Questions tagged [logic]

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

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62 views

Tableaux for normal modal logics [closed]

Does ⊢ ◻p ⊃ ◻◻p hold in Kρ? Check with tableaux and if the tableau does not close, define and draw a counter-model.
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How to derive P > (Q > R) from (P > Q) > R in Fitch?

I am having a little bit of difficulty coming up with a Fitch-style natural deduction proof. Presumably, I need to use a few conditional introduction rules, but I am not sure what I can get out of ...
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What is the justification for the claim that observing something that is both a raven and black increases the likelihood that all ravens are black?

Suppose that I have access to a machine that allows me to input a positive integer (perhaps up to ten decimal digits) and the machine will -- depending only on the input -- output a statement. If the ...
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29 views

How would I go about proving P>Q from the premise (notP v Q)? [duplicate]

A similar question had already been asked, but the solution involves steps I am unfamiliar with. in class, we have only been exposed to intro and elim rules, as well as contradiction rules. Here is ...
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133 views

Fitch Proof - Logic LPL 6.31

I am trying to complete the following proof in Fitch but am completely clueless on how to approach it. Any help would be appreciated! Thanks
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42 views

How can a undecidable theory be complete?

I don't understand how a theory can be undecidable (there is no effective procedure for determining if a sentence of the language is a theorem) and also be complete. How do we know all sentences are ...
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67 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 ...
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1answer
42 views

Why doesn't one assert in metamathematics that a sentence S is a logical consequence of the conjunction of a set of sentences?

In other words, why isn't there -- at least in standard textbook presentations of things like the deduction theorem and the compactness theorem -- a conjunction connective that is applied to sets of ...
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1answer
45 views

Contrapositive Fitch Proof

I can't seem to figure out how to get past this step. Any suggestions?
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2answers
148 views

To connect or to disconnect mathematics and platonism?

How [do philosophers] strongly support or refute the view that: mathematics is a bag of tricks for real-world problem solving; undecidable statements are an irrelevant and harmless side-effect of an ...
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1answer
93 views

Complement of “at least two people share the same birthday”

Suppose a room contains 𝑛 people. What is the probability that at least two people share the same birthday? So this is actually a question on probability, but I'm really confused in the logic and ...
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Is every reason reducible to a sequence of tautological statements? [closed]

I think of tautological statements as those statements which when explained should repeat themselves, and should intuitively explain the reason. For example, A = A because 'A is equal to A'; Dog is ...
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93 views

Do Aristotle's three laws of logic apply to statements about the future?

I have just read about Aristotle's Three Laws of Logic. I was wondering if statements such as "There is a chance of it raining in the next hour" can be evaluated using the three laws. Can you apply ...
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45 views

Logic Question in a fitch style system - disjunction elimination

I am having difficulty in formally proving two arguments. Firstly, given the premises A ∨ (B∧C) ¬B∨¬C∨ D derive A v D. I can see why it has to be either A or D, because if it's B and C, ...
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284 views

Proof Using Model Universe

Suppose I am trying to prove the following argument (∀x)(Cx → Dx), (∀x)(Ex → ~Dx), /∴ (∀x)(Ex → ~Cx) Now, let's also assume that I don't know if this argument is valid or not. Because of this, I try ...
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113 views

Difference between “neither true nor false” and “either true or false.”

What is the difference between "neither true nor false" and "either true or false."? I was reading about definitions And I read a line saying "Lexical definitions are either true or false". After ...
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60 views

Clarification on what is and isn't a logical statement

After reading the article from Wikipedia I feel more confused on what the scope of the definition of a 'logical statement' or proposition is. First, is the statement "It is raining" considered to be ...
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44 views

What is the difference between a function and a relation in first-order logic?

Consider this definition of first-order (or Herbrand) logic syntax. Here is the vocabulary: Definition (Vocabulary): A vocabulary V consists of: A set of relation constants {r1, ...,...
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The perfect definition of impossible [closed]

When i think about the true impossible, for me is a very dark area, that causes depression, because when we think about this simple question that begins whit, an example, "God creates the Human ...
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1answer
72 views

What's the difference between a second-order relation and a relation between objects?

I was reading an article in philosophy and found this: Some philosophers have denied that there is such a relation as identity. Thus Ludwig Wittgenstein writes (Tractatus 5.5301): "That ...
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77 views

How should one symbolize “and then” in logic?

Graham Priest observed that not all uses of "and" in English commute: (page 15) ...according to the truth table for &, 'a and b' always has the same value as 'b and a', namely, they are both ...
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2answers
51 views

What's the difference between “All A are B” and “A is B”?

I'm having trouble catching the difference between these two forms. I tried to draw some Venn diagrams but it's not helping. "All A are B" means A is contained in B. Does "A is B" mean A is also ...
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1answer
41 views

logical fallacy (or pseudo-logical, or rhetoric) corresponding to unduly extending my argument to make it false

This is probably similar to my preceding question: What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true? but I'm not sure ...
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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What is an example of a true contradiction in a paraconsistent logic?

