Quine: Reference and Modality
This paper forms chapter VIII of the book From A Logical Point of View.
The issues that interested Quine have had some prominence in recent threads. Quine occupies a curious position in the history of philosophy, with antecedents in Pragmatism but with sympathies very similar to the linguistic philosophy of Russell and Wittgenstein, and an attitude not so far from that of the Vienna Circle. Quine adopted both science and logic, seeking to show how a first order logic might regiment language in the service of scientific understanding. In the process he developed a number of influential arguments and tools, rejecting the analytic-synthetic distinction and Logical Empiricism, while developing a naturalised epistemology and metaphysics.
The present paper concerns one of the many aspects of his overall approach, his rejection of much of the logic of modality - of necessity and possibility. In the process he displays a very firm attachment to extensional interpretations of first order logic, while considering a broad range of examples from the use of ordinary language.
The paper was written at much the same time that Kripke and other logicians were re-writing the logic of modality using the powerful tools of possible world semantics, an approach that has since become the standard for philosophical considerations of modality.
My own interest is more in terms of Quine as an influence on his student, Davidson, and on how more recent modal logic might deal with the criticisms of modality levelled by Quine.
@J and I have been discussing this topic separately. I hope J will add some of their insights to the thread soon.
The PDF linked above does not easily permit quotation. If someone has access to a better rendition, please link it.
Anyway, there's a start.
The issues that interested Quine have had some prominence in recent threads. Quine occupies a curious position in the history of philosophy, with antecedents in Pragmatism but with sympathies very similar to the linguistic philosophy of Russell and Wittgenstein, and an attitude not so far from that of the Vienna Circle. Quine adopted both science and logic, seeking to show how a first order logic might regiment language in the service of scientific understanding. In the process he developed a number of influential arguments and tools, rejecting the analytic-synthetic distinction and Logical Empiricism, while developing a naturalised epistemology and metaphysics.
The present paper concerns one of the many aspects of his overall approach, his rejection of much of the logic of modality - of necessity and possibility. In the process he displays a very firm attachment to extensional interpretations of first order logic, while considering a broad range of examples from the use of ordinary language.
The paper was written at much the same time that Kripke and other logicians were re-writing the logic of modality using the powerful tools of possible world semantics, an approach that has since become the standard for philosophical considerations of modality.
My own interest is more in terms of Quine as an influence on his student, Davidson, and on how more recent modal logic might deal with the criticisms of modality levelled by Quine.
@J and I have been discussing this topic separately. I hope J will add some of their insights to the thread soon.
The PDF linked above does not easily permit quotation. If someone has access to a better rendition, please link it.
Anyway, there's a start.
Comments (234)
Sorry to interrupt your Thread, Banno. I honestly don't know what to do to get you to treat me as one of your colleagues, but no worries. I'm accustomed to such type of intellectual scorn.
Carry on.
This is the whole text of the book, 10.3MB
https://dn790009.ca.archive.org/0/items/FromALogicalPointOfView/
EDIT: For example, the .djvu file is 3.3 MB.
Lots to ponder in this essay. Just as a place to start:
Quine contrasts two statements (pp. 147-8):
(1) (?x)(x is necessarily greater than 7)
and
(2) Necessarily (?x)(x is greater than 7)
(1) is an existential generalization of a modal statement, and is either incoherent or false. (2) is unproblematic. To explain the difference, Quine makes the analogy with a game that must have a winner and a loser: It is necessary that some one of the players will win, but there is no one player of whom it may be said to be necessary that he win. Likewise, there must certainly be a number greater than 7, but we cannot say that any given number is necessarily that number. As Quine puts it,
Lets rephrase (2) in ordinary English: It has to be the case that some number is greater than 7 or perhaps It has to be the case that 7 is not the highest number. Why is it true? In what does the necessity lie? As Quine points out, the necessity here does not concern any attribute of the number 7. It is nothing like A bachelor is an unmarried male, where synonymy is supposed to result in analyticity or tautology. Synonymy is not the issue here. But we want to say that (2) is analytically true that is, true by virtue of its logical form since it doesnt matter what number we plug in; it has to come out true. If Quine allows (2) to be an example of a logical principle, then he would agree.
But have we really freed ourselves from any (questionable) definitional analyticity? Dont we need the concept/definition of number in order to know that there is no greatest number?
I believe we ought to say that Quines (2) is really shorthand for:
(3) Necessarily (?x)(x is a number) & (x is greater than 7)
Or does this commit us to the existence of some number? We could rephrase it, then (and Ill use English for simplicity):
(4) Necessarily, if some number exists, theres another one that is greater.
This preserves the analyticity we desire: Granted a number and what number means we know it cant be the greatest number.
But coming back now to tautology, if I write x is a number and then write There is a number greater than x, have I written a tautology? Are the logical constants alone what make the statements tautologous, regardless of what we plug in? I dont think so. We need number to have attributes, one of which is always exceeded or cannot be highest or some such. The logical form alone cant give us this. So greaterness is not about 7, as Quine says, but it is about number. You cant understand number without knowing what to do with greaterness. Is this analytic/definitional necessity?
Notice that this is not at all the same thing as saying, "You can't understand 'water' without knowing that water is composed of H20". Necessity, as Kripke shows us, may be a feature of either analytic or synthetic statements. So what gives "number" its peculiar type of analyticity? If statements like (3) are not true by tautology, but nor is math empirical . . . what's the best account? Would we be better off, for instance, with an argument that shows that any number x can't be the greatest number because there is no such thing?
Necessity and possibility quantify over complete propositions. Folk will be familiar with propositional logic, the p's and q's of p?q and so on. "Normal" modal logic (the system K) allows us to write ?p and ?p, so that the whole of the proposition is inside the scope of the modal operator.
Quoting J
This can be parsed as ??(x)(fx) were "f" is "greater than seven". This is well-formed, since ?(x)(fx) is complete.
Quoting J
The apparent parsing here is ?(x)?(fx). But "fx" is incomplete. The "x" is a variable, not an individaul constant. It's not that "x" could stand for anything - that'd be U(x)(fx). It's that we just do not know what x might be. It does not say that something is f, nor that nothing is f. That is, it is not a whole proposition. Hence it cannot be replaced by the p's and q's of propositional calculus, and cannot take a modal operator in normal modal logic. But the situation is more complex than that.
To a large extent this is a modern version of the de re/de dicto distinction. but we can be much clearer here using modal first order language than was possible in medieval times.
Despite these syntactic misgivings there may well be interpretations in possible world semantics in which ?(x)?(fx) can be understood. "There is something that in every possible world is f". The question then becomes how this is to be understood, and if it can be made consistent. From what I have been able to glean, if we step from K to S5 and permit ?(x)?(fx), then modal collapse follows.
The examples include quotation, what we might now call propositional attitude, and modality. It's worth noting that these are three distinct issues, and they might (do....) need to be addressed in different ways.
The thesis is summed up in the last sentence:
Yes. And this is amplified as follows:
I added "any" to Quine's statement because we can now appreciate that referential opacity characterizes (at least) three different situations: quotation, "belief"-type statements, and modality; as you say, they are three distinct issues.
Staying with modality for the moment, I'm curious how we should handle this idea from Kripke concerning what he calls "strongly rigid designators":
We know that a rigid designator has to designate the same object in every possible world. Thus, no one other than Nixon can be "Nixon". But Kripke is clear that Nixon, as such, did not have to exist. "Nixon" is not a strongly rigid designator.
Is a number strongly rigid? Kripke uses Quine's example from "Reference and Modality":
Kripke suggests that the answer, "intuitively," would be:
So, does "9" rigidly and strongly designate nine? That is, is there something about the number nine which makes us want to say that it must necessarily exist? We could do without Nixon, but not nine. This type of necessity seems problematic. Can it ever be anything other than stipulative? If there are insights from modal logic that would help here, please share.
Quoting Banno
Can you say more about this?
Isn't that what Quine doubts?
Is he wrong? How?
How does possible world semantics restore coherence in the face of referential opacity?
Asking for a friend.
Yep. He was pushing back against formal modal logic.
I'm not sure of the time line here. According to the forward, there were substantial revisions to the present article in around 1960-61. Kripke's A Completeness Theorem for Modal Logic was published in 1959. The Princeton Lectures, which became Naming and Necessity, were in 1970, well after Quine's paper.
It appears that the modal logic that Quine was addressing was mostly that prior to what we might be using now. And much, much clearer than Medieval modal logic.
So a new issue is how earlier problems might be parsed in formal modal terms, what those problems then look like and if there are ensuing issues.
I'm not too up on the de dicto/de re distinction, but it should be one of those that is amenable to formal description. Maybe @Count Timothy von Icarus will weigh in. For my part I understand that de dicto modalities have the whole proposition within the scope of the modal operator, as in K, applying across all possible worlds, while de re modalities apply to the properties of some individual - and here the terminology becomes ambiguous - and not always in every possible world. So in terms of syntax, de dicto is most similar to ??(x)f(x) and de re, to ?(x)?(fx), while in terms of semantics de dicto understands necessity as "true in every possible world" while de re might understand necessity as "true in this (or some) world", a cumbersome notion incompatible with S5.
Others understand this stuff in more detail than I.
OK. I quickly read through the SEP article and remembered why I'd never completely understood it in the first place. :smile: Glad to have some help from @Count Timothy von Icarus or anyone else.
Literally, de dicto is "of the said/expressed" and de re "of the matter/thing." For example, suppose some little girl says: "when I grow up, I want to marry the richest man in the world!"
De dicto, we could interpret this as the girl having perhaps a bit of an avaricious streak. She wants to marry the richest man in the world, whoever this happens to be. De re, this would be equivalent to "when I grow up, I want to marry Elon Musk!" bespeaking a fondness for our glorious DOGE master.
Re modality, clearly Elon Musk is not "the richest man in the world" by necessity. This is subject to change. The predication of "richest man in the world" of Musk is per accidens as opposed to per se.
You could also consider: "The number of states in the USA is necessarily evenly divisible by five."
De re, the sentence is equivalent with:"Fifty is necessarily evenly divisible by five," which I think most people would allow is true. De dicto this is clearly false. In the past, the US often had a number of states that was not evenly divisible by five, and once our glorious orange Augustus annexes Canada and Greenland it seems we will also be left with a number of states that is not divisible by five.
I am most familiar with how this ties into modality in terms of how it relates to the apparent conflict between divine foreknowledge and free will (or contingency as a whole). A key discussion here is St. Thomas's Summa Theologiae, Q.14 A. 13, .
If something is a fact, then to report that it is the case is to report that it is necessarily true. If Socrates is sitting, "Socrates is currently sitting" is true by necessity, but this is necessitas per accidens. By contrast, "man is an animal" is necessitas per se, de re (assuming for the sake of the example that all men are necessarily animals.)
That said, I don't know helpful this will be since modality is here considered in terms of necessary and contingent being/beings and causes (obviously a much broader notion of cause/principle than mechanism or constant conjunction alone), as opposed to possible worlds. I imagine the distinction would have different implications under different assumptions. I seem to vaguely recall Quine eventually rejecting the distinction on the grounds that it would imply essentialism.
But, if you're interested in the context:
Perhaps also helpful:
Quoting Count Timothy von Icarus
A question about this, though. "Necessity by accident" has an odd ring. Is the idea that, if "Socrates is currently sitting" is true, then as long as it remains true, it is necessarily the case that Socrates is sitting? The necessity would arise from the fact that there is only one way (allegedly) for a statement to be true, and that is by its stating something that is the case? I'm struggling to phrase the necessity in some understandable way -- maybe you can help.
"Man is an animal," in contrast, would be a good example of a Kripkean synthetic necessity. There is nothing analytic about the notion; it so happens, though, that we have discovered it to be true. And Kripke would go on to point out that we don't need this necessary truth in order to designate "man" -- we were able to do this quite well before we knew any science. Had it turned out that humans were not in fact animals, we would not have said, "Oh, we we were wrong in our identification of what a human is. We'd better call them doomans instead" Rather, we would have said, "We thought humans might be angelic or unique, but that is not so. They're still humans, just different from what we thought." (This is Kripke's "gold" example in a slightly different wording.)
Agreed.
Quoting Banno
Agreed, e.g.
(There is a winner in each play of the game, there is a richest man in each world, there is always a number greater than 7, or etc.)
Evidently Quine is ok with the kind of reading you (and Wiki) are calling de dicto.
However, not so sure about:
Quoting Banno
Whereas (I think) Quine's objection is to a typical de re reading, that there should be
Not because such a reading (there existing a winner of all possible plays of the game or a richest in all worlds or a greater than 7 in all worlds) is self-evidently non-sensical but because it has arisen through referential opacity, and hence behaves incoherently. E.g.
Does this objection hold up? If not why not?
... Hmm, chapter 6 of this book is called "Quine on de re and de dicto modality". :nerd:
It is perhaps becoming clear how two somewhat different uses of "necessity" are at work here. One has necessity as opposed to analyticity, the other has necessity as opposed to possibility. Early philosophy did not make this distinction, leading to difficulty. Aristotelian essentialism apparently does not differentiate analyticity from possibility.
'If Socrates is sitting, "Socrates is currently sitting" is true by necessity' would now be understood in terms of accessibility. There are possible worlds in which Socrates is not sitting. And in every possible world in which Socrates is sitting, Socrates is sitting. Putting this another way, if we consider only those possible worlds in which Socrates is sitting, then in every one of those worlds, Socrates is indeed sitting. So in a way of speaking, in those words in which Socrates is sitting, "necessarily" Socrates is sitting.
This would not be valid in S5, since every world is accessible. Indeed, "Socrates is sitting, therefore necessarily socrates is sitting" is invalid in K and S4.
To which we can add a third wrinkle, as I referred to earlier: necessity as opposed to tautology. '9 is greater than 7' is presumably analytic and likely necessary, but is it a tautology?
Quoting Banno
But:
Quoting Banno
Or Aristotelian logic:
Quoting Banno
Or Medieval philosophy:
Quoting Banno
---
Quoting bongo fury
A good question.
---Quoting Banno
Quine was as ignorant of Medieval logic as you are. He is not responding to it.
Quoting Banno
Good resources showing that Aristotelian essentialism is more robust than anything the moderns have stumbled upon are as follows:
Quoting Leontiskos
Klima spends more time with Kripke and Spade more time with Quine. It's no coincidence that those who do not know the past do not progress beyond it.
Can we please have mod attention to this persistent failure on Leon's part to address the topic at hand, and to indulge in personal insults directed at me?
Meh. I'll take this to PM in an attempt to keep the thread on topic.
Quoting Banno
They should also go back and address all the crap that Banno littered my thread with.
But in my paradoxes and Infinities course, I'm currently going over the different modalities of Ordinals which order Infinities in certain ways... and further, there is an intersection here with linguistics. The powerset of words is greater than the set of words because there are more sets of words (sentences) than there are individual words.
Modalities and referencing in math as it is with language... make a biforking chart for example to row 3... what happens down line 0 0 0 is linear and the modality is linear there is a transitive property that a is proceeded by b and b by c and the a is proceeded by c ...logically... but when we try to reference point 000 and point 110 or even 111 as if they were the same as point 000 simply because they're on the same row doesn't mean it will create a bijection from points 000 to 111 or 110 if we're declaring a linear modality while referencing things outside of the modality.
Quoting Banno
If you think that possible world semantics solves some problem that the Medievals could not solve without it, then you have to set out the problem, their solution, and the alternative possible worlds solution. Or as Bongo said in response:
Quoting Banno
Quoting bongo fury
Now it is fairly well established that Quine's understanding of Aristotelian essentialism was highly superficial. But you are welcome to try to do the work that Quine failed to do: set out a robust and well-referenced account of the solution that you find lackluster, and then show how your own possible worlds solution is supposed to be an improvement. As Bongo alludes to, I don't recall Quine seeing possible worlds semantics as being especially promising or advancing. Ironically, much of the recent neo-Aristotelianism flows from a growing dissatisfaction with the artificiality of possible worlds semantics. We are slowly correcting modern errors, first with Kripke's modal form of essentialism, and then moving with Fine and Klima towards more traditional and robust forms of essentialism, that do not rely on the overrated device of possible worlds. You seem to be stuck in positivistic decades that have been largely superseded by a hearkening back to richer philosophical traditions.
-
Quoting Banno
No, not the history of philosophy, but rather the history of 20th century Anglo philosophy. Again, one must read books written before 1900 if they are to make claims about the history of philosophy, and this very recent tradition you are immersed in is virtually unknown outside of the English-speaking world. If you have no knowledge of Medieval philosophy it's hard to understand why you make so many claims about it. It's a bit like the cat-lover who has never seen a dog and yet goes around telling everyone how much bigger and better cats are than dogs.
Any good references?
Quoting Leontiskos
David Oderberg also writes a fair bit on this topic, e.g. "How to Win Essence Back from Essentialists." Banno also has an old thread on a paper of Kit Fine's, which I believe to be too conservative.
