Questions tagged [logic]

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

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18 views

Is an “observer” always implied in scientific statements?

I'm not sure what it's called, but Russell famously resolved problematic statements like "The present King of France is bald," simply by saying that it contains a hidden assumption of ...
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Is there some non-classical logic where the van der Waerden theorem does not apply?

The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...
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Should we define truth (given it exists)?

Should we, human-beings, try to define truth (given truth exists in reality)? Personally, I don't think we should reduce truth to symbols and syllables because I think it will take us into weird ...
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How does Davidson's Slingshot argument escape Russell's Theory of Definite Descriptions?

Hi I am trying to understand Davidson's Slingshot argument. Apparently it is said that Russell's Theory of Definite Descriptions does not face the problem that Davidson highlights. For instance, if we ...
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How do I translate “all and only” and “if and only if”?

Hi is the translation for "if and only if" (iif) the same as "All and only" i.e. both requires the bicondtional?
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What are some non-trivial examples of the use/mention error?

Examples of use/ mention fallacies one often encounters are toy examples, such as : (1) The Morning Star is Venus. (2) Venus is a 5 letters word. (3) Therefore the Morning Star is a 5 letters word. (1)...
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Soundness and Completeness of Tableaux

Tableaux to my knowledge are both sound and complete. The statement: "If P is valid then tableau for -P eventually closes". Does this statement prove that tableau is sound and complete or ...
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Is the statement “If you are against criticizing the media, then you are against free speech” begging the question?

I have a question to any fallacy experts out there: I was in a recent discussion about media bias and the perceived harm to media by the president's statements about fake news and media bias. I made ...
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Is the included derivation feasible? If so, would my proof be correct?

The simple derivation seems correct and intuitive, and yet I feel as if something is off. I would greatly appreciate it if someone could double-check the provided formal proof. Thank you in advance ...
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What is my fallacy? LSAT Reasoning Question: Titanium Ink

I have a question regarding an LSAT Reasoning question and it drives me crazy Question is: Until recently it was thought that ink used before the sixteenth century did not contain titanium. However, ...
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3answers
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Do philosophers think physical laws are logical statements?

I had some questions like: Do philosophers think that the rules of the universe are always logical or can they be somehow divorced from logic? The rules of physics seem to follow the laws of logic, so ...
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I talk to every goblin every day. Question about “vacuously true”?

A short question about vacuously true. (1) I talk to every goblin every day. (2) I talked to every goblin yesterday. Goblins don't exist. So universal claims like (1) and (2) are vacuously true, ...
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In how many and which ways can a logic be non-classical? Are there systems for organizing them?

I asked on MathSE What are the various respects under which a logic can deviate from classical logic, thus being “ non-classical”? and received one short answer. So, I'm interested in responses from ...
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Approximately directed graph of logic types

I'm not sure if this is the right stack to post this question. Given there are many types of logic; Syllogistic, Symbolic, Modal, Deontic, Temporal, Epistemic, (non)monotonic, formal, informal, FOL, ...
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Was Peirce the first to distinguish objective and subjective possibilities?

I was reading IEP article about C.S Peirce where some of his logical notations for modal logic are presented, and one them seem to make a distinction between a subjective formula and an objective one....
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Fail to understand Tarski's substitution argument for logic apriorism and a rebuttal against it

I have been reading Bueno and Colyvan's Logical Non-apriorism and they mentioned that Tarski has the following argument for logic apriorism: If, in the sentences of the class K and in the sentence X, ...
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Is having “skin in the game” always beneficial in “thought and action” as Taleb seems to think?

I was skimming through the tweets about Taleb when I saw one from one of his former [friends][1] which was about Taleb's "skin of the game" that was about it say that is neither necessary ...
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What are some possible motivations for Peirce's use of only one operator(his NAND) to recreate the “and”, “or” and “not” operators?

