true, in a world in which aliens do exist, that there are other worlds in which they don't?
That's the same as asking if there are worlds in which aliens don't exist. We are supposing that aliens might not exist, so by stipulation, yes, there is at least one world in which they don't, and that continues to be true even in a world in which they do.
Yes, and I think it's false, and so I think your premise is false.
When I say "I believe this but I might be wrong" I'm not saying, in a roundabout way, "I believe this but I am wrong". That I might be wrong has nothing to do with whether or not I am wrong. I'm just admitting to the possibility of being wrong (and not in Banno's "I'm actually right, but there's a possible world where I'm wrong" sense but in the "I might actually be wrong" sense). ?¬p does not entail ¬p.
I think what's happening is that you're misinterpreting "it's possible that I have a true belief that might be wrong" as something like ?(p ? Bp ? ¬p), but this symbolism actually say "it's possible that I have a true belief that is wrong" and is, of course, false. You should be interpreting it as "?(p ? Bp ? ?¬p)" which is true if ¬?p.
Michael might think he is making a modal point when he is making an epistemic one. On that basis we might interpret
Quoting Michael
as just saying that one is not certain of one's beliefs.
Trying to be charitable, that might explain why he does not recognise the modal answers to his question - it's not really a modal question.
Just a suggestion. The alternative is that he is infatuated with the muddle he has created, and doesn't want to see the answer. It happens.
Quoting Banno
That's exactly what I'm saying as I made clear here:
Quoting Michael
there, at the very start of this thread, you set the discussion up in modal terms.
While modality has been used in deontic and temporal logic I am not aware of any interpretation of modal logic in which ? is said to represent certainty.
Have you an example?
I don't think they have. I said this:
These two are true:
1. I believe that aliens exist
2. I might be wrong
One of these is true:
3. Aliens exist
4. Aliens do not exist
It is possible that these 3 are true:
1. I believe that aliens exist
2. I might be wrong
3. Aliens exist
If these three are true then I have a true belief that might be wrong.
@Srap Tasmaner's response was to say that if 3 is true then 2 is false, which entails via modus tollens that if I might be wrong then I am wrong. This is false. I believe that aliens exist but I might be wrong. It does not follow from this that aliens do not exist.
So answer me: can I be wrong?
Indeed. Sometimes one's beliefs are in error.
Either this is a valid argument:
1. I believe that aliens exist
2. I might be wrong
3. Therefore, aliens do not exist
Or it is possible that these three are all true:
1. I believe that aliens exist
2. I might be wrong
3. Aliens exist
If you believe that the first is a valid argument then I think yours is the belief in error.
"I might be wrong" here means, it is possible that aliens do not exist. That is, there is a possible world in which aliens do not exist.
If you add the further premise that aliens do exist in this world, you can draw two conclusions: (1) they are possible; (2) this is not one of the worlds in which they do not exist. That's it. If I suggested otherwise, I must have expressed myself poorly.
I should add: if you don't like my translation of (2), and would prefer it to be something like "It is possible there are no aliens here, in this world" then, in the presence of a further premise that there are or are not aliens here, this can only be understood as an epistemic possibility -- that is, as a way of saying I don't happen to know.
Again, when I say "I might be wrong" I'm not saying "I'm actually right but there's a possible world where I'm wrong". I'm saying "I might actually be wrong".
You can understand it as epistemic possibility if you like, but using the phrase "I don't happen to know" is misleading given that:
Either this is a valid argument:
1. I believe with justification that aliens exist
2. I might be wrong
3. Therefore, aliens do not exist
Or it is possible that these three are all true:
1. I believe with justification that aliens exist
2. I might be wrong
3. Aliens exist
If we accept that it is possible that all three are true then we accept that it is possible to have knowledge (a justified true belief, given by 1 and 3) that might be wrong (given by 2).
(2) breaks down into cases, right?
(2a) I'm not wrong, and aliens do exist here.
(2b) I am wrong, and aliens do not exist here.
Are both of those cases consistent with premise (3)?
No, they are not. By disjunctive inference, we are forced into the (2a) branch.
Edit: I've tried to summarise my view below so you might not need to address this comment.
Are you saying that "I might be wrong" means "I'm not wrong"? That doesn't seem to be at all consistent with ordinary use or intention. And if it were the case then this would be a valid argument:
I believe with justification that aliens exist
I might be wrong
Therefore, aliens exist
Or are you saying that "I might be wrong" means "either I'm not wrong or I'm wrong"? That would be consistent with (3), and so my claim that we can have knowledge and might be wrong is true.
But is that all it means? You and others have repeatedly rejected the claim that we can have knowledge and might be wrong, and have said that if we're not wrong then we can't be wrong, and so clearly mean by "I might be wrong" something other than "either I'm not wrong or I'm wrong".
And I wonder if this is consistent with ordinary use and intention. Do these two mean the same thing?
I believe that aliens exist but I might be wrong
I believe that aliens exist and either I'm not wrong or I'm wrong
:up: I also know of no attempts in the current AI developments where they are trying to emulate the human concept of belief. I do think that belief is strongly associated with fear, instinct and even intuition so I don't think computing science and artificial intelligence can completely ignore 'belief' if they wish to emulate human consciousness effectively but I see no place for fear, instinct, intuition or belief in mathematics. Mathematicians YES, absolutely, but mathematics, NO.
It's easy to 'model' human thought processes by substituting words like 'not,' 'and,' 'at least one example exists' with keyboard symbols such as ?, ¬ etc. It's no more than a convenient text substitution system or 'shorthand.' It seems to me that there is nothing new in modal logic language that can tackle questions such as 'The Paradox of Omniscience.'
I've tried to collect the entirety of my thoughts below. Perhaps you would clarify exactly which step you take issue with?
One of these is a valid argument, where knowledge is taken to be justified true belief:
Argument 1
I believe with justification that John is a bachelor
My belief might be wrong
Therefore, John is not a bachelor
Argument 2
I believe with justification that John is a bachelor
My belief might be wrong
John is a bachelor
Therefore, I have knowledge that might be wrong
If we accept that Argument 1 is invalid then how are we to interpret "might be wrong"? One interpretation is "is not certain", and so the argument is:
I believe with justification that John is a bachelor
My belief is not certain
John is a bachelor
Therefore, I have knowledge that is not certain
Another interpretation is "is possibly false", and so the argument is:
I believe with justification that John is a bachelor
My belief is possibly false
John is a bachelor
Therefore, I have knowledge that is possibly false
At this point it is important to understand that there is a distinction between "is false" and "is possibly false". "is possibly false" just means "is not necessarily true", and so the argument is:
I believe with justification that John is a bachelor
My belief is not necessarily true
John is a bachelor
Therefore, I have knowledge that is not necessarily true
In other words, I know that John is a bachelor and it is not necessarily true that John is a bachelor.
Nothing so far should be controversial (except to the extent that the fallibilism of the first interpretation is controversial).
However, there is some ambiguity with "is possibly false", as shown by the prima facie difference between these two claims:
a. There is a possible world where my belief is false
b. It is possible that my belief is actually false
If when I claim that my belief might be wrong I am making a claim such as (a) then the interpretation of "might be wrong" as "is not necessarily true" above is sufficient, but if I am making a claim such as (b) then something more must be said.
It may be tempting to simplify matters by saying that (b) is false if my belief is true, but then this argument would be valid:
I believe with justification that John is a bachelor
It is possible that my belief is actually false
Therefore, John is not a bachelor
If this is unacceptable then how are we to interpret (b)? Perhaps as the claim that there is a possible world where the actual world is one of the possible worlds where p? This second layer of possible world semantics is admittedly confusing. Is it coherent? If not then how are we to interpret (b)? Perhaps it is to be interpreted as "my belief is not certain" as explained above?
1. "might be wrong" means either "is not certain" or "is not necessarily true"
2. It is acceptable to say that we can have knowledge that is not certain (if we're fallibilists)
3. It is acceptable to say that we can have knowledge that is not necessarily true
4. It is unacceptable to say that we can have knowledge that might be wrong
There is a contradiction.
A partial solution is to abandon fallibilism:
1. "might be wrong" means either "is not certain" or "is not necessarily true"
2. It is unacceptable to say that we can have knowledge that is not certain
3. It is acceptable to say that we can have knowledge that is not necessarily true
4. It is unacceptable to say that we can have knowledge that might be wrong
Although if, as my gut intuition suggests, certainty is only possible if the truth is necessary, we have a complete solution:
1. "might be wrong" means either "is not certain" or "is not necessarily true"
2. It is unacceptable to say that we can have knowledge that is not certain
3. It is unacceptable to say that we can have knowledge that is not necessarily true
4. It is unacceptable to say that we can have knowledge that might be wrong
But I think that if we wish to remain fallibilists then we must reject (4) and say that it is acceptable to say that we can have knowledge that might be wrong.
It may be tempting to find a third meaning of "might be wrong" that allows us remain fallibilists without rejecting (4), but such a meaning will then entail that this is valid:
I believe with justification that John is a bachelor
My belief might be wrong
Therefore, John is not a bachelor
So K becomes a modal operator?
(Or might as well.)
E.g. Kp (or ?p) meaning not even secretly not p (or ¬?¬p).
By analogy with necessarily p meaning not even possibly not p.
Then omniscience is cool, because there are no secret errors. Green zone gone when all p are Kp (?p):
Just as you are observing that omniscience will be cool if there are no possible errors.
Either way, no error problem.
You might object: but my green zone doesn't really contain any errors. It isn't inside the not p circle. So my 'secret errors' (absent omniscience) are no such thing.
But that was my point about your 'possible' errors being unintuitive enough, already. Their being both p and possibly not p is sufficient grounds for worrying at length about relevant angles on "might be wrong". We don't need to assume that modal logic will solve the problem, though. Modality is the problem.
Quoting Michael
The ambiguity here is crippling.
Let's say there need not be aliens, but there are. That they exist is a contingent fact, not necessary, and we can know this contingent fact.
If you accept that Kp ? p, then given Kp, you "must" conclude p, by modus ponens. That "must" is a sort of necessity, but it's logical necessity; it is different from the sort of necessity that the existence of aliens lacks. (Perhaps it would be more modern only to say that you may introduce p. In place of logical necessity, we would have logical permission or logical entitlement. In epistemic lands, that might be close to "warrant" or even "justification".)
If you define knowledge that p to include a stipulation that p is true, then it is analytic that when you know that p, p is true, and that's yet another sense of "necessity", very close to logical necessity, but perhaps different, as no specific logical principle is invoked.
And of course, if you have P in hand, either as a premise, or derived, perhaps from your knowledge that P, then at that point we can apply the law of noncontradiction to deny that P is also false, and we'll usually say, P "cannot" be false, or that it cannot not be true, which is either a case of logical necessity, or the law of noncontradiction (perhaps also double negation) merely expressing the meaning of "true", "false", and "not", in which case this is analytic. Whatever.
I clarified that in the previous comment:
Quoting Michael
This entire thread has been devoted to confusing "I have knowledge of something that need not be the case" with "I have knowledge of something that may not be the case."
(sorry, deleted the previous comment)
I think our conflict is in regards to the prima facie difference between saying:
a. There is a possible world where my belief is false
b. It is possible that my belief is actually false
Given Kp ? ?¬p I trust that you accept (a) is true even if my belief is true?
But I suspect that you claim that (b) is false if my belief is true?
No one raises an eyebrow on hearing "I think there are three left, but I could be wrong," or "I'm pretty sure there are three left, but I could be wrong," or even "I'm almost certain there are three left, but I could be wrong."
