Questions tagged [logic]

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

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Is there a way to prove that I'm not in a simulation or a vr of some sorts in which everything I see, feel, etc aren't real? [duplicate]

My question is could all I think of as real in this world, the pain, the happiness, sadness all just be part of some futuristic vr of some sorts that is making me think i am thinking and doing all im ...
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Set of all hidden assumptions in a statement

Imagine a person "A" who says to a person "B" the following statement: "It is true that the house in front of me has three windows". If you think about it, this statement is true for a person "B" only ...
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Existence in logic [closed]

It seems so easy: Define a universe U := {x | "x" <=> x & we can't infer a contradiction from it}, then the existential quantifier is the existential predicate "there is/exists". Exist-x ...
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The understanding of logic presupposes a kind of understanding of natural language, doesn't it?

Our understanding of logic needs at least a basic understanding of words over a finite alphabet,natural language and numbers. For example,when we write down (one way) the definition of the atomic ...
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Contradiction vs Inconsistency [closed]

Patrick Hurley. A Concise Introduction to Logic (2014 12 ed). pp 346-348. Can someone please distinguish contradictory vs. inconsistent statements more markedly and intuitively than the pages below? ...
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2answers
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Deductive argument in which every step and premises are explicitly stated?

Is there in philosophy a word/term describing an argument in which all the premises and rules for derivation from those premises are stated explicitly so that even a computer can check it? I know that ...
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Does the conditional statement “If not-p then p” have a name?

For there to be not-p it is necessary that there be p. It is easy to show that "If not-p then p" is true, and conversely "If p then not-p" is false. Further the contra-positive of "If not-p then p" ...
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3answers
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Is ¬(a = b) the same as (a ≠ b) in logic

Are these the same in predicate logic with identity: ¬ (a = b) a ≠ b I'm not quite sure whether they can be used interchangeably in proofs. Any help would be great!
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Hypothetical Condition Leading a Result

To me the language in the following statement suggest a logical fallacy of some sort. I am not skilled in such matters, so I thought that someone in this forum might provide some insight. Thanks for ...
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“It is possible that this sentence is not true”

This is a "modal liar sentence" that I'm trying to use to illustrate how liar sentences are not well-formed. It seems like a nifty species to consider, and I never came across it before, but so... The ...
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The Dratted Liar Again

Is there a formal or semantic difference between these sentences? This sentence is false. The sentence containing these words is false. EDIT: It seems the question is too ambiguous to be ...
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4answers
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Is there an issue with the Socratic method arguing against points?

So, I've noticed something, looking at the classic example: Do the gods know everything? Yes. Do some gods disagree with others? Yes. So gods disagree about what is true? I suppose they must. So gods ...
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prove using natural deduction truth functional logic

can someone help me with my practice problems pls prove using natural deduction truth functional logic A → (B → C), D → B ∴ A → (D → C) 1 A → (B → C) 2 D → B 3 A 4 D 5 ...
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Indirect Proof with contradiction in premises

The premises are as follow: 1. A 2. A > ~B 3. B 4. C The conclusion is (A & B) & \~C My teacher proceed to use solve it using Indirect Proof. 5. ~[(A & B) & ~C ] AP 6. ~B ...
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Why does “Daisy has four legs” not entail “Daisy has more than two legs”?

I have been going through one of the books and I found an example of conclusion C that is not entailed by a premise P. Daisy has four legs. So daisy has more than two legs. Surely though, the ...
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What is a logical ground?

I've been stumbling upon the expression and am now asking myself what it's meaning is. What does mentioning a logical ground refer to? Perhaps anyone could try to break down the possibly multilayered ...
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Distinguishing arguments and explanations

For this question suppose that an argument is a rationale in which the reason presents evidence in support of a claim made in the conclusion, and an explanation is a rationale in which the reason ...
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Fundamental Weakness in math?

Every proof in mathematics is an implication of the form A -> B where B is the proven statement and A is the premise (which can consist itself of many conjuncts like axioms, inference rules, theorems ...
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Can “A (logically) implies B” and “not-A (logically) implies B” be both true?

Suppose we have the following statements. They are logical implications. 1) A implies B. 2) Not A implies B. Can they both be true? I think no because if one of them is true then also its ...
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Modal Logics Isomorphisms

What does it mean to say that the different branches of modal logic (temporal, epistemic, etc.) are isomorphic? I looked for the answer on The Stanford Encyclopedia of Philosophy, but couldn't find ...
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Where is the Liar Paradox?

How would one go about proving that the Liar sentence is paradoxical? I ask because to me it obviously isn't one so I'd need a decent proof to change my mind. I've always been baffled as to why it's ...
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6answers
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Is 'All sentences are false' false, true or paradoxical?

Usually you read that the sentence S: 'All sentences are false' is false because if true you got a contradiction, but if false it's not since it would just mean that not all sentences are false, e.g. ...
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Should one be able to obtain a sociology or philosophy degree through verbal measures without classes or written tests? [closed]

I'm really just trying to find out what someone thinks is accurate an efficient according to the comparison of some critics, an or professionals. ...
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Intuitionistic derivation of ~~~A --> ~A

I need to give an intuitionistic derivation of ~~~A --> ~A by using natural deduction. I know that in intuitionistic terms ~~~A --> ~A converts to ~~~A → ~A i.e ⊦ ((A → ⊥)→ ⊥→ ⊥) → (A → ⊥). These ...
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Aristotelean obversion: not vs non-

Apr 30: Aristotelean contraposition consists of obverting an initial proposition, converting this obversion by switching the places of the first and second propositions (keeping any negation), and ...
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Is political correctness a result of a more rational society?