It was found in Peirce's unpublished papers that he defined the NAND operator and discovered that all classical logical operators could be replaced by combinations of NAND. What are some possible ...
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FOL translations (double predicates)

I'm learning first order logic right now and I'm stuck on some translations. Key: G(x) : x is a galaxy M(x) : x is a moon P(x) : x is a planet S(x) : x is a star B(x,y) : x is bigger than y O(x,y) : x ...
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FOL Translation

I'm learning first order logic right now and I'm stuck on a translation. Key: P(x) : x is a planet M(x) : x is a moon S(x) : x is a star O(x,y) : x orbits around y Only stars have planets orbiting ...
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Self-evident vs. self-explanatory vs. …?

How far apart are these descriptions? I was approaching the issue from the perspective of erotetic logic, and my intuition is that self-evidence is when a proposition is evident from its erotetic ...
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Can we define the notion of an “omnipotent God” in terms of computational power?

A classic omnipotence paradox asks, "can an omnipotent God create a stone so heavy that He cannot lift it?" The problem here is that we take omnipotence to mean "capable of anything ...
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Explanation of Littlewood's profound philosophical joke

In "A mathematician's Miscellany", By J. E. Littlewood, I found this piece of conversation between Littlewood and Wittgenstein: "Schoolmaster: Suppose x is the number of sheep in this ...
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How to deduce V from (U → V ), (¬U→V) using Deduction theorem?

We have these axioms and modus ponens: Axiom 1 is: P→(Q→P) Axiom 2 is: (P→(Q→R))→((P→Q)→(P→R)) Axiom 3 is:(P→Q)→(¬Q→¬P) Modus ponens is: from P and P→Q infer Q Edit: I still couldn't solve it, so I ...
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Which unary or binary logical operators existed in logic before 1854 besides 'and', 'or', and 'not'?

Logical operators are a central focus of logicians, and two important books with innovative thoughts on logic include Begriffsschrift (1879) by Gottlob Frege and The Laws of Thought by George Boole in ...
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Proving (P → Q) ↔ ¬ (P ∧ ¬ Q) in Fitch with no premise [duplicate]

I am struggling with this one for days and keep getting stumped |_ | |_ P → Q | | |_ P ∧ ¬Q | | | : | | | # | | ¬(P & -Q) | (P → Q) → ¬(P ∧ -Q) | |_ ¬(P ∧ ¬Q) | | |_ P | | | : | ...
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Why is first-order logic interesting to philosophers?

This site had a question: Is First Order Logic (FOL) the only fundamental logic? Let me ask the opposite: Why is FOL still interesting or useful to philosophers? For example, the "ancestor" ...
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Rudimentary Proof in SL

So I'm currently being introduced to SL and asked to prove a statement. A simple question with the premise L & W and L ⇒ ¬ F. I am asked to prove W & ¬ F. Could someone verify my solution? So ...
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Yablo's theory of aboutness: Upper bound and lower bound on subject matters

What does it mean that the following two condition defines respectively a lower bound and an upper bound in the set of subject matters of a sentence S in Yablo's theory of aboutness, and why, given ...
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1answer
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Question Concerning Validity and Logical Arguments

I have some questions about the study of logical reasoning and arguments. Is it true that no two false sentences are logically equivalent? For example, "A square has 5 sides" and "I ...
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According to logic and argumentation theory, how does one build strong arguments?

I'm very new to philosophy and the formal study of argumentation. In every essay so far, I've argued against a thesis. I attack the validity or strength of premises and the soundness or strength of ...
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147 views

Is logic relative like Einstein's Special Relativity or is it absolute?

Is logic relative like Einstein's Special Relativity or is it absolute? I am thinking it is absolute, but at the same time I am inclined to think that it's not as simple as you may think.
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Is there a non-transitive frame in which schema 4 is true? Or an irreflexive frame in which schema T is true?