Edit: Banno's claim that the Medievals lacked a "modal first order language" betrays a very curious form of ignorance. At bottom is the fact that Medievals were explicitly uncomfortable separating natural language from logic in the way that someone like Frege, Russell, or Quine was wont to do, and therefore they did not arrive at artificial constructs like possible worlds semantics. Such artificial constructs (and their weaknesses) flow from the idea that logic and natural language can be separated. To take one example, modal logic was highly developed by the late Medieval period, but it was not reified into rigidly formal constructs. Cf. "Natural Logic, Medieval Logic and Formal Semantics."
In math when we say 1 is less than 2, and 2 is less than 3 and then say 1 is less than 3, we're showing a transitive property in logic... according to a linear modality of referencing the points 1 2 and 3. We can say 1 is lesser in relation to 3...
The biforking model top of the model is a fork... ^ each left branch from a fork is 0 and each right fork is a 1
So row 1 would be 0 on the left side of for, 1 on the right row 2 would have a fork coming from side 0 and a fork coming from side 1 both are labeled the same 0 to 1 left to right...
You end up with a pyramid of forks... fork 0 0 0 would follow all the left forks, and all spots on that path are linked by a line upon the forking branch from the tip of the pyramid to far left extreme of the pyramid base, if you took the path 1 1 1 youd take the right forking path all the way to the right extreme of the pyramid base... traveling down the points 1 1 1 in row 1 then 2 then 3 all follow a path on a line and all reference each other with transitivity between row 1 and row 3... such that whats in row 2 proceeded row 1 and what's in row 3 proceeded row 2 ... but if you go down the far left, even though you're using linear modality the third spot on 0 0 0 the far left base of the pyramid, doesn't mean we can cross reference between spot 3 on path 000 and spot 3 on path 111 at the far right base... because there's no transitivity betwen the spot at 111 with the spot at 000. I can make a picture if needed, would probably make it way easier to understand hat I'm saying.
What follows when we cross reference say a word, using the wrong modality might be like a categorical error or fallacy of equivocation...if say row 3 ended up as 3 different definitions of the same word ...
Which is to say... say you used X logic to get to a definition of a word... a word that had 8 ways to be used across the different parts of speach it could cover...
All 8 definitions would rest in row 3 of this pyramid we just constructed...
That doesn't mean each definition can be used as a reference for the word in the sentence.
Yeah, it's a good point. I'm not sure where to go with that, so will give it some more thought. Quoting DifferentiatingEgg
Have you a link?
Quoting DifferentiatingEgg
There are arguments that the number of sentences in a natural language can be indenumerable. There was a thread on that a few years back. I'll see if I can locate it. It might be of interest to your course.
Yes, how tautology fits is part of the subtext.
Row 1: Good
Row2 forked into: Adjective Noun
Row3 contains 2 definitions forked under adjectival form of good (1.thorough and 2. Desired Quality) and 2 definitions forked under noun form of good (3. an advantage 4. a moral principle)...
Just because you can use a linear modality to reach adjective definition 2:"desired quality/should be" doesn't mean you can logically reference the noun definition 4 "a moral principle" when your argument details definition 2. There's no transitive property between definitions 2 and 4 through linear modality...because they travel down different forks all together...
OK, except the last sentence? When you say "reference for the word" do you mean intension (in logic)? Some words presumably wouldn't have any extensions.
Yes, a diagram would surely help but I don't want to put you to any additional trouble.
Can't get it to post here but I tossed it up on imagebb: https://ibb.co/5hP4c2yX
From the Tip of the pyramid to get to "desired quality" the modality to get there is linear ... an we can say to get there you go down a left branch (0) and a right branch (1) so traveling a linear path we get to 01: "desired qualities". Which is an adjective of Good. If we travel from the tip to the right twice 1 & 1 we end up at spot 11 at moral principle, which is a noun of good...
You can not logically reference or interchange definitions of Good at position 01 and 11 with the other... due to the fact that they're on completely seperate branches.
Ordinals are used to order Infinities ...
And since words and sentences are basically infinite, you can use the ordering styles of ordinals for linguistics and I believe that's what Quine is doing.
my bad, I kinda got lost in my own tanget, but what I was getting at is that I believe Quine ended up taking inspiration from the mathematical logic that appears in the study of paradoxes and infinities and (more) to inform on his logical modeling of linguistics... I wasn't trying to detail what Quine's model expressed, but I had noticed there were a lot of similarities between my current philosophy class and Quine's approach.
Oh, very much so. His academic reputation began with his New Foundations, an alternative axiomatisation of set theory. Unlike ZF, NF apparently allows a universal set without paradox, which fits nicely with Quine's holism. It makes use of stratification, which like the system you describe, creates a hierarchy. It has some interesting implications in regard to paradoxes.
Thanks :up:
How could you do quantum theory without modality? Isn't possibility central to it? If this is off topic, please ignore.
I think it was because possible worlds are figments of imagination. Too much dubious ontology.
The key here may be
Here Quine is I believe throwing his lot in with Russell and Kripke, accepting a descriptivist logic without individual terms.
He goes on to examine quotations, attitudes and modality, finding each again wanting...
Also, double dang New Foundations is Dense as f... hehe... yeah, I'm just now dipping the tips of my toes into Set Theory, kinda started in the middle... it seems with paradoxes and infinities, but I'm picking it up, it's much more taxing than I thought, like when I first picked up Nietzsche... I'm having to learn things that would have made this easier had I already understood them.
Been great learning it though, cause it's all really great tools for mental pushups and the ability to take a scalpel to language. In such a way that provides one with a certain mastery of its use. I never even fathomed using math to understand language in such ways. One can literally set it up like an equation. Sure, I've done sentences in with logical operators before, but I hadn't even considered:
Sentence = (conditional) + Subject + Predicate +(modifiers). (As a basic example)
Before redefining he appealed to sameness of stimulus between speakers. The new defines observation sentences for the single speaker:
Thus to ascent to the definition of "Good" as "Desired Quality" one must first have stimulated the original node (Good) then node 0 (Adjective [first left]) then to node 01 (Desired Quality [first right after first left])
So the total set of receptors in this case are "Good -> Adjective (Node 0) -> Desired Quality (Node 01)" Thus trying to swap meaning through a different set like "Noun (node 1)" -> "Moral Principle (node 11)" isn't logical because it groups a different total set of receptors.
We have, for the case of attitudes,
and
But Philip is aware that Cicero denounced Catiline. What he is unaware of is that Cicero and Tully are the same person. The difficulty here is the misfiring of the reference.
Quine says "the difficulty involved in the apparent consequence (29) of (9) recurs when we try to apply existential generalization to modal statements" (p.147). I'm not convinced that the difficulty in attitudinal issues is the same as that in modal issues. As explained above,
will result in modal collapse if the domain includes more than integers. In a modal context substitution will maintain truth, provided that we keep track of the domains and individuals being addressed, and hence the accessibility between possible worlds. This is not the case in attitudinal opacity...
I'm aware this is ill-expressed, and in need of much refinement, but I will post it anyway, as a signpost. My suspicion is that Quine has treated quotation, attitude and modality as if they were all examples of the failure of extensionality, but that since Kripke, we have a clearer way to deal with extensionality using possible world semantics, and so can treat modality separately to quotation and attitude.
Welcome back.
As Quine explains it, doesn't the collapse occur regardless of the domain? It has to do with existential generalization itself, no? But maybe I'm missing it.
(I'm somewhat regretting being here - the forums are overrun with idiots. Good to have a few folk, such as your good self, to talk to)
Quoting J
I suspect that this is how Quine pictures his criticism... much more depth is needed here. We will need to go over Kripke's solution again, and how rigid designation fixes the same individual in multiple possible worlds, each in effect a different domain.
Go back to 's "if Socrates is sitting, then necessarily socrates is sitting". How might this be described in possible world semantics? In effect the antecedent, "if Socrates is sitting...", confines us to only those possible worlds in which Socrates is sitting. And in each and every one of those worlds, Socrates is sitting. This is a way to make sense of "if Socrates is sitting, then necessarily socrates is sitting", while maintaining the definition of necessity as true in every possible world.
In that small subset of possible worlds in which Socrates is sitting, necessarily, Socrates is sitting, and modal collapse is avoided by not considering those worlds in which Socrates is not sitting, and so avoiding the situation where he is both sitting and not sitting.
But for any other set of possible worlds, Socrates will be both sitting and not sitting, and modal collapse will ensue.
Necessity can be understood as "true in all possible worlds that are accessible from a given world", and if we then restrict accessibility to only those worlds in which Socrates is sitting, then (by that definition of necessity) necessarily, Socrates is sitting.
So I think that Quine is mistaken, if he thought that collapse occurs regardless of the domain... or of accessibility.
(Thats a dreadfully unclear post - repetitive and obtuse. I hope it gives some indication of where this thread might go).
I'm not using "domain" very well here, either. We need a logician - I wonder if @TonesInDeepFreeze is available?
I missed your post, my apologies.
Yes, it's not non sense. I hope to show that it's not referential opacity that is the problem in modality - becasue modal logic is extensional and preserves truth, and substitution in modal contexts can be made functional.
So Quine argued that quotation, attitude and modality all suffered referential opacity. But recent modal logic is explicitly extensional, and so referentially transparent. Hence, I would seperate modality from quotation and attitude.
So we the truth that there will be a winner of the lottery. And the falsehood that Fred Smith will necessarily win the lottery. The difference can be shown clearly in the scope of the two statements when parsed. Taking "L" as "Wins the lottery" we can write the truth "necessarily, someone will win the lottery" as ?(?x)(Lx) and taking "a" as a name for Fred Smith, we can write "La" for "Fred Smith will win the lottery" but ?La is false - it is not true in every possible world that Fred Smith will win the lottery.
There's a lot of qualification that we might do well to throw in, excluding those possible worlds in which there is no lottery or in which the lottery is found fraudulent and void, and so have a lottery but no winner.
And yes, the issue becomes how we might pars
And it seems clear that even if Fred Smith is the winner, he is not the winner in every possible world, and so it is not true that there is a player (who happens to be Fred) for whom it is necessarily true that they are the winner.
Putting this in terms of scope, we can say ?(?x)(Lx) is true but that (?x)?(Lx) is false. The different placing of the ? says it all.
But you see more here, I suspect.
Might be worth considering this article, perhaps after Quine. On a quick look it seems more polemic than analytic. On my browser pp40-41are missing. But perhaps we will find the answer to the question I;ve been asking for a few threads now, what exactly is an essence?
Pages 40-41 are available to me.
Anyway, back to the article.
So are there referentially opaque modal contexts? By that we might understand, are there modal contexts were substitution salva veritate fails?
And what we have is that substitution works in modal contexts provided the scope of the modal operator is a whole proposition, and the substitution is rigid.
Here's Quine's objection. We had ?(4+4=8). Since "the number of planets =4+4", we ought be able to substitute salva veritate "the number of planets" for "4+4" in a modal context, deriving ?(the number of planets=8).
The reason substitution fails is that "the number of planets" is not a rigid designator. But "4+4" is. Consider the rigid "7+1=4+4". Here, substitution works salva veritate: ?(7+1=8).
Without the notion of rigid designation, Quine did not have the tools needed to see how substitution in modal contexts could be transparent.
Equivalent rigid designators can be substituted, preserving truth, in a modal context.
So applying the principles from the previous post, water = H20
Allow me instead to address the evening star, Hesperus...
So does the reply in the previous post apply here? Well, is "the evening star" rigid? This is I think the ambiguity on which Quine trades - and sorting that, together with Kripke's argument that we can have necessary yet synthetic truths, will get us to transparent substitution in modal contexts.
"The evening star' is a description, picking out the brightest star in the western evening sky, which for half the time is Venus. Of course, many objects might satisfy the description - Jupiter and Saturn, perhaps, when suitably positioned and Venus is visible in the morning; or Sirius, the brightest of the stars, might all be suitable candidates. But The Evening Star - capitalised as a proper name, and also called "Hesperus" - is Venus; that very thing, and not Jupiter, Saturn or Sirius. "Hesperus", then, is a rigid designator, as is "the Evening Star".
So if there is life on Hesperus, then there is life on Venus. If there is life on The Evening Star, then there is life on Venus. And Necessarily, if there is life on Hesperus, there is life on Venus. And Necessarily, if there is life on The Evening Star, then there is life on Venus. And so on.
And we can apply existential generalisation here. If there is life on Hesperus, then there is something on which there is life - or there is an x such that x has life on it. And necessarily, if there is life on Hesperus, then there is something on which there is life.
But of course (31) has the ? inside the scope of the existential quantifier...
mis-post
OK, I can see that. Going back to the integer domain, though:
Quoting Banno
I'm not sure why including more than integers would be the same kind of domain change as the one involving Socrates sitting. In the latter case, the domain has been restricted to certain possible worlds; what would be an equivalent (or similar) restriction for integers?
I think you're saying that "the evening star" (description) is not a rigid designator, but "the Evening Star" (name) is? So "the evening star" is like "President of the US in 1970"; another celestial body could be the evening star (the celestial body in the west), but only the Evening Star can be the Evening Star, just as only Nixon can be Nixon. And this plunges us right into questions about possible worlds. We know what we mean when we say "Someone other than Nixon might have been president in 1970", but do we know what we mean when we say "Something other than the Evening Star (aka Venus, Hesperus) might have been the evening star"? That is not the same as saying "Something other than the Evening Star might have been the brightest object in the evening sky" -- as you point out, other objects could satisfy this description; we know what that would mean. We seem to want the term to function both as a description and -- in upper case -- a name. Whereas "Nixon" is only a name; "Nixon" doesn't describe him in any further way.
Quoting Banno
It is interesting that 39% of the references to the molecular structure of water on TPF are given as 'H20' (H-twenty) rather than as 'H2O'. It makes those discussions elusive to a search.
I recall that when I wrote that I was thinking that (30) restricted the domain. But looking at that again, i can't fill it out. So the conditional in "If Socrates is sitting then necessarily Socrates is sitting" - if this is to make any sense at all - restricts us to only those worlds in which Socrates is sitting. Now (?x)(x is necessarily greater than 7) can be parsed as ?(x<7) - in every possible world x is greater than seven, and then bound to "there is an x" so 'there is an x such that in every possible world x is greater than seven".
So I now think you are correct, and I was mistaken.
We have analytic and synthetic necessities. Perhaps we might use "tautology" only for analytic necessities, such as that there in every possible world there is a number greater than seven, and not for synthetic necessities, such as Hesperus = Venus?
Quoting J
The brightest star in the western evening sky might not be Hesperus - it might be Jupiter. But Hesperus must be Hesperus, and The Evening Star must be Hesperus... Well, being the evening star does not seem to be essential to Hesperus, or Venus. Not in the way that being made of wood is essential to the lectern in Identity and Necessity, or being H?O (is that ok, ?) is essential to being water... If the lectern were ice, it would be a different lectern, if the liquid were not (mostly) H?O, it would not be water. But if Venus were not the brightest star in the western evening, it would still be Venus.
"The brightest star in the western evening sky" is not a rigid designator, but "The Evening Star" is.
That true statements are necessarily true is an interesting topic. In Book IV of the Metaphysics, Aristotle points out that, taken alone: "it is true that Socrates is standing" adds nothing to "Socrates is standing." Basically, there is an implied assertoric force in fact statements.
For truth is: "to say of what is that it is, and of what is not that it is not" (Metaphysics IV). Likewise, to say "a man" versus "one man" changes nothing, and the same is true of "a man" and "an existent man." And here we get part of the ground for the Doctrine of Transcendentals re "Being, One, and True."
But this is probably not the most helpful example, since it's pretty opaque. An easier one would be that a man with many siblings is necessarily not "the oldest living sibling" if he is dead. Yet neither is he necessarily dead. The man was alive at one point, and perhaps at some point, when he was alive, he was the oldest living sibling. However, the accident of his death necessarily precludes his being the "oldest living sibling."
Modality was often conceived of in terms of act/potency, not in terms of simultaneous/synchronic "alternative possibilities" (possible worlds ), but rather in terms of diachronic potentialities. Hence, a man is not equally "possibly living and possibly dead," for, to be in act as "living" necessarily excludes being (actually) dead. So too for all contraries: hot and cold, dark and light, etc.
I would just add that what seems like a small difference here might be seen as having huge consequences. Freedom in ancient and medieval thought was often conceptualized as something like: "the self-determining capacity to actualize the good." In modern views, it is often "the ability to do otherwise (other than what is actual)," and this has tremendous import for how people see all sorts of philosophical issues (e.g. Sarte wanting to dispatch any human essence to safeguard freedom, whereas on the earlier view having an essence is a prerequisite for any human good for freedom to achieve).
Avicenna makes a distinction here between necessity per se ("in itself") and necessity per aliud ("by another"). If you throw a rock through a window, it will necessarily break (physical necessity), but the window is not "necessarily broken" per se.
Modern conceptions of modality in terms of possible worlds will probably be inadequate to capture these distinctions. As Plantinga explains, if something is "possibly necessary" in this frame, it is necessary. For, to be "possibly necessary" is "to be necessary in at least one possible world," but then to be "necessary" is "to be in every possible world" (this seems to me analogous to the frequentist account of probability, which has been so popular after the early 20th century). Yet this is clearly not the sort of distinction folks like Aristotle, Al Farabi, and Avicenna are trying to elucidate, since these attempt to look to the why of necessity.