But no one ever says "I know for a fact there are three left, but I could be wrong."
Why not?
I suspect because of what I said here:
But even though we don't say it, I think that this argument shows that such a claim would be true:
1. I believe with justification that John is a bachelor
2. My belief might be wrong
3. John is a bachelor
4. Therefore, my true (from 3) justified belief (from 1) might be wrong (from 2)
The issue, then, is to unpack what "might be wrong" means, which I have tried to do above.
I don't understand how you can deny the conclusion. Maybe you're equivocating and so mean something different by the "might be wrong" in "my belief might be wrong" to the "might be wrong" in "my true justified belief might be wrong"?
Unless you think, as you seemed to before, that this is valid:
I believe with justification that John is a bachelor
My belief might be wrong
Therefore, John is not a bachelor
What would render a world impossible? Are possible worlds all those which are allowed logically? If so, how does one express the possibility of one having made an error in logic?
Also on this, the entire point of Moore's paradox is that there is something that we would never say as prima facie it would be absurd even though it isn't a logical contradiction and is sometimes even true. Perhaps the same sort of thing is going on here.
What does 'logically true' mean here?
Premises 1 and 2 reflect your beliefs
Premise 3 is a statement of fact that is independent of your beliefs
This makes your conclusion (as written) a bit misleading, because it's written as if you know* #3. If you know #3, then it is not possible for you to be wrong.
*("to know x" = to justifiably believe x & x is true & not a Gettier case)
I'm not presenting any of those premises as something like personal belief-assertions. They are intended as statements of fact, as is usually the case when we make arguments like these. Would it be clearer in the third-person, and perhaps with a material implication?
One of these is valid:
Argument 1
a. Jane believes with justification that John is a bachelor
b. Jane's belief might be wrong
c. Therefore, John is not a bachelor
Argument 2
a. Jane believes with justification that John is a bachelor
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's justified true belief might be wrong
The language is misleading because there are two different modalities within the argument: epistemic and metaphysical. I think this is the source of your confusion.
The statement (a), "Jane believes with justification John is a bachelor" needs unpacking. I infer that this means: "Jane believes John is a bachelor" and that this is a categorical belief. A categorical belief doesn't express any degree of doubt at all.The fact that this belief is justified, implies that - based on her background beliefs, that she believes it is necessarily the case that John is a bachelor. This reflects epistemic necessity (a weaker modality than metaphysical).
The statement (b), "Jane's belief might be wrong" sounds equivalent to: "it is metaphysically possible that Jane's belief is false". How could she be so certain, and yet still be wrong? Because there could be additional facts she's unaware of, or because one or more of her background beliefs is false.
So....
Argument 1 is invalid. The conclusion does not follow from the premises.
Argument 2 is invalid. If John is a bachelor, then her justified belief is true - it is not metaphysically possible for it to be false.
If you disagree, I suggest rewording your arguments with clarification of the modality for each modal statement.
Argument 2
a. Jane believes with justification that John is a bachelor
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's justified true belief might be wrong
I'll rephrase it:
a. Jane believes with justification that John is a bachelor
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then a) is true and b) is true and John is a bachelor
Does the conclusion follow?
The part in bold makes no sense. (a) is the premise "Jane believes with justification that John is a bachelor". A premise is treated as true, so why make it the consequent of a conditional?
Then the other part of the conclusion is vacuous - it just repeats the antecedent of the conditional (If John is a bachelor, then John is a bachelor).
a) I am a man
b) I am British
c) Therefore, if I am 30 years old then I am a man and I am British and I am 30 years old
It makes perfect sense. It's valid.
So in this case:
a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief that John is a bachelor is justified and Jane's belief might be wrong and John is a bachelor
We can combine "Jane's belief that John is a bachelor is justified" and "John is a bachelor" to make "Jane's belief is justified and true":
a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief is justified and true and Jane's belief might be wrong
We can combine "Jane's belief is justified and true" and "Jane's belief might be wrong" to make "Jane's belief is justified and true and might be wrong":
a. Jane's belief that John is a bachelor is justified
b. Jane's belief might be wrong
c. Therefore, if John is a bachelor then Jane's belief is justified and true and might be wrong
Initially, I was trying to help you understand the modal scope issues that were present. I suspected you were confused about this, so was trying to politely help. Sorry if I offended you.
The issue is what to make of arguments that go like this:
1. P.
2. (1) might be wrong.
...
And yet the conclusion has been met with such resistance. Why is that? Perhaps others are equivocating and reading something into the "might be wrong" in the conclusion that isn't read into the "might be wrong" in the premise.
And if it's "vacuously" true that Jane's knowledge might be wrong then it seems worthy of posting to me, but to each their own.
Quoting Srap Tasmaner
Not quite, as it's not asserting p and then asserting that p might be wrong. It's asserting that there is this belief and then asserting that this belief might be wrong (which is not the same as saying that that there is this belief might be wrong, as would be suggested by your wording above).
But I do think it has to do with the meaning of "might be wrong", which is why here I addressed various interpretations and here set out the paradox in that when we translate "might be wrong" using one of these interpretations there is no issue, but when we consider it untranslated it is rejected. Why is that? As above, perhaps others are equivocating and reading something into the "might be wrong" in the conclusion that isn't read into the "might be wrong" in the premise.
Such as
(p ? ¬?p) ? ?¬p
To be fair.
Or even
1. p
2. ¬?(p)
Or
1. p
2. ¬?(1)
You would think, right? I did. But @Michael has been very clear that this is not what he means.
This says, perfectly clearly, that p holds in the actual world, and there is at least one possible world in which ~p. The second conjunct on the LHS says "p need not be true". What Michael wants is for p to "maybe" be false in the actual world, even though there's a premise that says it's true.
It's also clear that Michael wants wants p as a premise in addition to some premise along the lines of "S believes that P" because he wants to say something about true beliefs, about knowledge "possibly" being wrong. Even in recent formulations that don't have p as a premise, it's in the conclusion as a discharged assumption.
I think it turns out modal logic is not the right tool for this job and its introduction has just confused things. It may be possible to formalize the argument neatly, but it'll be in some sort of epistemic logic, and I don't know those. (That is, even less than the tiny bit I know of modal logic.)
Bob has a belief, called "Bob's belief", that it's Thursday.
Bob's belief is right if and only if it's Thursday.
Bob's belief is wrong if and only if it's not Thursday.
Argument 1
Jane's belief might actually be wrong
Therefore, Jane's belief is false
If Argument 1 is invalid then Argument 2 is valid
Argument 2
Jane's belief might actually be wrong
Therefore, if Jane's belief is true then Jane's belief might actually be wrong and Jane's belief is true
The consequent of the conclusion of Argument 2 is simply the conjunction of the premise and the antecedent, and so the meaning of "Jane's belief might actually be wrong" in the conclusion means whatever it means in the premise.
So which is valid?
The only way in which they can both be invalid is if "Jane's belief might actually be wrong" is necessarily false.
Quoting Michael
Absolutely.
(b) is a misuse of "possible" in this context, because of the "actually" there.
There are no leftover possibilities in the actual world. It is defined by which possibilities it actualizes and which it doesn't. A statement that has a different truth value from the one it has in the actual world, is a statement that belongs to and partly defines a different possible world.
I tried to work around this issue by suggesting that the epistemic dilemma can be cast as trying to figure out which sort of world the actual world is. That might work, for all I know, but I suspect it's reinventing the wheel. @Kuro seems to be much more knowledgeable about this stuff than me.
Then there's an issue with the claim "I believe p but I might be wrong".
It shouldn't be interpreted simply as "I believe p and I'm not wrong but there is some other possible world that isn't the actual world where I'm wrong".
And I don't think it should be interpreted simply as "I believe p but I'm not certain" as the claim prima facie says something about the subject matter of the belief rather than one's reasons for holding it.
So how do we make sense of such a claim?
But see this is not an argument.
If Jane's belief that P may be false in the actual world, that only says it is not necessary that P and P's truth-value is, at this point, unknown. It doesn't even get us the possibility that P in this or any world.
Quoting Michael
I believe that P but I do not know that P.
If you acknowledge right off the bat that you might be mistaken, you pre-emptively abandon the claim to know, without waiting for the evidence to decide things either way.
You might even claim to have high confidence that P, but not, as you note, certainty. That really could be treated as a different issue, because there are cognitive claims we are inclined to make even assigning low confidence, given the totality of the evidence, but swayed by some sort of salience. I'm thinking of things like "I suspect it was Billy that left the refrigerator open, but really have no idea how it happened."
It is. Its like saying Im a bachelor, therefore Im not married.
So which of arguments 1 and 2 is valid?
My legal name might be "Srap Tasmaner" but it isn't.
That's logically the same form as the conclusion to your argument 2, and it's fine, so long as we know what we're about. In a context like this, "might be" is deliberately misleading. I don't think that's what you want. You want something that expresses epistemic modesty.
I might wire you £1,000 today but I won't.
And no, it isn't, and it isn't.
I haven't read every post, but the posts I read seem due to a lack of understanding of modal logic. I explained the problem in my first post.
That first argument was a reference to your claim here. When I asked you if that meant that "I might be wrong" entails "I am wrong" you responded with "I think that's the converse of what I was at least trying to say."
If you don't like me referring to it as an "argument" then I'll call it a "sentence" and say that either it is true or Argument 2 is valid.
Quoting Srap Tasmaner
It's not "deliberately misleading" if I explicitly say "the meaning of 'Jane's belief might actually be wrong' in the conclusion means whatever it means in the premise".
If you want to say "Jane's belief might actually be wrong" in the conclusion means something like "Jane's belief might have been wrong had things been different" then you are saying that this is what it means in the premise, which I think is false.
The converse would be that "I am wrong" entails "It is possible that I am wrong", which of course is true. Actuality entails possibility. Possibility doesn't entail actuality.
As for the rest, I believe the posts you're talking about may not have been the clearest I've written, because I was still (am still!) trying to figure out what's going on here. There seems regularly to be a problem with the sense in which truth excludes falsehood -- the truth of P in W makes it "impossible" that P is false in W, but that "impossibility" is not modal, only logical. There are no available possibilities within W.
If my keys are in my pocket, they cannot not be in my pocket, can't be on the dresser or on the table, even though they only happen to be in my pocket and might not have been. See how that works?
Is any of this even related to what you want? "I might be wrong," "I could be wrong," and similar formulations are about me, about the limits of my knowledge, and my knowledge in turn is knowledge of the actual world, but if I'm wrong it's because the world is different from what I thought, not because of some counterfactual something or other.
Maybe that's putting it too strong. It's how the world is or isn't we're interested in. If you ask me to guess the next card you're going to deal and I say "ace" but it's a 2, I can truly say, "If it had been an ace, I would have been right." And there has been work on knowledge that relies on that sort of thing. I'm just not sure any of this is in the neighborhood of your interest in fallibilism.
To clarify, the context I was referring to was saying that something I know to be false "might be true," as in the example about my legal name.
Colonel Flagg joins the poker game in the swamp and sits down next to Klinger.
Flagg: Hey, up close you're a guy.
Klinger: Far away too.
I am trying to make sense of this:
Argument 1
Jane's belief might be wrong
Therefore, if Jane's belief is true then Jane's belief might be wrong
The argument is valid but the conclusion is counterintuitive despite its consequent simply being a restatement of the premise.
