I'm curious to see what some other people think about this. — 83nt0n

Me too: https://thephilosophyforum.com/discussion/comment/377693

I'm actually tempted to call it the 'problem of deduction'. — 83nt0n

Different to this, though?

https://www.semanticscholar.org/paper/The-Enduring-Scandal-of-Deduction-Is-Propositional-D'Agostino-Floridi/6ff51e3f704044fac00b2c7430cf1ac775283820

Yes, I think so.

What Carrol leaves out is that the tortoise is playing the part of an interlocutor who refuses to be bound by the rules of the game. It's not possible to play a game with someone who refuses the rules of that game. We're left with Achilleus's dawning recognition - daylight for him not yet entirely arrived - that playing such a game is a waste of time. And for so long as Achilleus plays he is wasting his time, which the longer it goes on, the harder it is to disengage, and the more bitter the disengagement. Most of us have had experiences along these lines. It's a sign of youth not to understand what's happening.

Homer's Achilleus, we might note, was not by nature a time-waster.

It seems that the tortoise is revealing a problem with deduction, specifically modus ponens. In order to accept Z you must accept modus ponens (C). Then in order to accept Z you have to accept modus ponens (D). It seems that we must use either circular reasoning or an infinite regress to support modus ponens.

Can you force me to agree the sky is blue (on a sunny clear day)? You cannot. Does that mean there is a defect in your perception or description or understanding of colour?

You're right, I cannot force you to agree the sky is blue. That doesn't necessarily mean there is a defect; maybe there is a defect in the method of argumentation.

So I've come across a story (What the Tortoise Said to Achilles) that may pose some problems for deductive logic. — 83nt0n

It is not a problem for deductive logic so much as an observation about it: There is a difference between a premiss (such as A or B) and a logical leading principle (such as C and D and so on). The latter is also called an inference rule, and all other deductive inference rules can be derived from modus ponens once certain axioms are established. One must recognize that such rules are intrinsically truth-preserving in order to understand and employ deductive logic. The turtle is only compelled to accept Z if his goal is to adopt true beliefs.

Deductive logic seems to require modus ponens to justify modus ponens. As in: 1) If a rule of inference is truth-preserving, then it is an acceptable rule of inference. 2) Modus ponens is truth-preserving(from truth tables). 3) Therefore modus ponens is an acceptable rule of inference (from 1 and 2). This is the problem posed by the tortoise. Accepting C (in the story) is accepting modus ponens. However, because of the problem with modus ponens, the tortoise must accept D, E, etc. to arrive at Z.

Deductive logic seems to require modus ponens to justify modus ponens. — 83nt0n

Again, that is why it is a leading principle or inference rule for deductive arguments in general, not an additional premiss (or infinite series of premisses) in each individual argumentation that employs it.

Maybe I was obscure. Logic is a kind of game, i.e., an activity governed by rules, as is math, geometry, and lots of other things. But there are people who won't acknowledge the rules - some even post here! - and the lesson, sometimes learned the hard way, is that it is a fundamental error to fail to recognize that with such people, the game is not what you think it is, and it is a mistake to keep playing it. The corollary being that the intransigence of some people is not reflection whatever on the game itself.

As to inference or any other rules of any game, they can be questioned, refined, improved, whatever, but the bedrock on which they lie is acceptance.

So I've come across a story (What the Tortoise Said to Achilles) that may pose some problems for deductive logic. I'm actually tempted to call it the 'problem of deduction'. I'm curious to see what some other people think about this. https://wmpeople.wm.edu/asset/index/cvance/Carroll — 83nt0n

Are we trying to use deductive logic to prove that we shouldn't use deductive logic in this story?

Absolute truth exists, but it is very often hard to obtain.

The tortoise is not being intransigent; it seems that he is exploiting a weakness in the rules. Or I guess you could say he is questioning the game itself.

Yes but the point is that modus ponens is not justified in the first place.

I'd say we're using simple questioning to argue that deductive logic is flawed. However, if deductive logic shows that deductive logic is flawed, then deductive logic is flawed.

Yes but the point is that modus ponens is not justified in the first place. — 83nt0n

Tell us what you imagine "justified" to mean.

By justified I mean entailing that a person can believe the proposition and stay rational. The justification is what connects a belief to whether or not it's true. You might ask how something might be justified, I'd say I don't know. I am a skeptic. All methods of justification seem flawed to me, including deduction.

By justified I mean entailing that a person can believe the proposition and stay rational. — 83nt0n

How do you justify that definition?

