Questions tagged [logic]

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

Filter by
Sorted by
Tagged with
14
votes
8answers
15k 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 ...
13
votes
12answers
17k views

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 ...
0
votes
1answer
117 views

We cant' think in nothing! [closed]

If you ask someone to describe someone else, or just tell him who is that person? what is the natural answer? of course he will respond which person?, because he never saw him before. And it's clear ...
0
votes
1answer
105 views

What is the name of the argument that disallows the current state or condition of things as it is independent of reason?

I remember a few years ago I came across a description of a framework of argument that disallowed the use of the current (or any other) state in the argument given that the state is independent of how ...
9
votes
4answers
3k views

Why is Modus Ponens valid?

I am having trouble understanding what defines Entailment operator. On Mathoverflow I posted this question on what I perceive to be paradox of entailment. Consider: Modus Ponens: P therefore Q P ...
5
votes
5answers
2k views

How to understand numbers that become really large?

If we begin with a notion of number N that we denote F(N) as a function of time, can a decidable procedure exist on definability of the growth of numbers? Inspired by Tipler's Omega point and Thomson'...
4
votes
2answers
237 views

The paradox of the raven and Kratzer's account of “if-then”

I have just read Angelika Kratzer's paper "Conditionals". In this paper Kratzer rejects the traditional account of the "if-then" construction in English as a two-place material implication operator, ...
2
votes
1answer
2k views

What are the truth tables for “necessary” and “sufficient”?

Here he says that: If you have A is sufficient for B it means that every time you have A you will have B, without exception: A -> B If you have A is necessary for B it means that every ...
4
votes
8answers
3k views

Is there a name for an argument like “A implies B; B implies A; therefore A”?

Is there a name for the following false syllogism? A implies B and B implies A therefore A For example: If unicorns exist then they have horns, by the definition of a unicorn. But in order for ...
0
votes
2answers
3k views

Is there any logical flaw in the arguments in this story between a professor and a student on the problem science has with God? [closed]

I found the following story on this site An atheist professor of philosophy speaks to his class on the problem science has with God, The Almighty. He asks one of his new students to stand ...
2
votes
1answer
148 views

What kind of definition is a definition based on a Turing-test?

Given that an extensional definition is one that defines the definienda by enumerating (partially or exhaustively) examples that belong to it (i.e. the list defines the concept), and intensional is a ...
4
votes
4answers
814 views

How can I demonstrate that a grammatical sentence lacks logical value?

To begin with, consider Chomsky famous construction: "Colorless green ideas sleep furiously". All the words respect a grammatical construction. But "colorless green" seems like a contradiction. If ...
11
votes
4answers
1k views

What is the fallacy in comparing evolution to a fairy tale?

I found the following statement on this Creationist site. If a fair maiden kisses a frog which instantly changes into a handsome prince we would call it a fairy tale. But if the frog takes 40 ...
5
votes
7answers
6k views

Can something be actually possible yet logically impossible?

By actual possibility I mean the possibility which is implied by ability or power. By logical possibility I mean whether concepts of reality contradict each other or not. I believe that knowledge ...
4
votes
2answers
259 views

Formal treatments for Stoic Logic

Philosophers such as Susanne Bobzien have provided work that provides a basis for axiomatising Stoic logic, however, the treatments I have seen focus on exposition of ancient works, with little ...
8
votes
3answers
1k views

What is the philosophical problem with Skolem's Paradox?

I guess there are two questions here. QUESTION 1: Skolem's Paradox shows that countability is relative in first-order logic, but where is the relativity? In this first question, I will do the ...
2
votes
2answers
539 views

Descartes's *Cogito* from a modern, rigorous perspective

In Descartes's Meditations, in order to establish a firm foundation upon which he could build a framework to determine philosophical and material truths, he begins by removing all of his then-current ...
-2
votes
3answers
847 views

Can there exist Nothing in Something? [closed]

Is it possible for Nothing to exist in Something ? e.g. if something is the whole set can nothing be an element of it ? If you take Nothing from something something remains. If nothing cannot exist ...
4
votes
2answers
1k views

Question on learning type in Plato Cave Allegory

My question is based on the Cave of Plato. In this myth I see two types of learning. The first type of learning is the person that is released from the cave and climbs up to the light. The second ...
3
votes
3answers
938 views

How do mathematical objects relate to the real world?

I am just going to give an example of what I mean using Skolem's Paradox. I DO NOT want to get into Skolem's Paradox itself or its "resolution." Skolem's showed that countability is relative in ...
12
votes
4answers
2k views

“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 ...
1
vote
1answer
4k views

What is the best way to learn logical fallacies? [closed]

I want to learn logic better, I know a few fallacies but I've read no books mostly just stuff on the Internet. I see them everywhere, but sometimes I don't know what the fallacy is called. I am a ...
6
votes
1answer
11k views

What is the symbol (c with a line through it)?

Can someone please advise as to the meaning of the symbol here? Please note that this is a symbol utilized in logic or possible calculations utilizing triangles (though still logical). Its not the ...
4
votes
3answers
772 views

Is it possible to use intuitionistic logic in some everyday situations?

Intuitionistic logic is the same as the usual boolean one apart from excluding the excluded middle, that is not(p) or p is not neccessarily true, so that boolean logic is a specialisation of the ...
10
votes
3answers
332 views

Can one still derive paradoxes from the amended version of Naive Set theory given by Cantor in a letter to Dedekind?

