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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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?

While reading Logicomix, I came across a scene that I don't quite understand. Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
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What, if anything, is the difference between studying logic mathematically and studying it philosophically?

There seems to be a distinction between studying logic mathematically and studying it philosophically and, in practice, it is reasonably clear which framework one is using when one studies logic. I've ...
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Why should universal generalization work for abstract objects?

I am reading a logic book in my free time and usually the inference rule of universal generalization is motivated by real-life examples: Imagine having the statement that all people with brown hair ...
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How did Descartes made a logical skeptic argument against logic, without falling into a paradox, in his Metaphysical Meditations? Is it actually valid

René Descartes seems to have made some arguments against logic and mathematics in his Metaphysical Meditations, however it seems that these arguments are still logical, and the problem is whether that ...
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Why aren't Kripke semantics "syntax in disguise"?

The Wikipedia article on Kripke semantics suggests that they were considered a major breakthrough in part because algebraic semantics were seen as merely "syntax in disguise". But Kripke ...
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59 views

Laws of logic literature recommendations

What are some books/papers/articles I could read to develop an informed perspective on questions like "where do the laws of logic come from? Do they have a deep connection with the structure of ...
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363 views

What did Godel mean by intensional paradoxes?

I have read recently a chapter in Hao Wang: A logical journey: From Godel to Philosophy , where Wang mentions his discussions with Godel on intensional paradoxes, but I have no clue what exactly they ...
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5answers
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potential violation of law of excluded middle

Consider the following sentence: "Either Santa Claus is hungry or Santa Claus is not hungry." This seems to be a straightforward application of the law of excluded middle. However, it also ...
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1answer
56 views

A proposal for the meaning of life [closed]

I propose that the meaning of something is "all of the information related to it", and thus that the meaning of life is "all of the information related to life" - all of the causes ...
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1answer
254 views

What is mathematics? What are some of the most predominant philosophical definitions of mathematics?

Philosophers have given the nature of mathematics a lot of thought. As a beginner exploring philosophy, one of the questions which presents itself is 'what is X', and in this case, X is mathematics. ...
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505 views

What is the philosophical basis of the relation among reasoning, formal logic, and Turing machines? [closed]

Turing's machine is a generalisation of the concept of 'computation'. 'Formal logic' seems to be some sort of form of 'computation'. How are reasoning, computation, and formal logic related? Are forms ...
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can S5 be the weakest logic?

If we were to prove that an argument is a logical truth only in S5 logic out of (K, T, S4, and S5). does that make S5 the weakest of these four logics in which the argument is a logical truth?
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First-order semantics for plural logic

There are commonly thought to be two kinds of set-theoretic semantics for second-order logic: the standard one, where relation (and function) variables range over the entire power set of a model ...
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1answer
52 views

Jackson's simplification of Lewis' triviality result

I'm reading chapter 11 of The Blackwell Guide to the Philosophy of Language by Frank Jackson, and once he touched upon Lewis' triviality results he writes: However, this definitely doesn't look that ...
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1answer
117 views

Why do equivalent propositions sometimes differ in apparency?

I study maths, and I have found that a useful way of thinking about two propositions A and B being equivalent is to regard them as being two different ways of saying the same thing, or equivalently, ...
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2answers
309 views

Question on Godel's Remark on Algorithmic Nature of Mind

Gödel claimed that what the Theorems do entail (specifically, the Second Theorem) is that mathematics is inexhaustible: It is this theorem [i.e., the Second Theorem] which makes the incompletability ...
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1answer
102 views

Is Tarski's theory of truth widely accepted

Tarski's truth theorem asserts that a truth definition for a (reasonably strong) theory cannot be formalized within that theory. It seems that Tarski's theory of truth has met with a lot of criticism. ...
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Tarski's sufficient conditions for the Liar paradox and self-reference

Tarski gave three sufficient conditions in his 1944 paper The Semantic Conception of Truth for the Liar paradox to occur: The language in which the Liar sentence is stated in is semantically closed, ...
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Is logic about a priori mind?

What is logic? One can imagine Turing, Godel or Post writing a paper on logic. What provides the "validity" to the content they write? One proper answer to this question is the a priori &...
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3answers
131 views

In the context of philosophical logic, what does 'extra-logical' mean?