While reading the Wikipedia article on trivialism I noticed the following: In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is ...
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4answers
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Is metaphysics justified in its conclusions?

I'm curious of the modern meta-philosophical viewpoints on metaphysical knowledge. That is, is it possible for arm-chair theorizing or rational pure thought alone to gain true knowledge about any ...
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What is the logical distinction between “the same” and “equal to?”

We all understand that Given A = C, and B = C, Then A = B. However, A is not “the same as” B. Example: A is the question, “What animals have feathers and can fly?” B is the question, “What was the ...
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245 views

Is there any exception that proves or suggests that the law of non-contradiction does not always apply?

Is there any exception that proves or suggests that the law of non-contradiction does not always apply? I am thinking, because the law of non-contradiction is very similar to the law of excluded ...
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5answers
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Is this ad hominem or in general acceptable behavior during an argument?

Person A: What is considered socially acceptable should be common sense regardless of outside influences. Person B: What is considered common sense or obvious can be very different depending on ...
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Does a biconditional necessarily imply a causal relationship?

Supposing A if and only if B, is it necessarily true that either A causes B or B causes A? I'm considering this question where the truth values of A and B are both True, not both false. In theory, ...
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2answers
275 views

Is there a difference between equality and identity?

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

Is there any exception that proves or suggests that the law of identity not always apply?

The law of identity is rather simple, so I feel like there can be absolutely nothing that can contradict it or suggest it to be false, it's like a tautological truth that doesn't say anything. But is ...
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100 views

Is there any exception that proves or suggests that the law of excluded middle does not always apply?

Is there any exception that proves or suggests that the law of the excluded middle does not always apply? I am wondering if this rule is an absolute truth that is always true in our world or in any ...
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1answer
35 views

Logic terminology: does “conditional” etc refer to the operator or the WFF?

To be precise.... Do the terms we use to talk about the truth-functional operators (conditional, negation, conjunction, disjunction, biconditional) refer to the operator in isolation, or the WFF that ...
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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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45 views

Correct way to Interpret statements not containing Quantifiers

What's the correct interpretation of "seemingly universal" statements that do not use quantifiers? For example, p:"Roses are red". Is this equivalent to q:"All roses are red."? What's the correct ...
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67 views

Which is the correct/better way to represent the following argument?

p1. If an omni-god exists, then evil cannot exist p2. evil exists c. an omni-god does not exist I'm pretty sure its modus tollens and is represented as follows, p -> q ¬q ¬p But my friend is ...
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What paradoxes arise from quantifying over EVERYTHING?

This question is in context of the umbrella view of objects, that there exists a general category that everything falls under. Here are the quote and link that peaked my curiosity. Finally, note ...
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A Paradox for Anti-Realism?

Semantic Anti-Realists hold that a claim has a (constructive) proof if the claim is true. I wonder whether this position runs into a version of Yablo's supposedly non-circular version of the liar ...
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4answers
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Suppose ‘Some S are P’ is true. Determine the truth-values of the following (if possible)

I just want hints to make sure I'm going in the right direction. All S are ~ P. I got true Some S are not ~ P. I got false No P are S. I got false Some P are ~ S. I got true No S are ~ P. I got false
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273 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. ...
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Are accurate statements about fictional entities false?

"Homer Simpson is Marge Simpson's husband." Is this a true statement since it accurately describes the fictional character, Homer Simpson, or is it false since there is no Homer Simpson in reality to ...
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Who first proposed that A → (B ∧ ¬B) ⊢ ¬A was the principle of proof of some theorems?

The proof of various theorems are nowadays routinely described as "proof by contradiction". For example, the following theorems: https://en.wikipedia.org/wiki/Proof_by_contradiction The ...
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280 views

Can all formal systems be generalized as specified relations between finite strings? [closed]

https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics) In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be ...
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103 views

Rewriting a set of propositions that includes a circular proposition

"For any proposition P, if I believe that P then this paragraph (everything that is written between the quotes) entails that I believe that P. I believe that I exist. For any proposition P, if I ...
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Why does the Principle of Explosion not make Mathematical Logic inconsistent?

In Reductio ad Absurdum (RAA), we determine that a proposition P is false when it derives a contradiction. If we use this same derived contradiction as the premises to the Principle of Explosion (POE),...
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Noam Chomsky vs 9/11 Truth movement. Is Noam's Logic legit?

When Noam Chomsky was asked about what he thought about the collapse of building 7 at the University of Florida in 2013, he replied that only a minuscule part of the scientific community backed up the ...
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192 views

A comprehensive introduction to relationship between math and experience

I am a mathematician with interest in physics and pure logic and exists one problem: the connection between math and physics. Math concerned on pure universal truths and physics concerned on ...
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114 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 ...
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Is there a difference in the definition of “some” between Aristotelian and modern logic?

My logic prof told me that "some are" does NOT necessarily mean "some are not".... Ie. it could possibly mean "ALL are", but not necessarily (ie. we are not certain that all are) However, recently I ...