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
33
votes
14answers
19k views

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 ...
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 ...
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, ...
15
votes
2answers
961 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 ...
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 ...
13
votes
7answers
5k views

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 ...
12
votes
3answers
748 views

How come intuitive thinking is related to constructing a proof?

I am researching Constructivism and Intuitionism. I can't understand why Intuitionism and Intuitionistic Logic are named as they are. Intuitionistic logic requires constructing a proof of every ...
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 ...
11
votes
7answers
2k views

Do premises need to be valid conclusions themselves?

I'm pretty new to logic. I recently purchased "A Concise Introduction to Logic" by Patrick Hurley based on reviews. So far I'm liking the book. I'm really focusing hard on the first chapter to get a ...
10
votes
7answers
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: ...
10
votes
4answers
1k views

How do we separate rules of logic from non-logical constraints?

I think that very often the idea of 'constraint' appears in mathematics. For example, when a triangle is considered, 3 points are constrained not to be co-linear, and then we try to discover the ...
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 ...
9
votes
7answers
3k views

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 ...
9
votes
5answers
553 views

Why don't we have consensus in more complicated areas of logic?

When I once realised I don't really understand how and why proof by contradiction works, I started reading about it. And apparently I wasn't the only one who felt there's something wrong about it - ...
9
votes
5answers
620 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 ...
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
330 views

Logic and Computation : a philosophical viewpoint

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'...
8
votes
2answers
807 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 ...
8
votes
2answers
779 views

What are the philosophical implications of using inconsistent mathematics?

Why mathematicians would prefer at times to work with inconsistent systems (from which I assume everything can be proven unless changing the logic used)? In particular, how could working with an ...
7
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?
7
votes
1answer
605 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?
7
votes
2answers
708 views

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 ...
7
votes
2answers
968 views

In predicate logic, do we necessarily have to restrict the domain of discourse?

Can we combine formalized statements in predicate logic from widely different domains of discourse (say, one regarding integers, one regarding the fruits in one's garden) by using logical rules/...
7
votes
3answers
752 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 ...
7
votes
5answers
441 views

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 ...
6
votes
8answers
3k views

What is the explicit reasoning behind proof by contradiction?

From my understanding, proof by contradiction consists of the following steps. 1. Show that p -> q, where "->" is the conditional. 2. Show that q is false. 3. Deduce from a truth table that p must be ...
6
votes
4answers
991 views

Do logically incoherent statements still have meaning?

My reading of Carnap's "The Elimination of Metaphysics Through Logical Analysis of Language" suggests to me that it is possible to form sentences in a language that are grammatically correct but ...
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 ...
6
votes
4answers
2k views

A proposition is non-falsifiable. So what?

Does Karl Popper argue that non-falsifiable theories are not true/have no truth value, or simply that they are not provable? Put another way: according to Popper, could a non-falsifiable theory ...
6
votes
2answers
509 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 ...
6
votes
3answers
258 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 ...
6
votes
3answers
1k views

Can you list examples of problems that can not be solved within a formal system but human beings have solved through construction or creativity?

This kind of problem is mentioned in a book I have read, but the book did not give a concrete example. If any such problem existed, this might help me understand human creativity. I think it would ...
6
votes
4answers
350 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 ...
6
votes
5answers
695 views

How could mathematics and logic exist without us, if they are concepts created by us independent of reality?

Would maths and logic exist if we didn't exist despite we created them, and do not have correspondence with reality?
6
votes
1answer
290 views

What exactly is a first-order logic?

Can someone explain in simple terms what exactly is a first-order logic? From my amateur standpoint, I think that first-order logic is a some kind of a system of symbols and general logical rules and ...
5
votes
5answers
245 views

Is Modal Logic Logic?

What makes "Modal Logic" Logic? Why are symbols that stand for "necessary", for example, taken as symbols of Logic (of the same level of symbols that stand for "exists")? What are the limits that ...
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 ...
5
votes
3answers
409 views

Are there any strong reasons to still consider logical monism or a “One True Logic” in light of all the non-classical logics that have been developed?

I know there has always been some debate concerning whether or not a certain logical system (like classical logic) is the correct one, especially when it comes to propositional claims about the ...
5
votes
1answer
120 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 ...
5
votes
1answer
2k views

What are lucid examples of non-truth functionals?

I wanted to understand the concept of non-truth function (which I found when reading about conditionals in logic). The definition of non-truth function that I have is (from reddit): If a connective ...
5
votes
1answer
983 views

What distinction is there between logic, philosophy of logic and philosophical logic?

I'm not clear on where logic in the broad sense of the word stands with respect to philosophy. I do know there is mathematical logic which would be a subset of something. If philosophy of logic and ...
5
votes
3answers
312 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 "...
5
votes
2answers
157 views

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://...
5
votes
2answers
364 views

Is there a difference between equality and identity?

Is there any difference between equality and identity, or are they the same concept?
5
votes
2answers
288 views

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. ...
5
votes
5answers
205 views

Proof that deduction is valid in all possible realities?

I was wondering, how can we know that deduction is a valid way to argue for something in all possible realities? How do we know that, in some alternative universe, something is not both ~P and P? How ...
5
votes
1answer
109 views

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 ...
5
votes
2answers
220 views

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 ...
5
votes
4answers
759 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
2answers
856 views

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 ...

1
2 3 4 5