The ideas of potentiality and modality on the one hand, and probability on the other, are obviously related. If something is necessary, it occurs 100% of the time, if it is impossible it occurs 0% of the time. If it is possible, but not necessary, it must be somewhere in between. Hintikka unhelpfully labels to Aristotelian view a "statistical view " on the grounds that Aristotle recognizes this fact, and it's unfortunately all over analytic treatments of modality in earlier eras, making them out to be much more like the dominant (and problematic"Bernoulli's Fallacy" is a great book here) frequentist paradigm in modern statistics than it actually is.
In particular, Aristotle rejects wholly unrealized potencies because he thinks the cosmos is eternal, so everything that could happen has had time to happen, but very many of his interpreters (particularly Jews, Muslims, and Christians) reject this view. More problematically, it might seem to presuppose that things are necessary or not [I]in virtue[/I] of such frequencies, not vice versa (mixing up quia and prompter quid, cause versus effect). This is sort of akin to identifying valid arguments as "those arguments which never have a false conclusion when the premises are true" as opposed to those where the conclusion "follows from" or can be "inferred from" the premises.
Obviously, you can describe the example above in terms of possible worlds. If a man is dead in the actual world, he is not the oldest living sibling in all accessible worlds. Or "there are no possible worlds where the man is both dead and the oldest living sibling" (a frequentist explanation). This is sort of a flattening though. You could try to trace the distinctions through accessibility relations, but it's really the "because," "in virtue of," etc. questions re necessity that they attempt to address, which is not addressed by comparing frequency across datasets.
It's a similar topic approached in a different way. There are actually four modes of per se predication (as well as per se accidents) and they don't map neatly to modern distinctions. "Analytic" statements would fall under per se primo modo, which relate to essential definitions (e.g. a triangle having three sides). By contrast, Kripke, in keeping with his epoch, puts epistemic concerns front and center as opposed to metaphysical ones. For instance, it flows from the essence of fire that it is hot, but what it is to be fire is not identical with what it is to be hot, else all hot things would be fire. All foxes are made of flesh and bones, but what makes a fox a fox is not possession of flesh and bones (hence, we can recognize foxes' eidos in stone statues).
That the Categories and Porphyry's Isagoge were considered introductory, foundational texts in logic, not metaphysics, is perhaps indictive of the difference in approaches.
In general, the common sin of the medievals is not to fail to make distinctions, but rather to make so many that it becomes difficult to follow them. Where Hume (and Kant, following him) has a two pronged fork grounded in epistemic concerns, they have a minimum of six, generally grounded in metaphysical concerns. But also, essences are known through the senses, not as a priori analytic truths. The Peripatetic Axiom is: "there is nothing in the intellect that was not first in the senses.
Analyticity roughly (but imperfectly) corresponds to predication per se primo modo, which is just one mode of per se predication (there are also per se accidents), and the Islamic philosophers in particular have many distinctions vis-a-vis modality. Some (e.g. Al Farabi), largely do exclude necessity from an indeterminate future, however they still have necessity through causes, not solely through definitions. In some sense, principle/cause must be prior, since the Many that possess disparate definitions are downstream of their unifying principles (One).
There is obviously some relation. If to be a triangle is to have three sides then a triangle cannot possibly have four sides. Likewise a light room can not possibly be dark, in that the two contraries do not admit of being both in act simultaneously (but note that in contrary, as opposed to contradictory, opposition we can meet somewhere in the middle). If something is necessarily in act, its contrary is necessarily excluded, but this relation need not have anything to do with analyticity. Not being a square, hypercube, circle, dodecahedron, trapezoid, etc. is necessary for all triangles, but is not "what a triangle is."
Quoting Count Timothy von Icarus
Isn't the broken window captured by accessibility - from those worlds in which the rock goes through the glass, all accessible worlds contain broken glass. In some possible worlds, the oldest sibling is alive, in others they are dead - and from the latter, only those worlds in which the oldest sibling is dead are accessible. This captures the "becasue" and "in virtue of". Accessibility would seem to capture the notion of being "downstream" that you think absent. What am I missing? I gather you would say that the cause of the glass breaking is absent; that the nature (essence?) of the rock and the window necessitates the glass breaking? But that's just saying that in every world accessible from that in which the rock goes thought the glass, the glass is broken...
The upshot would be to consider systems other than S5, in which all worlds are accessible from all other worlds. So in effect your position seems to be that S5 does not capture certain ways of dealing with necessity.
I still do not follow what an essence is on your account. Is having three sides part of the essence of triangle, and becasue is it analytic that a triangle have three sides?
Added: That is, if you like, essences, even as you set them out, are descriptions of modal properties, of those consequences that follow from being classified as a rock or classified as glass.
Returning to my question about "accidental necessity," let's consider your example of the rock and the window.
Quoting Count Timothy von Icarus
This introduces a concept of "necessity" that is unclear to me. Which of these two things are you saying?:
1) The act of throwing a rock through a window is, by definition, the breaking of that window.
or
2) If a rock is thrown at a window, the window will necessarily break.
Since you use the phrase "physical necessity," I'm guessing you mean #2. A definitional necessity such as "'through a window' means 'breaking a window'" presumably isn't to the point here.
If I've got that right, can you explain the necessity in #2? Why must the window necessarily break? Is there some sort of ceteris paribus series of premises built into the necessity? Would we equally want to say that "The sun must necessarily rise tomorrow"? These necessities, if that is indeed what they are, seem very different from either "9 is necessarily greater than 7" or "Water is necessarily composed of H2O". Why would all three be described as "necessary"?
That might work. Or "tautology" may be more trouble than it's worth, since it has two common usages that are easily conflated. In logic, a tautology is meant to be true by virtue of the logical connectives alone, so very similar to analytic necessity. But when we ask if two statements are tautologous, we usually mean something different. We're asking if they "say the same thing", a much looser conception. "9 is greater than 7" is analytically true, and so is "10 is greater than 7", and for the same reason. It would be impossible to understand one without understanding the other. But do they say the same thing? Kinda sorta -- depends on how you want to frame "the same thing". They surely say the same thing about arithmetic.
The error here then is to supose any name may be substituted. What can be substituted salva veritate is a rigid designator. So much for singular terms.
The error here is to think that analytic and necessary are the very same. So much for quantification.
Those all seem like physical necessity to me. Some things can pass through others without breaking them. For instance, a beam of light from a flashlight will pass through a window just fine, and a rock could pass through a layer of water without "breaking it" (it might break the surface tension, but this would reform).
The fact that a rock's passage through a window entails it breaking has to do with what rocks, windows, and the surrounding cosmos are. Rocks and windows, being more or less heaps of external causes, wouldn't be the sorts of things that we would tend to think of as possessing self-determining natures (although possession of a nature/essence is also not a binary).
Why not exactly? To be sure, there might conceivably be something that could stop the sun from rising. A large exo-planet could utterly destroy the Earth, leaving nothing for the sun to rise on I suppose. Perhaps similar cosmic-scale events could occur as well. But barring any of these, the sun will rise. To deny this would be to deny that the past determines the future, and it's hard to think of anything there is more evidenced to suggest than this relation. Yet that's part of the nature of physical necessity. What comes before dictates what comes after. Indeed, even when we speak of non-temporal dependence and causality we nonetheless use the language of temporal ordering, e.g. "prior," "consequent."
And, given how we learn about the world, how we learn to speak and reason, etc., it seems fair to assume we learn about consequence and entailment through the senses. This sort of relation is [I]abstracted[/I] from the senses.
Right, hence the distinctions in terms of the modes of predication or something like Avicenna's necessity per aliud versus per se.
The latter two examples involve what is true of multitiudes and water intrinsically. The former case is necessary in the sense that the present appears to in some sense contain the future. Causes contain their effects in a way akin to how computational outputs are contained in the combination of input and function perhaps. It has to do with how the cosmos is, as a whole.
On the pancomputationalist view, which is fairly popular in physics, past physical states determine future ones (or a range of them) in exactly the way the output for some algorithm given some input is determined (and necessary). Perhaps this is so, but the philosophy of information has so many open questions that it's hard to know what this really means, and the use of digital computers as the model for being seems pretty suspect to me. Back when the steam engine was new the universe was conceived of as a great machine, the human body as a great engine, and while this got something right, it left out quite a bit.
You could consider "George Washington was the first President of the United States." Is it [I]possible[/I] for this to become false? If not, then it seems it is in some sense necessary, although it also seems to be something that [I]was[/I] contingent in the past. A way this might be explained is to say that it is not possible for any potency to have both come into act and not come into act. So if Washington was the first president (and he was) this is necessary de dicto (although not de re, since president is not predicated of Washington per se).
Quoting Count Timothy von Icarus
But if something could stop the sun from rising -- or, in the case of the rock and window, prevent the rock from breaking the window -- why would we call the event "necessary"? You can of course stipulate that "necessity" can refer to something that is overwhelmingly likely, such as the sun rising tomorrow, but I can only reply that this isn't what discussions about necessity are usually about.
Quoting Count Timothy von Icarus
This is what I meant by ceteris paribus conditions. Sure, if certain conditions hold steady, then certain results will occur. This is the same as saying that in some possible worlds the sun will rise, while in others it may not -- which is hardly "necessity". This has nothing to do with denying that the past determines the future; if some unlikely intervening event occurs, that will be the past in that possible world.
I think the best argument against this view of physical necessity is to ask: Where do you draw the line? Exactly how likely does a certain set of circumstances have to be before you're willing to declare the result "physically necessary"? Even phrasing it this way seems contrary to the idea of what "necessary" is supposed to mean, but let's grant it. You want to say that, in our world, the sun rising tomorrow is physically necessary. Suppose we get warning of a breach in spacetime -- has the likelihood decreased? Suppose the rapture occurs? Still "necessary"? You see what I mean: You have to make a judgment call on each of these possibilities, or else outright deny that they are possible, which you don't want to do, and rightly so. I would argue that this approach takes us much too far away from how "necessity" is used and understood.
Quoting Count Timothy von Icarus
"The former case" refers to "9 is necessarily greater than 7", yes? Are you positing "7" as being in the present, and "9" in the future? And that 7 thus causes 9? I must not be understanding your meaning here.
Quoting Count Timothy von Icarus
Certainly. As Kripke helps us understand, this could become false in two different ways. 1) We might discover that someone else briefly held that office, but this fact was suppressed for conspiratorial purposes. 2) We might discover that the man who first held the office was not the man we designate as "George Washington". It turns out that the real George Washington was murdered as a young man, and replaced with an impostor.
These are absolutely ridiculous suppositions. But something doesn't become necessary just because the possible counterexamples are ridiculous. Necessity is supposed to mean that there are no counter-examples -- that it is not possible for the truth to be other than it is.
Perhaps you don't accept that as a working definition of "necessity." But then I think the burden of argument is on you to make a case for why extremely likely events should be given the same name as absolutely necessary events.
That wouldn't be it though. Necessity is not just a case of high probability. Obviously, many things might stop a ball that has been thrown at a window from breaking the window. It could hit a bird, like that time Randy Johnson accidentally killed a pigeon with a fastball. The point is rather that if none of those things happen, and the ball goes through the window, then the window will necessarily break.
It might be easier to think in terms of the "necessary versus sufficient" conditions of counterfactual reasoning. If a plant is to grow, it is necessary that it receive water. If causes are sufficient to bring about a seeds' germination and growth, it will necessarily occur.
Or, you could consider St. Thomas' framing in terms of act and potency in the commentary on Book IX of the Metaphysics. Here is an example he uses: a human body will naturally tend towards health (and homeostasis) if nothing hinders it. Medicine is thus in some sense primarily the removal of external impediments of the movement from potency to act. This is a case of necessity involving natures.
Yes, the synchronic view of possible worlds is different. One can of course collapse any distinction between metaphysical, existential, physical, etc. necessity and try to explain it solely in terms of frequency across synchronic possible worlds. In which case "necessary" only applies to what is true in all possible worlds (and hence whatever is possibly necessary is necessary tout court). This seems to me like an impoverishment of concepts though.
Sure, if what "necessary" is [I]supposed[/I] to mean is just whatever a narrow clique of Anglo-Americans Baby Boomers decided it must mean in their infallible wisdom :grin: (I am being facetious here, to some degree, since Leibniz did have similar notions earlier). Avicenna or Al Farabi would disagree.
They're different views of modality; they will not agree in every respect.
I never said that though. I said that if conditions are sufficient to bring about the sun's rising then it will necessarily rise, and that this can be explained in terms of physical necessity in that things necessarily act according to their nature. It has nothing to do with things that might not happen being necessary. Likewise, if the sun rose, it is necessarily true that it rose.
No, sorry I was referring to the sun rising. The reference to popular theories in physics might make more sense now :rofl: .
This just seems bizarre to me. A lie is true if enough people believe it and then becomes false when people discover it is false?
A misattribution is correct until it is corrected?
I don't recall Kripke ever advancing such a claim, but it would essentially amount to defaulting on truth being anything other than the dominant current opinion. "Adolf Hitler was the first US President" would "become true" if enough people thought it was true, which seems to veer towards a sort of Protagotean relativism.
I think you're missing the point by focusing on epistemic issues. Discovering that something you thought was true is not true is not the same thing as facts about past events becoming true or false. The latter implies that becoming occurs in the past, not just in the present, which seems like a contradiction in terms.
Suppose it is indeed true that George Washington was the first president. There is no conspiracy, no misattribution, no epistemic issue. This is true and we know it. Is it possible for this to become false in the future? Might it one day be true that Adolf Hitler was in fact the first US President?
The sun rose yesterday. Is it possible that it did not rise yesterday, that the proposition "the sun rose yesterday should [I]become[/I] false be the sunset today?
If it is not possible, then it is in some sense necessary. If you just look at frequency over possible worlds, where "possible worlds" gets loosely imagined as "whatever we can imagine" then it will be impossible to identify this sort of necessity though. But what then, are all facts about the past possibly subject to change in the future?
Why would we think that? It seems obviously false. Hence, a notion of physical and accidental necessity is needed.
Is there a "possible world" where the sun didn't rise yesterday and we just think it did? Only for the radical skeptics.
This can be tied into the Ship of Theseus as a way to explain how rigid designators get their designation. That is to say, why is "Venus" or "The Evening Star" a rigid designation to begin with? What makes it rigidly designated? In every possible world Venus is X. But what is X? That "essentialness" of Venus? It is the causal conditions for which the term "Venus" is picked out amongst other things in the world. Thus causality seems to play the foundational role in all of this designation. There is a chain of events leading back to the baptism of the object that leads it to be rigidly designated to that object. Ok, well that works for proper names. How about scientific kinds like H20? I guess it can be the same causal foundation that links the name by necessity.
The tie in with the Ship of Theseus is, that if Venus was to miss X component or Y component or Z component is it still Venus? Well, according to Kripke, that would be a contingent circumstance, and thus not what makes designator pick out that object. So what is it? Again, it seems to be causality in a chain of events starting from its initial baptism or naming.
You might capture this in terms of accessibility, yes. The question then is if we might want some notion of physical necessity (i.e., related to changing, mobile being) as an [I]explanatory[/I] notion.
My last response to J above points out part of the case for this. If "George Washington was the first US President" is true, and it is not possible for it to [I]become[/I] false, it is in a sense necessary. However, it is clearly not necessary in terms of being true de re. Being president is a relation. And it is not true in every imaginable possible world.
In terms of essences, the articles Leo posted are quite good, particularly the ones by Spade and Klima.
Can Gandalf also have a necessity of Gandalf like Water is H20? If so, what is the thing that makes both point to the referent and rigidly designate to it? It isn't physicality. Is it causality? The initial "dubbing" of referent to the name? Why must physical things be the only things to be rigidly designated?
And then of course, if causality is the key, can this be questioned? What if in all possible worlds, causality does not hold or some such?
Well, you could follow Quine and try to get rid of proper names and say that: "there is some X that gandalfizes." Spade's article, which is quite good, points out some of the ways in which Quine's approach is more similar to Platonism. The variable, being a sort of bare particular (substratum, bearer of haecceity) sort of takes on the role of matter (the chora), with properties fulfilling the role of forms.
Sheer "dubbing" runs into the absurdities of the "very same Socrates" who is alternatively Socrates, a fish, a coffee mug, Plato, a patch on my tire, or Donald Trump, in which case we might be perplexed as to how these can ever be "the very same" individual.
The problem with the broadly "Platonic" strategy is that it does indeed have difficulty explaining how particulars exist and if the substratum lying beneath them to which properties attach is either one or many. This is complicated even more by certain empiricist commitments that would seem to make proposing an unobservable, propertyless substratum untenable. Without this substratum though, you often end up with an ontology that supposes a sort of "soup" prior to cognition, with the existence of all "things" being the contingent, accidental creation of the mind (e.g. The Problem of the Many, the problems of ordinary objects, etc.).
