Glad we are on a philosophy forum and can adjust to the big picture and zoom in where necessary — schopenhauer1
Nice idea. So for your understanding here you are saying that mathematics are basically "arbitrary" forms of logic (that sometimes map to reality)? — schopenhauer1
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
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.
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'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.So my problem again here is the use of "foundational". — schopenhauer1
That's kinda the point of logical pluralism. — Banno
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
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
...your joke post in the Lounge... — schopenhauer1
...mostly shows how poorly folk hereabouts deal with logic. — Banno
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
something is happening internally/cognitively that is going on prior to the formalization process of symbolic logic. — schopenhauer1
B1. There is no true/correct logic. — Leontiskos
That'd be logical nihilism. — Banno
Therefore, there are true/correct logics. — Banno
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
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
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
Where you used it to adjudicate over logics:Where have I given primacy to the PNC? — Leontiskos
If they do, then the PNC has been destroyed. — Leontiskos
You are not here to addressing the topic of this thread, by your own account.Are you disagreeing with my argument or not? — Leontiskos
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. — Leontiskos
Where you used it to adjudicate over logics — Banno
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
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.
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
The inference depends on accepting PNC. — Banno
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
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