I am having trouble understanding what 'extra-logical' actually means in the context of philosophical logic. Case in point: Bueno and Colyvan argues in their paper Logical Non-Apriorism and the ‘Law’ ...
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2answers
316 views

Does Quine's Predicate Functorese maintain the existence of relations?

Quine's predicate functorese has been proposed as a "feature-placing" language for ontological nihilism (Strawson, Azzouni, Dasgupta, Diehl). This is often used to eliminate objects and ...
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1answer
103 views

Is it there a "completely expressive" formal system / logic language?

I wonder whether it exists a formal system such that all (or a considerable number of) the others can be considered as a subsets or fragments of it. I would say that, for instance, First-Order logic ...
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4answers
184 views

Stephen Yablo's Aboutness and logical subtraction

I was finishing reading Aboutness by Yablo, but there is an intuitive definition that I do not get: He says on page 148 that: What is this relation of adding falsity, or being additionally false, or ...
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57 views

Confidence margin for logical verification

I'm starting to read Wittgenstein and I keep circling around a problem, which I'll lay out with the following ideas: a. Logical space is the totality of external reality. b. A proposition is logical ...
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Formal logic - a priori or a posteriori

I am aware of the classical classification of logical calculus as apriori. I have also read pretty much anything I could get my hands on regarding "logic", including "New Essays on the ...
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Do not understand Truth value gap theorists' response to the Strengthened Liar

Truth value gap theorists assert that the Liar sentence is neither true nor false - it has no truth value. But here comes my first question: If we take a sentence's meaning to be its truth condition, ...
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Is the distinction between fact and opinion, and objectivity and subjectivity universal or cultural? [closed]

I noticed in certain cultures that I interact with here in Malaysia, it seems that the distinction between fact-opinion and objectivity-subjectivity is non-existent. Whereas in STEM and the scientific ...
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1answer
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What is the exact form of law of non-contradiction that dialetheism rejects?

Dialetheism asserts that there are sentences that are both true and false, e.g. the Liar. This seems to, quite obviously, go against the law of non-contradiction (LNC), and indeed Priest seems to ...
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167 views

Is deductive logic, and more specifically propositional logic, ultimately derived from induction?

Is the system of propositional logic itself induced, beyond its manipulated assumptions? It seems to be the case that we use propositional logic on the basis of two facts - firstly that it seems to ...
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3answers
157 views

Infinite Regress in Language and Logic?

I had this idea, and it seems novel to me, but I'm wondering if there is a philosopher that addresses this issue already because I think it's kind of interesting. When making a logical statement, you ...
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2answers
371 views

Why are some things considered "impossible" even in other universes?

For example, I often hear that life could not develop in a universe where the fundamental constants were even slightly changed, or where certain physical laws were different. But if we're dealing with ...
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100 views

What is the philosophical term used to describe flawed logic?

A freak snowstorm strikes Washington, D.C. Climate change deniers hail it as evidence of global COOLING, not warming. It seems logical since snow is popularly associated with cold. However, it seldom ...
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81 views

an argument that is clearly valid but invalid in a sentence logic

I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...
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Can we make statements for persons/objects that cease to exist?

I am asking this question because I thought what truth value would have a have a quantifier over a set that contains persons that are dead. For example suppose I state: "For every x that is ...
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55 views

Is there some non-classical logic where the van der Waerden theorem does not apply?

The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...
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Hegel's counter proof of the old Logic

In his book on Logic,Hegel makes a counter proof of the old way of defining Logic. I have trouble understanding in which way Aristotle or Descartes were wrong according to him. Could someone explain? ...
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2answers
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Fail to understand Tarski's substitution argument for logic apriorism and a rebuttal against it

I have been reading Bueno and Colyvan's Logical Non-apriorism and they mentioned that Tarski has the following argument for logic apriorism: If, in the sentences of the class K and in the sentence X, ...
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Why is first-order logic interesting to philosophers?

This site had a question: Is First Order Logic (FOL) the only fundamental logic? Let me ask the opposite: Why is FOL still interesting or useful to philosophers? For example, the "ancestor" ...
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Yablo's condition on "Truth about a subject matter"

In section 2.4 of "Aboutness" Yablo offers the following analysis of what does it mean that a statament is true about a certain subject matter/topic: So, what is the proposition we are ...
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61 views

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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174 views

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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2answers
105 views

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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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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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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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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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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300 views

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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123 views

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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1answer
341 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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