To understand the issue we need to understand what the premise is saying. One interpretation is:
Argument 2
There is a possible world where Jane's belief is false
Therefore, if Jane's belief is true then there is a possible world where Jane's belief is false
The conclusion is acceptable, but I think that the premise is an inaccurate interpretation of the original. The premise "Jane's belief might be wrong" isn't just saying that there is a possible world where Jane's belief is false; it's suggesting that the actual world might be such world, and so we need something like:
Argument 3
It is possible that Jane's belief is actually false
Therefore, if Jane's belief is true then it is possible that Jane's belief is actually false
I understand that this might be adding a second layer of possible world semantics, but I don't know how else to phrase it. I know that there have been attempts to make sense of modal logic without possible world semantics, so maybe that is what is needed for claims like these.
Perhaps, as you suggested, this is now an epistemic matter, and the interpretation is something like:
Argument 4
Jane's belief is not certain
Therefore, if Jane's belief is true then Jane's belief is not certain
This, at least, appears to have an acceptable premise and conclusion, although I'm not sure if it's an accurate interpretation of Argument 3.
The paradox, though, is that whereas we may be willing to accept Arguments 2 and 4, we appear unwilling to accept Argument 1 (as shown by the resistance I am getting). Why is that?
Right. This is
1. P
2. (anything at all, true or false) ? P
But, it is now "misleading" because if Jane's belief is true, its being false is no longer a real possibility in this world, only elsewhere. What's more, we only say things like "Jane's belief might be false" when we don't know whether Jane's belief is true or false, so it is very odd to take it as a consequent of Jane's belief being true.
There's also this general counterintuitiveness about unnecessary disjunctions: "Today is Thursday" entails "Today is Thursday or Caesar was a goat." Uh huh. And we have that here: "P is true, so it might be true or it might be false." (Twirls mustache.)
Quoting Michael
And it doesn't say much and it's not what you're actually interested in.
Quoting Michael
Yeah, I don't think you can or want to do that, and if you can't then you still can't say a proposition that is true in W can be false in W. It's just the way true and false work, and the whole point of introducing W as, in essence, a set of assignments of truth-values to propositions.
I get what you're going for, I do. But if Jane's belief is true, Jane's belief can only be false counterfactually. We already know how to say that, and it's "Jane's belief might have been false," or "could have been false."
Quoting Michael
Maybe I'm missing the boat, but as I indicated before I don't think we're wedded to falling back on degrees of confidence or certainty or any of that. Despite the popularity of that approach these days, my gut is that this is a different issue. What about the shy schoolboy who does in fact know what the capital of Arkansas is, but doubts himself?
Quoting Michael
Yes, 2 says nothing and is not what you want anyway. 4 is another issue, I think, though lots would disagree. 1 and 3 are what matter.
1 is fucked up in various ways that amount to abuse. 3 ends up not being what you want because the epistemic issue you were after has been swallowed up by counterfactuals. Your options are to give in and treat "might be false" as "don't know", for whatever that gets you, or try to develop 3 into something coherent about knowledge and counterfactuals. Don't reinvent the wheel though. Look at sensitivity and safety, for instance here, if you really want to throw your life away on this.
Yet something like this seems to be what we are saying when we say "I believe this but I might be wrong". We are claiming that the actual world might be other than how we believe it to be.
So if Argument 3 is invalid then either "if I might be wrong then I am wrong" is true or "I might be wrong" is necessarily false.
They can both be true, yes, but you have to be careful. If Jane's belief is true in ?, which it is by stipulation, it cannot be false in ?. If it can be false, also stipulated, it must be false in some ?, where ? ? ?. That is to say, counterfactually.
But there's a way to say this that is misleading or even abusive. The magician tells you the coin is in his left hand or in his right, even when he knows which is the case, because he intends not to inform you. I could say, "Michael, honey, I might have overdrawn our checking account," when I know perfectly well that I have, but don't quite want to admit it. *
I don't think we have much use for arguments that rely on degenerate cases like "If Caesar was a goat then today is Thursday," today being Thursday.
Quoting Michael
I have offered, I think half a dozen times, a distinction between the world being different from how we think it is and counterfactually different from how it is.
What's different about your version here is that the world might be different from how we think. And that's to say we don't know how the world is, else we would be in a position to judge whether we had been mistaken, and in a position to contemplate counterfactual worlds.
And this gets us no closer to your goal of fallibilist knowledge, so far as I can tell.
* Should have added: I know that I might have, because I've done it. Actuality entails possibility.
No, it doesn't "mean the same thing," but it might or might not be different from how I think it is implies that I do not know whether it is how I think it is.
Unless of course you're being abusive. I listen to a quiz show sometimes in which the host says things amounting to "Well the answer might be C ..." in order to get the guest to give the correct answer of C. (It's a friendly show. If it weren't, he might say something like that to trick the guest into giving the wrong answer.)
If we have actuality in hand, if we know the facts, what would motivate us to talk instead in terms of possibility? There are good and bad reasons for doing so ...
If we do not know the facts, it is obvious what our motivation for considering possibilities is.
It's the meaning of the phrase that matters here, not what its assertion implies about the speaker.
Do you at least understand the difference between "the actual world might be other than I believe it to be" and "there is a possible world that is other than how I believe the actual world to be"?
Quoting Srap Tasmaner
Then I don't understand the issue you have. If Jane's belief might be wrong and if Jane's belief is true then Jane's belief is true and might be wrong. Why do you disagree so much with this contraction?
Quoting Srap Tasmaner
Throw in justification to the above.
If Jane's belief is justified and if Jane's belief might be wrong and if Jane's belief is true then Jane's belief is justified and true and might be wrong. Again, why do you disagree so much with this contraction?
Because you have been very clear that you mean Jane's belief, which is true in the actual world, might be false in the actual world, and that's not an option. If it's true in ?, it cannot be false in ?; if it's possibly false, in addition to being true in ?, it's false counterfactually in some ? where ? ? ?.
Quoting Michael
I think I do.
For instance, there could be a possible world that is other than how I believe the actual world to be because I am wrong about how the world is, and this world is that "other" world.
The actual world is a possible world. There are possible worlds I know I don't live in, and possible worlds I can contemplate that, for all I know, are this one.
I don't understand your modality.
You are right that Jane's belief, which is true in the actual world, isn't false in the actual world, but what do you mean by saying that it can't be false in the actual world? That something isn't false isn't that it can't be false (unless it's necessarily true).
You seem to have this notion of modality that sits somewhere between p and ?p?
Then using that understanding, we have three options:
Option 1
It is possible that Jane's belief is actually false
Therefore, if Jane's belief is true then it is possible that Jane's belief is actually false
Option 2
It is possible that Jane's belief is actually false
Therefore, Jane's belief is actually false
Option 3
It is not possible that Jane's belief is actually false
Assume, for the sake of argument, that Jane's belief is "John is a bachelor".
Which option is correct? It must be one of them.
Based on what I understand of your position, you're saying that if the actual world is as Jane believes it to be then it isn't possible for the actual world to be other than Jane believes it to be?
If so then via modus tollens if it is possible for the actual world to be other than Jane believes it to be then the actual world isn't as Jane believes it to be, and so Option 2 is correct.
Only the law of of noncontradiction. It's a matter of, let's say, "logical" necessity. What is true cannot be false, even if it might have been false. No such law prevents a sentence from being both true and English, say. But by the same token an English sentence cannot be a Russian sentence.
Quoting Michael
No. If Jane's belief is actually true, it can only be counterfactually false, not actually false. It's what "counterfactual" means.
Quoting Michael
No. We do not know that Jane's belief is necessarily false, so we do not know that it is not possible that Jane's belief is actually true.
This is tricky though, and can be put a little more clearly the other way around. There are worlds in which Jane's belief is false; the actual world might be one of those worlds. "Might be" here is epistemic; it's about our knowledge of what sort of world this one is, not about what sort of world it is. There are two steps: determining what sorts of possible worlds there are, and then determining which of those we happen to live in. We simply do not have enough here to conclude that this world is the sort of world in which Jane's belief is false. The other kind of world may be possible, and this might be one of those.
(For what it's worth, the epistemic issue is forcing me to talk about possibilities that might or might not be, which is terribly uncomfortable, but I'm not sure how to get around it. I wondered aloud once before whether we could just capture the epistemic options in more sets of possible worlds, but that's more work than I feel like doing unless I have to, and I don't even know that it works. Again, very likely reinventing the wheel here, as this sort of stuff is a very hot topic today in epistemology.)
Quoting Michael
So this is not freestanding but the fallback if I reject 1 and 2.
Option 1 I have a problem with because even if JB is only contingently actually true, it cannot be actually but only counterfactually false. I am not committed to JB being necessarily true.
Option 2 tries to take the logical necessity of Option 1 and turn it into metaphysical necessity. That is, there are conditions under which I have said JB cannot be actually false (namely JB being actually true), therefore if JB can be actually false, those conditions must not be met (JB is not actually true). But JB need only be contingently actually true to block JB being actually (rather than counterfactually) false, so I am still not committed to JB being necessarily true.
If JB were necessarily true, it would not be possible for it to be actually false. Since I am not committed to JB being necessarily true, am I committed to anything else that would make it impossible for JB to be actually false? Nothing I can think of, so it's "no" to option 3 as well.
Quoting Michael
Also no.
I understand your quandary here, I think, but it's mainly down to use of modal sounding terms in different senses. The fact that whenever P is true in W, it cannot be false in W, comes right out of the definition of W, which includes P carrying a value of "true". That's just not the same thing as saying that P is true in all possible worlds; it's only saying that the worlds in which it is true are defined by its being true there, and if you need it to be false then you're in another set of worlds.
I am barely qualified to be explaining this stuff and feel like I'm on the verge of making a hash of it.
Would really appreciate it if someone more knowledgeable chimed in.
You accepted here that "Jane's belief might be false" and "Jane's belief is true" can both be true, so I don't understand your objection. Do the below two phrasings mean something fundamentally different to you? Obviously the first phrasing has as a premise the antecedent of the second phrasing's conclusion, and the second phrasing combines the second premise and the conclusion of the first phrasing into a material conditional, but the meaning of "Jane's belief might be false" is identical in every occurrence, and if one is valid then so is the other.
Phrasing 1:
Jane's belief might be false
Jane's belief is true
Therefore, Jane's belief might be false
Phrasing 2:
Jane's belief might be false
Therefore, if Jane's belief is true then Jane's belief might be false
World 1
Jane's belief might be false
Jane's belief is true
World 2
Jane's belief might be false
Jane's belief is false
I doubt either of us has been perfectly consistent about this, but I can explain what I'm thinking.
When we say "P is true," for instance, I am taking that as "P is true in the actual world." I think that's generally what's intended with an unadorned "true" or "false." When it matters, I'm saying "actually true" or "true in W," something like that.
When we say "P is possibly true," with no other restriction, I am taking that as "true in some possible world," and the set of possible worlds in which P is true may or may not include the actual world.
So, in our earlier exchange, I took "Jane's belief is true" to mean true in the actual world, and "Jane's belief might be false" to mean false in some (other) possible world. They can both clearly be true, on this reading, even though JB being actually true means the actual world is not one of the worlds in which JB is false.
Quoting Michael
Phrasing 2 is a degenerate argument in which JB's truth plays no role.
Phrasing 1 is fine because I'm reading "might be" as counterfactual. If you change that to "Jane's belief might actually be false," I'll say no.
Quoting Michael
I'd rather you be more explicit. It is absurd that in this sort of conversation we are not in every case saying "true in W" instead of unadorned "true." It would make many points much clearer.
