Glad we are on a philosophy forum and can adjust to the big picture and zoom in where necessary — schopenhauer1

Yep. At least that's the hope. :grin:

Nice idea. So for your understanding here you are saying that mathematics are basically "arbitrary" forms of logic (that sometimes map to reality)? — schopenhauer1

Metamathematics, not mathematics. Something like "game formalism (SEP). It is something like the study of the logic of symbol manipulation.

I tried to set out my view of logic in my first post here:

Historically logic is the thing by which (discursive) knowledge is produced. When I combine two or more pieces of knowledge to arrive at new knowledge I am by definition utilizing logic. — Leontiskos

On this view the "binding" is part of logic, given that discursive knowledge cannot be produced without it. But there is a distinction between intellection and combination/separation, and we justifiably think of the latter as logic.

To try to get at it in just a few words, we usually think of knowledge of simples as one thing and the manipulation of that knowledge of simples as another thing. That's fine; they are distinct. I call this knowledge of simples "intellection" as opposed to "ratiocination." But even when all the simple pieces on the board are set and ready for manipulation, I would contend that we have still not left intellection behind. Why? Because an inferential move or rule involves intellection. The manner in which we move from premises to conclusions is not endlessly discursive, or not entirely related to ratiocination. We must understand that the inference is valid in order to undertake it, and this understanding is part of intellection. Logic of course tends to calcify or standardize rules of inference, thus forgetting the importance of understanding them. Basically, the closer we move to that "binding" between the formal logical system and reality, the more immersed we are in intellection, and this includes an understanding of inference.

The actual truth-value of these sentences isn't in question when talking about logic. It's the form between the sentences under the assumption that if the premises are true that the conclusion follows. But since the moon is not made of green cheese the question of being -- what is -- differs from the question of validity, and logic is this study of validity.

But this isn't how logic is studied. For instance, take Curry's paradox as an example. The problem is that the common idea that "valid arguments with true premises yield true conclusions," results in absolute absurdities like "if this sentence is true then Albany, New York is in Mongolia," being used to prove "Albany, New York is in Mongolia." Harty Field and J.C. Beall have written a lot on this one. Yet if we totally abstracted all content away from "truth" (something I'd argue we aren't even mentally capable of) it seems impossible to recognize these sorts of problems. If you don't consider content at all, how do you even recognize when you're able to prove the absolutely absurd and have a problem? Sure, we could recognize triviality (i.e. when we can affirm every claim that is expressible in the language of the theory) in some abstract sense, but we wouldn't have any idea why this is problematic (and paradoxes of absurdity exist in non-trivial contexts anyhow). Hemple's ravens, and probably a lot of stuff involving logic and induction would be other examples where there will be similar issues. Or accounts of implication.

That said, I get the distinction, and I think it's a useful one to some extent. Nevertheless, when logicians want to discuss truth, and validity as "truth preserving," one has to understand what is meant by "truth." One can declare one's logic "pure" and free from metaphysics, but honestly it seems that all this accomplishes is making one's presuppositions opaque and immune to scrutiny (and, relevant to this topic, does so in a way that I think is often question begging re logical nihilism).

If "truth" is just left as an empty lable, "existence" in existential quantification likewise just a symbol with rules attached to it, etc. what exactly are we preserving? An AI can spit out systems without any regard to truth. Would it be doing the purest form of logic by jettisoning all metaphysical baggage? But then why even say it has anything at all to do with truth preservation; logic is just reduced to computation.

Of course, the deflationary approach to the above problems might be just to say: "well, 'Albany, New York is in Mongolia,' is simply true in some systems. Truth depends on your theory. If you want to talk about the absurdity of that statement then you won't be talking about logic."

I think it should be obvious though that this begs the question on logical nihilism, since it deflates truth and the realist is trying to make a claim about what is true universally.

We might try to get around this by divorcing "truth in logic" from "metaphysical truth," but I am not sure how effective this will be if the topic of debate is logic itself, as in the context of this thread, lol.