The justification is what connects a belief to whether or not it's true. — 83nt0n

How do you justify that assertion?

You might ask how something might be justified, I'd say I don't know. — 83nt0n

How do you justify that response?

I am a skeptic. — 83nt0n

How do you justify that self-characterization?

All methods of justification seem flawed to me, including deduction. — 83nt0n

How do you justify that judgment?

If that is your definition of justified, then modus ponens is entirely justified, since it always takes us from true beliefs to true beliefs. For suppose toward a contradiction that P and if P, then Q are both true, but Q false. Since P is true and Q is false, it follows that if P then Q is false, contrary to what we have assumed. Therefore, if we believe in P and we believe in if P then Q, we are rationally justified in believing that Q.

Expanding a bit, it is always possible to justify our rules of deduction by soundness proofs, which are typical in mathematical logic.

How do you justify that definition? — aletheist

This is how I am choosing to use the word.

How do you justify that assertion? — aletheist

Again, this is how I am using the word.

How do you justify that response? — aletheist

Because I don't know. And no I don't know that I don't know. Maybe I do know, I just don't know it.

How do you justify that self-characterization? — aletheist

I am not saying this as an assertion; skeptics compose sentences like this not to assert something but to describe the way it appears.

How do you justify that judgment? — aletheist

That's why I included the word seem. I could be wrong, but others have not met the burden of proof.

If you have questions about skepticism, check out the YouTube channel carneades.org and his series in defense of skepticism. However, this is not really the topic of this discussion. I am specifically interested in discussing deduction.

If that is your definition of justified, then modus ponens is entirely justified, since it always takes us from true beliefs to true beliefs. — Nagase

You seem to be using modus ponens to support modus ponens. 1) If that is your definition of justified, then modus ponens is entirely justified. 2) That is your (read:my) definition of justified. 3) Therefore modus ponens is entirely justified (from 1 and 2 modus ponens).

Also you seem to assume that if a rule goes from true beliefs to true beliefs, it is justified. Once again, this is using modus ponens to prove modus ponens. This is the point behind Carroll's story. For Achilles to justify modus ponens, he has to assert modus ponens.

No offense intended when I say this: you seem to be driven more by hubris in contrast to the pursuit of knowledge. If you've articulated your perspective to the best of your ability I can't follow your reasoning. It's almost as if you hold the stance that nothing has meaning since everything is built on presuppositions that are built on further abstractions.

I think Tim layed it out nicely: no matter what game we play the rules must be established first before any player can proceed.

If your beef is exclusively with modus ponens, then rest assured that it is dispensable (well, sort of, for some systems).

But that does not seem to be your problem with modus ponens; rather, you seem to be wary of using any rule of inference at all (incidentally, note that this is not my reading of Carroll's story at all---I think he is pressing the need for distinguishing axioms from rules of inference). Behind this wariness there seems to be some kind of linear propositional support requirement, namely that "a proposition or theory must be supported by inference from accepted premises to a conclusion, and that the conclusion not appear among the premises, premises of the premises, etc." (Paul Gregory, Quine's Naturalism, Chapter 1) The name derives from the fact that this requirement imposes a linear structure on our knowledge, i.e. P < Q iff P supports Q. It is well known that this requirement leads to skeptical conclusions, in the form of the Agrippan trilemma. Ironically, you seem to apply modus ponens to this argument (If there is a requirement for linear propositional support, then we must embrace skepticism; there is such a requirement; therefore, we must embrace skepticism), whereas it seems to me that it would be better to apply modus tollens and reject the linear propositional support requirement. (For what is worth, that is precisely Quine's strategy in "Epistemology Naturalized".)

My stance is that I do not know anything, but I (really) want to have knowledge, so I continue the search. I wouldn't say that nothing has meaning, because it is possible that something is intrinsically meaningful, but I am just ignorant.

I think Tim layed it out nicely: no matter what game we play the rules must be established first before any player can proceed — ISeeIDoIAm

Yes, I tend to agree that rules need to be established, but the question is how do we go about establishing the rules. How do we establish a system of logic that allows us to know?

Good point. But I am also skeptical of the linear thinking; I use probably because I'm hardwired that way.

Ironically, you seem to apply modus ponens to this argument (If there is a requirement for linear propositional support, then we must embrace skepticism; there is such a requirement; therefore, we must embrace skepticism) — Nagase

I don't necessarily think that propositions need linear support. In fact, it seems that this kind of linear analysis is flawed (because of Agrippa's Trilemma and other problems), however, nonlinear analysis seems to me to be unable to avoid circular reasoning. If I am mistaken, please enlighten me. I am relatively new to philosophy; I have been an autodidact for about a year now.