Hence, the Aristotelian idea of particulars as more than bundles of properties, as possessing an internal principle of intelligibility, self-determination, and unity (although they are not wholly self-subsistent).
The problems of broadly Platonist approaches are perhaps less acute in philosophies with a notion of "vertical reality" (described quite well in Robert M. Wallace's books on Plato and Hegel). They seem particularly acute in physicalist ontologies that want to be "flat."
One solution is essentially hyper voluntarist theology with man swapped in for God. So, instead of "a deer is whatever God says it is," we get "a deer is whatever man says it is."
But then the problem of contingency as far as what properties makes a Gandalf.
Quoting Count Timothy von Icarus
Not so much if it the "dubbing" entails a chain of causal events that lead back to the dubbing. Of course you can ask all sorts of things like, "Can the dubbing be mistaken?" Can there be a faux dubbing that never really happened and all are mistaken in a contingent world?
Quoting Count Timothy von Icarus
Yep, how does an object not simply decay into only its properties. However, we can say the patterns present themselves in forms, and these forms are delineated and made into technologies and testable experiments. That seems to indicate that the world is presenting something beyond mere convention or habit of thought. But this can of course go into Kantian Idealism, and how the mind by necessity structures the world vs. various realisms, etc. Either way, both would be contra mere conventionalism, I would think.
Quoting Count Timothy von Icarus
Indeed, but what is this internal coherence? It's asserted but not explained other than its needed to say this object is this and not that.
Quoting Count Timothy von Icarus
Yeah, are there principles behind the physical aspects at work, etc. Some people propose a mathematical one, etc.
Quoting Count Timothy von Icarus
One might retort that realism is shown through outcomes that are out of our control but lead to technologies and repeatable testable results. Interesting enough, I wonder if this kind of response can even work for Gandalf or Bilbo. Bilbo is a hobbit, hobbits are this but not that. One cannot make a hobbit to X if he cannot do X, thus if a TV series takes the stories and breaks them, they are panned as inauthentic.
Of course not. Our wires got crossed here. Your wrote:
Quoting Count Timothy von Icarus
I took you to mean, "Is it possible for this putatively true statement to be shown to be false?" and responded accordingly. I thought you were giving it as an example of a "physically necessary" truth.
I now see you must have meant, "Is it possible for this true statement to become false in the future?" which requires a totally different answer.
The rest of your response bears this out. We have no disagreement. True statements can't become false in this sense (barring some bizarre extremes we might imagine, which aren't to the point). If it is the case that I am sitting in a chair now, that statement, with appropriate tense modifications, stays true. A more interesting question is, Was it true before I sat in the chair? This is a version of the question that arises in philosophy of history: Is it true to say that the 1st president was born in 1732? Yes, we reply. Well, but was it true in 1732? Hair begins to be pulled out . . .
Quoting Count Timothy von Icarus
This is a different matter, and quite interesting. First, help me with the grammar. Is there a typo or a word missing in your final question, about change in the future? I can't quite parse it.
Quoting Count Timothy von Icarus
Well, yes. How would that make it impossible?
Quoting Count Timothy von Icarus
I wish you had said what you now say, as it would have avoided misunderstanding. What you did say was, in response to my asking if 'The sun must necessarily rise tomorrow' was on a par with 'The rock must necessarily break the window':
Quoting Count Timothy von Icarus
Which says nothing about sufficient conditions to bring about the sun's rising. This is no big deal, I'm sure you meant to be clear, as did I.
Quoting schopenhauer1
"Venus" rigidly designates Venus becasue we choose it to work in that way; nothing more. We are using the word "Venus" to mean that exact same thing in every possible world in which Venus exists. There may be a causal chain leading to a baptism in the actual world, but there need not be any such causal chain in every world in which Venus exists. Once it's "picked out", it is designated rigidly. I'm not sure if this is what you are saying, of if it disagrees with what you are saying. So Theseus' ship may change completely, and yet it continues to make sense to refer to it as the Ship of Theseus, using that name as a rigid designator.
is correct. I should have avoided the rock/window example, as it has lead to folk confusing physical and logical necessity. Quine is concerned here with logical necessity.
Quoting Count Timothy von Icarus
Not so much. Causation is a whole other topic.
Quoting Count Timothy von Icarus
This mixes a few different notions of necessity. First, it is not a necessary fact that George Washington was your first president (Assuming you are 'Mercan?). We can stipulate a possible worlds in which he just sold apples. But you add "become", and here we can use accessibility. We can stipulate that from any world in which Washington became your first president, only those worlds in which he was the first president are accessible - we stipulate a rule of accessibility. If we do this then it follows that from that world, all accessible worlds have Washington as your first president - for those worlds, necessarily, Washington was your first president. Doing this puts limitations on the worlds that are under consideration - as it should. One of those is that in no world in which he was your first president, could he not be your first president. This should be obvious from considerations of consistency... And it is not true in every possible world, since that would be a different stipulation.
All this by way of showing how possible world semantics sets out what is problematic with Quoting Count Timothy von Icarus
It's down to accessibility.
Nothing here so far involves essences.
Quoting schopenhauer1
They need not be. Anything that can be given a proper name can be rigidly designated. Kinds, such as gold or H?O, can also be rigidly designated. But again, while causality may be the answer to how it is that a name refers to an individual, once that link is established, the causal chain becomes unnecessary. So Hesperus = Phosphorus even though the casual chains to their baptism differ.
Quoting Count Timothy von Icarus
But the problem then is that you have thrown the babe of rigid designation out with the bathwater of explaining reference.
Quoting Count Timothy von Icarus
If someone were to misuse a term in this way, wouldn't that be apparent? Sure, someone could use "Socrates" to refer to some fish, but it would quickly become apparent that they were talking about something other than the philosopher. Doesn't "Deer" man whatever we choose it to? Note the collective "we".
Quoting schopenhauer1
Very much, yep. Essence remains unexplained, apart from the occasional hand wave to "x=x". So the best explanation we have is still from Kripke.
Sorry for any misunderstanding. There are, of course, views that deny any such sufficiency, on the grounds that cause is just observed constant conjunction that may vary at any time. As points out and I said earlier, one can get at this with accessibility. The benefit I see in conceptualizing modality in terms of potentiality and actuality is that you are then explaining modality in terms of a principle that is already in play and useful throughout metaphysics, philosophy of nature, and epistemology and because it seems to how much closer to the necessity of common sense counterfactual reasoning.
And yes , the example with Washington would not involve essences. Physical necessity involving natures would come into play with something like counterfactual reasoning about growing a bean plant. Watering the plant is a necessary condition for its sprouting and growing. We can well imagine a world where this is not the case, where Jack throws the beans on the ground and a bean stalk reaching into the clouds sprouts up. Yet watering your beans seems to be a necessary prerequisite for their growing in reality.
Likewise, to St. Thomas' point on Metaphysics IX, if we come across a dead man, we know that there is necessarily [I]some[/I] cause of death. It might be foul play or it might have been a heart attack or stroke. However, he won't have died "for no reason at all." This seems trickier to capture in terms of accessibility, but in terms of potentiality and actuality it is just the notion of entelécheia, "staying-at-work-being-itself."
But it isn't? One might say the Physics and the 2,000+ years of commentaries and extensions on it is flawed, but it certainly presents both explanation and argument.
It is the "once picked out, it is designated rigidly" that I am trying to go back to. "What" is causing this rigidity of the designator? And thus I brought up what I think is integral to Kripke- the causal theory of reference. Thus the foundation seems to me, to be causality that is the root of this rigidity.
Quoting Banno
Ok, so if the causal chain becomes unnecessary, what makes it still a rigid designator? Because if you use anything other than causality, I would be at a loss to how it is so. If a proper name refers to the same thing in all possible worlds, there needs to be a reason for why it does. The reason is the causal chain. One may not be able to actually trace it, but that's what creates the referent to be rigidly designated. Ship of Theseus has a causal link that goes back to X dubbing. Now, it gets tricky as to when THE Ship of Theseus as a philosophical concept is actually designated versus some ship of Theseus, but that's just the application of the concept.
Yes - accessibility again. Beans are such that if we would be successful bean famers we ought consider only those possible worlds in which beans need water. This is an issue of practicality rather than ontology. Think of physical necessity as pruning the tree of logically possible worlds...
Quoting schopenhauer1
Rigid designators are not discovered, they are stipulated. When one asks what the world might be like if Thatcher had lost her first election, one is stipulating a world in which, if anything, Thatcher exists in order to lose the election. The stipulation is what makes it a rigid designation.
This is choosing amongst a set of grammars - semantics - that we might make use of. In other approaches, such as David Lewis' proposal, there is no rigid designation. Using rigid designation keeps stuff consistent and fairly intuitive. That's not to say that it doesn't have a few issues, but very few in comaprison to other approaches.
Definition of Stipulation:
a condition or requirement that is specified or demanded as part of an agreement.
Quoting Banno
So it looks like your theory here is that we agree (i.e. follow a convention), that such-and-such is picked out across all possible worlds. However, the convention doesn't convey where the rigid designation comes about. If I say X = Sam, Sam is referring to X because of the causal chain that dubbed it so somewhere in the history. This gives it the rigid designation in the first place. Otherwise, X = Sam is just a hollow analytic statement.
Sorry, lets' try to be clear here - the rigid designation comes about as a result of the stipulation. That the name refers to the object might well be the result of a baptism and causal chain, but that plays no part in the name being treated as a rigid designator.
So you can say Sam := X; then ask "In some possible world, what if Sam were not X?" And still be referring to Sam.
I guess what I mean then is how is it that the stipulation is constrained to "Sam" and not something else? Which seems to be the question there. Causal-historical chain of events seems to be Kripke's answer.
Well, "In some possible world, what if Sam were not X?" is a question about Sam...
Keep in mind that the casual theory of reference was a quick explanation for a possible alternative tot he descriptive theory of reference, and never filled out by Kripke.
I don't see a problem here. "Sam" refers to Sam, "Washington" to Washington, that's just what we do with those words. If there is a problem as to which Sam or which Washington is being named, that may be sorted to our mutual satisfaction by having a chat.
If I said "Sam is X", and you say "No no, Bob is X". How do we sort this out? Well, someone misremembered or mislabeled something here. Maybe I thought Sam was Bob this whole time. What resolves this is the causal set of events that leads Sam to have been referred to Sam and not something else like Bob. I think we are kind of saying the same thing, but I am giving the mechanism for the stipulation. If I said, "No no, I know Sam is Bob, but I am not calling Sam Sam but Bob from now on", well, that would just be another causal-historical event that connects Bob with Sam.
It's not a problem for Quine if you think we are just labeling stuff and it's just convention. For Kripke, I would think there needs to be a mechanism for which the same word is necessarily that referent in all possible worlds. That mechanism is the causal-historical events that goes back to its dubbing (or in this case its possible "redubbing"). Even if we say Harry was Bob was Sam, we can have a world in which Harry and Bob and Sam refer to the same thing, but they didn't know the previous iterations. At some point in the history the name was dubbed, and the name was used by stipulation, and in this case, that name was changed, and then used by stipulation. And then again. In fact, what if the original name was lost to time, but then someone remembered that this was the original name of that person? Well, the causal theory allows it to be a rigid designator that will always rigidly designate that person. Sam was the initial dubbing, Bob and Harry were subsequent dubbing, and by convention others have used it, and all these convoluted namings of that same person would hold as that person and not another because of its stipulation in causal-historical events.
The mechanism is the stipulation.
If by stipulation you simply mean convention, then I think we are kind of saying the same thing. The convention is itself part of the causal-historical events. The dubbing is how it started, the convention is how it is used and ongoing part of the the name being carried on.
No worries. I wish I too was a model of clarity!
"If it is not possible, then it is in some sense necessary."
Count Timothy von Icarus
This proposal is a neat and simple way to bring out different alleged senses of "necessity." We look at event X; it is no longer merely "possible," since it has occurred, been actualized; therefore we're tempted to say that it must be necessary, since it has been removed from the realm of possibility.
But what exactly is the "necessary" part here? Compare two statements:
(1) "It is necessary that X occurred."
(2) "It is necessary that, since X occurred, it cannot un-occur, or not be the case."
Statement (1) is pretty clearly not what the proposal means. My cat is named Bunny, but it could have been otherwise.
Statement (2), though, does seem to express what we mean by the original proposal. Now that my cat is named Bunny, we can't rewrite the past so that she is named Methuselah. Her being named Bunny is "necessary" in that sense.
In fact, before I develop this any further, let me ask whether you think (2) is a fair elaboration of what you meant by "If it is not possible, then it is in some sense necessary."
(37) is curious. "An object, of itself and by whatever name or none, must be seen as having some of its traits necessarily and others contingently, despite the fact that the latter traits follow just as analytically from some ways of specifying the object as the former traits do from other ways of specifying it." But after Barcan, and then Kripke, we might permit an object to have necessary yet contingent traits. That gold has a certain atomic number is contingent, yet necessary. Some properties (like being H?O for water or having 79 protons for gold) are essential to the object, despite having been discovered empirically rather than analytically derived.
There's that words, "essential".
If anyone is following this, they might well be interested in the section from the SEP article on Quine's misunderstanding of Barcan, and related topics. In particular, Barcan argues that Quine is mistaken to think that modal logic is committed to Aristotelian essentialism.
And so we arrive at the Barcan Formula, ?(??)A?(??)?A.
There's a lot here to work through.
Obviously, you can rename a pet, but it seems accurate in the sense that something that has happened cannot possibly have not happened. It has already been actualized.
However, I don't think we'd want to limit this sort of consideration only to the past.
Consider: "In order for the green conscripts to be effective in battle it was necessary for Napoleon to train them into a disciplined army first."
This is the sort of sentence historians commonly write. Are they deficient in their understanding or does this make sense?
I think it makes sense, but it can be taken in ways that don't. For instance, it can hardly mean "in all possible worlds this set of individuals needed to be trained by Napoleon to become a combat-effective fighting force." It seems possible that this set of men might have received training at some other point, by some other means, or that they might have some sort of preternatural aptitude as soldiers and not require formal training.
Rather, I think we can correctly interpret it as: "Given the conscripts lacked combat skills it was necessary for this potentiality (to be good soldiers) to be brought into act because potentialities necessarily do not go from potency to act without some sufficient cause." Basically, people who lack skills necessarily don't spontaneously gain them for no reason at all, but will only gain them through certain actualities (a sort of physical necessity). This is falls under the more general principle that actuality must lie prior to any move from potency to act, else things could happen for "no reason at all."
And this sort of relationship between actualities and potentialities can be layered on in many ways, which is what we often see in complex counterfactual reasoning.
In all the possible worlds in which green conscripts were effective in battle, Napoleon had first trained them into a disciplined army. It's just access, again. The only worlds in which green conscripts were effective in battle were those accessible from the worlds in which Napoleon had first trained them into a disciplined army.
Whether it's true or not is a different issue.
But it can be set out clearly with possible world semantics using accessibility.
It [I] might[/I] be expressible in terms of accessibility, (although I would say you are losing things); that's not really the point. Framing modality in terms of possible worlds requires a radical, counterintuitive retranslation of counterfactual reasoning into terms speakers themselves are unlikely to recognize as true to their intentions, while at the same time requiring either a bloated ontology of "existing" possible worlds, or some other sort of explanation of what they are.
Why must we be under a commitment to understanding modality in these terms? Certainly not because this is how modality has been historically or widely conceived, or because it's what most people mean by the common usage of the term.
I will throw out a very similar example. You can also explain probability in terms of frequency alone. This will work quite well in some situations, when you are picking colored jelly beans blindly out of a jar for instance. "A randomly chosen jelly bean has a 25% chance of being red" just means "25% of the jelly beans are red."
Frequentism is not the only way to understand probability however. It only really becomes popular in the 20th century due to some quite contingent events (I don't think its eventual dominance is unrelated to the switch to viewing modality in terms of possible worlds either). One can claim "probability is just frequency" just as one could try to claim that "modality is just possible worlds."
But there are several other views of probability: propensity, subjectivism, logical, etc. and it's far from obvious that these aren't better ways to look at things. Frequency can, for instance, be explained as the result of propensity. Frequentism often leads to grave mistakes because it is very counterintuitive for certain sorts of issues.
For instance when we say "Trump had only a 20% chance of winning the 2016 election," do we (must we?) mean something somehow parsable into frequentist terms? E.g., "in only 20% of possible worlds including the election did Trump win," or "if we ran the election 100 times these polls suggest Trump would win 20 of the 100."
These are, IMO, bizarre rewriting exercises that dogmatic frequentists have to engage in as a means to hold up the assertion that probability and potentiality just [I]are[/I] frequency. A propensity view suits one-time events far better, or the Bayesian view. Possible worlds sometimes looks a lot like frequentism, only of a sort particularly concerned with what occurs with 0% or 100% frequency. It also has to rely on bizarre rewriting exercises.