That said, I get the distinction, and I think it's a useful one to some extent. Nevertheless, when logicians want to discuss truth, and validity as "truth preserving," one has to understand what is meant by "truth." One can declare one's logic "pure" and free from metaphysics, but honestly it seems that all this accomplishes is making one's presuppositions opaque and immune to scrutiny (and, relevant to this topic, does so in a way that I think is often question begging re logical nihilism). — Count Timothy von Icarus

I prefer to think of it as putting it to the side as something that can be discussed separately -- which isn't to say our choice of a logic is metaphysically innocent or anything. When you're trying to put it all together into some kind of coherent picture usually you can see how there are some natural implications of an idea; some ideas seem to "get along" better together than others.

My task here is to point out that the nihilism isn't absurd on the basis of anti-realism/realism, that nihilism is different from pluralism, that pluralism is a worthy contender whether we are realists or anti-realists, and that logical monism isn't obviously true.

I've read you as saying that logical nihilism leads to a lack of knowing -- that we would be unable to track what is relevant with respect to knowledge if there were no logical rules. I think the case of Humean skepticism is a good one to point to for demonstrating that knowledge need not have anything to do with our habits of inference -- we build knowledge around causation, but it could very well be that we find out we were mistaken in that knowledge.

Now, just because we were mistaken that does not then mean that things weren't real. It just means that our knowledge doesn't necessarily track what's real. So if we wash our hands before treating a bleeding wound to remove the humors from our hands since it causes diseases we will know something which is false, act on it, and in the process eliminate microorganisms which cause diseases.

The whole causal mechanism is a myth, but we manage because we are the ancestors of those who were lucky enough to reproduce in this environment (and they didn't know much either, so I'd guess -- though I don't know)

In fact we could look at induction as a survival strategy which violates the basics of logic all the time since it's an invalid inference. :D

Or, at least, I put those sorts of things under the heading "informal logic" which is the study of how people actually make inferences which includes a lot more on the "content" side (since that's how you demonstrate why such and so is a fallacy). It just seems that we'd be able to accommodate informal logic, or this kind of "content based" logic regardless of our position with respect to monism, pluralism, and nihilism in logic.

So my problem again here is the use of "foundational". — schopenhauer1

I'd only used "foundational" in response to posts here. Even in propositional logic, axiomatic systems are but one of many, and in those systems there are ma y variations as to which axioms are chosen. Modus Ponens is common, but not essential. Sequent Calculus does not rely on Modus Ponens, but derives it. Natural deduction usually has modus ponens as a propositional rule. Tableaux has a rule concerning what we can write after an implication, more or less in place of modus ponens.Lambda Calculus has nothing analogous to Modus Ponens.

And most certainly, not all logics are axiomatic.

All this by way of suggesting that proposing a foundation for all logics is to invite logicians to undermine that very foundation.

That's kinda the point of logical pluralism.

That's kinda the point of logical pluralism. — Banno

Sure, but wouldn't that be if we believed that logic was completely conventional? Here we can split up something like "natural logic" (the rationalizing we can do as a certain species regarding the world), and "formal logic" (the kind of axiomatic (or non-axiomatic) based logics that we formalize with symbols and rules?

I was proposing that the foundation for formal logic can perhaps be found in a natural logic, or something like this.. a foundation outside the formalized logics themselves.

I would contend that we have still not left intellection behind. Why? Because an inferential move or rule involves intellection. The manner in which we move from premises to conclusions is not endlessly discursive, or not entirely related to ratiocination. We must understand that the inference is valid in order to undertake it, and this understanding is part of intellection. Logic of course tends to calcify or standardize rules of inference, thus forgetting the importance of understanding them. Basically, the closer we move to that "binding" between the formal logical system and reality, the more immersed we are in intellection, and this includes an understanding of inference. — Leontiskos

Yes so I guess to equate with your terminology, "Whence intellection"?

If you like. "Natural logic" will collapse into "formal logic" as soon as you take it seriously. The "rationalisations we make" are the very subject of formal logic.