So, I know that I can construct a frame {W, R, I} which is not transitive and in which schema 4 is not true (more specifically, Axiom Schema K and Axiom Schema 4 are not both true). I also know that I ...
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Can the paradox of the gentle murderer be resolved using the sentence-type/token distinction?

Quick recap: the paradox in question can be formulated like so (I think; look in the SEP article on deontic logic for a better recap if this doesn't work): If Jill kills Jane, she ought to kill Jane ...
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2answers
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Formal versions of exotic logical connectives in natural language

Formal logic tends to be concerned with minimal or at least almost-minimal sets of logical connectives. The standard logical connectives are and, or, implies, iff, neg (I couldn't use Latex for their ...
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Name for a logical fallacy: confusing measures in argumentation

I have encountered a line of reasoning in my research which seems to be fallacious. An example is if you wanted to know something about the general health of an individual, you could measure many ...
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What's the right term in logic for this phenomenon?

The statement "My mother is my parent" is always true, however, the opposite statement "My parent is my mother" is not always true because my father is also my parent. What's the ...
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Can a category of non-difference exist in Western logic?

Indian philosophy has a logical category of non-difference (related somewhat to abheda) in which something is different from something else but identical to it as well. An example is that of the the ...
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Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) [closed]

Prove that the following is a logical truth (tautology) using a natural deduction derivation: (B → C) ˅ (¬B → C) How do I prove this using statement logic? I know I need to start with a supposition ...
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108 views

Tarski's convention-T and inductive definition

I am studying the famous tarskian theory of truth ad there is a thing not clear to me. 1)Why does the T-schema "'S' is true if an only if S" specifies the truth-condition for the sentence 'S'...
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TFL - Natural Deduction Problem Solving

I am using a website called Carnap.io for submitting my proofs for natural deduction for TFL. It keeps telling me the proof for the following premise is wrong: ⊤ ⊢ (A ↔ ¬B) → (¬A → B) but I'm not sure ...
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Natural Deduction for TFL

Is the proof below correct for the following premise?: ⊤ ⊢ (B → ¬B) → ¬B 1 B → ~B :AS 2 B :AS 3 ~B : → E1,2 4 ⊥ 5 ~B :~I1-4 6 -- 7 (B->~B)-> ~B :->I1-...
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What is the difference between these two types of proofs?

While employing induction method for proving, is deriving the string(formula) "Fn → Fn+1 " any different from showing that if Fn holds true, then so does Fn+1 ? By showing I mean that we use ...
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What does the symbol “:=” mean in formal logic?

:= What does the "colon-equal symbol" mean, and how is it used?
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What is an author? [closed]

If you make a program to write a book, are you considered the author? I’m sorry if this is off topic, but I couldn’t tell if that was included in the ‘on-topic’ list of acceptable questions, and I ...
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Is uniqueness necessary in the case of God — the Creator?

====================================================================== Let us assume God as the Creator. Suppose: By similar/same process; with the same materials, God A, God B, and God C created ...
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Functional Abbreviation for Inst Expression in Turing's Paper [closed]

In Turing's 1936 paper On Computable Numbers Page 30-31, and its Correction Page 1-2 For a Turing Machine M, Inst(i,j,k,LEFT,l) means that if M scans symbol j under m-configuration i, then the symbol ...
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Prove that p → □p is not derivable in system K?

The only way I could think of doing this is to show that p → □p with the K axioms would imply a contradiction, but I don't think that's true. Not sure how to get started on this. Do I just have to ...
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2answers
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Knowing versus understanding the composition of the universe

The mass-energy content of the Universe is approximately this: 5% normal matter, 20% dark matter, and 75% dark energy. Because we don't know much about dark matter and dark energy, apart from the fact ...
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Are inferences in everyday life often combinations of inductive, deductive and other possible methods of inference?

Logicians have distilled methods of inference into some fundamental kinds like deduction and induction. In everyday conversation, though, we are constantly making inferences both inductively and ...

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