It also often seems to get things completely backwards. There are no possible worlds without x [I]because x is necessary[/I], not "x is necessary because no possible worlds exclude it" (this is essentially just a special case of the frequentist dogma that probability just is frequency, which has been appropriately lampooned in recent years). This, in turn, leads to having to explain complex cases (although perhaps fairly simple in naive counterfactual reasoning) with ever finer webs of relations. This is the opposite of the goal of explaining complex things in terms of more general principles, e.g. principles like "conscripts who aren't soldiers don't spontaneously know how to be good soldiers without being taught because potential isn't spontaneously actualized without a cause sufficient to its actualization; a cause is necessary."
If you try to sprout pinto beans by putting them in an incinerator, this will not work. Anyone is free to rebut this by successfully starting a garden by first incinerating their beans. Otherwise, the claim seems pretty secure.
So why commit ourselves to a conceptual apparatus where we must say: "Actually, the impossible is actually possible because we can string together the words 'I incinerated my beans to sprout them'" and thus be committed to the "existence" of some "possible worlds" where the impossible is possible?
Why collapse all necessity into one sort? It seems clear that there are different sorts. A triangle cannot have four sides. This is impossible in a way that seems to vary from how incinerating beans cannot possibly result in their sprouting however.
If the probability function is defined so as to quantify the mathematical proportion of possible worlds having a particular property, then we are dealing with logical probability, but not necessarily frequential probability. For example, if there are three possible worlds of different colours, then why should the existence of these three distinct possibilities automatically imply that each colour is equally likely or frequent? In my opinion, the fallacy that logical probability implies frequential or even epistemic probability is what gave rise to the controversial and frankly embarrassing Principle of Indifference.
On the other hand if the probability function is chosen to represent non-mathematical facts concerning observational frequencies, then we have frequentialist probability but not logical probability.
In my opinion, there is no such thing as epistemic probability or propensity probability, because I think that the belief-interpretation of probability consist of a poorly articulated muddle of logical probability, frequential probability, and unarticulated subjective bias that at best expresses the mental state of the analyst rather then the phenomena he is predicting; of course mental states and reality are sometimes correlated but not always.
The best way of expressing ignorance with regards to the likelihood of a possible outcome is simply to refrain from assigning a probability, and the best way of using Bayesian methods is to interpret them as inferring frequency information from logical information expressed in the design of the sigma algebra over the sample space, plus observational frequency information expressed in the probability measure.
Then how are you supposed to update your ignorance when you encounter new evidence?
Bad judgement can apply to any interpretation of probability. Infamous examples include people being sent to prison for years, having their lives ruined, because of poor interpretations of probability. Perhaps these examples only tend to involve frequentism because it is already dominant, or perhaps it speaks to its being truly counterintuitive?
A famous case from the UK involved a woman being convicted of murdering her own children after two of them died of SIDS. The lead witness in the case, an expert in statistics, argued for conviction on the grounds that the frequency with which a woman of her demographic background could be expected to lose two kids to SIDS was incredibly low, meaning the odds of foul play should be considered far higher. But this is simply bad reasoning, since the question should be "given a woman has already lost one child to SIDS, what is the chance that they will lose another?"
Actually, families that experience SIDS are much more likely to experience it again, and there are causal explanations for this that don't involve foul play (although, it seems obvious that people who murder their kids are also more likely to do so in the future as well). The explanation that the prosecution offered in terms of population frequencies was clearly deficient (leading to exoneration).
A proponent of frequentism might argue, however, that the problem is simply that the wrong population was chosen by the expert. The population in question should have been "mothers who have already lost their first child to SIDS." So, the frequentist can say the mistake is looking at frequency in the wrong population. The obvious rebuttal here is that the population of "mothers who lost their first child to SIDS" is relevant [I] because[/I] this population has a much higher propensity to experience SIDS. That is, population selection often has an implicit notion of propensity that is built in.
You see the same thing with the Monte Hall Problem, Mr. Brown's kids, etc. Originally you had PhDs focusing on probability writing in to give the wrong answer to this question. The answer only seems obvious now because everyone gets taught it in intro stats. But of course, if you use Bayes' Theorem, something you can teach to a middle schooler, the correct answer is easy to come by.
It doesn't, at least not in the Principle of Indifference as described by Leplace, Keynes, etc. It's the simplest non-informative prior. Obviously, it cannot be applied to all cases, rather a special set of them. But the general reasoning used here tends to be at work in more complex non-informative priors.
Anyhow, part of the reason why subjectivist probability has made such a comeback is through information theory. On a frequentist account, the question of "what is the relevant distribution" vis-á-vis information becomes extremely fraught. For the (now I believe minority) group that wants to deny information any "physical reality" the argument is that, for every observation/message, the values of each variable just are whatever they happen to be, occuring with p = 1. Hence, mechanism is all that is needed to explain the world. I think Jaynes' work is particularly instructive here.
Exactly. There are indeed plenty of ways to misapply the Principle of Indifference, or cases where it will not be appropriate. There are other non-informative priors, PI is just easiest to teach for simple examples. However, critiques of it often simply include information in the example that would necessarily preclude using PI in the first place, which doesn't really say anything more than "if you misapply a rule is doesn't work right."
Knowledge is represented in terms of
1) A deductive system, that apart from the logical connectives is comprised only of constants, sets, types and functions, e.g such as a model of a road network.
2) Statistics that report how the deductive system is used, e.g traffic statistics.
It makes no sense to represent ignorance. To me that's a contradiction in terms.
Structural Equation Models are another reasonable example, provided one steers clear of non-informative priors and sticks to making deductions rather than making inductive inferences; Personally, I think Bayes rule should only be used when inferring a conditional distribution of a known multivariate distribution, for what does it mean to say that " Hypothesis A is inductively twice as probable as Hypothesis B when conditioning on an observation"?
Quoting Count Timothy von Icarus
The Principle of Indifference is supposed to be a normative principle for assigning probabilities on the basis of ignorance. As soon as a non-informative prior is used, posterior probabilities are epistemically meaningless in general, even if their distributions are useful for convergent machine learning.
The way i interpret non-informative priors is in terms of the following analogy:
Imagine using a net to catch a fish in a lake. Using a big net that covers the entire surface of the lake is analogous to using a non-informative prior. Reeling in the net to obtain the fish is then analogous to Bayesian updating. But would you really want to say that the net represents your indifference as to where the fish is? rather, isn't the net simply part of a mechanical procedure for ensuring the fish is caught, irrespective of your state of mind?
- Perhaps a Bayesian will remark that the net represents the fisherman's credence as to where the fish is. I think my reply would be to say that the meaning of "the fisherman's credence" should be given in terms of where the net is, rather than the meaning of the net being in terms of "the fisherman's credence" which I have no prior understanding of.
Also, why choose the simplest prior? Occams Razor? what justifies the use of that?
In fact, if one isn't interested in asymptotic Bayesian convergence and has no frequency information, then why use a prior at all? Why not just stick to saying what one knows or assumes, and gamble without saying anything else?
You place a lot of weight in intuition. What, then, if my intuition differs from yours? Which is to be preferred?
What would one make of someone who suggested that predicate logic "framing predicate logic in terms of p's and q' requires a radical, counterintuitive retranslation of sentential reasoning into terms speakers themselves are unlikely to recognise as true to their intentions, while at the same time requiring either a bloated ontology of "propositions" , or some other sort of explanation of what they are?" One would hope that they had misunderstood what was being done, and try to explain tot hem that if someone's intuition is that a modus tollens argument was incorrect, then the intuition might well be questionable.
Of course it might also be that the intuition has been misinterpreted in applying the modus tollens, and here the predicate logic might be of use to set out where that misinterpretation sits.
But it will not do to say that one will not accept predicate logic simply becasue it does not suit you.
"Why must we be under a commitment to understanding sentences in these terms? Certainly not because this is how sentences have been historically or widely conceived, or because it's what most people mean by the common usage of the term."
Teach an introductory logic course and you will quickly find that applying patterns such as modus tollens to sentences is not intuitive to many, nor how people string sentences together. A large part of your teaching sentential logic is correcting those intuitions.
Predicate modal logic and possible world semantics give us strong and coherent ways to use the language of modality. We know it is coherent, we know it works, from the structure of the formal language. If soldiering needs to be taught, then so does reasoning.
No, it is the same in probability theory. There, the "set of possible worlds" refers to the sample space, where a "possible world" is normally referred to as an event or element of the sample space. A coin flip or stochastic process refers to a random variable, namely a function whose domain is the sample space and whose codomain is another set, usually the reals or the naturals.
So the input to a stochastic process is a particular possible world, of which the output is a set of observations of that possible world.
Any accessibility relation defined on a set of possible worlds can be interpreted as placing restrictions on the probability measure defined on (a sigma algebra of) sets of the possible worlds.
(post recently edited due to a mistake when describing the codomain of random variables)
Wearers possible worlds in modal logic are stipulated, are not mutually exclusive and sit within a structure R which determines what worlds are accessible, one from the other.
Even counterpart theory would have these modal characteristics. Neither approach to modality involves a structured space of possibilities.
This looks to be the mistake in 's "Trump had only a 20% chance of winning the 2016 election". (Let's move away from using Trump in our examples. please... He gets much more attention than he deserves.) That is, it misses the part where modality is stipulated, not found.
Yes, you're right to challenge my previous post, as I realize that I wasn't quite correct in my interpretation of possible worlds in probability theory. But I still see no fundamental incompatibility.
Ultimately, i think the question we're addressing is "Can a set of possible worlds be adequately modelled in terms of a sigma algebra defined over a sample space?"
I think the key is to think of an element of the sample space as a trip through possible worlds that obeys the accessibility relation. This is essentially how finance uses probability theory when modelling movements of a stock price, where an element of the sample space is a sequence of binary values representing a sequence of price directions. Following this approach,
- An event is a possible trip through possible worlds.
- The sigma algebra defined on the sample space represents the possible history of the trip at each stage.
-A stochastic process represents possible histories of observations as the trip proceeds.
- An additional element can be added to the sample space to represent termination of the trip.
Thank you. I very much appreciate this simple gesture towards agreement.
This is what needs tracing out, to be sure.
In considering this I have been struck by how accessibility in modal logic resembles a Markov process, with states resembling possible worlds and transition probabilities resembling Accessibility relations. A directed graph resembles a Kripke frame... but Markov processes are not binary, unlike modal logic. Would that I had a stronger background in the maths involved.
Again, there is a lot going on here.
"In fact, before I develop this any further, let me ask whether you think (2) is a fair elaboration of what you meant by "If it is not possible, then it is in some sense necessary."
- J
Quoting Count Timothy von Icarus
Good, glad I understood you.
So we're working here with a sense of "necessary" that means "impossible to change." As you point out, past events may not be the only things about which this can be said, but let's stick to that for now.
The first point which arises about this usage is that it seems to rely for its truth on certain beliefs about the physical world. I'm thinking of something like: "The causal 'flow of time' is unidirectional, toward what we call the future. Nothing can reverse this causality, and nothing can return to a previous moment in the flow and 're-cause' something in a different manner."
Do we know this to be true? I would say we do not -- we know so little about how time functions, physically -- but let's grant it. Is it, then, a necessary truth? This, notice, would be a necessary truth that guarantees a whole host of other necessary truths, but on quite different grounds. Do we need it to be a necessary truth? Could the (in 2025 allegedly necessary) truth that "Washington was born in 1732" depend for its necessity on a contingent truth that "Nothing can be uncaused or re-caused"? Well, why not?, we might reply. Why shouldn't a contingent truth ground a necessary truth? Isn't it the same case as the (contingent) truth that GW was born in 1732 causing the (now necessary) truth that "GW was born in 1732"?
But there's a flaw here. We're equivocating. We don't want to say that GW's birth in 1732 caused anything here other than the truth of a subsequent statement to that effect. Whereas, with a law about "causality and the flow of time," we do want to say that this law, whether necessary or contingent, literally causes events to become necessary subsequent to time T1 -- that is, when they in fact occur.
So, pausing again before I go on -- do you think this is a reasonable analysis of some of the issues involved in "necessity" statements involving the past? I know that some of this is modeled more precisely in Logicalese but I have my reasons for wanting to stay with English, as you'll see . . .
But surely, ignorance is directly related to probabilities. If an event has a probability of 1, you can predict it perfectly; if all the probabilities are equal, then its like maximal unpredictability.
Quoting sime
The probability that some hypothesis was the cause of your observation; and even if your prior is wrong, probability theory is the only logical way of changing probabilities when you see the evidence if you know the likelihood afaik.
I find myself agreeing with Barcan, that Quine is mistaken to think the choice is between an Aristotelian essentialism and rejecting quantified modal logic altogether. And so the issue becomes the various and diverse notions of essence and how they might cohere and confute one another.
I love this thread. When I first started doing philosophy, I despised the historical uses of "necessary", because they discolored the readers' lenses, through which my writing was being read. I remember thinking I needed to invent my own term(s) in order to avoid having my writing filtered through such sense(s).
Quite the interesting discussion involving the different senses of "necessity" and "necessary".
The misunderstanding between J and Von Icarus was quite helpful for me. I suspect that such misattributions of meaning/sense often go unrecognized and result in an ongoing unarticulated misunderstanding.
Anway, just complimenting the thread and its participants. I'm very interested and will continue to read along in the background. I've nothing to add. Better listen and learn a bit more about the historical context(s) involving the senses of "necessary" that later plagued the interpretation of my early writing.
Hope you and the wife are happy and healthy.
Cheers.
Avoiding Cyclones by cancelling our travel plans, as it turns out. As a result I find i have time on my hands.
Thanks - I didn't really expect many to pay much attention to this thread, to the extent that I would not have started it but for @J's interest.
Your suggestion is essentially equivalent to what I suggested in my last post, and indeed the likely tool for constructing the sample space i was referring to.
A Markov Kernel on a measurable space (S,B) onto itself, i.e. (S,B) --> (S,B), is a direct way of defining a state-transition probability matrix on a generally infinite set S. But as you indicate, what is needed is a binary valued state-transition matrix rather than a probability matrix. This just means swapping the state-transition probability measure B x S --> [0,1] for an unnormalized binary valued measure B x S ---> {0,1}. By iterating this 'markov process', one obtains a trip on S. The construction I suggested earlier that directly identified trips with events, has one sample space that consists of the product of n copies of S:
S1 x S2 x .... Sn.
in which the sigma algebra of possible trips obeys the accessibility relation.
Quoting Apustimelogist
The distribution of an unknown random number generator could equal anything. If an analyst knows that he doesn't know the rng, then why should he represent his credence with a uniform distribution? And why should the ignorance of the analyst be of interest when the important thing is determining the function of the unknown distribution?
Quoting Apustimelogist
Ever heard of imprecise probability?
I feel like this kind of issue can still be talked about in the same kind of framework; for instance, Bayesian model selection where you are using Bayesian inference to select priors and models you want to use; and things like hyperpriors and hyperparameters.
Quoting sime
I don't think it rings a bell
That's what I thought. "One simple space" - so the step-wise structure disappears? That would presumably be the case if we implemented S5 in this way. Our trips through the space would correspond to moving within one big equivalence class. To model the sort of thing @Count Timothy von Icarus has been suggesting* we might use S4; we would have Reflexivity and Transitivity, but no more, and therefore some structure. This might allow something closer to our intuitions for physical necessity.
So if S={a,b,c,d} and the accessibility was {a,b}, {b,c},{c,d},{d,d} by transitivity and reflexivity, then not all states are accessible form each other - not {d,a}, for example, and accessibility is nested - {b,c},{c,d} implies {b,d}.
The result could model a causal hierarchy.
Oddly, the lack of symmetry means this is not reversible - a time-like direction?
I'm finding this quite unexpected, and intriguing. If we move to S4.3, and ?p???p, we bar looping back, reinforcing the time-like directionality. In effect it implies a sort of entropy...
Too speculative, I think; And on reflection I am not sure it achieves more than S4.3 might by itself...except that paths might be traced probabilistically.
*(added) so we might have "If Socrates is sitting, then Socrates is necessarily sitting" in S4.3, but not in S5. Necessity that persist forward.
The favoritism he has in mind, if we could quantify in modal logic, would be:
I have a number of questions about this analysis, but let me start with this: What does Quine mean by "must be seen"? Is this referring back to the act of quantification? Is this a doctrine (like "To be is to be the value of a bound variable") that would state, "To be a bound variable in modal logic is to entail a choice of some necessary predicate(s)"?
A lot of weight must rest on intuition. A [I] rational argument[/I] in support of rational argument must presuppose the authority of rational argument. You cannot rationally justify reason in a non-circular manner. One cannot justify all the laws of thought, or one's inference rules, without at least starting from accepting some of them. Like Gadamer says, one needs prejudices to even begin.
The classical inference rules are not counterintuitive. They are so intuitive that man studied them for millennia and largely came to the conclusion that they could not be otherwise. What is counterintuitive is having to translate things into logical form and properly apply the rules.
