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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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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Are there examples of ideas that rationally-trained persons agree on?

This question is meant for a bit of fun as a comedic corollary to JDH's top-voted question, "What would it take in a book to convince a rational person that it had been written by or directly ...
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Is this proposition analytic or synthetic?

Consider the following statement: Cats have four legs This is an analytic statement, since its truth can be established by looking at the subject and predicate; one does not need to look further ...
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Santa Claus does not exist. Therefore, something does not exist. Valid?

My professor defines logical validity (in the English language) like so: 'An argument is logically valid if and only if there is no (uniform) interpretation (of subject-specific expressions) under ...
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Logic and Computation: a philosophical viewpoint on Curry-Howard isomorphism

The link between logic and computation is stronger than ever, especially since the establishment of the Curry-Howard isomorphism specifying that proofs can be seen as programs and formulas as program'...
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Is it rational to use disjunctive imperative sentences?

Suppose you tell someone, "Go to the store or go to the creek." Now, if this person is otherwise predisposed to one option, and your command triggers this predisposition, then by issuing the ...
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How do we know that this is the truth? [closed]

I am not a philosophy student, academically. But I have watched a lot of videos and studied some of the content regarding the here and there philosophy of the existentialism, religion, relations of ...
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What are the advantages of Aristotle's term logic over predicate logic?

I have read Wikipedia's term logic entry, and the quote by Gareth Evans in the Revival section that's supposed to argue for term logic's advantages over predicate logic: "I come to semantic ...
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If you used intuitionistic logic in real life, would you not sound absurd?

Intuitionistic logic does not include the law of the excluded middle and double-negation elimination. I imagine a real-life conversation with an intuitionist might go like this: Amy said you didn't ...
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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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Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

A book I'm reading mentions the following: A major barrier to the development of first-order logic had been the concentration on one-place predicates to the exclusion of many-place relational ...
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How to reconcile the fact that mathematical proofs are logical implications with the lack of a formal calculus equivalent to the logical implication? [closed]

Theorems follow from axioms. That is, theorems are the logical consequence of axioms. Thus, mathematical proofs are essentially deductive. Proofs are all essentially logical implications. There is ...
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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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What are the differences between philosophies presupposing one Logic versus many logics?

I was wondering in light of the historical developments of logic since ancient Greeks and well into the nineteenth and twentieth centuries: What kind of a philosophy assumes only one Logic, and what ...
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Can classical logic hold without causality?

Consider a universe where causality failed to hold. Would that universe be described by classical/standard logic? Or would we have to use a radically different logic where causality was not necessary? ...
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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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151 views

Is it true that if an argument is invalid, any argument of that logical form must be invalid?

I am stuck over whether these statements are true: First: "If an argument is invalid, any argument of that logical form must be invalid." Second: "There may be invalid argument with ...
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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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Why is it that the statement “All goblins are yellow” does not contradict the statement “All goblins are pink?”

From what I know, I think it has something to do with vacuous truths, but my understanding is not quite there yet.
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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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Why did we define vacuous statements as true rather than false?

I have been trying to understand why implications about the empty set are treated as "true". It seems to me intuitively that vacuous statements should be false. For example consider the sentence: ...
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can an argument containing a contradiction be valid argument

I know that validity has nothing with truth of the conclusion or with how good argument is in general, and an argument is valid iff the truth of its premises guarantees the truth of its conclusion. ...
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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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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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1answer
123 views

Do mathematical objects exist after their definition? [duplicate]

Suppose we have a system with a set of axioms. Now we begined to define new terms. E.g. in maths we have a particular set of axioms and then we define what a function is. But do all the functions ...
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Does truth exist without proof?

When we prove something (e.g. in maths) we show that a particular statement is true. But if we couldn't prove that statement that doesn't mean that the statement would be false right? So is proof a ...
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How much of a nonstarter is this argument that tautologies are (true-ish but) not true?

I am wondering how much of a nonstarter you think this argument is. I am also interested in suggestions concerning articles or books to read. (More recent works preferred, as I can follow their ...
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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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One-paragraph explanation of the principle the counterexample by modern logicians? [closed]

Is there any good, one-paragraph explanation of the principle and importance of the counterexample in logic by a modern logician (19th to 21st century)?
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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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Is atheism the null hypothesis on god's existence? Can the null hypothesis be accepted? Is the proposition “god does not exist” falsifiable?

 Is Atheism the Null Hypothesis?  Is Atheism Falsifiable?  Does Atheism Carry the Burden of Proof? Atheism has distinct definitions which can be categorized as follows: • Weak/Soft ...
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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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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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What is the difference between Law of Excluded Middle and Principle of Bivalence?

Law of Excluded Middle: In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, ...
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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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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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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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What does the truth-value of a material implication represent?

This question comes from my attempts to understand what the truth value for a material implication with a false antecedent represents. I have seen several justifications for this convention, usually ...
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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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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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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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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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Why isn't Cantor's diagonal argument just a paradox?

Cantor's diagonal argument concludes the cardinality of the power set of a countably infinite set is greater than that of the countably infinite set. In other words, the infiniteness of real numbers ...
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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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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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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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What exactly is informal logic and is this what I'm looking for?

I've been reading and researching about formal and symbolic logic for some time now, mainly out of interest in rationality. But I've come to a point where the various logical systems seem more like ...

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