Yes, I am aware of the insanity in the question. However, that is precisely why I am asking. The insanity stems from the popular idea, especially amongst academics or the type of people you might find ...
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Is there an intuitive justification of Peirce's Law?

I recently encountered Peirce's law, which states for a given proposition P, if there exists a proposition Q such that P follows from "if P then Q", then P is true. Alternatively: ((P→Q)→P)→P. Below, ...
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Non-consistent mathematical axioms

It is known that axioms are the building blocks of mathematics. Differents sets of axioms different "games". What I don't understand is how do we know that we pick axioms that are consistent? . Does ...
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Is RAA just MT?

If I say P and it leads to ~ Q then I have a false conditional . So imagine I want to prove ~ P then I show that Q is false as in If P then Q ~ Q ~ P We can do it the other way too If ~ P then ...
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The Concept of Trivialism

I understand trivialism is the position that everything is true, but I don't understand how it arrives there conceptually. The trivialist realizes that our natural (L)anguage (combined with our ...
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What is the ontological status of the laws of logic? [duplicate]

Are the laws of logic abstract objects that exist independently of physical things? Are they the same in all possible worlds? Are they man-made constructs, nothing more than ideas in our minds? Or ...
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Four statements that contradict each other

This question was inspired by Three statements that contradict each other I’m wondering if there is any set of 4 statements that contradict each other when taken as a whole, but any combined 3 of ...
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Predicate Logic

How do I derive this? Pr 1 ∀x(Fx -> ∀xGx) ∴ ∀x(Fx -> ∀x(Gx \ / Hx)) My attempt: However I cannot used universal derivation due to the free x. I think using ass id and qn would be better ...
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How to solve this Predicate logic derivation

I want to derive the following: ∀x(Fx ↔ (¬Gx ∨ ¬Hx)). ¬∀x(Gx ∧ Hx) → ∃x(Ix ∧ ¬Gx) ∴ ∃xFx → ∃x(Ix ∧ Fx) This is my attempt: Any suggestions as to how I continue and derive this? I cannot figure out ...
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Classification of deductive reasoning types

Please, could you help me make sense of/classify types of deductive reasoning? When studying mathematical logical, I have noticed there is this Hilbert's axiomatic system (Hilbert calculus) with its ...
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Why do we call the axiom Br in modal logic “Platonic Thesis”?

The Axiom Br (or B) in modal logic is sometimes called "Platonic Thesis", I wonder it is because of its semantical property (being symmetrical) but I couldn't find anything related.
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Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days (NOT duplicated)

First of all, please don't close this question cause I don't get the explanation given in: Use the Fitch system to prove the tautology (p ∨ ¬p) I have been trying to solve this exercise for days ...
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Use the Fitch system to prove the tautology (p ∨ ¬p). Stalled for days [duplicate]

I'm having trouble solving this one. I've been stuck in step 9 for days now. Any help is very much appreciated.
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I know that he knows that I know that he knows

Not sure if this is the right place for this question but here goes... Some time in the past I've stumbled upon some site/article/post/etc that discussed the issue of 2 parties having (or not) some ...
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Which fallacy was committed here?

In a discussion at the start of the COVID-19 outbreak there were people with the opinion that everyone was overreacting. I'm sorry but this is a massive over reaction in my opinion. Pneumonia kills ...
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What is the counter-argument against the argument of design? [closed]

The argument of design has several features, keying on relative complexity and tuning for use, from which one infers a designer. If we find a sand castle on a "simple" beach, which had an unusual ...
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Logical Mathematical Proofs [duplicate]

Prove the following theorem: ⊢ (P → Q) → (¬ Q → ¬ P) Prove the following equivalence: (P ∧ Q) → R ⊣ ⊢ P → (Q → R) Prove the following set of sentences inconsistent: {P → (Q → R), ¬ R ∧ (P ∧ Q)...
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Predicate Logic Proof Help! ∃xAx ∨ ∃yFy , ∀x(Ax → Fx) |= ∃xFx [closed]

I am unable to prove it :( I think I need to assume - ∃xFx but what follows later on?
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Existence as a Predicate [duplicate]

Can I just create a predicate "Existence" defined as: E = {x|x was, is or will be}? I don't feel it would lead to anything weird, using logic. Take for example Sokrates: This guy existed, so he's ...
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Is it reasonable to conflate being and truth?

Let x be something that exists unequivocally. Then "x exists" is true, but does it make sense to say x itself is true? And vice versa - the proposition "x exists" is true, but is there a sense in ...
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What's more fundamental than logic and mathematics?

I just studied some basic abstract algebra, and it opened up my eyes into concepts more fundamental than found in Boolean algebra and elementary algebra, showing deeper insights about them both. Is ...
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Good Translations of the Organon

I can't seem to find a translation of Aristotle's famous Organon that is consistently given good reviews. Does anyone have any recommendations?
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fitch arrow proof

using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C7 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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If-then statements meaning in everyday vs mathematics

In mathematics when a "P implies Q" statement is true it means that every time P is true, Q is true also. What about everyday usage? For example consider the statement: "If it is raining, then I am ...
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A Classical Notion of Dividing Travel Up into Infinite Divisions

1) A man wants me to go from a to b in a straight line. 2) Suppose he can, first he needs to go to (a-b)/2. 3) Suppose he can, secondly he needs to go to (a-b)/4. 4) There are infinitely many integers....

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