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Questions tagged [logic]

For questions about logic, whether it concerns syllogistic logic, mathematical logic or the nature of logic itself.

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17
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5answers
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Can a lack of knowledge or understanding invalidate a positive claim?

Consider the example of causal determinism. It can be phrased in many ways, all with identical meaning: - The idea that "every event, including human cognition and behavior, decision and action, is ...
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How is the claim “I am in New York only if I am in America” the same as "If I am in New York, then I am in America?

It makes absolutely zero sense to me. It would make sense if "I am in America" is the antecedent and the consequent is the former. Even though it wouldn't be sound, it would make logical sense. I ...
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What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?

Suppose that someone initially states that "fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight ...
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Is God either immoral or not omnipotent?

The usual (Christian) justification for suffering/evil in the world created by a benevolent God is freedom of the will. However, the more interesting question is not about the source of evil (which ...
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Are all paradoxes reducible to one “fundamental” paradox?

I may need to refine this question, since I am mostly grappling with a murky intuition and haven't yet done the real work. When I encounter many of the well-known paradoxes, such as Zeno's dichotomy, ...
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What fallacy dismisses problems by presenting “bigger” problems?

Wasn't really sure how to phrase this, but I'm thinking of an instance in which someone diminishes a problem by presenting one of larger scope - as a rather shoddy example, "x political problem in ...
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1answer
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When it is correct to use Tarski's undefinability theorem versus Gödel's incompleteness theorem?

Smullyan (1991, 2001) has argued forcefully that Tarski's undefinability theorem deserves much of the attention garnered by Gödel's incompleteness theorems. That the latter theorems have much to say ...
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1answer
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Difference between implication/conditional and logical entailment?

What is the difference between the implication/conditional truth function and the notion of logical entailment? My naive understanding as a computer programmer is that the conditional is a function ...
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If a person claims to know anything could it be disproven by saying 'prove that we are not in a simulation'?

Everyone starts out at 0 and if anyone wants to say that they know something they have to prove that claim. Is the counter to this person claiming that they know something logically correct? Person ...
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Is 'equality' ultimately grounded in empirical observation?

Let's say I invent a concept X in my own imaginings. The only property it has is X-ness; it is defined as 'that which is represented by X'. I have just defined that to be the case. It seems to me, ...
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What is the philosophical equivalent of mathematical proofs?

In mathematics, there seem to be five standard methods of proving or refuting an argument: a proof by induction, contradiction, counter example etc. Are there some typical proof methods that exist in ...
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963 views

When given limited information, is the simplest solution that matches that information most likely correct?

Is there any basis in philosophy for the idea that when given limited information, the simplest solution that matches that information should be presumed correct or most likely to be correct? For ...
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Do “if everybody did it” arguments commit a fallacy?

Who is committing a fallacy in this discussion, and what kind of fallacy is it? A: There's nothing wrong with killing people at random B: If everybody did it, you would too most likely be a random ...
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Name for reverse Ad Hominem, (i.e. praising the defense)?

Is there a standard name for a fallacy of the same form as an ad hominem, except that instead of denouncing the opposition, it praises the defense? Typically an ad hominem ("against the man") fallacy ...
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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 ...
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What Precisely Does “Semantics” Mean?

What do logicians mean when they refer to the notion of "semantics"? I don't find the definition "the connection between words and meaning of those words" to be that satisfactory here. Informally, ...
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I have trouble understanding this fallacy: “If A, then B. Therefore if not-B, then not-A.”

About "If A, then B. Therefore, if not-B, then not-A": From what I understand the conclusion is wrong, because it is not said that A is a sufficient condition for B, (and there may be other ...
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10answers
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What fallacy is assuming something is the case because of past events

I'm sure this is a simple question. What I am referring to is disbelieving someone on Day 20 because they have lied every day previous to Day 20. Another example is the boy who cried wolf. The 50th ...
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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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2answers
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Is “propositions of logic are tautologies” (Wittgenstein) literal or mystical?

At 6.1 in the Tractatus, Wittgenstein says, "The propositions of logic are tautologies." When he says this, is he referring to the fact that the axioms of propositional logic as presented, for ...
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Is using analogies a bad logic reasoning?

When discussing with someone, I like to take the argument they use and put it in another context, to see if it works, and if it doesn't, ask why the argument should be valid in one context but not in ...
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Why should I believe my own conclusions?

Consider the metaphysical question of whether God exists (just as an example). There are, and have been throughout history, billions of atheists, billions of Christians, and billions of people with ...
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How fundamental is logic?

I had always perceived logic as something that exists outside mathematics, physics/the physical, human consciousness, and everything. So when someone in my class posed the question whether logic can ...
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1answer
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How do quantifiers work in predicate logic?

Predicate logic is somewhat like propositional logic, except that where propositional logic only works on the level of whole sentences (e.g. A = "Socrates is mortal", B = "All ...
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Do the laws of logic exist independently of human or animal consciousness?

Are the laws of mathematics and logic, such as if a=b, and b=c, then a=c just constructs of the human mind, or does the universe hold an innate logical structure to it, which the physical part of the ...
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What are the practical applications of modal logic?

