Questions tagged [logic]

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

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In what contexts or disciplines does “One may assume X” imply “One may ignore the possibility of any statement contrary to X being true”?

In computer programming, it has become fashionable for compilers (processors of computer language) to apply the following form of reasoning: A language standard would permit a compiler to assume that ...
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What type of fallacy does the phrase “I don't live to eat, I eat to live” fall into?

I would say it's a non sequitur but I believe there's a narrower term for it.
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Why did Hilary Putnam change of opinion towards Quantum Logic?

Hilary Putnam is known for having proposed a radical change in our thinking about the physical universe: He proposed that the universe was fundamentally based on Quantum Logic, and not in Classical ...
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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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131 views

Comparisons between two notions of existence

I have the following, rather naive question: To what extent can the a priori existence of mathematical objects be reasonably compared with the seemingly a posteriori existence of objects established ...
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Does following logic necessarily require one to conclude that they are objective and have no bias?

In social psychology, naïve realism is the human tendency to believe that we see the world around us objectively, and that people who disagree with us must be uninformed, irrational, or biased. It is ...
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Did any logician object to the idea that if two contingent propositions are true, then they imply one another?

Both the following sentences are true: On January 22, 2020, the earth is orbiting the sun. On January 21, 2020, Trump was the 45th president of the United States of America. So did any ...
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Is a model of inference needed for reasoning?

In logic we can't make any deductions without rules of inference, predicates, and formulas. In probability/statistic we can't make any inferences without assuming some probabilistic model which might ...
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How do I prove :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C)?

How do I prove, :((A ⊃ B) ⊃ C) ⊃ (B ⊃ C), using symbolic logic derivations where ⊃ represents a conditional i.e. A ⊃ B = A implies B? The first line of my derivations is the assumption, (A ⊃ B) ⊃ C)....
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Trying to formalize a certain sentence in predicate modal logic

I have the following sentence which I want to formalize in predicate modal logic. The sentence is: What is good for you is not necessarily good for others" My attempt at formalizing this is as ...
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In non-platonism, can undecidable statements have truth value?

Most sources I can find about Gödel's incompleteness theorems summarize the result as "there exist true arithmetical statements that have no proof." It seems coherent to say that there exist ...
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2+2=4 why is this a deductive logical inference? [closed]

I googled a a deductive logical inference https://www.google.com/search?client=firefox-b-d&q=a+deductive+logical+inference%3F and couldn't understand a thing. But I presume it's because if 2+2 ...
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Proving A ⊨ B iff ⊨A → B

Let A and B represent arbitrary formulas. Also let 1 ≡ True and 0 ≡ False Prove that A ⊨ B iff ⊨A → B For my proof, I break down the biconditional into two conditionals and prove each conditional. ...
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From Ignorant to Researcher in Modal Logic

I am a student in a French university in pure mathematics. I recently came across modal logic and more particularly doxastic logic. But, the only masters of logic offered are reserved for students of ...
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How do proofs about logic fit into a logical framework?

I'm learning logic from Michael O'Leary's A First Course in Mathematical Logic and Set Theory. In chapter 1 he carefully explains the meaning of logical implication (p ⊨ q), logical inference (p ⟹ q), ...
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Heraclitean, Parmenides, and Aristotelian change? Is there an alternative?

Dear philosophy stack exchange, I've been considering of late the problem of change as presented by Heraclities and Parmenides as well as the supposed solution to the problem by Aristotle himself. I ...
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Does a formal fallacy definition for “X has not happened (with potential time constraint Y), so Z will not happen (now or in near future)” exist?

Does there exist a formal definition for (what I would say is) a logically fallacy that would fit to the following structure of statements: "X has not happened (with potential time constraint Y), so ...
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Before Gödel, was undecidability of axiomatic systems an issue at all?

Before Gödel, was the issue raised that there may be undecidable statements within axiomatic systems of thought? Gödel managed to answer affirmatively by proving that the assumption of the ...
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In Quine's ontology, why does a 'recognition' of something lead to ontological commitment while a 'feeling' does not?

We are discussing Quine's On What There Is in a metaphysics class I am in. I felt like I understood what he meant, that if something has to be predicated for in a sentence, we are ontologically ...
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Where did Suárez say the principle of non-contradiction does not apply to the Trinity?

Fr. Réginald Garrigou-Lagrange, O.P., says, in Le Sens du Mystère et le Clair-Obscur Intellectuel: Nature et Surnaturel p. 128 fn. 1 (Engl. transl. p. 142 fn. 41): St. Thomas never would have ...
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Is there a logical argument for the limit of knowledge?

It is justifiable to assert that certain knowledge could not be disseminated without the invention of writing. One could say that humanity needed the knowledge of writing before further knowledge ...
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Has there been any philosophical guidance regarding when to use logic vs empirical testing?

One obvious disadvantage of testing a given claim with scientific constraints is that one may never know the number of possible constraints to try, in which combinations, and in which order to modify ...
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Name for this Logical Fallacy

Suppose there is a non-empty subset A of U. Let A' denote the complement of A in U. What is the name of this logical fallacy? X is true for A therefore not X is true for­­­­­­­­­­­­­­­­­­ A' ...
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Logical fallacy: X is bad, Y is worse, thus X is not bad

I have heard this type of argument too many times: You are criticising X using well researched facts and arguments. Your interlocutor, states that Y is much worse with equally well researched facts ...
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About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
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Did Stephen Hawking think that logic is contingent on physics?

