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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Any concrete, real life example of Peirce's Law?

What would be a real life, concrete example of Peirce's Law? ((p → q) → p) → p There is a Wikipedia article on it, if you are unfamiliar with it: https://en.wikipedia.org/wiki/Peirce's_law There ...
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Can animals follow logical rules of inference?

I've been trying to recall a thought experiment, which I very vaguely remember to have come across either in Davidson or Dennett, that considers the following scenario: A hound is chasing its quarry ...
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Deductive reasoning & conditionals

What would be a good example of explicit deductive reasoning that doesn't seem to be possibly interpreted correctly as a conditional (If A, then B)?
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How to draw a truth table on Stack Exchange? [migrated]

I need to draw/input tables, such as truth tables in order to ask and answer questions about logic. Can someone please instruct me on how to make a truth table on this site. My goal is to make a truth ...
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Is it logically permissible to neither believe nor disbelieve a proposition X? Or does this violate the law of excluded middle?

Given a proposition X, one can either believe it or disbelieve it. Is it logical however to neither believe X nor disbelieve X? Is it logical to neither believe proposition X nor its negation ~X? I ...
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Equivalence Thesis

What is, if any, the canonical justification accepted in mathematical logic for the Equivalence Thesis, asserting (1) that indicative conditionals are truth-functional logical expressions and (2) that ...
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Semantic rules overdetermine the truth value of Liar Paradox

I am reading Graham Priest's In Contradiction (p.14) and he mentioned that the semantic rules of 'this sentence' and 'is True' overdetermine and underdetermine the Liar Paradox and its counterpart ...
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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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If-then statement and time between antecedent and consequent

Suppose the following statement. "If I kick the ball then the ball will hit the wall." Can this sentence have a truth value? I mean the time that I kick the ball, it hasn't reached the wall so the ...
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Contradiction vs Impossiblity

When we do proof by contradiction we think in the following way: Suppose we know that Q is true. We assume that not P is true and through implications we conclude not Q is true. Now how we proceed ...
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Was Hans Reichenbach really a logical empiricist? Did he really think that logic was empirical?

I was reading an article in the Stanford Encyclopedia of Philosophy about Hans Reichenbach 1, and I have a specific question about it that I would like to ask. There, it is said that: Reichenbach ...
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The understanding of logic presupposes a kind of understanding of natural language, doesn't it?

Our understanding of logic needs at least a basic understanding of words over a finite alphabet,natural language and numbers. For example,when we write down (one way) the definition of the atomic ...
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Non-consistent mathematical axioms

It is known that axioms are the building blocks of mathematics. Differents sets of axioms different "games". What I don't understand is how do we know that we pick axioms that are consistent? . Does ...
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What is the ontological status of the laws of logic? [duplicate]

Are the laws of logic abstract objects that exist independently of physical things? Are they the same in all possible worlds? Are they man-made constructs, nothing more than ideas in our minds? Or ...
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If-then statements meaning in everyday vs mathematics

In mathematics when a "P implies Q" statement is true it means that every time P is true, Q is true also. What about everyday usage? For example consider the statement: "If it is raining, then I am ...
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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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How/Why is the explanation/prediction of physical phenomena not deductive?

Why is the explanation of the triboelectric effect or the electrostatic effect(indicative examples) not deductive? How so we have a set of premises and from them follows the conclusion which is what ...
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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 ...
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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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Where is the fallacy in Seth Yalcin's counterexample to the modus tollens?

Where is the fallacy, do you think, in Seth Yalcin’s argument (2012) that the Modus Tollens is not a generally valid form of argument? Seth Yalcin’s counterexample to the Modus Tollens (MT) https://...
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Excluded middle versus bivalence [duplicate]

In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true. This principle should not be ...
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Are mathematical axioms arbitrary?

I've been thinking recently about whether or not mathematical axioms are arbitrary. I'm trying to figure out what axioms in systems are derived from and just how arbitrary they really are. My main ...
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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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Can we know that law of non contradiction is true a priori?

I have seen some arguments for why should we accept law of non contradiction, and it seems to works in almost all areas. But some argument for it is like an argument for principle "nothing comes from ...
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How do Descartes' definitions of 'a priori' and a 'posteriori' effect the current generalized understanding of these two distinctions?