But more to your point, the reason I bring up probability is simply because it is a good analogy in terms of the sort of disagreement here. Were I a subjectivist, a frequentist, etc., I could give exactly the sort of response you've given. "Ah, but that can be framed in frequentist terms." Indeed, both subjectivists and frequentists have some sort of explanation to cover every case. If they didn't, it would be a decisive deficiency. Nonetheless, some explanations require much more "stretching" than others. And there is also a similarity here in that both sides make use of the same methodology and formalisms, and then sometimes point to the formal apparatus to say "see, this works, so the interpretation must be correct." But of course, the fact that Bayes' Theorem is useful doesn't really say much to undercut frequentism.
This is similar to Spade's point re Quine's sort of austere Platonism. Perhaps he is wrong about why Quine chooses this sort of theory of predication, but supposing he is right, it would be an example of the cart pulling the horse. In this case, metaphysics would be dictated by the particular formalism one is familiar with. This is "I have a hammer, so the world must be composed of nails.
And, to the contrary, Klima and other Aristotelians claim that this framing of modality, and of essence in terms of modality, is in fact hostile to Aristotle. But this shows the problem of pointing to formalisms to attempt to adjudicate metaphysics. Here we see an influential philosopher claiming that a formalism must be abandoned precisely because it seems to him to lead to metaphysical conclusions he disagrees with.
Klima's point is that contemporary modal framings of essence seem to be leading to a sort of conceptual blindness vis-á-vis classical notions of essence, and that one difficulty is the demand that realist theories be translated into systems made by nominalists with a nominalist bias. And right here we can see just one example of a nominalist saying "let's ditch this system because it isn't consistent with the proper metaphysics."
Yet then philosophers will turn around and point to their preferred formalisms, designed with these biases and aims in mind, and try to call on them to adjudicate metaphysical questions. "Look, truth is not relational, it cannot ultimately apply to the adequacy of intellect to being, because in this formalism it applies to propositions and has an arity of one."
Obviously, this sort of appeal to formalism will be particularly inadequate if the camp using it has themselves claimed that such formalisms are just a few among an infinite number of possible creations that must be selected for on the basis of some vague criteria of usefulness
I think the Principal of Non-Contradiction is enough. Something cannot happen and have not happened. George Washington cannot have been the first US President and not have been the first US President (p and ~p).
The idea of the "past changing" would seem to imply some sort of second time dimension by which there is a past that exists at some "second time" ST1 and then changes at some later time ST2. But if the past changes and George Washington was not the first president then he was never president.
Philosophers of time have discussed if such a notion is even coherent, but at any rate I see no reason why we should trouble ourselves too much about it. It seems on par with questions like: "but what if the world was created 5 seconds ago and then all our memories shall change in another 5 seconds?," "what if an evil demon has messed with all my concepts and I don't really even know what a triangle is?," or the misologist's "what is reason has no authority and does not lead to truth?" or "what if nothing is really true or false?"
My personal thoughts are that, if one walks down the cul-de-sac of radical skepticism, there is no "certain" way out. The various coping mechanisms created by modern thought's love affair with radical skepticism are all subject to the challenge: "but what if it is radically wrong?" Reason has the capacity to question anything. Yet I also think that philosophy is under absolutely no obligation to start from radical skepticism. And I think having to maintain that:
"It is possible that giving my child milk tonight shall transform them into a lobster.";
"It is possible that if I recite this incantation, Adolf Hitler will become the first President of the USA, retroactively changing history."; or
"It is possible that I did not eat this dinner that I just ate"
Are all out in the realm of "radical skepticism." Certainly, on a common sense usage of "possible," I should not worry about the possibility that giving my child milk will transform them into a lobster, nor do I think the actual necessity in play here is inaccessible to the human mind (else the project of the sciences and philosophy would be doomed). Likewise, my having both ate and not ate my dinner seems straightforwardly contradictory.
I am not sure if this is a good way to go about it. You're splitting everything up into individual propositions. So, you have it that the specific individual proposition involving Washington's birth is necessarily true in virtue of the particular event of Washington's birth. This is not how it is normally put at least. The necessary relationship between the truth of a proposition and the fact that what it describes obtains is generally framed as a general principle. It's true for all true propositions, in virtue of the fact that they are adequate to being. Causes are many and are instantiations of principles, but necessity "flows" from principles.
Existential, metaphysical, and physical necessity are normally described as ordered, which I think is the right way to look at it. One is able to describe physical necessity through appeals to more general principles, rather than as some sort of heap of propositions that can either be true or false and necessary or contingent. That George Washington can't have been both born in 1732 and not born in 1732 is explicable by the more general principle that a thing cannot both be and not be in the same way, at the same time, without qualification.
Agreed. But don't we also have to agree that this is not necessarily true? Otherwise, where do we draw a conceptual line between what is necessary and what is overwhelmingly likely? But by all means, let's not worry about any wildly unlikely things.
Quoting Count Timothy von Icarus
Bracketing whether this is ever normally put (!), I don't see what's wrong with it. Isn't it an instance of the general principle? It seems clear enough. The general principle, if I understand you, would be "a proposition is necessarily true if the fact that it describes obtains." (This invokes the "adequate to being" idea, which I find a bit opaque, but no more so than any other attempt at a correspondence theory of truth.)
"Quoting Count Timothy von Icarus
Here's the real rub. I can't remember how much of the Kimhi thread you followed, but one of the major themes was whether PNC applies to both logical and physical space, and why. We know ~(p and ~p) (in most logics), but why is it that physical occurrences cannot both obtain and not obtain? Is it because of the PNC, or is the explanatory arrow reversed, with the PNC being as it is because it reflects something about the way the physical world must be actualized? Or, ideally, both -- we're equipped with rational equipment that is perfectly suited to the way the world in fact operates?
"GW was President in our world, but there are other worlds in which he was not." When we say this, are we saying the same thing as "The (logical version of the) PNC applies in our world, but there are other worlds in which it might not"? Or, if we don't like possible-worlds talk, is saying "GW might not have been president" the same kind of statement as "The (logical) PNC might not apply"? There's a pretty stark difference, seems to me, and it's tied directly to how we should understand "necessity." But I'll pause here and see what you think.
I'll go over the argument once again for you. You suggested that a possible world semantics for modal logic was counterintuitive. I'm asking you what might be concluded from this, by considering how one might react to someone who claimed that the classical inference rules were counterintuitive. You cannot say that someone is wrong concerning their intuition. If they do think classical inference counterintuitive, what a teacher might do is work through some examples to show them how classical inference leads to coherent deductions, allowing one to express one's ideas consistently.
Similarly, all a teacher can do for someone who finds possible world semantics of modal logic counterintuitive is to show that the results are coherent and consistent, and hope that the pieces that seem counterintuitive fall in to place, becoming intuitive as the logic is learned.
You would I hope agree that logic is a discipline, that it requires some effort to follow and understand and that it does considerably more than simply to reinforce one's intuitions.
Nor will mere intuitions do as a basis for any shared argument, given that our intuitions are not all held in common. Intuition cannot serve as a basis for rationality.
Modal logic, including possible world semantics, is an accepted part of formal logic, with a very strong foundation and application across diverse fields, including many outside of philosophy. Choosing to use it is not so much like choosing between frequentist and Bayesian approaches to probability, as choosing between integral and differential calculus. You may use the tool appropriately to the task, with confidence.
The other philosophers here are quite entitled to differ with Klima on several points. Most obviously, they may question whether his notion of metaphysics is indeed "proper"; they might also ask whether his articulation of "proper metaphysics" really does not match our best, consistent and coherent account of modality; and they might point out that if a theory does not fit well with out best logic, that provides us with ample reason to question not the logic, but the theory.
That was in reference to Quine though. "This system implies 'Aristotelian essentialism,' (at least as he understood it), therefore it is flawed."
Now that is a fine point to make. If formalism implies a position one takes to be false, it is indeed deficient. The point is rather that one cannot then turn around and point at an "approved" formalism as evidence of the rightness of a metaphysical position.
This same point is made re Quine's methods in metaontology. That "there exists at least one Hercules that is strong" implies an ontological commitment to the existence of Hercules, but not strength, is obviously not neutral.
It seems worth pointing out that PNC will apply throughout all possible worlds.
Quoting Count Timothy von Icarus
Yes. But if a metaphysical position, understood formally, entails a contradiction, that is reason to reject the metaphysical position. Which is to say that our metaphysics ought not be inconsistent.
Before we continue, it would be useful to set out what "Aristotelian essentialism" might be, in its variations. It is not monolithic, and we may well find some agreement .
Barcan seems sympathetic, but Kripke less so. In formal terms, we can differentiate between fixed and non-fixed domains.
Fine would have us consider essences in terms of definitions rather than necessary properties. Now it remains that it is very unclear to me what an essence is for you, but I suspect that you would find Fine more to your liking than Barcan. Fine wants to rescue essences from modality.
Quine reiterates his argument, further extending it to attributes. To be extensional, one ought be able to substitute equivalent terms without altering truth values, but Quine argues that this does not work in modal contexts. Hence for Quine modal contexts are "intensional".
One way to think about the distinction between intensional and extensional contexts is that a predicate in an extensional context refers to the very objects picked out, while in an intensional context the predicate refers to the attribute doing the picking...
Suppose this is our domain...
We can give the beads proper names by numbering them from left to right. The beads are 1,2,3, 4,5,6,7,8,9. Intensionally, the red beads are those for which "having the attribute red" is true. Extensionally, red = {1,2,3}. it just is those beads.
Quine takes the example
and the identity
and constructs the falsities
and
For those beads, that a bead has the attribute of being red is discovered by looking to see what colour the bead is. It is therefore not analytic, but synthetic. Being a member of {1.2.3} on the other hand, is analytic. Being red and being a member of {1,2,3} are not the very same.
Notice also {1} might have been blue. But it would still be a member of {1,2,3}.
For Quine, any attribute might have been otherwise, and so for Quine there are no essential properties. But every item in the domain is a bead; so while it is possible for 1 to have been blue, it is not possible for 1 not to be a bead and still be 1. 1 is necessarily a bead, and not not necessarily red. Being a bead is part of the (Aristotelian?) essence of 1, but being red is not.
Of course, Quine would point out that we arbitrarily limited our domain to beads. And he would be correct. What counts as an essential attribute is decided not by examining the beads, but in the linguistic act of setting up the domain. Essence, then, is an arbitrary part of the language game.
Quoting Banno
Interestingly, we could number a set of objects extensionally without knowing what they were. So "being a bead" (or any other common noun) wouldn't come into play. Must something serve as an "essence", though? "Object"? "The thing I am speaking about"? Relates to Kripke.
I might have missed a response somewhere, but I'm still curious about this, from Part 3.
Quoting J
I'm please.
I chose it also in order to draw comparisons to PI§42 regarding simples. What is the simple here? What are the individuals? We treated the beads as the individuals. I left out the string entirely; the domain might have been set to {beads, string}. I might equally validly have treated the colours as individuals - that the domain was {blue, red}. What counts as an individual in the domain is stipulated.
Quoting J
No, you didn't. I had intended to come back to this. It needs a longer post delving into the context. Next post, maybe.
So this is a long argument setting out w "the only hope of sustaining quantified modal".
The page referred to just before your quote...
Quine's view of Aristotelian essentialism, it seems. So what is the "reversion to Aristotelian essentialism"? That some of the properties of a man are necessary, and some contingent.
What Smullyanis proposes (back a few paragraphs) is very close to Kripke's rigid designation. Quine would reject this on the grounds that some description must be associated with any proper name in order to "fix" it's referent. This wasn't rejected until Donnellan and Kripke's discussion of the topic, a few years later.
Quine's text is not helped by the juxtaposition of necessary and contingent, and the association of analyticity with necessity.
So let's be a bit pedantic and oppose necessity with possibility, and define these in terms of possible worlds, while also and distinctly opposing the analytic and the synthetic, such that the analytic is understood by definition while the synthetic is understood by checking out how things are in the world.
And as for contingency, let's leave it aside until we have a better foundation.
How's that looking?
Quoting J
is, then, what musty happen if modal logic is to avoid the issues with quantification that Quine raises - in this Quine is more or less correct, and the strategy Kripke adopts is pretty much the one Quine sets out - there are properties of things that are true of them in every possible world.
Whether these properties are "essential" is another question.
but this is wrong. It should be:
I'm fine with this, as long as we understand that this terminological clarification has only sharpened the questions; it's not an answer in itself. We still want to know which things that we learn about the world (synthetic knowledge) turn out to be necessary, a la Kripke and (I guess) Aristotle, and what this says about possible worlds. Is there a possible world in which water is not H2O? Kripke says no. So is there a possible world in which a human is not a rational animal? I don't know if Kripke weighed in on this, but I would say yes.
Quoting Banno
So my suggested paraphrase, "To be a bound variable in modal logic is to entail a choice of some necessary predicate(s)" would be correct. And I think we're both saying that "necessary predicates" might turn out to be so ontologically minimal that they wouldn't fit the concept of "essential properties" at all.
Good. This highlights the distinction.
And of course we might have done otherwise. We might have used the word "gold" for a group of different metals, but as it turns out we use it only for samples of that metal which has 79 protons in its nucleus. Did we discover, or did we stipulate, that it is "gold" that has an atomic number of 79? When scientific knowledge advances, are we changing the rules of our language, or are we uncovering facts that were already true? - but these are not mutually exclusive. We might arguably be doing both. In discovering that gold has 79 protons in its nucleus, we thereby changed the way we talk about gold.
What introduces necessity or possibility is the way the domain is interpreted as much as which properties are involved.
This seems to presume a fixed domain - that the very same things exist in every possible world. If that is not presumed, then there might be bound variables that belong to possible but not actual individuals. ?x?P(x) might be true in some possible world, yet not in others. In which case it's not true that the bound variable x is necessarily P. There are possible worlds in which nothing is P.
A proper name, according to Kripke, is a rigid designator. It picks out the thing named in all possible worlds. This does not mean, of course, that the thing named occurs in all possible worlds. It merely means that, if Banno exists in a world, the name must designate him and not some other. Importantly, Kripke points out that the property we use to designate that man . . . need not be one which is regarded as in any way necessary or essential. But at the same time, he says that the proper name itself wont do as that property:
As we know, Kripke believes we should refer back to the origin story of a person in order to say what that independent determination is.
Now demonstratives are also rigid designators, according to Kripke. If I point out the window and say, This cloud, I have baptized the cloud and given it a rigid designation. The same caveat applies here as with proper names: The cloud may not appear in a given world, but if it appears, the designation that cloud is rigid.
I have two questions about this.
1) Is the origin story here simply a matter of my pointing and declaring? Doesnt that seem the same as simply declaring a proper name, which Kripke says is circular? Then, if the independent determination of the referent is something else in the case of that cloud, what is it? Do we have to start talking in terms of molecular structure? But that is very un-Kripkean; that would be like using a telescope to identify a table; its not how we designate things.
2) Presumably there can be a possible world in which that cloud occurs but I do not. Does the cloud remain rigidly designated? There seems something odd about this. Do we want to say that, because I appear in a different possible world to baptize the cloud, my action carries over in some way to a world in which I never did so? There must be a better way to understand this.
Clarifications and insights welcome.
I'm not quite sure what you meant there, but to clarify, a sample space S can fully and faithfully represent any relation that is defined over a countable number of nodes, in terms of a set of infinite paths over those nodes.
However, speaking of probability theory in the same breath as modal logic seems to be uncommon, in spite of the fact that modal logic and probability theory have practically the same models in terms of Boolean algebras with minor changes or small additional structure that has no bearing with respect to the toy examples that are used to demonstrate the meaning of the theories.
Notably, the logical quantifiers of any decidable theory that has a countable number of formulas can be eliminated from the theory by simply introducing additional n-ary predicate symbols. And since modal logic refers only to fragments of first order logic, then unless the modalities/quantifiers are used with respect to undecidable or uncountable sets of propositions, then they have no theoretical significance and one might as well just stick to propositional logic. To me this raises a philosophical paradox, in that the only propositions that give the quantifiers/modalities philosophical significance are the very propositions that the quantifiers/modalities cannot decide.
Supose we put the beads in the image above in a bag, and pull out a bead. We know, since we know the number of beads, that there is one chance in three of the bead we pull out being red.This is classical, a priori probability. If we did not know the arrangement of the beads, we might apply some probability theory to an experiment in which we pull out a bead and return it to the bag, and over time we see that one in three of the beads we pull out is red. This is frequentist probability. A third, related approach might be to decide that there is a fifty-fifty chance of picking out a red bead, then to pick out and return the beads, adjusting one's estimation of the probability of picking out a red bead on the basis of the result. This is the Bayesian approach.
These are the sorts of things we do when reasoning about probability. We go out and experiment on the way things are, and describe the result one way or the other.
When we reason about modality, we do something a bit different. We stipulate, rather then experiment. We say things like "Supose you pull out a red bead..." We are not concerned with how the world actually behaves, but with how it might behave.
The similarity in models between probability and modality may lead us not to notice that what we are doing in each case is somewhat different. The one is an activity of discovery, the other an activity of stipulation.
