Questions tagged [logic]

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

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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
110 views

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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279 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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1answer
88 views

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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97 views

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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290 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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1answer
106 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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335 views

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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335 views

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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5answers
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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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1answer
124 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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1answer
43 views

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 ...
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179 views

How to denote the idea of nothingness in formal terms?

I was thinking about the question "Why is there something rather than nothing?" , and have read about some theories that existence is the case because non-existence is logically impossible So, I ...
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15answers
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Is every sentence we write or utter either true or false? [closed]

Please read the complete description before putting any answer / comment, Thank you. I've been just thinking through this question which I can frame it like this: Can I write or utter any sentence ...
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115 views

Why is Math not Logic? [duplicate]

So I've heard, "Math is not logic," because logic has no notion of order. However, consider the following argument: There once was a man on a mountaintop. He came down, murdered a villager's cat, and ...
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3answers
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Determining the validity of the arguments in the exercises of The Norton Introduction to Philosophy

The first exercise is "Spot the valid argument(s)." The following are the arguments. I think all of these arguments are valid. Am I right? (i) If abortion is permissible, infanticide is ...
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4answers
174 views

Mathematical proof of a philosophical theory

Can I prove a philosophical theory mathematically? If yes? How? For example, can the theory of materialism be proved mathematically?
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1answer
130 views

Why is Law of Large Numbers a Law and Central Limit Theorem a Theorem… when they look like the opposites?

In probabilities, the Law of Large Numbers (which has a "weak" and a "strong" version) tells that the more samples you take of a fact (under a model you state), the closer you are to the actual mean ...
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3answers
92 views

Contradictory statements with Nested Quantifiers

Edit: Thanks very much to everyone for the answers! As a follow-up question, I'm curious if there are Aristotelian methods for finding contradictories to statements with nested quantifiers. As, thanks ...
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Are verb tenses actually irrelevant in logic?

In my Introduction to Logic course, we learned that verb tenses are irrelevant when symbolizing and deducing arguments. However, it seems to me that the verb tenses could sometimes choose whether or ...
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What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
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Does intuitionistic negation of A mean that there does not exist a proof of A?

Section 13 of Kleene's Intoduction to Metamathematics introduces briefly Brouwer's informal intuitionistic school of thought. There he writes that the interpretation of not A is meant to be taken as ...
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What is the logical law proving “if not p then q” is equivalent to “p or q”?

I know that (¬p → q) ≡ (p v q) from comparing the truth tables. But is there a law that states this? Something like the laws of propositional logic: idempotent, associative, commutative, distributive, ...
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56 views

Can “moral reasoning” be defined as a perception?

https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1527-2001.1996.tb01017.x I saw this research paper titled "Moral reasoning as perception", and I was wondering how is it possible to conceive "moral ...
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How disjunction works with the conditional excluded middle

I'm studying the semantics for counterfactuals, and I'm slightly confused about how certain inferences supposedly make the Conditional Excluded Middle (CXM) fail. Formally, we can write the ...
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Clarifications on 1) Modus Ponens, 2) Modus Tollens, 3) Inductive, 4) Incomplete based on examples

My second lecture on Hypothetico-Deductive methods (based on Popper's falsification theory). In the class, we were given the following examples. We had to classify which examples belong to 1) Modus ...
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What is Robert Nozick alluding to by a “vast generalization” of Feynman’s path integral?

I was reading a book from the philosopher Robert Nozick (Invariances: The Structure of the Objective World), and there was something that confused me. Around page 159 he argues that every logically ...
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Does the Law Of Excluded Middle Apply to the Principle Of Identity and Non Contradiction? [closed]

This argument will seem confusing, precisely because it observes the laws of identity being subject to equivocation. If this is kept in mind, the following should make more sense and explain why the ...
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164 views

Did physicist Eugene Wigner think that every mathematical structure existed as an isolated universe?

I have read that Eugene Paul Wigner thought that all mathematical structures had physical existence. Does that mean that he believed in a multiverse containing all mathematical structures as separate ...
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Mechanics of Perception

How is perception formed? By perception I mean 'thought' or 'idea' of the World. What I see by itself does not contribute anything to thought. Only an acknowledgement can contribute to structuring of ...
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50 views

Reasoning for Inductive inference?

Just out of curiosity, if I should replace the deductive inference related questions to inductive inference, then which are true? Inductive inferences rearrange current knowledge in such a way that ...
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61 views

Liar paradox from a different view/resolved?

Informally, the statement T: T: "this statement is not both true and not true" a) T is not true if and only if it is both true and not true b) T is true if and only if it is not both true and not ...
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Question about conjunctions

Would this principle be true for conjunctions: For any proposition p, if p is a conjunction with at least three conjuncts, then there are more distinct conjunctions that can be created out of the ...
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173 views

Do Most Philosophers Ignore the Rules of Dialectical Logic?

In metaphysics it is well known that all selective conclusions about the world as a whole are undecidable. Most philosophers infer from this that metaphysics is incomprehensible. I believe this is a ...
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109 views

Russel's paradoxical set from a different view

Suppose naïve set theory, let's do a tought experiment: Informally, let's define a set € such that € contains all the sets that don't contain themselves.(yes, all but not necessarily only those), ...
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Would this be an invalid or valid argument? [closed]

All mathematical truths are knowable. All mathematical truths are eternal. So All that is knowable is eternal.
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A deontic premise that leads to a necessity from a permission

I wanted to devise some rules for myself, then formulate those rules using formal symbolic logic, and one of the rules that I have set for myself is : "Do not say what is unnecessary", in other words :...
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Why is it argued that an argument has one and only one conclusion?

Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true ...
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What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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Is it true in some sense that the only “truth” people are capable of knowing is the “truth” that they assume to be true?

What are some viewpoints on the following assertion in philosophy and logic? Anything people argue to be true is only their assertion based on some axioms or premises which they assume to be true (...
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Does Barrow and Tipler's “anthropic principle-multiverse” entail the existence of all logically possible universes?

I've read several texts that indicate that the anthropic principle (applied to cosmology, and more specifically, to the multiverse) yields the existence of all logically possible universes (most like ...
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156 views

How do you measure circular reasoning? [closed]

How do you measure circular reasoning?
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What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results?

What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results? You would think philosophers wouldn't ever criticize or try to debunk logic ...
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What is the difference between a premise and an assumption in logic?

It seems to me that an assumption is an untold premise in my argument. Is it right?
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Why there is no suberogation function?

Going off the definition of logical validity that depends on true premises going to true conclusions, there is no imperative logic. However, it seems that some "imperative arguments" look regular ...
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An erotetic argument about the liar paradox

I noticed something about the liar paradox, when the liar sentences are taken as questions. Let’s start with the liar index, “This sentence is false.” Allow this to be questioned: “Is this sentence ...
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1answer
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What is the difference in logic between strong and weak negation?

My main concern is to separate different forms of logic. I am hoping to use negation as a way to do that. In the abstract to "Web Rules Need Two Kinds of Negation", Gerd Wagner writes ... there ...