The noted and highly respected pluralist, Dr. Richard Mckeon, in his introductory comments to the International Institute of Philosophy's 'Entretiens in Jerusalem, in 1977, quotes from Descartes ...
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In non-platonism, can undecidable statements have truth value?

Most sources I can find about Gödel's incompleteness theorems summarize the result as "there exist true arithmetical statements that have no proof." It seems coherent to say that there exist ...
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Can/Do there exist any quantifiers other than “there exists” and “for all”?

I'm curious about why there are only the two logical quantifiers there exists and for all. Intuition and human language support the idea that these quantifiers make sense, but otherwise it seems ...
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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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Justification for the paradigm of abductive reasoning

In Chance , Love and Logic, Peirce defines reasoning into two categories: analytic and non-analytic. All forms of reasoning have three fundamental components: rule, case, result. Analytic reasoning ...
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Which of common rules of inference are rejected on some philosophical grounds?

My question is: is there a mathematical or philosophical basis for rejecting any of the following rules of inference? If yes, then what is the argument for rejecting any of them? I am asking this ...
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Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

Two concepts F,G are equinumerous if there exists a one-to-one correspondence between the objects that fall under F and G. Equinumerosity is one the most fundamental building blocks of Gottlob ...
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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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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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What is the difference between 'accidental' and 'contingent'?

What is different between 'accidental' and 'contingent'? I thought that accidental contains intentional notation while Contingent does not. But there could be an intentional action that turns out to ...
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Rhetoric: How to frame redundancy in an argument as deficiency?

How can we categorize redundancy in an argument as deficiency? That is, weaken the argument because of its redundancy? Suppose X is an argument that boasts coherence and clarity, but it has various ...
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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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Is a tree proof or natural deduction a semantic method of proof?

Peter Schroeder-Heister writes in an article on "Proof-Theoretic Semantics" the following: Proof-theoretic semantics is inherently inferential, as it is inferential activity which manifests itself ...
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Is Herbrand semantics a kind of term formalism?

Michael Genesereth and Eric Kao describe Herbrand semantics as follows: Herbrand semantics is an alternative semantics for First Order Logic based on truth assignments for ground sentences rather ...
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Did early Wittgenstein view mathematics as “sense-less” or “non-sensical”?

G. E. M Anscombe makes the following distinction between Wittgenstein's use of sense-less (sinnlos) and nonsense (unsinnig): (page 163) We must distinguish in the theory of the Tractatus between ...
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Although Russell's paradox has the virtue of simplicity, is it a distraction from other paradoxes of naive set theory?

Given that Russell's paradox exhibits a contradiction in naive set theory, the interpretation of the binary relation "∈" called "membership" (where the expression "x ∈ m" is pronounced as "x is an ...
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What philosophical axes did 19th century mathematicians have to grind?

Tim Button's presentation of set theory motivates the subject by providing a history of 19th century mathematics where the notion of limit allowed definitions of the derivative and continuity. These ...
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Do Aristotle's three laws of logic apply to statements about the future?

I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply ...
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What's the difference between a second-order relation and a relation between objects?

I was reading an article in philosophy and found this: Some philosophers have denied that there is such a relation as identity. Thus Ludwig Wittgenstein writes (Tractatus 5.5301): "That ...
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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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What is an example of a true contradiction in a paraconsistent logic?

While reading the Wikipedia article on trivialism I noticed the following: In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
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Is there any exception that proves or suggests that the law of non-contradiction does not always apply?

Is there any exception that proves or suggests that the law of non-contradiction does not always apply? I am thinking, because the law of non-contradiction is very similar to the law of excluded ...
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Is there a difference between equality and identity?

Is there any difference between equality and identity, or are they the same concept?
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Is there any exception that proves or suggests that the law of excluded middle does not always apply?

Is there any exception that proves or suggests that the law of the excluded middle does not always apply? I am wondering if this rule is an absolute truth that is always true in our world or in any ...
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Why are there two fundamental laws of logic?

We have the law of non-contradiction and the law of excluded middle, but looking at it, it seems that both of them are the same thing, or at least one of them logically implies the other. Is there a ...
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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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