If you like. "Natural logic" will collapse into "formal logic" as soon as you take it seriously. The "rationalisations we make" are the very subject of formal logic. — Banno

Interestingly though, your joke post in the Lounge kind of proves a point where formal logics can lead to errors by simply abiding by the rules without interpretation (possibly the natural logic?) used to make the content work (become sound/make sensible). And thus something else is going on that isn't just the formal logic (natural logic that is)...

Also, being a bit of a devil's advocate from my past positions (contra evolutionary psychology), there is no way our species evolved "to use formal logic", rather we have rationalization capacities that happened to be able to form formal logic. It is this rationalization capacity that I am interested in- empirically understood through various methods of anthropologists, evolutionary biologists, cognitive scientists, and the like (possibly).. I'll take even armchair theories as stand-ins for now, but that is the foundation I mean.

...your joke post in the Lounge... — schopenhauer1

...mostly shows how poorly folk hereabouts deal with logic.

...mostly shows how poorly folk hereabouts deal with logic. — Banno

I get it, but I think this point still stands and is important:

ules without interpretation (possibly the natural logic?) used to make the content work (become sound/make sensible). And thus something else is going on that isn't just the formal logic (natural logic that is)...

Also, being a bit of a devil's advocate from my past positions (contra evolutionary psychology), there is no way our species evolved "to use formal logic", rather we have rationalization capacities that happened to be able to form formal logic. It is this rationalization capacity that I am interested in- empirically understood through various methods of anthropologists, evolutionary biologists, cognitive scientists, and the like (possibly).. I'll take even armchair theories as stand-ins for now, but that is the foundation I mean. — schopenhauer1

I'm not keen on evolutionary teleologies.

I'm with you in terms of, I'm not much for evolutionary psychological "just so" theories, but if it's not some sort of naturalistic/biological reason we can reason, we still have some capacity that is there by the very fact that we can develop logic, so whatever way it got there, something is happening internally/cognitively that is going on prior to the formalization process of symbolic logic.

something is happening internally/cognitively that is going on prior to the formalization process of symbolic logic. — schopenhauer1

Language.

- These topics really can't be addressed in bite-sized forum posts. How do we obtain the simples which logic then manipulates? That is a very large question. I suppose if you search my posts for "intellection" you will find places where I tried to elaborate on it.

-

This is how I want to see a disagreement between Banno and myself:

1. If we have discursive knowledge, then there is a true/correct logic.
L1. We have discursive knowledge.
L2. Therefore, there is a true/correct logic.

1. If we have discursive knowledge, then there is a true/correct logic.
B1. There is no true/correct logic.
B2. Therefore we do not have discursive knowledge.


Then the question is simply whether L1 or B1 is more plausible. The problem with Banno's approach is that, even for any merits it has, it precludes knowledge, and this is much more absurd than the alternative. Of course B1 is not exactly logical nihilism as presented in the OP, but I see no real reason to engage G. Russell's theories on their own terms. I am here because of a tangent that was redirected to this thread, not because of the OP. I would be more likely to address an argument if Banno presented it himself.

B1. There is no true/correct logic. — Leontiskos

That'd be logical nihilism. What is being suggested is logical pluralism.

You might try
1. If we have discursive knowledge, then there are true/correct logics
L1. We have discursive knowledge.
L2. Therefore, there are true/correct logics.

That'd be logical nihilism. — Banno

Yep, that's what I said.

Therefore, there are true/correct logics. — Banno

I think Count has addressed this nicely:

I guess a "strong" pluralism would declare that there are multiple equally valid/applicable logics but no morphisms between them? I just find it hard to imagine how this could be the case, since it seems that, by definition, they must have similarities in virtue of the fact that they are equally applicable to the same things. — Count Timothy von Icarus

So we end up with this:

• The "true/correct logics" either contradict one another or they don't.
• If they do, then the PNC has been destroyed.
• If they don't, then we are no longer talking about logical pluralism.

