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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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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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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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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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 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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Are the “laws” of deductive logic empirically verifiable?

"Is Logic Empirical?" strongly suggests a question that I would like very much to get a handle on. That phrase is a title of an article by Hilary Putnam, and, according to synopses/reviews, the ...
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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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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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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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What is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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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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Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?

The proof of various theorems are nowadays routinely described as "proof by contradiction". For example, the following theorems: https://en.wikipedia.org/wiki/Proof_by_contradiction The ...
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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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What is the difference between Aristotle's theory of categories and Russell's theory of types?

A partial answer might come through an introduction. Well, we know that Russell's efforts to understand the contradictory appearance of the class of all classes not members of themselves (a notion ...
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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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Can knowledge about argumentation be sufficient for philosophical logic without too symbolic or mathematical concepts?

The most important element for expression of truth is trough an argument, with premises and conclusion. Argumentation requires to avoid fallacies and adhere to the truth. However logic if treated as a ...
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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 ...
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Introductory book on philosophy of logic?

I know that there are quite a few questions like this here already, but I haven't yet found an answer that would satisfy me. I'm looking for an introductory logic book. My main goal is to work ...
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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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Are there paradoxes involved in allowing for an unrestricted domain in predicate logic?

I've put some thought into this, and just want to make sure I'm on track, or if I need to be corrected. Basically, my answer is this: Yes, you need to always specify a domain when formalizing into ...
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A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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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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Is there a logic of married bachelors?

I'm sure this question must have a simple clarification, but I am largely unfamiliar with the branches of formal logic and not sure where to look for it. We know that "All bachelors are unmarried men"...
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Wittgenstein criticizes Coffey's work 'The Science of Logic' in its assumption that every proposition requires a subject and a predicate. Why?

Why does Wittgenstein believe there can be propositions that lack a subject or predicate? What examples does Wittgenstein give in support of this belief?
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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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Can paraconsistent or other logics make the impossible happen?

A paraconsistent logic system it is defined as "a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic 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 book recommendations for learning Hegel and Wittgenstein?

I'm currently interested in Hegel's Dialectic and Wittgenstein works. I'm mostly looking for things related to logic, language and the foundation of mathematics. What do you think I should read from ...
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Why is it argued that an argument has one and only one conclusion?

Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true ...
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What is the difference between a logical truth and a tautology?

Some papers I read seem to be referring to a distinction between logical truths and tautologies. At first I thought something was wrong since I thought they are the same by definition. I checked the ...
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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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Tractatus 3.333 and Russell's paradox

Can anyone explain to a non-logician how Tractatus 3.333 refutes (or fails to refute) Russell's Paradox? Please explain his use of symbols!
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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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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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Exactly what was Wittgenstein's argument against identity?

Roughly Speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing. (Tractatus, 5.5302 and 5.5303) Like Russell ...
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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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Is there a generally agreed upon solution to Bradley's Infinite Regress without appeal to Paraconsistent Logic?

I'm interested in Priest's solution using paraconsistent logic, but before I embark on that, I wanted to know if there was a generally agreed upon solution in more "classical" schools of thought. ...
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What are the problems with Tractatus?

Tractatus, in a way, says World isn't what is out there, but is the world you imagine. World is what you would tell another person when you will recount this world. (It is what you would 'know' of the ...
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Is there anyone who believes that all modal statements are meaningless or trivial?

It is often useful to interpret statements in various modal logics using possible-world semantics. For instance "it is necessary that P" means "P is true in all possible worlds", "it is possible that ...
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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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Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
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If I said I had $100 when asked, but I actually had $200, would I be lying by omission? [closed]

If you had $200 cash on you right now, and I asked you if you had $100 on you, would the correct answer be yes (always/no matter what other conditions there are), no (always/no matter what other ...
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Ontological status of variables

Background This question has its origin in this post. More specifically, in giving answers to the following questions, In what way does the collection of all sets consist of sets? What are ...