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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14 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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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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276 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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81 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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4answers
168 views

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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102 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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301 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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96 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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177 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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56 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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146 views

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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61 views

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
108 views

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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158 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
131 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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352 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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91 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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72 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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1answer
78 views

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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50 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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43 views

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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115 views

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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5answers
263 views

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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57 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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165 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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95 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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185 views

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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4k views

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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227 views

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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258 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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115 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
258 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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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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151 views

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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237 views

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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80 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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1answer
126 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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405 views

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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33 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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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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49 views

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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584 views

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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368 views

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

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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152 views

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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