Agrippa's Trilemma
Agrippa's trilemma aka Münchhausen Trilemma.
Regarding proofs,
A. there are only 3 possibilities
1. Infinite regress (every premise requires an argument; every premise of that argument requires a separate argument; so on ad infinitum)
2. Axiomatic arguments (assume a specific set of premises)
3. Circularity (the argument's conclusion is just a restated premise)
B. None of the three (1, 2, and 3) are satisfactory
Ergo,
C. Nothing can be proven
---
Refutation
If Agrippa's trilemma is a sound argument, all arguments fail including Agrippa's trilemma itself [self-refutation; Agrippa, you just shot yourself]
---
Refutation of the refutation of the refutation ...
1. To claim Agrippa's trilemma is self-refuting I have to craft an argument, call it X, to do so but since I assumed Agrippa's trilemma for that, I've conceded that no argument will do the trick and that includes argument X. In other words the refutation itself is self-refuting.
Intriguingly, this refutation of the refutation is itself self-refuting for the same reason; however dogmatists are still not out of the woods because the refutation of the refutation of the refutation is also self-refuting, again for the same reason ... ad nauseum/ad infinitum :vomit:
2. If I use reason to prove reason's worth it would be a circulus in probando (picture baron Müchhausen extricating himself out of the marsh by pulling his own hair).
WTF? :chin:
Regarding proofs,
A. there are only 3 possibilities
1. Infinite regress (every premise requires an argument; every premise of that argument requires a separate argument; so on ad infinitum)
2. Axiomatic arguments (assume a specific set of premises)
3. Circularity (the argument's conclusion is just a restated premise)
B. None of the three (1, 2, and 3) are satisfactory
Ergo,
C. Nothing can be proven
---
Refutation
If Agrippa's trilemma is a sound argument, all arguments fail including Agrippa's trilemma itself [self-refutation; Agrippa, you just shot yourself]
---
Refutation of the refutation of the refutation ...
1. To claim Agrippa's trilemma is self-refuting I have to craft an argument, call it X, to do so but since I assumed Agrippa's trilemma for that, I've conceded that no argument will do the trick and that includes argument X. In other words the refutation itself is self-refuting.
Intriguingly, this refutation of the refutation is itself self-refuting for the same reason; however dogmatists are still not out of the woods because the refutation of the refutation of the refutation is also self-refuting, again for the same reason ... ad nauseum/ad infinitum :vomit:
2. If I use reason to prove reason's worth it would be a circulus in probando (picture baron Müchhausen extricating himself out of the marsh by pulling his own hair).
WTF? :chin:
Comments (36)
Euclid did pretty well with the second method. That another set of premises is possible doesn't make fidelity to the one's adopted unsatisfactory.
Yep, math (Euclid) is axiomatized, to the extent possible. However, assuming a set of axioms in other areas flies against the principle (PSR) that all statements need to be proven (no flat assertions allowed).
God exists! Don't you want to ask why?
What does PSR refer to?
The principle of sufficient reason.
Before anybody tries to prove anything with it, wasn't Leibniz saying that everything that exists must have some reason for being here because the thing that exists could easily not exist with another set of conditions?
Si, si, señor!
Ship of Theseus, only now we're making improvements + we're doing it while still sailing. :up: and yet I don't see anyone respond in a satisfying manner to Agrippa's challenge to the dogmatists.
Does it not matter who is putting forth a dogma and what it is?
It sounds like you want an unconditional boundary.
I'm just exploring the possibility of escaping from the clutches of skepticism. Do you see a light at the end of this tunnel?
Well, I do not share the ready optimism of Leibniz, but he did show that all alternatives do not need to be cancelled for something to be viable. The limits of negation apply to all. Which is sort of one of your points.
Pyrrhonian? Academic? Cartesian? Humean? ... Rortyan?
:zip:
Suppose we have an epistemic principle, like evidentialism, saying that for any P we believe, we need to have evidence that P: if this thesis of evidentialism itself doesn't actually have evidence through evidentialism, then either evidentialism is self-refuting or is not of global-scope (e.g. there are exceptions to the rule). But our epistemic principles should be our most general and topic-neutral principles, so we're in a very problematic spot if we lack any global principles for good reasoning.
But consider that, given evidentialism, it turns out we do actually have evidence of evidentialism for us to believe in evidentialism. This is clearly a case of epistemic circularity, but it is the only coherent route for us to take. It's not bad to have an epistemic circularity at all, in fact, we should be very worried if our epistemic principles failed to verify themselves!
Note: I'm not saying evidentialism itself is true here: it's used as a prop for an example defending epistemic circularity. Evidentialism itself does not entail epistemic circularity, there are evidentialists who are foundationalists, infintitists or other non-coherentists
No! This is not correct, the PSR is not an epistemic principle regarding justification. The PSR is a metaphysical principle regarding explanation, that is, any facts in reality out there are explained by other facts (these can be causal explanations, grounding explanations, or what not).
For instance, the fall of the apple is caused by, say, the properties of its mass, the laws of physics and what not, and these facts conjoined together explain the apple's falling.
This is completely different from principles regarding epistemic justification. For instance, we may think we need a reason for all our beliefs, including us believing the apple fell, and perhaps our reason for thinking this is that we think our senses are reliable (reliabialism), we're using induction (Bayesianism), so on.
The first is an explicitly metaphysical principle not about what we should believe & standards of justification but about the explicability of reality, the other are epistemic principles about our beliefs and justification
By the way, the PSR is usually restricted to contingent facts. Proponents of the PSR do not generally think necessary facts, like 2+2=4 or the law of identity require further metaphysical explanation, but only contingent facts like eating dinner today, though not everyone restricts it, obviously
Very interesting.