According to this book*: Extrasensory Perception: Support, Skepticism, and Science, it says that Stephen Hawking thought that logic was contingent on physics, i.e that logic depends on the physics of ...
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Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...
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What fallacy in Pascal's Wager allows replacing God with the devil?

I wanted to know the name of the fallacy or fallacies the Pascal's Wager in the sense that it can be applied to motivate one's belief in many things. A similar argument to the original Wager can be ...
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Wittgenstein and “linguistic trap”

In a book on philosophy I've lost by now I encounter an argument about "linguistic trap" idea attributed to Wittgenstein, that is, such a trap is supposed to be "taking linguistic convention or ...
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108 views

Is it possible for an argument to be logically valid but not truth-functionally valid?

Truth-functionally valid: there is no truth value assignment for which the premises (of an argument) are true yet the conclusion is false. I am told that there are arguments which are logically valid ...
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Term for evidence that isn't understood

Imagine someone asks how you can believe that whales evolved from land animals. You tell them about "missing link" fossils that chronicle whales' evolutionary journey. This is solid evidence - to ...
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Does anyone have an example where a sufficient condition comes first?

Example: Sufficient Condition of A+ MUST MEAN Necessary Condition of Studying occured Temporally speaking, either condition can occur first, or the two conditions can occur at the same time. In our ...
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Is there a term for such a logical fallacy?

I'm wondering if there is a terminology for the following logical fallacy: Joe: Statement "X" must be true because it is clearly laid out as such in mutually reliable source "Y". Sam: Joe, the ...
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logical atomism explanation with examples

I read a bit of logical atomism by Russel but would appreciate if someone explains with examples of what is meant by it. For example it says:" According to logical atomism, all truths are ultimately ...
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Do all epistemologies suffer from the “regress of justifications” problem?

Aristotle describes the regress problem in his logical work Posterior Analytics I.2: b5. Some hold that, owing to the necessity of knowing the primary premisses, there is no scientific knowledge. ...
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Do I need to read The Organon to understand Aristotle's philosophy?

I recently read through the collected works of Plato and really enjoyed learning about his philosophy and ideas. I'd like to do the same for Aristotle and have started reading through his works as ...
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Can something be true if it does not follow logic?

Can something be true if it is not logical? Can something be true if it does not follow logic? if I can't deduce it logically? or if it contradicts logic? In other words: if someone says statement X ...
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Does philosophy belong to empirical science or formal science?

According to Wikipedia, science can be divided into empirical science (such as natural science and social science) and formal science (such as mathematics, logic, statistics). I was wondering if ...
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Is there a logical fallacy to identity politics?

My understanding of Identity Politics goes as follows: A is a member of/identifies with group X B is not a member of/does not identify with group X A frames challenge S in terms of X Because B doesn’...
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Learning Logic, A Pathway

I would like to devote a greater amount of time to further learning logic. I have experience with mathematical proofs and thus have an understanding of logic to the degree necessary for proofs. I ...
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Where is the weakness in the ontological proof for God's existence?

I read the ontological proof for God's existence. As much as I understood, it says that if you consider that existence is part of essence, then the most complete essence should also exist. Now, I see ...
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How do I complete the remainder of this quantified Fitch proof?

This is where I get stuck, how do I finish this proof? I only have access to intro and elif rules, not DS or anacon or others.
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Is double negation always applicable to commitments?

If I commit to X, am I always committing to not ~X? In classical propositional logic, double negation always the same as not negating at all. I'm curious if this principle applies to commitments. ...
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What is the difference between the resolution rule and the elimination in natural deduction?

I understand that elimination is: p v q ¬q then p and resolution is: q1 v q2 v q3...qn ¬q1 v q2 v q3...qn then q2 v q3...qn I see no difference, but my teacher is telling us don't use the ...
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Why do people use the material implicaton over alternatives?

It isn't because it works. There are numerous alternative, fully-functioning implication systems. If people have a problem with conditionals with false antecedents, and with true consequents, always ...
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What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
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What reasons do I have to believe that ~p->~q and pV~q are equivalent?

I understand the reasoning for why pVq implies ~p->q, but not the converse. What reasons are there to believe ~p->~q implies pV~q, other than to make the whole material implication system neat?
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Is there a semantically complete system of direct-method deductive logic?

Does anybody know of a system of direct-method deductive (propositional) logic, in other words, a system that does not require (or even incorporate) conditional (and indirect) proof method(s) and that ...
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What is an enumerative definition?

W. Kent Wilson in his book argues for developing an enumerative definition of concepts. An enumerative definition formulates its meaning by enumerating the objects or phenomena that fall under the ...
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Is God's existence either impossible or necessary?

This is meant as a supplement to a modal ontological argument to show that God's existence is either logically impossible or necessary. Am I committing a fallacy or a logical error of some kind or ...