Consider the following definition of set given by Cantor in a letter to Dedekind: If on the other hand the totality of the elements of a multiplicity can be thought of without contradiction as '...
3
votes
3answers
296 views

Do Gödel's incompleteness theorems support the idea that the examination of a 'system' should only be undertaken to arrive at the inconsistency?

Roughly, Gödel demonstrated that in a logical system, that contains a model or arithmetic, there are statements which may be true, but are unprovable within the system. If a statement is not ...
11
votes
16answers
11k views

Does the notion of an all-powerful God conflict with the idea of free will?

In Abrahamic religions, God is often believed to be wholly omnipotent. People also seem to believe that humans have "free will", especially insofar that they feel they are in control of their own ...
7
votes
1answer
306 views

David Lewis' conception of properties as classes [closed]

David Lewis' conception of abundant properties which he identifies with sets/classes ("no matter how oddly defined") is not quite clear to me. Since according to this position there cannot be - in no ...
-2
votes
4answers
3k views

Can the existence of God be proved from mathematics? [closed]

This question of highest importance for everybody could not be answered in MO and will not be answered in Mathematics.SE. I can understand why the set-theorists there dive and attack it like vultures. ...
6
votes
3answers
459 views

Does Cox's theorem implicitly assumes the three classic laws of thought?

I read about Cox's theorem a long time ago in "Jaynes Probability Theory: The Logic of Science". It was used to justify the so-called "logical" interpretation of probability. My impression was that ...
13
votes
2answers
8k views

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? ...
32
votes
3answers
4k views

How did first-order logic come to be the dominant formal logic?

Early formal systems like Frege's Begriffsschrift or the Peano's work on the axiomatization of the natural numbers used axiom system with an underlying second-order predicate logic (from today's point ...
7
votes
3answers
727 views

Are there any known deficits of “relevant logic”?

The principle of explosion is the law of classical logic and similar systems of logic, according to which any statement can be proven from a contradiction. Some early formal systems like Frege's ...
1
vote
1answer
986 views

Is “nothing” easy to understand? [closed]

Let's first define nothing as the absence of something. Not talking about universe here. How early on do we grasp this concept of nothing? Are there people who get old without that basic ...
0
votes
2answers
760 views

Is implying the same as asserting?

I need to understand if implying something, knowingly or unknowingly, is the same as asserting it. I also need to understand if it is merely semantics or there is a philosophical rigor to it. EDIT: ...
10
votes
1answer
2k views

How does Robert Nozick explain the Gettier problem?

Nozick agrees that the Gettier counterexamples to the JTB analysis of knowledge are cases where someone has a JTB but does not know. What is his explanation of what has gone wrong in those cases? ...
13
votes
4answers
930 views

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. ...
9
votes
3answers
3k views

Is reductio ad absurdum a valid logical proof?

It strikes me that atheists often in the religion debate will try to characterize religion in a funny or silly way, often comparing religion to belief in fairies or unicorns or flying spaghetti ...
2
votes
5answers
14k views

Is it possible in any way to justify murder using reason or logic?

Some believe that murder is only committed due to an emotional or moral action, but can you ever justify it with reason?
9
votes
3answers
792 views

Possible worlds in logic

In modern logic there is often talked about possible worlds. I understand this idea in this way: Every proposition may be true or false. Possible world W is a set of all propositions where there is ...
2
votes
3answers
293 views

How to be a good critic?

How can we be a good critic when facing people's rigid beliefs? I'm interested in how to attack (logically) their dogmatic beliefs to have a "good" influence on their minds, because if we just attack ...
2
votes
2answers
189 views

an argument about a logic question

I've had an argument with someone and I would like to know for sure if I'm right. I don't know if you have heard of the board game "Catan", it's not really important. Well, long story short, at the ...
7
votes
2answers
5k views

Can an eternal god destroy himself? [duplicate]

Possible Duplicate: Is the definition of God consistent? (primary) also: An immovable object and an irresistible force God's paradoxes and their implications To many, at first sight, ...
24
votes
4answers
4k views

What are the philosophical implications of category theory?

I have heard about topoi being the ideal entities to use for foundations of mathematics (since we are able to reasonably interpret our theories in them), so I imagine there might possibly be some ...
15
votes
6answers
966 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 ...
9
votes
4answers
1k views

Syllogism from Lewis Carroll

I was reading Code by Charles Petzold, and on page 86 he references a syllogism from Lewis Carroll: All philosophers are logical; An illogical man is always obstinate; Therefore, some obstinate ...
3
votes
1answer
169 views

What is a mathematical or logical name for the process of proving a statement by exhausting the domain?

I am trying to understand logic and I came across a set of actions that I describe below that I can't get my head around. Suppose you have a bag of multiple colored balls. Situation 1. Argument: ...
10
votes
1answer
3k views

What is Kant's argument about the relationship between logic and reason?

At Wikipedia, I read: Logic arose (see below) from a concern with correctness of argumentation. Modern logicians usually wish to ensure that logic studies just those arguments that arise from ...
8
votes
5answers
2k views

A bizarre question asked at a job interview about conditional probability [closed]

I was recently asked a "logic puzzle" type question at a job interview which seems to be a slightly mangled version of a N-coin puzzle (intended to test the subject's knowledge of conditional ...
2
votes
1answer
61 views

Term for a reduction to an unanticipated result

I'm looking for a term that describes the logical argument I am making. Both to just have a way to describe it and ensure that it is indeed a sound argument. Somewhat formally the argument is as ...