Questions tagged [philosophy-of-logic]

Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.

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How do dialetheists determine which contradiction is true?

I have been reading a lot about dialetheism lately. I know for a fact that dialetheists do not believe that every contradiction is true. (Surely there is a difference between asserting that Liar is ...
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Which rational thinkers (theologians, philosophers, scientists, mathematicians etc.), prior to 1850, disagreed with Aristotle's logic?

Did any intellectual luminary ever articulate any major disagreement with Aristotle's logic prior to the inception of modern mathematical "classical" logic? Which rational thinkers, such as ...
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What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
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Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...
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Looking for references for some remark of Quine's

I'm looking for a comment I think I remember Quine having made. He's talking about our understanding of proofs. I think he says something along the following lines... If you understand many different ...
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What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
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Is there such a thing as unary logic?

Is there such a thing as unary (as opposed to binary, ternary, …, n-ary) logic? cf. Is there any reason for the heavy focus on binary relations in formal logic?
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32 views

Possible Models

A model consists in one or more possible worlds. Necessity in a world is determined by its associated set of possible worlds. I am curious whether there is any work that involves an account of ...
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Arguing that English does not satisfy the Tarski condition by appealing to truth value gap

I am reading Graham Priest's In Contradiction (P.12), where he is asserting that English satisfies the Tarski condition (a variant of semantic closure) and thus contains true contradiction. He ...
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192 views

What are the eventual purposes of symbolic logic?

What is the teleology of logic? Every body of knowledge has to have a teleology for which it's designed. The body of knowledge in logic doesn't clearly have any teleology or any purpose to which it ...
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Aristotle's Categories and Linguistics

I have actually two questions: What he calls substances or non-substances seem to me as, now what we call a matter of language. So what he calls substances could be seen as concrete nouns, and non-...
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91 views

What paradoxes arise from quantifying over EVERYTHING?

This question is in context of the umbrella view of objects, that there exists a general category that everything falls under. Here are the quote and link that peaked my curiosity. Finally, note ...
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162 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
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Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
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121 views

What is the relation between expressive completeness and semantic completeness

A formal system is expressively complete if and only if it is capable of expressing, as a formula, everything that is the subject of that formal system. A deductive system is semantically complete if ...
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35 views

Why do we seek to “limit” our scope for the search after truth?

In philosophy and science, we quite often make systematic approaches that limits our thoughts to be as accurate as possible. Examples are endless - basically every logical system, every ...
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163 views

What are the differences (if any) between classical and modern predicativity

I am researching Predicativity and I've encounterd defenition for classical predicativity and for modern predicativity but I can't understand the differences between them. Thanks
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550 views

Some questions on “context” in Mathematical Logic

Recently I was having a discussion with user21820 in this chatroom. There very naively (in the sense that I didn't choose carefully each word of my following statement) I expressed the opinion that, ...
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258 views

Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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What is the 'axiomatic' or epistemological foundation of Analytic philosophy, what is its practice and purpose?

In researching the origin and purpose of the Analytical Tradition in philosophy, all that appeared was that it traces its origin to the 'Tractatus' offshoots following Wittgenstein and Russell, and ...
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49 views

Philosophers & the material implication

Is there still today any philosopher specialised in logic making any substantial argument against the notion that a material implication is a logical implication?
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Baconian Logical Fallacy

I have been reading about logical fallacies lately, and I saw the Baconian fallacy listed here (of course on everyone's favorite site, Wikipedia). The description provided reads: "using pieces of ...
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77 views

Are axioms more important than definitions?

To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
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Question on the “Property of an Object” and the “Action of an Object” (+the “State of an Object”)

I have confronted a philosophical problem related to the definition of the "property of an object." What I believe is: The capability of an object (the capability to desire) is the property of an ...
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Is there a method for identifying the logical form of everyday speech sentences?

Is there a method for identifying the logical form of everyday speech sentences? Did any logicians attempt to establish such a method? Bertrand Russell gave a few examples of that but nothing ...
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116 views

Bibliography about non-mathematical applications of logic:

I have been recently playing with modal and temporal modal logics in the context of "organisms" (mostly after some study of entelechy in Aristotle and relatedly, some ideas of current biology). I have ...
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Using logic to do metalogical proofs? Is there a circularity problem here?

(1) If modus tollens were not correct, then I could have (P-->Q), ~Q and P. (2) But I cannot have (P--> Q) , ~Q and P. For, in that case, I would have (~P v Q) and ~Q and P; which means I would have ...
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Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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227 views

The sea battle paradox and the soundness criterion

Again a short look at Aristotle's resolution (one of many) of the sea battle paradox: In one famous example about a hypothetical sea battle, [Aristotle] observes that the necessary truth of a mere ...
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What counts as a logically necessarily true statement and what is not?

"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death." Is this statement considered logically necessarily true? I personally ...
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238 views

Is Classical Logic the proper model of the deductive logic of human reasoning?

Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it? The expression "Classical ...