Quoting Michael
Worlds? Not sets of worlds?
For the first, if JB is true in W1, no it cannot be false in W1. How could it be?
For the second, I'll address the bit I skipped over with W1. What exactly do you mean by "might be"? I cheated a little in W1, because the second premise allowed me to construe it as "not violating the law of noncontradiction." But really what is "might be" supposed to mean within a given world?
If you want these claims to be true within a single world, I think we have to take "might be" as indicating our epistemic position, because it makes no sense at all to count a world as its own counterfactual. Worlds are collections of facts, not possibilities. Sets of worlds represent possibilities, depending on how the facts are distributed among them.
I can continue to read W2 as I read W1, that it does not violate the law of noncontradiction for JB to be false. But these "worlds" are specified using unnecessarily ambiguous language. I wish this language were just nonsensical, but it happens that there are things we want to say that can be made to fit (the logical and epistemic issues), and that are sometimes what people mean when they talk this way. Since we know there are several different types issues in play, there's no reason for us not to be much clearer.
The skeptic claims that we might be brains in a vat. There are two different ways to interpret this claim:
1. There is a possible world where "we are brains in a vat" is true
2. It is possible that "we are brains in a vat" is true in the actual world
I think it obvious in context that they are making a claim such as 2). So with that in mind, I will rephrase the above:
World 1
a) This world might be other than Jane believes it to be
b) This world is as Jane believes it to be
World 2
a) This world might be other than Jane believes it to be
b) This world isn't as Jane believes it to be
---
Option 1
Both World 1 and World 2 are possible
Option 2
Only World 2 is possible
Option 3
Neither World 1 nor World 2 is possible
(only World 1 being possible is technically an option but I suspect we can dismiss that option outright).
3. There are possible worlds in which we are brains in vats, and we do not (or, perhaps, "cannot") know that this world is not one of those.
See how that separates the concerns you have mashed together in (2)? You must first argue that brains-in-vats worlds are possible (that it is coherent, and maybe a bunch of other stuff), and then further argue that we have and possibly can have no knowledge that our world is not one of those.
"Possibly true in W" is not nearly clear enough, not for this kind of discussion, and I'm tired of disentangling the various strands of meaning.
Not gonna address your worlds that "might be" this or that. Clarify your terminology or I'm done.
This is acceptable except your use of the word know. I think we are not certain is a better phrasing.
This is the approach I took back here:
My belief is justified
I am not certain
John is a bachelor
Therefore, I have knowledge that is not certain
And here:
The paradox, then, is that:
1. "might be wrong" means either "is not certain" or "is not necessarily true"
2. It is acceptable to say that we can have knowledge that is not certain (if we're fallibilists)
3. It is acceptable to say that we can have knowledge that is not necessarily true
4. It is unacceptable to say that we can have knowledge that might be wrong
And back on page 1:
Maybe the problem is with the interpretation of the English sentence. These two dont mean the same thing:
It is possible that I know everything and am wrong about something
I know everything and it is possible that I am wrong about something
The former is false but the latter seems possible.
I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know everything even if I am not certain about anything.
If this is the approach you want to take now then I dont understand what youve been arguing against. Perhaps a misrepresentation of my position? I made it clear, again back on page 1 that I wasnt suggesting anything like ?(Kp ? ¬p).
And I think you should have raised an eyebrow at "cannot". That would pretty much force us to start sorting worlds by our epistemic condition and then determining (1) whether worlds in which we know we're brains in vats are possible, and (2) whether worlds in which we are brains in vats but don't know it are possible, and so on and on. There is, I understand, quite a bit of literature along exactly these lines, none of which I've spent any time with.
Quoting Michael
I think that's true.
Some of what I've been saying has become clearer to me, but not to you, as we went along. Some of it is just subtle enough that I think I've expressed myself poorly at least a couple times, but I have been trying to be more precise with each post.
I think I have been mistaken, even in that last post, in how I imagined we would keep the issues of how the world is and our knowledge of it separate. I still think we should keep them separate, but it's becoming clearer to me that they are both ways of sorting and partitioning sets of worlds -- different ways, yes, but the only way forward is to treat them similarly if separately. Otherwise there are too many things I can't say without serious cheating.
As far as I can tell, and you'll correct me if I'm wrong, your position and your understanding of the issues involved has changed not at all since the OP, despite everything I and others have posted. You still appear to be baffled that anyone would disagree with anything you've posted and just post it again, as here.
If you have something new to say, I'll listen, but for now I've put as much work into this as I intend to, and I'm not going down the rabbit hole of modal conditions on knowledge without very good reason.
You and others have said things like if p is true then p cannot be false which Im not sure how to understand.
If its something like p ? ¬?¬p then its false.
If its something like if p is true then we are certain that p is true then its false.
If its something like ¬?(p ? ¬p) then its not addressing anything Im saying.
If its something else then please tell because then I honestly have no idea what youre trying to say.
It's something like ~(P & ~P). It's really that simple.
Ive never said anything to suggest otherwise which is why I dont understand the objections.
Maybe the problem is with the interpretation of the English sentence. These two dont mean the same thing:
a) It is possible that I know something and am wrong about that thing
b) I know something and it is possible that I am wrong about that thing
The former is false but the latter seems possible as the arguments show.
I suppose the latter is the implication of fallibilism. If knowledge does not require certainty then I can know and not be certain.
It seems you and others are misinterpreting my position as saying something like a).
I think on ordinary usage, b) is also false.
If I know it's raining outside then I can't be wrong that it's raining outside. Knowledge entails truth.
So consider instead a scenario where something isn't known. Suppose Alice flips a coin, observes the outcome (i.e., knows what it is) and then places her hand over the coin. She then asks Bob, who hasn't observed the outcome, whether it is heads or tails. He could reasonably say, "I don't know. It could be heads or it could be tails, with equal likelihood of either."
Bob's second sentence is true since he's not in a position to rule out either possibility or prefer one possibility to the other. One of the possibilities is the actual outcome, he just doesn't know which one that is.
Whereas for Alice, there is only one possibility - the outcome she observed.
Jane's belief might be wrong or it might be right. If Jane' s belief is right then it's not true that it might be wrong. If Jane's belief is wrong, then it is not that it merely might be wrong, but that it is in fact wrong. It is only appropriate to say a belief might be wrong, if we don't know whether it is right or wrong.
You said that if we have a justified belief it might be wrong, which is true; but a justified belief is not knowledge, since knowledge is defined as a justified true belief. It is not the case that a justified true belief might be wrong. So many pages on this thread on account of a very basic confusion; it's puzzling!
A true belief entails truth as well. I guess that it's raining outside and I might be wrong. Even if I guessed correctly. Otherwise "I might be wrong" is only true if I guessed incorrectly, i.e. if I am wrong.
So, either "I might be wrong" can be true even if I have a true belief or "I might be wrong" is only true if I have a false belief.
Quoting Janus
See above.
The first option is fine when understood as an expression of uncertainty as in, "I believe it is raining but I'm not certain". But not in the sense of, "My true beliefs could be false".
What does "could be false" mean? Either "there is a possible world where it is false" or "I am not certain that it is true". In both cases "My true belief could be false" can be true.
If you just mean that my true belief could not be both true and false then I agree, but "my true belief could be false" doesn't mean "my true belief could be both true and false".
The "could be false" in "my true belief could be false" means the same thing it does in "my belief could be false". Therefore, if "my belief could be false" being true does not entail that my belief is false then "my true belief could be false" could be true.
Either of those two senses are fine. But "My true belief could be false" is a conceptual claim. Compare "John could be married" to "Bachelor John could be married". There are possible worlds where John is married (and others where he is not). But there are no possible worlds where John is a bachelor and married.
I know, but "bachelor John could be married" doesn't mean "there is a possible world where John is a bachelor and married".
There is a difference between:
a) John is a bachelor and could be married
b) John could be a bachelor and married
a) The ball might be red.
This proposition is true whatever the colour of the ball in the box. It is true if the ball is red and it is true if the ball is blue.
If you want to say that a) is false if the ball is blue then you are saying that if the ball might be red then it is red.
If you accept that a) is true even if the ball is blue then you accept that there is a possible world where the ball is blue and a) is true; you accept that there is a possible world where the ball is blue and the ball might be red.
Yes.
Quoting Michael
No, I'm saying that it is false that "the blue ball might be red", just as it is false that "The number 2 might be odd". There's a difference between conceptual and empirical claims.
a) The ball might be red
If you accept that a) is true even if the ball is blue then you accept that there is a possible world where the ball is blue and a) is true.
And then I don't see a difference between these phrasings:
1. The ball is blue and a) is true
2. The ball is blue and the ball might be red
3. The ball is blue and might be red
4. The blue ball might be red
Do these mean different things to you, and so have different truth-conditions?
Do you think that the number 2 might be (or could be) odd?
Quoting Michael
They mean the same thing to me. But I (and I suspect most people) would interpret them as asserting a contradiction (in the conceptual sense I mentioned above). Whereas you seem to be interpreting them in a Moorean sentence sense. While such sentences can be true, no-one would ever assert them. People would either say the ball is blue (when they knew it was blue) OR say the ball might be red (when they didn't know it was blue), but not both together.
Yes, exactly that. Moore's paradox was the inspiration for this discussion.
"I believe it is raining and it is not raining" is logically consistent and possibly true, but not something we would ever assert.
"Jane's knowledge might be wrong" is logically consistent (unless knowledge requires certainty) and possibly true, but not something we would ever assert.
No, because the number 2 is necessarily even. My examples are only ever where the truth of the claim is not necessarily true. Hence in the OP:
1. Kp (premise)
2. ¬?p (premise)
3. Kp ? ?¬p (from 1 and 2)
:up:
Quoting Michael
OK, so there is a number written on a piece of paper hidden in a box. That number is either 1 or 2.
a) The number in the box might be odd.
This proposition is true whatever the number in the box. It is true if the number is 1 and it is true if the number is 2.
Would you agree or disagree with that?
But if by definition you take p, Kp and Bp to correspond to your actual world, then no contradiction arises with respect to the discrepancies with a possible world you talk about.
Quoting Michael
Not according to many people's grammar of "belief" including mine, although you appear to have company with a certain group of subjective Bayesians, who when designing an experiment insist on talking about their mental states rather than the experiment itself, much to the bemusement of any non-Bayesians present who merely wish to discuss reality.
Personally, if I am prepared to say "I believe X", then i am also prepared to assert "X" and "X is true". So according to my prescriptive usage, Moore's sentence is inconsistent. Only in the past or future tense would i invoke belief concepts.
a) the number in the box might be odd
b) the number in the box is 2
Which contracts to:
c) the number in the box is 2 and might be odd
And even:
d) the number 2 might be odd
However, 2 is necessarily even and so we have a contradiction. And even if we understand "might be" in terms of one's own certainty rather than logical possibility we have:
e) I am not certain that the number 2 is even
Which may, in fact, be false.
How do you think this is resolved? I wonder if perhaps these don't mean the same thing?
1. The ball is blue and might be red
2. The blue ball might be red
3. The number in the box is 2 and might be odd
4. The number 2 might be odd
I'm happy to reject 2 and 4.
So in terms of my original argument, I'll still commit to 5 but reject 6:
5. My belief is true and might be wrong
6. My true belief might be wrong
Seriously?
Actually, no. I think I can still accept 6. Because it means one of these two things:
1. There is a possible world where my true belief is false
2. I am not certain that my true belief is true
By recognizing that it's due to identity ignorance.
