Questions tagged [philosophy-of-logic]

Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.

Filter by
Sorted by
Tagged with
9
votes
2answers
851 views

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 ...
14
votes
2answers
2k views

What is the philosophical ground for distinguishing logic and mathematics?

I was wondering why the field of mathematics and that of logic are perceived as two distinct fields. Although could be pleased with the intuition that logic is rather meta-mathematics, still would ...
15
votes
2answers
988 views

What are the current topics in philosophy of logic?

I'm contemplating another attempt at completing my long delayed MA in Philosophy, and I need a new thesis topic. As a student I excelled in advanced symbolic logic, but my connection with academic ...
3
votes
2answers
870 views

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 ...
16
votes
7answers
2k views

Is Logic Empirical?

We use the logical system that we know from observations (empirical data) holds true in the world we live in (please correct me if I am wrong). Hence the axioms of logic we choose are themselves ...
5
votes
6answers
1k views

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 ...
8
votes
5answers
2k views

What is the difference between the “is” of predication and the “is” of identity?

What is the difference between these, the "is" of predication and the "is" of identity? For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
1
vote
2answers
385 views

References for the justification of the use of Logic

Following that question : How to justify the use of logic? I'm looking for references of the justification of the use of Logic (the question above didn't ask explicitly for resources but rather for a ...
15
votes
10answers
16k views

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, ...
1
vote
3answers
208 views

What justifications have been given for using particular systems of logical calculus?

I think that using any particular system of logical calculus should be properly justified. This justification should be seen as particularly important and pressing in science and technology, and ...
0
votes
0answers
111 views

Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
12
votes
8answers
3k views

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: ...
7
votes
3answers
771 views

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 ...
1
vote
3answers
279 views

Is Deductive Reasoning Alien to the Material World?

A quick survey of literature: Goel V. Anatomy of deductive reasoning. Trends Cogn Sci. 2007 Oct https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2685028/ García-Madruga JA, Gutiérrez F, Carriedo N, ...
5
votes
4answers
789 views

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 ...
5
votes
3answers
321 views

What does the term “mathematical logic” mean?

What is "mathematical logic"? Is it the logic of mathematical reasoning, or is it the claim that mathematics and logic are identical? Also, is "quantificational logic" a particular type of "...
2
votes
3answers
277 views

How do we know that if the statement “A → B” is correct, “¬B → ¬A” is correct?

All examples that I can come up with confirm that If "A → B" is correct, "¬B → ¬A" is correct, but is it possible to rigorously prove that negating a true implication always will result in another ...
1
vote
1answer
73 views

Can different varieties of modality be used with existential quantification?

I'm wondering if it makes sense to talk about worlds which aren't this one being real. It seems like you can claim that something possibly exists. Now I'm wondering, because it seems to amount to ...
1
vote
1answer
559 views

What is the intension of the concept “intension”? [closed]

I think that it should be possible to assign to all concepts a plausible intension, consisting of just one or two words. However, in textbooks or encyclopedias I never found such focused appointments ...
9
votes
2answers
4k views

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 ...
14
votes
12answers
11k views

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.
8
votes
10answers
1k views

Does the Fallacy Fallacy make logic useless?

I should add that I'm not a formal student of philosophy and haven't studied it in any serious depth. I just like logic, and logical fallacies. I like to spot them, and I like to debate using them, ...
8
votes
1answer
368 views

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'...
6
votes
2answers
514 views

What does Russell mean by “term” in Principles of Mathematics?

Bertrand Russell in Principles of Mathematics defines a term as "Whatever may be an object of thought, or may occur in any true or false proposition or can be counted as one." Can someone elaborate on ...
4
votes
1answer
473 views

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 ...
4
votes
1answer
1k views

What, at present, are the major unsolved problems of logic?

In the 1900s, Hilbert published a list of 23 (later 24) unsolved problems in mathematics, which sparked increased research into each of them and the subsequent resolution of several of these problems. ...
9
votes
5answers
632 views

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 ...
7
votes
1answer
617 views

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?
6
votes
4answers
368 views

Is there any reason for the heavy focus on binary relations in formal logic?

As a fan of C. S. Peirce, I'm surprised that, at least triadic relations, aren't investigated as much as binary relations are. What I mean is that with binary relations, they have already been ...
5
votes
3answers
2k views

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!
4
votes
2answers
300 views

References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
4
votes
3answers
2k views

If the premises of an argument CANNOT all be true, then said argument is valid

Based on the fact that a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, I am ...
1
vote
1answer
316 views

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?
12
votes
1answer
1k views

What is the axiom of reducibility? And what philosophical controversies did it incite?

Trying to come to terms with basics concerning philosophy of logic, and wish to ask about some particular issue: What is in simple words the axiom of reducibility put forward by Russell? And what is ...
6
votes
8answers
5k views

Is finding truth possible?

Consider the following argument: If want to know that something is true, I need to first know what is truth. If I need to know what is true, I need to find the truth. (Is there ...
4
votes
1answer
196 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 ...
3
votes
1answer
437 views

The Truth-Falsehood Dichotomy and Logic

Some philosophers argue against truth bivalency, and say that not every statement must be true or false, but some statements can be untrue without being false, or truth-ambiguous, or both true and ...
3
votes
3answers
164 views

What do we mean when we say there's only one type of logic/mathematics and that they can’t change?

Do we want to say that if they changed, they would not be logic/mathematics (as we know) anymore? How can we be sure that there's no other type of logic/mathematics?
1
vote
0answers
162 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
1
vote
2answers
64 views

Are syllogisms independent of humans?

For example, if "All a are b" and "All b are c" then "All a are c". To make this syllogism, does a conscious being need to exist? Or is it inferred from the sentences?
0
votes
1answer
168 views

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 ...
6
votes
3answers
259 views

How is the nature of logical principles commonly defined in contemporary philosophy?

In contemporary philosophy, how exactly is the nature of logical principles defined? For example, the way I've commonly seen logical principles construed are as true propositions which described the ...
4
votes
1answer
207 views

What were the historical interpretations of Aristotle's definition of validity/logical consequence?

What were historically the various interpretations given to Aristotle's notion of validity, implicit in his syllogistic? Here is one authoritative translation of the relevant text: A syllogism is ...
4
votes
2answers
314 views

Prerequisites for Michael Dummett texts

I want to read Michael Dummett's The Logical Basis of Metaphysics. Is it hard to read ? I would like an answer for the same question regarding his other texts. Do I need a prior exposition to other ...
3
votes
4answers
527 views

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 ...
3
votes
1answer
95 views

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 ...
2
votes
1answer
196 views

What is the subject of Tractatus by Wittgenstein?

Is Tractatus about the Philosophy of language or Philosophy of logic. I was hearing John Searle's lecture and he said there are two strands in Philosophy of language :- 1. Logical theory of language 2....
2
votes
4answers
240 views

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 ...