I can appreciate the distinction you are pointing out between stipulation and observation. Indeed, classical probability theory explicitly accommodates that distinction, by enabling analytic truths to be identified with an a priori choice of a sample space together with propositions that describe the a priori decided properties of the possible worlds in terms of measurable functions that map worlds to values. By contrast, statistical knowledge referring to observations of the sample space is encoded post-hoc through a choice of probability measure. I think this to be the most natural interpretation of classical probability theory, so I am tempted to think of probability theory as modal logic + statistics.
In particular, we can define a proposition p to be analytically true in relation to a possible world w if p is "True" for every path that includes w (or 'pathlet' if transitivity fails), in an analogous fashion to the definition of modal necessity for a Kripkean frame. (But here, I am suggesting that we say p is analytically true at w rather than necessarily true at w, due to the assumption that the sample space was decided in advance, prior to making observations).
By contrast, we can define p to be necessarily true at w if the set of paths including w for which p is true is assigned a probability equal to one. Thus a proposition can be necessarily true without being analytically true, by there existing a set of paths through w that has probability zero for which p is false.
We need to be clear that, in those possible worlds in which I do not exist, "Banno" does not refer to anything.
Now go back to Quoting J
In standard possible world semantics, the domain will be different in some possible worlds. In those worlds there need not be an x that is P. That is, ?xP(x) would be false. It would not be the case that in every possible world something is P. If the domain is fixed - the same in all possible worlds - then a bound variable might have necessary properties; we might have ?xP(x) in every possible world.
When the domain varies, quantification does not necessarily imply that x has any essential properties, since x may not exist in all worlds.
So in the varying domain of standard modal logic, to be a bound variable does not entail a choice of some necessary predicates.
But I can see where this may come from. The Barcan formula, ?x ?P(x) ? ??x P(x), also relies on a fixed domain. may also be implicitly making use of a fixed domain - it is hard to say.
Kripke is not using a fixed domain.
Hence the need to note that there are possible worlds not blessed with my presence.
Quoting Banno
Good line for an obituary: "An eminent logician, the late X claimed he was necessary in all possible worlds, but alas, we now discover this is untrue."
This occurs as part of an extended discussion. Kripke does offer the causal theory as a solution, but there are problems.
I'd take a different track in characterising the failure to name Glunk as "Glunk" here. The issue at hand is what it might be to have effectively named an individual. It is worth stating something that is I hope quite obvious, but which tends to get lost in these considerations. A proper name works only if those in the community agree as to it's use. If a proper name does not in our conversations pick out an individual unambiguously, then it has failed to be a name.
The problem isn't the circularity - circular arguments are not invalid, just unsatisfactory, unconvincing. An individual might well decide to use "Glunk" to refer to that individual they call Glunk, but then they would be subject to the difficulties noted by Wittgenstein - yes, private language. Kripke is quite right that we need something else to "better have some independent determination of the referent of ?Glunk". But that determination need not be the origin story, as Kripke suggests. We might just as well depend on the community in which "Glunk" picks out Glunk. If we agree that "Glunk" picks out Glunk, the presence or absence of an origin story is irrelevant.
Here I am departing from agreement with Kripke.
Here I am using much the same argument that I have used to reject Kripkenstein.
Quoting J
A name is successful if it is used consistently and coherently by a community, and this regardless of the origin myth. The independent determination of the referent is the use in the community. Or if you prefer, and I think this amounts to much the same thing, we could use Davidson here, and say that the correct use of a name or a demonstrative is that which makes the vast majority of expressions that include it, true.
Similarly, perhaps the reference still works in your absence becasue the reference is communal. "That cloud" remains a rigid designator. I doubt Kripke would agree with this.
Non-rigid designators: Reassignable Pointers. Namely, mutable variables that range over the address space of other variables of a particular type. E.g, a pointer implementing the primary key of a relational database.
A rigid designator: A pointer that cannot be reassigned, representing a specific row of a table.
An indexical: A non-rigid designator used as a foreign key, so as to interpret its meaning as context sensitive and subject to change.
Yes, a proper name is a convention. There is nothing to it beyond whatever a given community agrees is a sufficient "baptism."
Quoting Banno
Hmm. I'm not so sure. The question is, Can "Community picks out Glunk" produce the same plausibility responses for us that "Glunk is picked out by his birth" does for Kripke?
Let me use the Queen Elizabeth example, as it's easier to quote directly. Kripke asks, "How could a person originating from different parents, from a totally different sperm and egg, be this very woman?" He acknowledges that others may have different intuitions about this, but for him, "anything coming from a different origin would not be this object."
So now we ask, "How could a person, Glunk, who is not so-baptized by his community, be this very person?" My intuition here is quite different from the Elizabeth-from-different-parents example. I would say that Glunk, under whatever name, is surely the same person. In other words, his name is not anything like an essential property. The name may be essential to how we designate him, but that's not the same thing.
Quoting Banno
This is all well and good if the issue is indeed about the correct use of a name. But I think Kripke is talking about something different. It's the de re vs. de dicto question, yes? There has to be something about a rigid designation that transcends nomenclature or terminology. I appreciate that a community-wide agreement to name something is not the same as my personal, private-language decision to do so. But they are the same sort of thing. I don't think you can get to "independent determination of the referent" simply by letting "independent" mean "independent of me." I read Kripke as talking about an entirely different, ontological independence. Which comes with its own problems, of course, but this is a start.
Well yes it is, becasue we make it so.
That's what Kripke did in positing possible world semantics as a way to give meaning to modal utterances. When you ask "What if Elizabeth had not had Elizabeth Angela Marguerite Bowes-Lyon (such an English name...) as her mother", you are thereby asking about Elizabeth... becasue you make it so.
And of course her name might have been Kate. In which case she would still be the very same person.
A name is not a property at all. That's why properties are represented as f,g,h and individuals as a,b,c... and names as "a","b","c"... Why? Becasue this is how the game is played; why does hitting the ball to the boundary count as a four? Why do to five cards of the same suit count as a flush? Becasue it's what we do. "What this shews is that there is a way of grasping a rule which is not an interpretation, but which is exhibited in what we call "obeying the rule" and "going against it" in actual cases."
The point may have been missed, so I'll restate it. "Independent determination" is irrelevant; what counts is that the folk in the conversation are talking about the same thing, to their own satisfaction. That is what it is to have effectively named an individual.
Quoting J
Kripke didn't understand Wittgenstein. That's why he felt obligated to write his other book, a book that was important for being so wrong.
If the name changes but she is still the very same person, then a name cannot be an essential property -- or, if you like, any sort of property. (Though I don't really see why 'is called Elizabeth by everyone who knows her' can't be a property. How is it different from 'has red hair'?)
But compare "She might have had different parents. In which case she would still be the very same person." You're not maintaining that this is true in the same way that the Eliz-vs-Kate case is true? Indeed, it isn't true at all, is it? We might mistakenly designate her as the same person, but that would be an error -- if we agree with Kripke about the importance of parentage.
indeed, because a name is not a property...
Quoting J
Property or predicate? How does the use of each differ? Extensionally, a name picks out an individual, and a predicate is a group (set, class...) of individuals. What is a property?
Supose we took a sample from Elizabeth's body and found that she could not have been the daughter of Elizabeth Angela Marguerite Bowes-Lyon... Who did we take the sample from? I think that as you specify your example with greater precession, you will find that the antinomy dissipates. Further, if it does not dissipate, then that very fact shows that you have not yet clearly stipulated what you are saying.
This is a good question. What would you say?
The response I gave above what that once we take into account that (24) is not a necessary truth, that 9 is not the number of planets in every possible world, we can see why the substitution fails for this particular case. It's a bit harder to see how this might work in the case of propositions. Partly that's becasue what a proposition is, is somewhat ambiguous, and what a proposition is is central to the argument. It's clear, for example, that
is false, as is
Now a proposition is supposedly different to an utterance or a sentence, in that it is what the sentence stands for or refers to, and not the sentence itself, so that for instance the sentence in English and the sentence in French may differ, while the proposition each expresses remains constant. So we might ask if it true that
I'm not sure there is any one answer to this.
As a result of such considerations I tend to use sentence rather than proposition.
Just to be clear: Do you read the '=' sign here to mean 'says the same thing as' or 'expresses the same proposition as'? Or would this difference, if any, not be significant? I'm looking for paraphrases that don't use "proposition."
Well yes - the planets.
We may end up with "The number of the planets > 7" and "Le nombre de planètes > 7" both referring to the proposition, while neither of them is the proposition; and then it is the proposition that refers to planets and perhaps to numbers. Why multiply entities unnecessarily? Both "The number of the planets > 7" and "Le nombre de planètes > 7" are about the number of planets, without the need for a proposition as intermediary. What they have in common is not some other entity we call the proposition, but that they say the same thing about the number of planets.
Quoting J
So back to the distinction between properties and attributes and classes.
Beads {1,2,3} and the beads with the attribute "being red" are extensionally equivalent. In the domain of beads, being red just is being bead 1, 2, or 3. Any "why" as to those beads and not 4, 5, or 6 or 7, 8 or 9 is for extensionally besides the point.
But are you entitled to the phrase "say the same thing" without explaining what it means? Synonymy again. Is this meant to be a brute fact? Some statements simply "say the same thing" and that's as far as we can go with it? This is where the proposition comes in handy.
But as I said, I'm happy with "says the same thing" and "expresses the same proposition" being equivalent.
The explanation is that they are extensionally equivalent. Planets = planètes.
I don't see a need. Planets = Planètes = {mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune}.
To put it differently, do we know that we're "saying the same thing" about X by checking X and comparing it to what you and I have said? A kind of rough-and-ready extension of a correspondence theory? Doesn't that presuppose that you and I mean the same thing?
Some folk insist that Pluto should be included amongst the planets. There's a conversation to be had there, as well.
Notice that this is not about correspondence, so much as what we take as granted. Not meaning, but use. We use "red" to refer to {1,2,3} and "Planètes " to refer to the planets.
I see the attractiveness of this position. But there's a synonymy problem still. {1,2,3} may be extensionally equivalent to "is red", but would you really want to say that "{1,2,3}" means the same thing as "red"? What about the lack of substitutivity? If the items {1,2,3} were green rather than red, we would discover "the same" extensional equivalence, but it would now be with "is green". Any number of items can be 1, 2, and 3, but that won't necessarily make them red.
In short, how is this different from the number-of-planets problem, where we agree that, as Quine says, "failure of substitutivity reveals merely that occurrence to be supplanted is not purely referential" (140)?
Quite simple... de dicto is incoherent cause it's a quotational account, so who knows what exactly he's referencing...
You cant tell which total set of receptors are triggered for the words in a quotational account... hence the popularity of disquotation. Apollonians flock to disquotation because of its form.
But in truth, every language is a quotational account... what observation sentences are true for every person in the world are very few. Even science as its truths delve deeper and deeper. Overturning older ways for the newer, better, faster, stronger method...
In reading Quine, there are times when the man will use phrases direct from Nietzsche, that trigger a total set of receptors (example "leading to strange new vistas") and it's my belief that Quine would consider his own perspective from his opposite under the mask of Nietzsche, to scrutinize his works. To overcome this problem of subjectivity from "Stimulus to Science."
That word. If everything hat applies to {1,2,3} applies to "...is red", then what more is there to "meaning"?
And yes, it is not necessary that {1,2,3} are red. They might have been blue. That's kinda the point, isn't it?
I think the power of an extensional first-order language is easily underestimated. It'll not do to just assume that extensional contexts are inadequate, it must be shown. It is not clear that there is ""failure of substitutivity" in the instances Quine lists. The whole substitutivity issue doesnt pose a deep problem if we understand "meaning" in terms of systematic extensional correspondence rather than some mysterious intensional essence.
But doubt this will convince you.
Just as I realized Quines philosophy is based on Set Theory and Mathematics to inform him on linguistics... with hardly any ability in set theory none the less. I simply realized that what I was learning about Ordinals is how Quine orders linguistics from the top down. His "total set of receptors" was the same as the total set of nodes in which one can say this references that
1. I'm going to throw shit on you vs. 2. I'm going to throw "shit" on you... what am I referring to by "shit" in number 2? I'll give you three guesses. If you can not get it right, then it's likely cause it's incoherent because I quoted shit... and thus, modality and reference do not trigger all the same set of receptors from De Re vs De Dicto.
That I detail every language as its own quotational account... well, you cannot know wtf "hintegedanke" means without knowing it in German because there is no word for it in any other language, or even "Aristeuein" for that matter but for the Greek. Even without that... how many words are there for a Bird? In other languages? I don't know... and I dont even know 1/10th or probably 1/100ths of all the words for Bird... the different modality of a language can render something incoherent just as a quotational account...
Unless you know the meaning within that modality... the same total set of receptors wont fire...
And thus if I switch modalities from English to French w/ That oiseau is flying... the plane? the insects, ... what exactly is flying when I don't know what "oiseau" is? I can make an educated guess based on faith and "what I know that can fly?"
Thus modalities have a certain resisting against identity when substituted...
If that's opaque then I can see why you take Russel's boneheaded criticism of Nietzsche. Because you're out here substituting your meanings and words for Nietzsche's own...
And as Wittgenstein shows us, every philosopher has his own language, a language that you have to familiarize yourself with otherwise you wont know wtf they're saying.
It's not so much a matter of being convinced. I feel as you did, in an earlier thread, where you said something to the effect of, I'm frustrated because I can't see a point that is so obvious to others. (This might have been in regard to Rodl's concerns about Frege.).
Quoting Banno
This would be the source of my frustration, here. No matter what angle I squint at it from, I keep seeing a need for "meaning" in order to give a convincing account of how intension works. But . . . better philosophers than I have contested this, so I'm going to keep pondering it.
One cannot use words without knowing the meanings.
Quoting Corvus
True, though, ultimately the meaning of a word is dependent upon the sentence it shows up in.
Quoting Corvus
If that were so, no one would ever learn the meaning of a word.
I can't decide if your talk of receptors is anachronistic or just incongruous. Let's keep this conversation to the PM - it's a bit too off-topic here.
Nonsense. Meanings can be learnt via inferences from observations on the real world and how others use the words in social situations.
Yep - The meanings of words are learned by using them...
I think so . . . Let me try it from the idea of qualia. I suppose you agree that, if I ask you to close your eyes and imagine "red," and then "green," the two color patches or whatever you come up with will look different in your imagination. That is because (I would say) "red" and "green" have different meanings, at least as far as "meaning" is commonly understood. Are we on the same page so far?
(Note that I am not a fan of qualia... https://thephilosophyforum.com/discussion/9509/nothing-to-do-with-dennetts-quining-qualia )
Quoting J
We agree that we know what "is red" and "is green" mean, sufficiently well to imagine them ourselves, and to pick them out in the visual field. (And I'm not trying to beg the question by employing "mean" as if we both understand it the same way. Please feel free to translate as you see fit.). If I understand you, you're saying that extensional equivalence explains this. Or at least that's how I interpret your:
Quoting Banno
The "more" would be the quale "red." In pointing to the beads, I happen also to be pointing to beads 1,2,3, but if you and I are discussing redness, that would be beside the point.
Perhaps another good place to pause -- do you see something awry yet?
The inference of the meanings are not the meanings themselves, are they?
And how can we say that what you pick out by "this" is the same as what I pick out?
I don't see that question as having any significance. That is, we can't talk about the hidden stuff, only the things around us that are red. When we think we are talking about the hidden stuff, we are mistaken.
It's not wrong to say that this (indicating the qual) is red; rather it's senseless.
( I do like the line of reasoning you are adopting.)
What is the difference between learning the meaning of a word and learning to use the word?
(, you might consider this, too. )
Meaning of a word is in conceptual level. Using a word is in application level. They are different.
How do you tell that someone has the "concept" red?
By seeing how they use the word, and what they do in the world with red things.
So again, what more is there to understanding the concept "red" than being able do stuff with red things...
Welcome to the wonderful world of Wittgenstein.
Not everyone agrees with Wittgenstein. If you don't know what red means, how could you use the word "red"? If you are a colour blind, how could you tell red objects? For you being able to use the word red means that you know what you mean by red from your experience of seeing red via your perception, and folks describing red objects as red.
So what.
Think on it some more. Colour blind folk do use the word "red" correctly - how can that be?
Wittgenstein was wrong.
Quoting Banno
They could be using the word red metaphorically, rhetorically or idiomatically to mean something other than the colour red such as red tape, redline, red-light district.
... and Red herring, red meat of course.
This seems to conflate several issues. Why is my description of my red quale a private rule? What would be the (correct, presumably) use of a public rule to describe the quale? I'm not seeing the alternative.
As for whether you and I are naming the same quale, wouldn't the answer be: Conceivably we aren't, but it's unlikely, given how color names are learned. And again, even if our meanings turned out to be different, it would have no bearing on whether we intended rather than extended (so to speak). When I point to the red beads and call them "red", this has nothing to do with their extension. Because, as above, the same beads might be green, with no difference in extension. If the extension were all that mattered, how would I know if they were red or green? So what then is the difference?