Pick your poison. Your thesis is that there are true/correct logics with nothing in common, such that we cannot call their similarity logic in a singular sense, and we cannot apply a rational aspect under which they are the same. But the natural language itself betrays this, for simply calling them logics indicates that they belong to a singular genus.

As I said:

For example, someone who believes in deductive, inductive, and abductive reasoning is not a logical pluralist. It is in no way controversial that there are different ways of reasoning.*

* Similarly, someone who utilizes different logical languages or formalisms for different arguments is also not a logical pluralist. — Leontiskos

The idea that different formal logics can each yield sound arguments without contradicting one another is not in any way controversial, and I would not call it logical pluralism.

So we end up with this:

The "true/correct logics" either contradict one another or they don't.
If they do, then the PNC has been destroyed.
If they don't, then we are no longer talking about logical pluralism — Leontiskos

Which is just to give primacy to PNC, and so to beg the question.

- Where have I given primacy to the PNC? Are you disagreeing with my argument or not?

Where have I given primacy to the PNC? — Leontiskos

Where you used it to adjudicate over logics:

If they do, then the PNC has been destroyed. — Leontiskos

Are you disagreeing with my argument or not? — Leontiskos

You are not here to addressing the topic of this thread, by your own account. You do not have to be here, and I am not under any obligation to address your posts.

Where you used it to adjudicate over logics — Banno

Do you agree or disagree with that inference? There is no adjudication, just a consequence.

You are not here to addressing the topic of this thread, by your own account. You do not have to be here, and I am not under any obligation to address your posts. — Banno

And yet you are the one who transplanted a different conversation into this thread. You are also the one who abandoned the OP of logical nihilism in favor of logical pluralism when I brought it up.

I'm curious, if you support that position, in virtue of what would true/correct logics be true/correct and false/incorrect ones not be?

Well, on that consequence it seems possible that logical pluralism, nihilism, monism, whatever have you, could be both true and false. So everyone wins... and loses.

Yep, haha. But maybe that's the point.

Great posts of late. Your time away has served you well. :up:

Can I suggest having a look at the discussion in the article that this thread concerns? Section 1.2, concerning the interpretation of logical laws.

On the interpretations view Γ ⊨ φ is true iff whatever (syntactically appropriate) interpretation is given to the non-logical expressions in Γ and φ, if every member of Γ is true, then so is φ.

"Support" is what one gives a football team. I find the ideas here very interesting, and they fit in with a bunch of other stuff. I reject logical nihilism, but there are also good reasons to reject logical monism. The article that this thread is concerned with tries to show a third path. Some have understood that.

I'm curious, if you support that position, in virtue of what would true/correct logics be true/correct and false/incorrect ones not be? — Count Timothy von Icarus

I'll just point out what a great question this is, and how it becomes even greater after being dodged. :smile:

The inference depends on accepting PNC. The article mentions goes into this in some detail, but doubtless you will not read that, either.

The only doge here is your refusal to engage with the content.

The inference depends on accepting PNC. — Banno

How so? "If the 'true/correct logics' contradict one another, then the PNC has been destroyed."

I have to accept the PNC to accept that claim? I think everyone can see that you are wrong here. Maybe stop dancing and start answering the simple questions being asked?

Edit: Unless you are actually presenting Aristotle's argument in Metaphysics IV, but I doubt it. If that is what you are doing you should be more forthcoming. More transparent. More philosophical.

That'd be logical nihilism. What is being suggested is logical pluralism.

You might try
1. If we have discursive knowledge, then there are true/correct logics
L1. We have discursive knowledge.
L2. Therefore, there are true/correct logics. — Banno

Are we confusing true/correct with simply consistent? All of our ideas agree therefore the symbols we use to represent them must construct actual truth, feels like a reach.

No, Leon. If you are going to use the claim to reject there being contradictory logics, then you have given primacy to PNC.

You may be right, but True/correct is Leon's term. There's plenty in the detail, and looking to it would turn this thread away form the mere bitch session it is becoming.