Which is to say, Alice knows that the number 2 is even, but not that the number written on the hidden piece of paper is even, even though it is 2. The difference is due to Alice not having identified the written number as 2.
Similarly, we know that blue balls are blue and true statements are true by understanding the identities involved. But Alice may not know that this particular blue ball is blue, or that this particular true statement is true because she hasn't yet identified the ball as blue or the statement as true.
a) If I know that John is a bachelor then John might not be a bachelor
This can be interpreted as:
b) If I know that John is a bachelor then there is a possible world where John is not a bachelor
c) If I know that John is a bachelor then I am not certain that John is a bachelor
Do you believe that either of (b) and (c) is false? Or do you believe that neither of these is the correct interpretation of (a)?
As far as I can tell that's a contradiction: know and wrong are mutually exclusive, oui?
Knowing and being wrong are contradictions, but knowing and possibly being wrong are not.
For example, it is possible that I am wrong in believing that you are American. It doesn't follow from this that you are not American. Therefore, it could be the case that both a) it is possible that I am wrong, and b) I am not wrong.
In my book, "possibly being wrong" is fallibilism which precludes omniscience sensu strictissimo.
Why does fallibilism preclude omniscience? Doesn't omniscience just mean knowing everything? If fallibilism is true then I can know everything even if I am not certain about anything (assuming, for the sake of argument, it is possible to know everything). Call it fallible omniscience if you like.
Or does omniscience mean knowing everything with certainty?
By logical implication, yes.
And what does certainty require? I suspect that what is true is necessarily true. In which case knowing everything with certainty (omniscience) requires that everything which is true is necessarily true. Therefore, if there is something which is true but not necessarily true then omniscience is impossible.
Empirical evidence/proof. Proof that remains irrefutable in all past/current and future scenario's is impossible, therefore omniscience is impossible as are all the omnis as are omnigods.
It's impossible that nothing is impossible. Paradox is simple impasse. It's just a logic hamster wheel.
I think you and @Srap Tasmaner should be :clap: :clap: ed and be given the TPF award for the most tenacious exchange on any thread I have read so far. I admire tenacity but I feel exhausted for both of you with 0 progress made imo.
Quoting Michael
OK, but its impossible either way because necessity is subjective and circumstantial. All possible circumstances cannot be predicted. So even if all truths were necessarily true, omniscience would still be impossible. So, we are left with the immovable object meeting the irresistible force impasse. An impossible scenario.
I think that is false.
Quoting Michael
I do. We don't doubt what we know.
p ? ?p
Therefore (b) is true if there is a possible world where John is not a bachelor.
And if fallibilism is true then knowledge does not require certainty, and so knowledge does not entail certainty. I can know and not be certain. Therefore (c) is true if I am not certain that John is a bachelor.
Just my thoughts...
Unless you can define what a deity is, and what it has in strengths and weaknesses, you cannot compare human frailties to a deity. You cannot define a deity, therefore you cannot compare it to mortal humans.
No one in this forum can define a deity.
While it s the case that man cannot change the laws of the universe, a deity, instrumental in the creation of the universe, can tweak, adjust, change or modify any law because the Supreme Being established the Laws of the Universe.
Respectfully,
R
That's normally the case with nonexistents.
Suppose reason and experience suggest to me that it is almost certain that some of what I believe is in fact false, but that I am not in a position to know which of my beliefs will turn out to have been wrong.
The conjunction of all of my beliefs is thus false, but only because at least one of them is false; the claim that I believe something false is an existential claim, and ranges over my beliefs disjunctively.
Put another way, I must believe that my beliefs taken together, in sensu composito, are false, while at the same time believing of each, in sensu diviso, that it is true, since these are after all my beliefs. If someone were to enumerate my beliefs, and question me about them one by one, at the end they would announce that I do not after all believe that one of my beliefs is false, because "my beliefs" is just the conjunction of a great many things I believe are true. This is a quandary.
A tempting approach is to say that since I believe a certain number of my beliefs are false, without knowing which ones, my attitude toward each of my beliefs should be that it might be one of the false ones. But this is problematic because a conjunction of all of these "might be false"'s leads to the conclusion that all of my beliefs might be false, which is not what I think at all. Quandary unresolved.
And the problem isn't restricted to these universal conjunctions. If I believe there is a needle in a haystack, I need not believe, of any subset of the haystack, that it contains the needle; the overwhelming majority of moderately sized "substacks" will not contain the needle. But I must at the same time believe that there is a substack that does contain the needle.
And all of this applies to facts, though I've been presenting it in terms of beliefs. Most subsets of my beliefs have conjunctions that are true, and most substacks of the haystack do not contain the needle.
We can also, in a sense, reverse our analysis: I could hold that my beliefs are generally true (de dicto) while refusing to endorse unreservedly any one of them taken individually (de re). As a matter of simplistic probability, if I figure 99% of my beliefs are true, I could say of each that the chances of it being true are 99 out of 100 and leave it at that.
Is there a way out of this?
I'm not sure. One thing that looks a bit suspicious to me is the temptation to treat our beliefs as a countable (either finite or countably infinite) set, something like a haystack that we really could examine member by member. It could be argued that in reasoning, we only deal with such finite or countably infinite sets, but I'm not sure that's true either, because reasoning always takes place within a context of quite vaguely defined background knowledge. I find the idea that beliefs could be enumerated as implausible as enumerating the real numbers. If that view is correct, the model relied on here is faulty. But I'm not certain. Despite my reservations about background knowledge, deliberate reasoning does consist in part of trying to restrict which of our beliefs are in play and which are not, so perhaps that objection misses the point, while quite rightly drawing attention to the fact that whether we reason successfully is sometimes down to whether we have properly drawn the boundary between what we include and what we exclude. (That is, have we kept out everything we should, and let in everything we should?)
There is some fuzziness in the analogies here too. If I know there is a needle in a haystack, then I know there is some subset of the haystack that contains the needle, but would I really claim to know, of any given substack, that it does or does not contain the needle? I have probability on my side, so there's justification about, but if I claim to know of each substack that it does not contain the needle, I am (1) effectively claiming there is no needle, and (2) I am wrong on at least one occasion. And here it begins to look like not so much a case of the occasion when we're wrong being unfortunate, as we usually think, as all the cases in which we were right being lucky. (Which suggests we were doing some part of the analysis backwards, that we have the wrong designated term.)
I haven't solved it yet. My real suspicion is that there is mistake in moving from "Somewhere among my beliefs there is a falsehood" to "I should think, of each of my beliefs, that it might be false." There's something wrong there, which is what motivated this ramble, but I don't have an alternative model to offer yet.
I think you're describing the lottery paradox there?
There are 1,000 tickets and one of them is a winner and you are not certain which. For each ticket n it is rational to say, given the 0.1% chance of being the winner, that ticket n is a loser.
And, of course, for each ticket one can say "it might be the winner" and "it might be a loser".
They could all be loser's ie, a rollover!
Obviously.
The usual sort of probabilistic analysis is well-known, and you can say, with enough hand waving, that there's a definition of "reasonable" in here somewhere, but that might not be true. And it's not what we were looking for.
In a sense I was suggesting that you might try to layer this probabilistic approach on top of a set of beliefs that are not themselves probabilistic (which beliefs about a lottery inherently are). I don't find that very satisfying because you are then forced into taking an attitude toward your own beliefs that inadvertently changes them. There are things I hold probabilistic beliefs about, but I don't think I must treat each of my beliefs as probabilistic because some largely unrelated beliefs are false. That's very weird. ("There's a chance that's not milk because my keys might not be in my jacket." What?)
So I'm still unhappy with the move from "Some of my beliefs are false" to "Each of my beliefs might be false." For a whole bunch of reasons, some of which have been on display in this thread.
This de dicto / de re sort of problem applies to facts as well as beliefs, which is similar to what you and @Andrew M were discussing. Drawing balls from an urn, it's fine to say "The next one might be red," but it doesn't really make sense to say of either a red or a blue ball that it might be red, even if it's the next ball. It just is or isn't.
It just is or isn't the case that aliens exist, and yet I can say "aliens might exist" and you can say "aliens might not exist" and we'd both be right. How do we make sense of what it means that things might be a certain way, given that they just are a certain way? I offered two explanations here:
a) There is a possible world where aliens (do not) exist
b) I am not certain that aliens (do not) exist
Does "aliens might (not) exist" mean something other than (a) or (b)?
And yet you resist the world's favorite choice for such a situation: "I do not know whether aliens exist," because you have an agenda. The word "might" in "Aliens might exist" describes our epistemic condition, not the state of the world.
Certainty describes our epistemic condition as well and that was one of my examples. I agree that we say "I might be wrong" when we don't know, but I don't know if "I might be wrong" means "I don't know". I think "I'm not certain" (or "it is not certain") is more accurate.
But even if we use your meaning, we still have:
a) if aliens exist then aliens might not exist
Which is intuitively false and yet possibly true.
And mixes modalities. I don't want to go through all this again.
How is it mixing modalities? You just said that "aliens might not exist" means "I do not know if aliens exist" and so the claim above is:
a) if aliens exist then I do not know if aliens exist
This claim is true. Therefore, "if aliens exist then aliens might not exist" is true.
Perhaps mixing modalities is what you and others do when you misinterpret this claim as something like "it's possible that if aliens exist then aliens do not exist", and that would explain why it's intuitively false; we intuitively misinterpret the claim.
Is it? It does not look true. What is the connection you're positing between the existence of aliens and my ignorance of that fact? An equivalent English sentence is "Aliens exist only if I don't know whether aliens exist." Does that sound remotely plausible?
What you mean is that you're taking "I don't know whether aliens exist" (P) as a premise, in which case, you can claim any conditional with P as the consequent is true, but all of them are uninformative, so this "argument" is abusive.
It's a material conditional, which is true if the consequent is true. Given that "I do not know if aliens exist" is true it then follows that "if aliens exist then I do not know if aliens exist" is true.
Quoting Srap Tasmaner
It shows that both "aliens exist" and "I do not know if aliens exist" can both be true. And so, given your definition of "might be" it shows that "aliens exist" and "aliens might not exist" can both be true.
And it's not supposed to be informative, just as Moore's paradox isn't supposed to be informative. It's just supposed to show, like Moore's paradox, that there is a claim (whether that be "if aliens exist then aliens might not exist" or "aliens exist and aliens might not exist") which is possibly true and yet intuitively contradictory.
Aliens exist
Aliens might not exist (? I do not know if aliens exist)
Therefore, aliens exist and aliens might not exist
The argument is valid (even if vacuous). The second premise is true. The first premise is possibly true. The conclusion appears to be a contradiction but it isn't, and it's possibly true.
How does it do that?
Quoting Michael
Meaning the conditional is true whether the antecedent is true or not.
So how do you think the truth of this conditional shows that the antecedent and the consequent can both be true? It would still be true even if it is necessarily false that aliens exist. What are you even talking about?
Quoting Michael
It is clearly possible for aliens to exist and for me not to know it. That's not only uncontroversial, for all I know it's true.
But what you've been chasing in this thread is me knowing aliens exist even though they might not. To get there you have to allow premise 1 to be the epistemic claim and force premise 2 to be something else.
If you've nothing new, I'm hopping off this particular hamster wheel.