I'm a computer science and philosophy double major. I know logic is paramount in computer science, but what about modal logic? Are there any practical applications in computer science and perhaps even ...
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“→” is the symbol for material implication. Is there such a thing as “immaterial implication”?

Why do we qualify "implication" with "material"? This seems to imply that there are other kinds of implication.
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Does a Background in Mathematics Make One a Better Philosopher?

I was a Philosophy major as an undergrad and became obsessed with the beauty of rigorous argumentation. There I didn't take a single class listed under the Mathematics department and was almost ...
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How do I go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx]?

I've been thinking about the ontological argument recently. I'm trying to go from ◊∃x□[∃y(y=x) ∧ Mx] to ∃x□[∃y(y=x) ∧ Mx] I choose that formulation because that seems to express x having the ...
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2answers
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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 ...
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12answers
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Are omniscience and omnipotence mutually inconsistent?

I see this in The God Delusion by Richard Dawkins: If God is omniscient, he must already know how he is going to intervene to change the course of history using his omnipotence. But that means ...
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Is rejecting A not equivalent to accepting ~A?

A fundamental misconception that many laymen hold is that rejecting claim A is equivalent to accepting its inverse, namely ~A. How can we formally differentiate these claims, which I believe are all ...
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6answers
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Is formal logic unsuitable for philosophical reasoning?

I'm taking a course at university about philosophical reasoning / argumentation. The professor came up with an example where formal logic was wrong: If Dave is in London, then he is in England. (...
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3answers
555 views

Are systems of logic that don't follow or extend garden-variety FOL possible?

As I know all humans share a unique logic and even less-educated people uses same common sense in their statements. For example, it is rational for anybody that if P is correct then P or Q is correct ...
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555 views

Are all fallacies created equal?

That is, are some fallacies considered worse than others, or does each fallacy have the same weight? For example, are formal fallacies considered "worse" than informal fallacies or vice versa? For ...
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3answers
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What is the difference between Law of Excluded Middle and Law of Non Contradiction?

In spite of reading the SEP entry under Contradiction several times I have difficulty distinguishing between the two. We can translate the Aristotelian language, with some loss of faithfulness, ...
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4answers
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What fallacy excludes “outsiders” from discussing “insider” issue?

I see this a lot on the internet, especially as of late with what's trending in the news: You're a man, so you're not allowed to comment on women's issues. You're a woman, so you're not ...
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2answers
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What is the problem with using circular reasoning? Is it “invalid”?

What, specifically, is the problem with circular logic/reasoning? I think it's invalid. For some reason, everyone knows that it's wrong to use, but is there anything more to it than that? ...
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Does Wittgenstein's Tractatus establish serious bounds for discussions of the supernatural from a modern point of view?

In today's mathematics, we have many variants of logic (propositional, first order, higher order, fuzzy logic, etc.). These are all self-consistent formal systems that are based on some set of axioms. ...
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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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“Because if you doubt that you're doubting, you're still doubting” - What is the analogous mathematical/logical expression to this sentence?

In an answer here, the following was stated: The essence of his [Descartes] argument is that you can doubt almost everything about the world, but you can't doubt that you're doubting. Because if ...
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6answers
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What practical methods can be used to prove a negative claim?

I realize that the burden of proof falls squarely on the shoulders of the person making the claim, but they often seem unwilling to do the footwork. It is difficult to prove a negative case except by ...
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When can we call an explanation “rational”?

There are a lot of questions involving rational judgment, rational choice, rational explanation, etc... And at the same time, it seems that "being rational" is a guiding principle for a lot of people. ...
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Gödel's theorem and God

I have seen it argued that Gödel's Incompleteness Theorems have implications regarding the existence of God. Arguments for the existence of God run mostly along the lines: "Because of Gödel's Theorem, ...
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3answers
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What is the difference between an Ordinal number and a Cardinal number?

I'm trying to understand the real difference between an Ordinal and a Cardinal, especially in relation with transfinite cardinals. The stuff on Wiki is a bit too complicated. Can anyone make it simple ...
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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 ...
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Is Galileo's argument about falling bodies logically flawed?

Galileo's famous argument against the Aristotle's theory of falling bodies goes like this. "Let's say heavy objects do fall faster than light ones. Then it seems the heavier weight will fall with the ...
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2answers
380 views

Was Locke right that analytic knowledge is vacuous?

According to Locke, it is impossible to obtain substantive knowledge from analytic propositions. Statements like "triangle has three sides" are analytic, but one cannot derive the Pythagorean Theorem ...
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846 views

What does Hegel mean by “Quality”?

In the Science of Logic, Hegel initially presents quality as existent determinateness. He further distinguishes two modes of determining quality in accordance with the moments of existence: ...
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1answer
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What are the differences between Tarski's 1933 and 1956 truth definitions?

The paper "The Seven Virtues of Simple Type Theory" mentions that it uses the same trick (due to Tarski) to define the semantics that is also used by first-order logic. I interpreted this a reference ...