My stance is that I do not know anything, but I (really) want to have knowledge, so I continue the search. — 83nt0n

How do you know that you do not know anything? How do you know that you want to have knowledge?

How do we establish a system of logic that allows us to know? — 83nt0n

We already have, but you claim not to accept it, even though you cannot avoid employing it.

How do you know that you do not know anything? How do you know that you want to have knowledge? — aletheist

I do not know this. I could be wrong. However, skeptics like me do not assert as true what we're saying. We just explain how it appears to us to be able to hold a conversation.

We already have, but you claim not to accept it, even though you cannot avoid employing it. — aletheist

Have we? Deductive logic (at least classical) seems unable to guarantee the conclusions it validates. I do admit that I probably cannot avoid employing it, but this has no bearing on whether it allows us to know.

A wise way to live so long as you have stable footing.

"I am the wisest man alive, for I know one thing, and that is that I know nothing."

I have had a similar thought pattern in regards to what you describe. How do we know what we see is true? How can we ever know what is absolute in this world of imagination and illusions? The short answer: we can't.

Trial and error is the only tried and true method of determining value in a reality that technically may not even exist. For all we know life could be a simulation. But that thought is pointless imo. I can't do anything with that. So I, like many others, chart my waters by experience rather than where the wind might take me. To do anything you need a basis (a reference point), no matter how wide you set your goalposts you need parameters to work from.

You can never truly know if you walk "the yellow brick road". If the game doesn't work well enough, the only course of action is to scrap the old rules and make new ones until you find a set that works. And if you can't find a better version than what exists then that's the state of things until they aren't. There's an infinite amount of ways a plan can fail, and only a handful where it works out as intended.

I do not know this. — 83nt0n

How do you know that you do not know this?

I could be wrong. — 83nt0n

How do you know that you could be wrong?

However, skeptics like me do not assert as true what we're saying. — 83nt0n

This is your third assertion in a row that something is true.

We just explain how it appears to us to be able to hold a conversation. — 83nt0n

Why should I believe you?

Deductive logic (at least classical) seems unable to guarantee the conclusions it validates. — 83nt0n

The inference rules of deductive logic, including modus ponens, are intrinsically truth-preserving; if the premisses are true, then the conclusion is necessarily true. What deduction cannot guarantee is that the premisses are true.

I do admit that I probably cannot avoid employing it, but this has no bearing on whether it allows us to know. — 83nt0n

Another assertion that something is true. Do you not realize that thoroughgoing skepticism is self-defeating? In order to be consistent you would have to be just as skeptical about skepticism as you claim to be about everything else.

"The inference rules of deductive logic, including modus ponens, are intrinsically truth-preserving; if the premisses are true, then the conclusion is true. What deduction cannot guarantee is that the premisses are true."

They are intrinsically true so long as the original presupposition rings true. I think that's the point he's trying to lay out. Like many layers stacked on each other: the whole thing comes tumbling down if the foundation is faulty.

They are intrinsically true so long as the original presupposition rings true. — ISeeIDoIAm

What do you mean by "the original presupposition"?

This is your third assertion in a row that something is true. — aletheist

Again, I'm not asserting my statements/positions as definitely true. This is how it appears to me. INCLUDING THIS.

Why should I believe you? — aletheist

Maybe you shouldn't.

The inference rules of deductive logic, including modus ponens, are intrinsically truth-preserving; if the premisses are true, then the conclusion is true. What deduction cannot guarantee is that the premisses are true. — aletheist

But the axioms that classical deductive logic employs are unsupported.

They are intrinsically true so long as the original presupposition rings true. I think that's the point he's trying to lay out. — ISeeIDoIAm

Exactly.

Another assertion that something is true. Do you not realize that thoroughgoing skepticism is self-defeating? In order to be consistent you would have to be just as skeptical about skepticism as you claim to be about everything else. — aletheist

Again, this is not an assertion. This is how it seems to me. I have to utilize appearances, as I have nothing else to allow me to hold a conversation. Skepticism the position doesn't seem to be self defeating. However, if skepticism as a way of action is incoherent, this is probably due to human fallibility. And I am skeptical of my skepticism (or at least it appears that way). It could be that someone does have knowledge, but as of yet I haven't found any.