Because I understand "aliens might not exist" as "I am not certain that aliens exist" as opposed to just "I do not know that aliens exist". So the argument would be:
I know that aliens exist
Aliens might not exist (? I am not certain that aliens exist)
Therefore, I know that aliens exist and aliens might not exist
Why do we say that we might be wrong? Because the evidence available to us has not proved our belief. Even if we want to say that something like 80% certainty is sufficient for our belief to count as knowledge, it seems strange to say that we could be wrong when we have 79% certainty but can't be wrong when we have 80% certainty simply because that's the somewhat arbitrary point at which our belief counts as knowledge (if it happens to be true).
I think the "can't be wrong" is only true when our belief is proved (i.e. it is 100% certain).
Yes.
Quoting Michael
I would say knowledge entails certainty. That is, when one comes to know that John is a bachelor, the alternative possibility is ruled out. From my earlier example, for Bob, the hidden coin's orientation could be heads or tails. Whereas Alice has reduced the possibilities to one - the coin's orientation that she observed.
Quoting Michael
Fallibilism means that we are capable of making mistakes, not that we might be mistaken in any particular instance. For example, we're capable of making a mistake when adding two and two. But if we conclude that the answer is four, then we can't be mistaken about that. Similarly, we can't be mistaken if we identify the blue ball as blue. To be certain means to have ruled out alternative possibilities (i.e., we don't doubt).
Suppose Alice says, "I know the ball is blue" or even just "The ball is blue". There is no indication of uncertainty there. Whereas if she says, "I think [or believe] the ball is blue" then that suggests the qualifier, "but I could be wrong".
Then knowledge requires certainty. If we are not certain that John is a bachelor then we do not know that John is a bachelor.
The argument I offered was premised on the notion that we can know things even if we are not certain, and so I accept that a rejection of that premise allows one to reject the conclusion.
Whether or not we'd want to reject that premise is another matter, but I see that you are willing.
A related question, then, is what it takes for us to be certain that something is true. My initial view is that we can only be certain that something is true if that thing is necessarily true, and so I can only be certain that John is a bachelor if it is necessarily true that John is a bachelor, although perhaps that's a matter for another discussion.
For a contingent truth q, there's a possible world in which q is false.
Is the OP getting mixed up between falsehood (in our world) and contingent truth (could be a falsehood in some other world)?
And I again think of the shy schoolboy: I'm inclined to say that he knows the right answer, even if his lack of confidence in himself leads him to doubt that he knows what he does in fact know.
Even if you're right, certainty is a necessary but not sufficient condition for knowledge. We generally believe that knowledge must be arrived at "in the right way" to count, to rule out lucky guesses. And we seem to have the very same problem with certainty. Many people are certain Trump won the 2020 election, but their certainty was arrived at in the wrong sort of way. If we still have to give an analysis of the right kind of certainty to get anywhere, will that analysis differ significantly from an account of the right way to arrive at knowledge? Maybe, but it's not clear to me.
:up:
Quoting Michael
That would be Cartesian certainty. But in ordinary language, we have at least two or three other uses:
(1) Alice was certain that she left her car keys on the table.
(2) The police ascertained the cause of the victim's death.
Per the first (psychological certainty), Alice can be mistaken and doesn't seem to require any epistemic standard. The second (epistemic certainty) entails success and requires an epistemic standard, but isn't Cartesian certainty.
For another potential use, Descartes says that moral certainty is certainty which is sufficient to regulate our behaviour, or which measures up to the certainty we have on matters relating to the conduct of life which we never normally doubt, though we know that it is possible, absolutely speaking, that they may be false (PW 1, p. 289 n. 2). SEP
Quoting Srap Tasmaner
Yes that's a good edge case. Though consider whether we would trust his answer if we didn't already know it ourselves. To me, it's like someone wobbling on their bike. Do they know how to ride, or are they about to fall off? Compare also a student who can successfully cram for an exam but soon forgets the answers, or who can parrot the right words, to someone who understands the subject and can reliably use and communicate what they know. Having knowledge seems more like the latter to me.
Quoting Srap Tasmaner
:100:
To your last comment, from the same SEP article as above:
Quoting SEP - Certainty
This is descriptive of something -- Ryle (and of course Wittgenstein) says similar things -- about how we judge another's understanding and ability. And, as you say, it does seem to capture something about understanding what you know and being able to apply it, and so on.
But it's too strict, isn't it? I can ask someone to remember a telephone number for me, and they needn't understand which part is the (American) area code, which the exchange, and so on. They needn't even know it's a telephone number or what a telephone number might be. They either know the digits by heart or they don't. As long as there's no guessing, they know it. They need to be able to recite it back to me, or to reconstruct it if they chose some odd mnemonic, so there's a still an ability-style test, but it's nothing so broad as really "getting" telephones and their numbers.
We know perfectly well that the sort of person who tends to know stuff, and the sort of procedure that tends to produce knowledge, can fail. (Hence this thread.) And we know just as well that an unreliable person who has an unreliable approach to knowledge is sometimes dead right. We might reasonably prefer the former as an approach to rationality, but we'll miss the boat on what knowledge is.
I agree. Alice can know the phone number qua a ten-digit number. But if when asked she says, "I think it's
So in that case we could say that she didn't know that she knew it. But with reflection on her (perhaps repeated) success at remembering it, she could come to know that she knows it. To relate this back to the OP, knowing everything would also require knowing that one knows in each case.
Quoting Srap Tasmaner
In the former case, when there is a failure, we just say that she didn't know it after all. So knowledge claims don't preclude that possibility. As you note, we're not infallible and our procedures aren't perfect. However, in the unreliable person's case, I would attribute that to luck and not be inclined to say they know it. Even a stopped clock displays the correct time sometimes, but it isn't connected to the world in an appropriate way.
Yes, absolutely. Someone who always thinks it's 3 o'clock will be right twice a day, but we couldn't say that they know it.
On the other hand, here's a variation on an old story, called "The Boy Who Thought Wolf": suppose our young shepherd is a nervous sort, and every time he hears a rustling in the bushes he concludes "wolf"; we note that his procedure is unreliable, and conclude that even when he's right, he doesn't know there's a wolf. Like the clock. But suppose one night a wolf comes striding out from the bushes. Now he knows there's a wolf.
We can imagine the criterion here (seeing the thing) being made into a procedure, and say that if it were a procedure it would be reliable, and so we consider this case knowledge as a sort of courtesy.
But that's all backwards. The truth is that we talk of his actual wolf encounter as a potential procedure precisely because we recognize that in this case he knows there's a wolf. Making a procedure of this just relies on what we already know to be productive of knowledge, namely, this kind of situation. The issue of process is entirely derivative.
This is the main point I was trying to defend: judging whether someone has knowledge is a very different sort of thing from judging ability and understanding, that sort of thing. Surely not completely separate! But still noticeably a different kind of thing. Knowledge can attach to discrete, one-off events in a way that many things just don't. (I've sidestepped talk of the senses, among other things, because I'm not even trying to provide some explanation or account or analysis of knowledge, just see how it works when it does. Roughly.)
Quoting Andrew M
I think, as a general matter, we should preserve both sides of the coin here, not just our fallibility -- the cases where we think we know and we're wrong about that -- but also where we have misplaced doubt, and do know something despite thinking we don't. Even forgetting and remembering has a place here: you can claim, honestly, not to know where Mike is today, and then remember that he has work -- that is, remember that you do know where he is.
Quoting Andrew M
Maybe omniscience can just keep climbing that ladder, knowing that p, knowing that you know it, knowing that you know that you know it, ad nauseam. That's a lot of of infinities though. On a model like this, omniscience might just be incoherent. Whatever.
Yes. In the case of the wolf example, the boy can be asked, "How do you know there's a wolf?" Then we can form our own judgment on the evidence.
Quoting Srap Tasmaner
Yes. For a different kind of example, consider a scientist couching an imminent risk in highly-qualified and conditional terms which the politician interprets as not needing to worry about it then. So the language use and expectations may change for different contexts.
Quoting Srap Tasmaner
Perhaps it could be tacit. If no doubt is exhibited in the use of knowledge, or the person would respond that they know something if asked, then that would count as knowing that they know.
I don't think it's a matter of doubt, just a matter of admitting fallibility. I would say that I know that my housemate is a bachelor, but I also accept that he could be lying to me and have a secret wife that he ran away from. Implausible, perhaps, but not unheard of. Does admitting of this possibility (and not just in the "there is a possible world" sense) somehow entail that I don't know that my housemate is a bachelor (assuming he isn't lying to me)? I don't think so. That I might be mistaken is simply an admission that I am not certain, not an admission of doubt.
So in such a scenario I would say that I know (and perhaps I do), but I'd also say that I might be wrong. Both claims are warranted.
I won't belabor this -- in part because I have so little else to say about it now (!) though I've already been saying something related over here, which no one found interesting except MU, who thought it was stupid.
I do want to say though that I think there's something a little funny going on in imagining judging a sort of canonical case of knowing. (Of the "Well I seen it, didn't I!" variety.) What I mean is something like this: you might take the boy's knowledge claim as inferential, and question him in order to recreate that inference and judge its soundness. So how does that go?
Why do you claim to know there's a wolf in the hills?
-- I saw him.
And how do you know that what you saw was a wolf?
-- I mean, I know what a wolf is.
What else can the boy possibly say? What's odd is the feeling that he would infer the presence of a wolf from his seeing a wolf. That makes no sense, because "see" here is used factively, just as much as "know". "I know it was a wolf because I saw it" is only useful in distinction from "I know it was a wolf because I heard it" or something like that.
I'm not saying that the senses are irrelevant, or that their "testimony" can't be scrutinized. I guess I am a little bit saying something Wittgensteiny -- that there's a point at which your spade is turned and there's nothing more to say. That point regularly involves the use of factive verbs. Either you know or you don't. Either you saw it or you didn't.
And factive verbs find use precisely on the strength of their canonical cases. Seeing something you recognize in adequate lighting conditions and in a normal state of mind counts as knowing, counts as knowing if anything does, and all the more difficult and nuanced cases we deal with (I just caught a glimpse of it, it was new moon and very dark, I had been crying, etc. etc.) are dealt with holding just this sort of case as the standard.
And counterfactual descriptions of knowledge seem to circle around the same idea. "If any of you had been there and seen what I saw, you'd be saying 'wolf' too." (And further afield: if we would judge, of anyone in such a situation, in any accessible world, that they would know there was a wolf, then you, in this situation, in the actual world, are properly said to know there's a wolf.)
I'm going to keep mulling over this "situation" business. I've always wanted to say that a key element of knowing is being in a position to know, despite the evident circularity. I might find a way to make that do some work.
Quoting Srap Tasmaner
I think that's an interesting example that gets at something quite basic about epistemic certainty being required for knowledge. If you add the condition that the person who always thinks it's 3 o clock also has a disorder which makes them see the display as 15:00, they would have the psychological certainty. they'd have a paradigm example of epistemic connection to the knowledge through their own perception (if an arbitrary person saw that, they would know), but we'd still want to reject that they know that it's 3 o-clock when it's 3 o-clock because their connection to reality itself is also evincing the claim that it's 3 o-clock by accident.
One of the issues this may create for an account regarding communal standards of epistemic certainty is that we'd still need to be able to preclude instances like the above, in which certain people would be excluded from counting as knowing things due to the facts about them precluding an appropriate access to reality (in some collection of scenarios).
You also couldn't establish the reason that their knowledge isn't knowledge if you happened to assess them at 3 o'clock using the same clock as them without other knowledge, since a non-disordered observer would be able to make claims of the same standard about the perceptual event regarding the clock. They'd both see it, they'd both be certain, the only difference is their position in the broader web of knowledge having norms.