Needing a reason for a reason not indicting all attempts toward those ends.
(Your comment went well beyond that observation).
All three work.
So the choices are: reason as a hypocrisy (it fails to self-justify) OR reason as a circularity (it self-justifies). Can we say that what we're dealing with here is a [s]vicious[/s] virtuous cycle?
Yes Agrippa's trilemma is self-refuting but only if you assume it to be true; but then the refutation would be self-refuting; this refutation of the refutation itself is also self-refuting; so on ad infinitum. The bottom line: once we assume Agrippa's trilemma, it precludes logic - no argument is permissible beyond that point and that means you can't refute Agrippa's trilemma. In fact this argument which I just made is also inadmissible and to complicate matters further even this one which I'm making is not to be taken seriously, so on and so on ... ad nauseum/ad infinitum. :zip:
What are our options? We have to prove Agrippa's trilemma is unsound. One way is to say there's a 4[sup]th[/sup] alternative i.e. Agrippa's trilemma is a false trichotomy. Any ideas what this 4[sup]th[/sup] option is?
Or we could follow Kuro's lead and say that the circularity isn't vicious but virtuous; at the very least, reason ain't no hypocrite (it demands of itself what it demands of others and ... meets those demands; how exactly, Kuro will tell us).
Quoting Agent Smith
Excellent: exactly my point. :)
Quoting Agent Smith
I think the error in Agrippa's theorem is in Point B. He said, "none of the three are satisfactory."
The solution to the problem, or the refutation of the trilemma is ridiculously simple. Substitute B with B1, where B1 says "all three are satisfactory, any one of them individually and any two in combination or all three."
This can't be decided by logic. This can only be decided by an arbitrary personal call which you hold true: B or B1.
1. Infinite regress
2. Circularity
3. Axiom
3, according to Agrippa, unsatisfactory, options. Nevertheless, the skeptics did have beliefs. Therein lies the rub! Pragmatism?
So...according to Agrippa. His word against mine.
Sorry, I did not see this. You beat me to it.
Sophia (wisdom)?
Quoting Banno
Agent Smith, you read more carefully, please.
Agrippa called them three possibilities of proofs. PROOFS. So they are not just a walk-in-the-park, or dancing in the rain, or having a sandwitch at Mrs. Yashinski's tea party. They are PROOFS.
There is no such thing as a proof that does not work. If it does not work, it is not a proof.
Agrippa called them Proofs. So it is given already, that they work, and do the job.
Then agrippa says it, quite inappropriately, that they are not satisfactory.
How can he say that? When he had already agreed that they are satisfactory, when he called them proofs.
There is no such thing as an unsatisfactory proof. In that case it's not a proof.
So... Agrippa commits a self-contradiction.
Seeing that is how you arrive at the truth.
I don't know what you are talking about. You are saying I am stupid compared to Agrippa? If you read my one previous post, you will see that it's quite the other way around. It was HE who dug himself in a logical contradiction, not me.
So... according to you Wisdom is to commit logical faults in arguments? (Rhetorical question. Just please don't assume I am stupider than any of the philosophers I criticize. I may or may not be, but just don't assume that. Aside from that insult, you are also committing an appeal to authority fallacy, when you say, "yes, GMBA, you seem to be right, but this other guy I quoted is wise, and you are not.")
What are our options?
1. Axioms (assume truth), but remember this is exactly that which is being rejected by [s]Agrippa[/s] reason. No flat assertions.
2. Circularity, but that's a big no no in logic. Again, reason applied to reason. This is a flat assertion, there's no argument, but that's a different story.
Thus the trilemma is established - it's got to be one od these 3 and nothing else and all 3 fall short of the mark, not because Agrippa says so but because reason says so.
Summary: Reason says reason is no good,
If there's a contradiction then it is this: Reason commits suicide - Agrippa has crafted a logical argument that logical argumentation fails. It's not Agrippa vs. Logic as you seem to be thinking, it's Logic vs. Logic. Kinda reminds me of the omnipotence paradox: if god defeats Himself, does He win or does He lose? Both? Neither?
The SEP article on skepticism concludes: There are no justified beliefs.
On an intuitive level, says a professor, how good is a system that self-destructs in such a fashion? Logic doesn't need enemies, it is its own worst enemy, oui monsieur?
The fact that you're asking for an argument to prove this kind of presupposes the thing being proven, but nevertheless, I'd cite Conee, who argues for reflective equilibriums which are epistemically but not logically circular (it's basically a type of a coherentist foundationalism which also doubles as a response to the Criterion problem).
Précisément! Circular! We knew that! Doesn't it remind you of Kavka's Toxin Puzzle? One only needs to intend to drink the poison/prove logic - it's the same as drinking the poison/proving logic.
How about if we say logic works? I am able to predict; in fact I think it's the other way round, I'm (very) predictable.
Truth (proven truth) exists in a priori considerations.
And in a priori considerations all three are acceptable. To my knowledge, at least two are acceptable.
If Peter is taller than Fred and Fred is taller than Paul then Peter is taller than Paul.
This is true, no matter whether there is indeed a Peter or a Fred or a Paul.
Yes, this is circular, and yet it is true.
Or take the other one. Axiom: the order of terms in a summation of numbers is immaterial.
Therefore it is true that the sum of 5+2+7 equals the sum of 7+2+5.
Yes, it is based on axioms, yet it is true.
Agrippa's trilemma fails in the realm of a priori proofs; yet it is irrelevant in the realm of empirical observations, because in that realm there are no axioms, and there is no circular logic. In fact, if you ask Hume, there is a chance that there is no causality in the empirical world, altogether.