What I'd really like -- what I think would help most for me to see this picture -- would be to hear your alternative account of how, for instance, we can label "red" without allowing that "red" means that color (or quale). And, anticipating you, if that account involves learning how a word is used, what is the "extensional version" of that? What do we teach a child when we teach them color names? "When you point to that, say 'red'?" And if the child replies, "Why?" what do we say?
Quine, in Word and Object, addresses how folk who are color blind use the word correctly.
Uniformity comes where it matters socially; hence rather in point of intersubjectively conspicuous circumstances of utterances than in point of privately conspicuous ones. For an extreme illustration of the point, consider two men one of whom has normal color vision and the other of whom is color-blind as between red and green. Society has trained both men by the method noted earlier: rewarding the utterance of red when the speaker is seen fixating something red, and penalizing it in the contrary case. Moreover the gross socially observable results are about alike: both men are pretty good about attributing red to just the red things. But the private mechanisms by which the two men achieve these similar results are very different. The one man has learned red in associate with the regulation photochemical effect. The other man has learned red by light in various wavelengths (red and green) in company with elaborate special combination of supplementary conditions of intensity, saturation, shape, and setting, calculated e.g. to admit fire and sunsets and exclude grass;
Well if your are to convince me of this I'd first have to be convinced that you understood Wittgenstein.
Quoting Corvus
... and so on. If I ask for the red pen, and they hand me the red pen, that's not metaphorical, nor is it merely rhetorically, and it certainly isn't idiomatic. It's pretty much literal and extensional.
Quite so; if someone referred to "the sensation S" for themselves alone, then the qual is private; and if they do it for others, isn't it just the colour red? Here's the problem with qualia: if they are private, then they are outside of our discourse, and if they are public, they are just our common words for this or that.
Quoting J
Rather we play with them, ask for the red block, offer them a lolly - but only the red one, and so on. We teach them to use the word. Then there is no "why?" as the task is of forthright interest.
Quoting J
...and it doesn't matter!. Becasue what counts here is the use!
That is, and here I'm grossly overgeneralising, the extension.
If one says one can use words without knowing its meanings, then he is wrong, whoever he is.
Quoting Banno
They must have been acquainted with something other than "red" to be able to do that by habit or guessing. That doesn't mean they know what "red" is. Their use of "red" could be based on the high chance of fluke guessing.
I agree. But to know a word is to use it, and to use it is to know it.
Quoting Corvus
...but nor does it mean that they do not!
We have a part agreement here, which is a rare event.
Quoting Banno
Actually it is difficult for me to imagine what colour blind would be like without being one myself, hence the point was purely from inference. You could be right. Please carry on.
Thanks.
So we need necessity in order to do physics; but we must debar it from logic. A difficult path to tread.
I think you are. I was "seeing the picture" up to this point, but you'll have to work harder to explain how use reduces to extension. I believe you still need to respond to the bead question: How do we make coherent a situation where the extension remains the same but the color changes?
Quoting J
I'm not seeing a problem with that. It might have been that beads 4,5, and 6 were the red beads. In which case, in that domain, "...is red" would be extensionally equivalent to {4,5,6} instead of {1,2,3}. And an extensional sentence about the red beads would have the same truth value as an extensional sentence about the beads {4,5,6}, and passes the test of substitution.
We want to say that there is more to being red than being {1,2,3}; but note that that "more" is intensional rather than extensional.
There need be no "intermediary step" of the sort you suggested,
Quoting J
Extensionally, Quoting Banno
The list of planets just is the "meaning" of both Planets and Planètes, and so since their number is greater than seven, both the English and French sentences are true.
There is a seperate issue, why Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune count as planets, while Pluto, amongst other things, does not. But given that we accept the list of planets, then
without further explanation. That is, if planets and planètes have the same extension, then "The number of planets is greater than 7" means the same thing as "The number of planètes is greater than 7" without further ado.
I agree, because what else could a proper name refer to? Some "essence of Banno"? But I'm suggesting that a color name is different, because in addition to referring to the various extensions of "is red," it also (appears to) refer to something intensional, namely the quale we can each call to mind. I know how much you value ordinary usage, and I would maintain that this is a clearcut case: No one scratches their head and says, "Yes, but what is Banno? What does 'Banno' mean? How can I use 'Banno' intensionally?" whereas we surely do talk this way about most terms that have definitions in addition to an extension. A proper name merely signifies without defining. So I still think the burden of argument is on you to explain why this way of talking has to be mistaken.
Quoting Banno
Yes. Does this mean you countenance an intensional use that is not extensional -- or by "we want to say," did you mean that we'd like to but we can't justify doing so?
After all, can you give a reason for saying that {1,2,3} are red, that does not involve showing us or at least looking at the beads?
No. So take me to the next step -- what does that tell us about "red"?
:smile: Isn't it your bed time...?
In one sense it tells us that there is nothing more to say about red; given the domain is only the beads, red just is {1,2,3}.
I agree that there is something annoying here, but I suspect that it cannot be well articulated.
Ha! Argumentum ad tempus requiescendi.
I will try to articulate the annoyance better, but probably not tonight, as the moon rises slowly over the Gulf of America . . .
Not a location I recognise. :meh:
Good night.
Compare Quine to Martin Lof, the inventor of intuitionistic type theory. According to Lof, analytic sentences, at least in the context of intuitionistic type theory, are de-dicto definitions that are regarded to consist of perfect information, as in a complete table.
So in terms of your beads example, Lof would regard your proposed function mapping numbers to colors as analytic. But it is important to note the utility of calling this function definition "analytic" is only in relation to existentially quantified propositions about the analytic definition, which Lof classifies as "synthetic". E.g the theorem "there exists three red beads" is synthetic for Lof in relation to your bead function definition, because to determine the truth of the theorem requires checking.
In general, Lof regards a theorem in relation to intuitionistic logic to be 'synthetic' if the theorem contains an existential quantifier whose existence requires a proof in relation to the analytic definitions provided. Lof regards a synthetic theorem to be 'a priori' if the theorem can be proved de dicto via a process of deduction using the supplied analytic definitions that makes no recourse to facts about the external world. This is of course the case with intuitionistic logic, since its deductive system is constructive, i.e. de dicto. Hence for Lof, most of the theorems of intuitionistic mathematics are synthetic a priori (with the exception being postulated mathematical axioms). Generally, synthetic a priori propositions are undecidable.
Of course one might question whether the rules of the deductive system are correctly applied or whether one's analytic definitions are correct, in which case one's definitions are treated as being truth apt synthetic propositions in relation to some other underlying analytic definitions. So the analytic-synthetic distinction Lof intended is pragmatic without implying an absolute metaphysical distinction.
I think that Lof's reasoning is very much in line with Quine, whose notion of "physical necessity" I understand to be synthetic a posteriori, being in relation to the external world, but nevertheless also in relation to an analytic definition of physical terminology that undergoes constant revision on the basis of a posteriori evidence.
For example I imagine that Quine would consider the theorem "All swans are white" to be an analytic definition in the sense that Lof referred to, namely that the theorem doesn't contain a non-negated existential quantifier and so cannot be regarded as "true" except in the de dicto sense. This of course doesn't imply that the theorem's negation is analytic, which consists of a non-negated existential quantifier that answers to de re evidence. To me, such examples suggest that when counter-examples cause theory change, the falsified older theory is often not even wrong, in that the older theory cannot express the counter-example that it is wrong about.
In practice, we allow empirical counterexamples to revise our concepts, meaning that the statement was never purely analytic to begin with. Quine might say that "All swans are white" was part of a revisable web of belief rather than something analytic. It's not that we stipulate that "all and only white waterfowl are swans", an unfalsifiable, analytic and false proposal.
In any case, the idea of using an intuitionistic logic here is interesting.
Apologies for any misleading. To clarify, in type theory synthetic judgments can be identified with existential quantification due to the fact all propositions are types: having a proof that proposition A is true is equivalent to constructing a term a of type A, written a : A.
When referring to existential quantification, Lof wasn't referring to an existential quantifier within a proposition, but to an existential quantifier over terms representing a proof of a proposition type. Furthermore, the terms of a proposition type are definitionally equal by fiat, i.e a proposition type is the equivalence class of all proofs of that proposition.
My example referring to the swans was potentially misleading for conflating the two sorts of existential quantification, but nevertheless valid. A term cannot be constructed for the proposition type "All swans are white", indeed for any proposition containing a universal quantifier over an infinite domain, unless the proposition is interpreted intuitionistically such that the proposition can be proved by mathematical induction.
Perhaps a better example is the proposition "Nothing can accelerate beyond the speed of light". In relativity, a proof of that proposition implies contradiction. Hence presumably, the negation of the proposition is analytic in the theory special relativity, meaning that the proposition doesn't imply the physical impossibility of faster than light travel.
I wonder if part of the problem lies in the choice of "red". I thought that picking an irreducible quale would help us see what's going on with "meaning," but maybe not. In a certain sense, "red" is like a proper name, in that it's "just there," and can't be defined further, at least not in a way that's relevant to the phenomenology.
So what if we pick "square" instead? This term has a simple definition, and doubts about possible squares are easily and publicly resolvable. Would you want to say that the extension of Square X simply is what we mean by (or define as) a square?
Perhaps bead eight is square. In that case, and given that our domain is just the beads, "...is square" and '...is eight" are extensionally equivalent, and whatever is extensional the case with square things will be extensively the case with bead eight.
So it does not look as if the choice of red is an issue.
Take note that "red" and "square" are not proper names.
Part of what is shown here is the poverty of phenomenological approaches that is simply bypassed by the extensional treatment. We don't need the messy thinking that accompanies trying to explain if and how what you see as red and what I see as red (...or square...) are the same. So ling as we agree that {1,2,3} are red and {8} is square, we can get on.
A whole philosophical quagmire avoided.
So type theory can be used to give a clear account of what is analytic and what is synthetic. This is different to what is necessary and what is possible, the concerns of modal logic. So we now have formal tools at hand with which we can make distinctions that were not available to Quine. Quine rightly dismissed the analytic/synthetic distinction as too vague, and consequently also dismissed modality, which he understood as closely related. Subsequent - or perhaps even consequent - developments have shown us ways to revive these ideas.
Here is the difference I see between "red" and "square". If someone is in doubt about "red", they aren't going to say "But what does 'red' mean?" They're probably not even going to ask, "How do you define 'red'?", though if they did, a definition of sorts is available, involving wavelengths. But people used "red" correctly long before this definition was known, so it's not a helpful response. The point, then, is that "red" does seem to be the sort of thing that has to get pointed to; it can't otherwise be explained or defined (phenomenologically).
"Square" is different. The doubtful geometer can and does ask, "What does 'square' mean?" and receives a definition that is phenomenologically relevant and simple -- check the sides and angles. For me, the conclusion is irresistible that, in addition to various extended things that are square, there is also an intension for "square", a meaning or definition that can be appealed to in doubtful cases, and that we would certainly use in teaching a child about squares.
This doesn't yet constitute a full-fledged defense of "meaning," but are you with me so far?
Quoting Banno
I know I've pointed this out before, but I think it's really important to keep in mind: Quine accepts the analytic/synthetic distinction when it comes to what he called "logical truths":
It is the second kind of alleged analyticity, typified by "No bachelor is married", which requires synonymy, that is the focus of Quine's objections.
Yep, tautologies are true because they remain true under substitution - and that is becasue of the very definition of extensionality. So a=a or p v ~p are analytic because no matter what you substitute in to a, it remains true. Same for any tautology.
But a Batchelor of Arts need not be married, and a bachelor might be married to his work.
That is, Quine accepts the analytic/synthetic distinction when it can be given a firmly extensional definition.
So far as I understand the sort of formal systems @sime has in mind, analyticity is defined in terms of construction rather than substitution. The identity a=a is always constructible, without the need for external verification. Not so for "p v ~p". Nor for "Bachelors are unmarried".
So yes, synonymy requires verification - "witness".
I think you're pointing to the fact that any definition will ultimately have to consist of simples. But why would that mean it wasn't a definition, or meaning? My suggestion is modest: anything which can be defined in terms of simples is therefore different from a simple itself. Thus, this may lead to an explanation of why we have a pretty good idea what "square" means, much less so for "red."
It's important that we don't get this mixed up with using these terms. Here, of course, we do fine with both "square" and "red," but to say that this settles the issue of meaning is to beg the question, surely; the question at hand is whether meaning is use.
BTW, if either one of us resolves this satisfactorily, I will write it up and send it to a major journal -- Breaking news! 20th century conflict settled! Wittgenstein proved right (or wrong, as the case may be)! :wink:
Wittgenstein already won this particular game by pointing out that it is not so much what we say as want we do that is of import.
I guess I never understood why this was supposed to be obvious, or even true. Why is doing more important than saying? Certainly we want to know what we're doing with words, but what we're trying to express with them has usually been taken as extending well beyond what we may do. Is there a way of expanding the above maxim with some argument or demonstration, rather than claiming it's something we can simply "point out" as a game-winning move?
Saying is a doing.
I win.
:wink:
But only on a particular interpretation of what it means to say something -- which is the very interpretation we're examining.
Draw? :wink:
Not really, I settled this like a month ago... showing Quine uses set theory to inform on linguistics which I infered from studying ordinals and Quine's detailing you cant reference words or substitute them through different modalities because the total set of receptors aren't the same. And some how that confused you greatly... because you obviously never read Quine except for like a few pages.
Reference via different modalities is generally fallacy of equivocation. Plain and simple. Not sure how this got a month of discussion to not even figure that out yet.
That is, in using Wittgenstein against Quine I've neglected the problems that might cause for Davidson.
So this hasn't finished.
And I still need to sort that last argument, from the final paragraph of the article.
So the winning move reduces to: "it's not so much what we do as what we do that is of import?" :rofl:
Do you think it is possible today to give an accurate (if perhaps still imperfect) account of why different people experience all red objects as red?
The (radical) empiricist wants to demand that many aspects of human experience are "off limits" for philosophical, or at least epistemic consideration. However, my view would be that, if we are able to understand the metaphysics and physics of sense knowledge and intellectual knowledge, then there is no reason for us to exclude phenomenology, quiddity, etc. from our analysis.
Anyhow, I would just note that it is easy to go further than Wittgenstein and begin throwing up radical empiricist critiques of him as well, to go "full behaviorist" (and "full eliminitive materialist") and to demand that language be reduced to use, which is actually just stimulus and response. After all, what else is "observable?" The challenge is thus: "Show me an observation of a 'language community' that cannot be explained in terms of stimulus and response and mechanistic causation? You cannot."
This would give us conclusions like "LLMs use language appropriately, so LLMs are language users," etc., and "LLMs are conscious so long as their behavior makes us refer to them as such. There are no "facts of the matter" about consciousness. In a way, it's the Cartesian view of animals expanded to include man.
The objection here is generally that: "the hyper empiricist is leaving out a whole swath of human experience, indeed the very arena where knowledge and understanding occur for us."
But I always find it ironic that this charge gets leveled at the hyper empiricist by the (less) radical empiricist.
No. This problem has been around for a while, as you know. "Maybe Jesse's 'red' looks like my 'green'?!!" But that doesn't stop us from being able to define "red": "the color at the long wavelength end of the visible spectrum of light, next to orange and opposite violet. It has a dominant wavelength of approximately 625750 nanometres," according to our friends at Wikipedia. This is what I meant by a phenomenologically irrelevant definition. We can accept the definition and still be unable to use it to judge the quale. So, what we can't "define" (if that's even the right word) is the subjective experience itself.
Fortunately, it only matters if we require absolute certainty here, which we shouldn't. It seems to me wildly unlikely that evolution would have selected for "personalized qualia" while retaining the same mechanisms for brain processing of the same available wavelengths for each person. That would be expensive and useless. Like the sun rising tomorrow, we can stop worrying about it, despite lack of certainty.
Quoting Count Timothy von Icarus
Actually, I'd be comfortable with the first conclusion, precisely because being a "user" tells us nothing about what's going on mentally. (In the case of the LLM, nothing.). The second conclusion would never be made by a "full eliminative materialist," though! They're not interested in what might or might not be conscious. For us, assuming we believe in consciousness -- then yes, we'd reject the notion that simply referring to something as conscious because it appears to pass all the tests is the same thing as being conscious. We'd also raise two eyebrows at the idea that we know what these tests are, anyway.
Ah well. Yet anther discussion of the phenomenology of colour will only help the length of my thread.
LLMs upset Douglas Hofstadter as he states his whole theory behind GEB is wrong or LLMs are conscious...
Hence over to Davidson, and interpreting natural languages in formal first order terms, as truth functional. And we arrive at the nineteen eighties.
I thought you'd be on board with that:
Quoting J
Quoting Banno
But maybe your "Ok" wasn't assent. I agree about not prolonging this with color phenomenology and Mary the Color Scientist and all that, but . . . do you assent that the imagined red and green are different experiences?
No. Red and green may be experienced, but they are not experiences - not qualia, because nothing is.
It's not just that the red in my imagining might be the green in yours, but that the comparison cannot be made. Red and green, like all words, are inherently communal, not private.
Quoting J
Too late.
A typo, I think? You meant "truth functionality requires that there not be substitutional opacity," no? Or else I really got lost!