@Andrew M
Quoting fdrake
I think that's pretty clear, and why I included "in a normal state of mind" as part of the canonical situation. Normal for who? Normal for me, with my strange disorder? More like, normal for us, really.
There are a couple of things I'm after here: one is thinking of knowledge in a rather old-fashioned way, the way we use the concept ordinarily, and the way we still teach young people, namely, that it is distinct from opinion and from guessing. I don't want to lean too hard on the way English happens to distribute its verbs, but everyday usage lumps "belief" in with opinion and friends; if knowledge shouldn't be in there, then knowledge is not some sort of super-belief, isn't at the top of an axis marked "confidence," isn't on that axis at all. And that dovetails also with the cases mentioned above, that it may very well be clearer to someone else whether I know something or not than it is to me. (See Robert Burns.) We can know that we know something, and we can have beliefs about our knowing, and these don't attach automatically to instances of knowing, so we're not automatically in a privileged position compared to others with respect to whether we know or not.
Forgetting and remembering have all kinds of cases. I can know someone's birthday and not remember it until really pushed by someone else; but I can also have really, completely, irrevocably forgotten something that someone else wants to insist I know because they learned it from me. (I expect that will become a more and more frequent experience for me, alas.)
Coming back to your issue, fdrake, I tried to gesture at another of those ordinary ideas about knowledge with my first counterfactual: if any of you had seen what I saw, then you'd know what I know. We want cases of knowledge not to be cases of gnosis! It should be accessible to almost anyone, and the knowledge I acquired, by virtue of the position I was in, is just the knowledge almost anyone would acquire. (This is a vaguely science related notion, that it shouldn't matter who makes the observation, that you can freely substitute one observer for another, so long as they follow the same procedures, that sort of thing.) But we have to say "almost" because there are things you have to know, and maybe things you have to be able to do, to acquire certain sorts of knowledge even in ideal conditions. If you don't already know what a wolf is, you won't know when you've seen one. And here again, you might report that there's something up in the hills, looked like a dog but different somehow, and someone more knowledgeable could correct that to "You saw a wolf, your first." [hide="aside"](I've actually had an experience close to this: was standing in the bay of a garage talking to the mechanic when the lizard brain jerked my head toward the back of the garage where a couple dogs were walking past the open garage door. One of them had a bit of a lope to its gait. The mechanic had seen my head jerk, so he said, "Yeah, that one's half wolf." Looked mostly like a German Shepherd, but the proportions were a little different and the way it moved was unmistakable.)[/hide]
So it turns out the canonical "situation" is not just the environment but involves quite about you, whether you have the capacity to acquire the knowledge available, whether you are receptive to it, and so on. Whether you were paying attention -- that one matters quite a bit. All of that goes into what we can't help but keep calling "being connected to reality the right way" to acquire knowledge. Or we could say that there are ways of interacting with your environment that are knowing ways and ways that aren't. Conducting surveillance is putting yourself in a position to know, and conducting experiments is creating situations where you can be in a position to know. Some of the difficulty of carrying off the acquisition of knowledge is not knowing enough to design those situations; you have only your current capacity to rely on in making the design, and if that's inadequate you might get an interesting result but not know it (the CMB story), or you might force the results to conform to your pre-existing knowledge, misinterpreting rather than simply missing the novelty.
Getting pretty far afield. I just want to capture the sense of saying something like, "Dad knows where the Easter eggs are, because he's the one who hid them," and that sense holds even if Dad forgets where he put a few of them. Similarly, "I know there's one in the flowers because I saw him put it there." These are cases of knowledge if anything is. They give the word "know" meaning. They are the sorts of cases you reach for to say what's missing when someone only has an opinion or an educated guess or a belief or a hunch about where the Easter eggs are. If Dad says, "I think I put one on the mantelpiece -- no, wait, I remember I was afraid it would roll off," that's less like switching from one belief to another and more like switching from one kind of state -- believing, opining, guessing -- to another kind altogether, knowing. You can still be wrong about whether you know, but the state you want to be in is not just a state of having different and better beliefs. That's the idea.
I think that's quite perceptive. The only contributions I have here are muddying the waters further and joining you in rambling. I agree with you that it's the case that a 'canonical situation' is required. As a tentative estimate of what a canonical situation is, I think it's an implicitly known set of context appropriate rules for generating a specific type of knowledge when it is engaged. If someone was in an such a relation to some knowledge item, they can be deemed to have known it. It is like participation in a rite.
I also think you're right with the claim that engendering a situation where something can come to be known (and what might block that situation) is a skill in itself. A kind of epistemology of contextual knowledge production, rather than one of linking statements to conditions of satisfaction through idealised argument. I might be able to design those situations for code - like finding a bug in a system I know well enough - but not others - like finding confounding variables in an experiment in neurology. I can perform some rites but not others.
In some respect, though, it doesn't matter that I can do those things, what would make the produced facts, claims, knowledge etc seems also to need to be generic and or/generalisable. You can't 'just know', even if you really truly know. The working needs to be able to be shown. I think we often take on trust that the working could be shown if needed. Like if I tell you I went to Lidl today, you'd probably take that as a fact and not even wonder if in fact I'd gone to Aldi, or even think about how I knew it was a Lidl. You can doubt whether I have performed the rite or not, but since most rites are taken on trust, you will take it on trust that I've performed the rite.
In that regard, it seems 'the collective' becomes acquainted and takes as a given a collection of rites of knowledge production, which trigger in certain contexts. You'd have no reason to doubt that I went to Lidl instead of Aldi today, unless I told you another time that I get the two confused all the time - and in that manner you'd be able to sensibly doubt that I was following the right rule of knowledge production to know I went to Lidl. I may have forgotten that I went to Aldi instead of Lidl, but I could sensibly be deemed to have known it under the trust that I had the capability to perform the appropriate rite.
Do you think something similar is going on with your dad hiding the eggs scenario? Insofar as dad performed a rite (placing the eggs) that makes him deem-able to know where the eggs are. Even if you ask him later and he forgot.
When someone justifies a knowledge claim like "I know where they are because I saw him put them there", what makes the "because" function as a justification is ultimately a (trusted) appeal to a connection between location knowledge of objects and sight of the person, which is a common rite of knowledge production regarding the location of objects.
When a person[hide=*](aside; is it necessary that a bearer of knowledge be a person? Institutions and collectives also can be deemed to have known things...[/hide] seeks to know something, I think you're right that they'll try to enter 'a state' in which they can come to know it. I think the production of that state is the successful performance of an implicitly sanctioned rite.
As an aside, I don't think the rites themselves can be true or false, only more or less accurate, more or less fit for task. It isn't like "I know where they are because I saw him put them there" has an easy parsing in terms of logic[hide=**](yet people seem to understand it without recourse to knowledge about differences between this world and the closest possible world in which causing fact didn't occur)[/hide] In that regard, the connection to reality which is ascribed to genuinely productive states of knowledge is effectively a sanctioning of that rite through (again publicly deemed) sufficient accuracy/reliability/fitness for task.
Well that's the thing. Some of what you say in your post has the feel of the "rites" (clever choice, that) underwriting knowledge production -- a bit like what Austin says about how only in specific circumstances does saying "I name this ship the Queen Mary III" make it so that the ship is now named "Queen Mary III."
But it's evident that we can judge whether a given candidate for a rite is knowledge producing. "You don't find out how many we have in the store by checking the receiving logs; you have to go and count them." What's going on there? I could claim that we are relying on a pre-existing understanding of knowledge to judge whether a rite works -- but it also looks like I'm proposing an alternative rite already known to work.
There's circularity here that leads to a bootstrapping problem. I have to know what knowledge is to know whether a rite candidate works; but all I have for an understanding of knowledge is pointing to rites known to produce it. How could I ever get from not having a rite that produces knowledge to having at least one I can use for reference? If I don't know what knowledge is, how can I possibly find out?
That bootstrapping problem infects every attempt at "explaining" knowledge -- for instance, if we take the talk of rites here as an explanation. [hide="aside"](It's why Cook Wilson said he thought the very phrase "theory of knowledge" was nonsense, and why Williamson ends up plumping for "knowledge first." --- I know only a little about these guys, so in part I'm trying to see if I can find my own path to where they end up before reading them. Some of what I'm writing has been kicking around in my head for a long time ...)[/hide]
Quoting fdrake
Now that's a biggie. For something to be a rite, we must be able to set out the steps in detail and teach those steps to the novitiate.
Is it true? It's at least true that if you follow the steps then you will acquire knowledge. But do you know because you followed the steps? Do the steps constitute knowledge acquisition? Is there maybe one step where we say, "Here, here's where the knowledge comes in"? Again, I think any such claims will be circular. How could you possibly come to know such a thing? So whatever the status of these rites, I don't think they can be an account or an explanation of knowledge.
One thing I think I'm resisting here is the suggestion (derived from Sellars) that "I know ..." is not really a factual claim at all, but an offer to defend or to justify my claim, to enter the space of reasons. In "I know X because Y," I'm not taking Y as being my justification or my warrant for claiming that X. I'm thinking of X and Y as being more intimately related than that. If I lack one justification, I might have another. You can swap out Y's. Reasons are things you can "come up with". The Y I'm interested in is not something like the basis for an inference, but more like an explication of what sense in which I'm using the word "know".
So the sense in which the steps of the rite must be capable of being made explicit, that could be that you must be able to say in what sense you meant the word "know". (Is there really more than one sense? Need to come back to that.) And since we do also make inferences based on evidence, can we tell the difference between distinguishing senses of "know" and offering justifications? "It was crowded and I didn't get a good look at him, but I heard him laugh and I'd know that laugh anywhere. He was there alright." Here's where I would start: one of the absolutely central elements of a knowledge claim like this is "I was there."
"I was there" is powerful. Imagine a vet listening to some guys at a bar, talking big about what we should have done in Vietnam or in Afghanistan. "You don't know what you're talking about," he says. "And you do? You some kind of expert?" "I was there." End of debate.
But again (and this is also, I understand, a key point for Williamson) knowing doesn't automatically mean you know that you know. (Knowing is not "luminous.") You can think you know, because you were there, but you weren't paying attention at the crucial moment, or you didn't recognize the significance of what you were seeing, and so on. We need there to be something definitive in the canonical situation, something automatic, but there are so many ways to fall short of that we have to be sensitive to.
One last bit on justification and "just knowing" without reasons. If we start from some position, with knowledge of some facts, say, and reason from there to something else we are prepared to count as knowledge, something we intend to rely upon, that's a bit like a "save point" in a video game. Calling it knowledge means precisely that you don't have to go back before that, and you can even jettison the reasons you relied on and just keep the conclusion. Knowledge of this sort is detachable from the reasons supporting it. When questioned, you have to check to see if you kept the original reasons; if you did, you have to reconstruct the inference, and if you didn't then you have to reconstruct the whole thing. Maybe it'll turn out your reasons weren't solid, or your inference was faulty. That happens. But in treating, let's just say it, such a belief as knowledge, you're in a way committed to not needing reasons for it anymore. It's a new save point you can treat as as-far-back-as-I-need-to-go.
And that could be one of those cases where we're reaching for a word, "knowledge", because the application here would have some structural similarity to its use elsewhere, even though the cases are actually different. In the situation where I know it was a wolf because I saw it, we are not making an inference and so there's no need to talk of reasons; in the case where we have made what we believe is a successful inference, we no longer seem to need the reasons (we have our save point) and so we call that "knowledge." But they're not really the same sort of thing at all. Knowledge has this strange dual nature, that it can be what you are most able or least able to defend, most willing or least willing to support with reasons.
Consider what it would take to be certain that your housemate was a bachelor. If it's never possible, then that's a Cartesian standard, not an ordinary standard. In everyday usage, "I might be wrong" qualifies the specific claim in an informative way - that there is some concrete reason why I don't want to fully endorse or commit to the claim. It's not a general claim of human fallibility - it's common knowledge that even the most careful investigations can sometimes lead to mistaken conclusions.
As SEP notes, there is generally "a reluctance to allow the contextually set standards for knowledge and certainty to diverge" (Williamson 2000, p. 254).
Here's the context for that quote:
I don't think it even needs to reach the "Cartesian" standard. It's really just the same point you made earlier (which I missed):
Quoting Andrew M
In the case of my housemate being a bachelor, I just have a greater conviction.
For sure. With the wolf example, I was distinguishing between the scenarios of the boy hearing a rustle in the bushes versus seeing the wolf. If the boy reports the latter then, yes, we should be satisfied that he knows it.
In line with what you're saying, I'd just add that Gilbert Ryle called terms like "see" achievement verbs. To see a wolf entails that there is a wolf there. (Though, of course, one could think they had seen a wolf, but be mistaken.)
:up:
I particularly like the bolded bit. If I understand what you're saying right, we clearly have a somewhat generic ability to assess whether a given rite is appropriate for producing a given item of knowledge. You gotta count to get the number, you don't check the acquired stock.
You gotta follow the bug back from what's producing it, not start somewhere random. You check if the shirt button is sufficiently fastened by inspecting if it's through the button hole, not by pulling your shirt down.
Each of those instances had a failure mode, a break in connection of the proposed conduct with the goal's item. I don't think it's possible to specify generic content of a failure mode that breaks the connection, but it seems to be possible to say that the connection of the rite from the desired knowledge item is severed. In that regard perhaps a rite fails when it is sufficiently severed from its desired knowledge item.
Now why I particularly liked the bolded bit is because it seems like you've caught a productive ambiguity in how this works. In retrospect it appears the rites are given, like they're an a-priori, but they also seem to be modified and passed on in the act of examining the rite. I'd never thought about the example of counting items in a store vs checking just the receiving logs before, but when I read it it's clearly a successful rite. The pre-existing understanding seems to be what semantic and epistemic resources an individual (or collective) can draw on while either creating or enacting a rite; the prior context of interpretation. But when using the prior context for interpretation, it is difficult to tell what is prior context and what is created synthetically in the act. A kind of alchemy of a particular event into an instance of, or failure to satisfy, a candidate practice for producing knowledge.
Quoting Srap Tasmaner
I think I agree with that, and I want to 'yes, and' it. The "I know" when someone says "I know" in a context of justification isn't just an epistemic move in the game; it's staking yourself on the prior epistemic moves. Manoeuvring yourself into a position where you expect to be deemed to know.
I am willing to bet that the expectation there falls on the trust of a previously enacted rite; that it was conducted appropriately and an appropriate rite. But not explicated in those terms, it's taken on trust. I think this is an intimately related phenomenon to the one you reference here:
Quoting Srap Tasmaner
Being able to declare a position (analogous to "I expect to be deemed to know (in virtue of this or that rite)") I think is also to declare that the position itself is valid, because its constitutive steps have been ensured by (expecting yourself to be) following a trusted rite.
That trust seems to be irreducibly social - insofar as it pertains to common access to a shared environment. but also irreducibly entity focussed - because the entities are shared in the that environment. It is simultaneously an elevation of environmental patterns into socialised principles of associations and a matching of socialised principles to patterns; for following a pattern to success or failure in a rite.
We have at least a couple different threads here now.
I'm tempted to respond directly to your proposed model here (especially because some of it is close to some things I nearly wrote about earlier), pitch in on refining and extending it, all that, but I'm going to resist that temptation for now.
One thing that bothers me a little is that the model seems very broadly applicable, which may be a strength, but means we might be missing something specific to knowledge. I think I could read most of what you wrote as applying to, say, rational belief. (And possibly to a great number of other things, ethical questions and so on.) Would you say there's a point in here that is specific to knowledge?
One thing I've been trying to capture is that there's something a little arbitrary about knowledge. If I know because I was there, even by chance, and you don't because you weren't, that's just the way it is. If I happened to look up and see the balloon before it went behind the trees, I know there was a balloon and you can only take my word for it or not, even if you were walking along beside me.
I keep reaching for these examples that are clearly matters of perception -- which is suspicious -- but there are also the examples related to remembering, so I don't think I'm actually talking about perception rather than knowledge.
What about that balloon? Could I provide reasons for you to believe it was there? Maybe, maybe not. You didn't even notice me looking up, but if there was a balloon, we could try to find it again. Even if we find a balloon, that won't prove I saw it, might not even be the same one, but that might give you grounds for believing me. And that might be a mistake -- could be I made it up and the universe provided a spurious balloon to join in the fun of having you on. But I just know one way or the other, at least about whether I saw it, and you can only conceivably have reasons to believe. We are up to two completely different things.
Do you see your model as talking about this, or as comfortably absorbing this as a particular case?
Yes, absolutely. I had Ryle in mind when I said "know" and "see" are both being used "factively". Point of interest that we might be disinclined to treat the identical construction, "I heard a wolf in the bushes" as factive. That is at least intended as a factive use, but we the audience are reserving some doubt that, say, wolves and foxes rustle bushes so distinctively. (But maybe to an experienced woodsman ...) For a more attractively factive use of "hear", consider how different is the sound of a bird searching for bugs among the dry leaves under a bush from the sound of a chipmunk just passing through. Or, for that matter, "I heard an owl up in the big oak tree last night."
I don't know if there's anything specific to knowledge in it. I also don't know if there's anything which distinguishes knowledge from (placehlder) produced by/enacted in a 'successful connection to the world' - because we use 'to know' as a summary of perception, as well as for synthesis of perceptions and judgements (counting), as well as for practical activities (know how to ride a bike).
Maybe something that would make it more specific to knowledge would focus on objectivity (like this thread does here), what is it that makes social practices generalisable, knowledge-productive and binding (deemed to know if enacted)?
Quoting Srap Tasmaner
There's something almost arbitrary about a process of knowledge production, yeah. It could be a case of 'garbage in, garbage out'. If you can declare a prior reality as fixed by taking something as knowledge, taking a position in the space of reasons - a 'save game' as you helpfully put it -, if there are errors in the save game, treating them as knowledge has the capacity to make them part of social reality. It can be that a factual error propagates and itself gets ritualised, or a faulty connection to the state of things is sanctified.
I've been envious of people who are prone to certainty in their convictions and actions for a while, to me it seems they have the ability to conjure social reality around them; no matter how distorted it is! Maybe this is the same thing.
I honestly should have said "contingent" where I said "arbitrary" -- but I liked how forceful "arbitrary" sounds, and it captured the peculiar way in which each of us is just blocked from knowing certain things. If you weren't there, you weren't; you can have all the rational beliefs about it you like, but you'll never know. That's just contingency, but it feels arbitrary.
Here's something for you to talk about: what I postponed in looking at your model was not so much the "rites" stuff, but the propagation mechanism, having been deemed to have performed a rite, trust, staking a position, aiming to be deemed, all that business. That's nice, but applies to lots of things, it seems to me. More than just to the performance of rites. Did I miss something there?
As for "rites": rites sound like the sort of thing one would generally perform knowingly and deliberately. That's one way of putting the circularity problem. But, as above, another thing I want to say is that you know a great many things accidentally, so to speak, not intentionally and deliberately. I rely every day on things I happened to have learned that I didn't set out to learn. I didn't look up in order to see the balloon that I didn't know was there until I looked up; I just happened to look up and there it was, and now I have knowledge that you don't. From the perspective of a third party, Bill, I could be said to have taken an action that resulted in knowledge, and if Bill's definition of "rite" is loose enough, then Bill can say I performed a rite. Roughly, I did the same thing and achieved the same result as someone who performed that rite knowingly and intentionally. But the fact remains, I could not have performed the rite intentionally, since I lacked the knowledge required to do so. (And we've circled back to circularity.)
Seem like we also ought to say something about rites as general and specific. If I perform the rite of looking in a box to find out what's in it, there's the general, as it were, "rite schema" and then there's the specific rite, a token of that type, I will perform with this specific box. This "application" step might be a place where we point to additional knowledge required to perform the rite (knowing it, that it applies, how to apply it, etc.), but it's also clearly an area for experimentation. If you wonder what's in there, you might reason, "It looks somewhat like a box; let's see if we can open it (like a box)." That step of analogizing, or of extending the known range of applicability of a rule, is obviously terribly fruitful, and one way to generate unplanned-for, unexpected knowledge, without requiring at least certain sorts of knowledge up front. You don't have to know that the rite will work, or even know that it applies, to try it out. So there's experimentation again, and maybe not quite a solution to bootstrapping, but a clear path for expanding your knowledge base. And that path is deliberate, and intentional, without any knowledge of what the result will be.
I was watching Sean Carroll's monthly podcast 'ask me anything september' and he was answering a question about 'Constructor theory.' I had not heard of it and looked it up on wiki:
As I read it, this thread came to mind and I wondered if constructor theory could be used to assess the plausibility of an omniscient system by means of a possible or impossible 'task' as this concept is employed in constructor theory. I have copied and pasted the couple of paragraphs below from: https://en.wikipedia.org/wiki/Constructor_theory which made me think of this thread:
[i][b]The fundamental elements of the theory are tasks: the abstract specifications of transformations as inputoutput pairs of attributes. A task is impossible if there is a law of physics that forbids its being performed with arbitrarily high accuracy, and possible otherwise. When it is possible, a constructor for it can be built, again with arbitrary accuracy and reliability. A constructor is an entity that can cause the task to occur while retaining the ability to cause it again. Examples of constructors include a heat engine (a thermodynamic constructor), a catalyst (a chemical constructor) or a computer program controlling an automated factory (an example of a programmable constructor).
The theory was developed by physicists David Deutsch and Chiara Marletto. It draws together ideas from diverse areas, including thermodynamics, statistical mechanics, information theory, and quantum computation.
Quantum mechanics and all other physical theories are claimed to be subsidiary theories, and quantum information becomes a special case of superinformation.
Chiara Marletto's constructor theory of life builds on constructor theory.[/b][/i]
and
[b][i]According to Deutsch, current theories of physics, based on quantum mechanics, do not adequately explain why some transformations between states of being are possible and some are not. For example, a drop of dye can dissolve in water, but thermodynamics shows that the reverse transformation, of the dye clumping back together, is effectively impossible. We do not know at a quantum level why this should be so. Constructor theory provides an explanatory framework built on the transformations themselves, rather than the components.
Information has the property that a given statement might have said something else, and one of these alternatives would not be true. The untrue alternative is said to be "counterfactual". Conventional physical theories do not model such counterfactuals. However, the link between information and such physical ideas as the entropy in a thermodynamic system is so strong that they are sometimes identified. For example, the area of a black hole's event horizon is a measure both of the hole's entropy and of the information that it contains, as per the Bekenstein bound. Constructor theory is an attempt to bridge this gap, providing a physical model that can express counterfactuals, thus allowing the laws of information and computation to be viewed as laws of physics.[/i][/b]
Do you think this has any relevance to your OP? I admit my thought that constructor theory may be a way to assess the plausibility of an omniscient system is based on very tenuous linking on my part as I am basing it on a loose reading of a theory I had not heard of before today.