Questions tagged [logic]

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

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How to prove (A v ¬ B), (¬ A v C), (¬ C → B) therefore (¬ D v C)

My idea is to use disjunction elimination on (¬ A v C)to obtain C, and then use disjunction introduction to obtain (¬ D v C), but I'm having a hard time obtaining C.
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189 views

Are mathematical axioms arbitrary?

I've been thinking recently about whether or not mathematical axioms are arbitrary. I'm trying to figure out what axioms in systems are derived from and just how arbitrary they really are. My main ...
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1answer
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Complete a formal proof of ~(~A&~B) from A in as few lines as possible

Prove ~(~A&~B) from A in as few lines as possible. ~ = negation & = conjunction v = disjunction | = line in a subproof Here's what I have: A - Premise |~A - Assume |~B ...
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5answers
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Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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Does Kripke hold a view of free logic?

if Kripke doesn't want to accept Barcan's formula(the changed form in free logic) - given his essentialism - one solution is free logic. So does Kripke say that he accepts free logic or?
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Inference Rules of Modal Logic

I'm currently reading the book "An Introduction to Non-Classical Logic." Currently, I'm being introduced to modal logic for the first time. This book seems to prefer to present the reader with the ...
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1answer
252 views

Why does Gödel's incompleteness theorem apply to multiple formal systems?

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor ...
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Identifying a contradiction - to demonstrate hylemorphism

I am trying to create a mind map that shows the shortest possible logical path of necessary entailments from the first principles of reason & nature, leading to the basic principles of scholastic ...
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140 views

Is this a logical fallacy: using your statement against you

Is there a logical fallacy in this situation? : Person 1: This group is judgmental. Person 2: Your saying the group is judgmental is judgmental. I am not sure how to explain what appears off in ...
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Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce ...
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4answers
233 views

Can we know that law of non contradiction is true a priori?

I have seen some arguments for why should we accept law of non contradiction, and it seems to works in almost all areas. But some argument for it is like an argument for principle "nothing comes from ...
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Conditionals and logic

When second and third conditional sentences are used, are they logical? If he won the lottery, he would buy a new car. The reality is he is not buying a new car. So we can safely say he hasn't won ...
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Okay if someone does something by accident are they responsible?

This always confused me if a child breaks a vase the parents say "Well it's an accident it's not your fault.". Assuming the person is not negligent if someone does something bad like break a vase or ...
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Question about an argument with a conflicting premises and conclusion

I have a homework problem where I have to state if an argument is valid, conclusive or neither. However I am struggling to wrap my head around this one. The argument goes: Generally, a flood ...
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87 views

What is the difference between “derivation” and “inference” in logic?

What is the difference between "derivation" and "inference" in logic? I see these two words and they confuse me and then there are terms like "derivation rule" and "rule of inference". What are the ...
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Is this the correct way to phrase a logical argument with multiple syllogisms?

I'm not familiar with phrasing arguments in the form of traditional logical syllogisms, so I'd like to ask if this formulation is correct, or if it can be expressed more concisely. Note, I'm not ...
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263 views

Mathematical models of dynamic algorithmic processes

This question primarily concerns dynamical or time-dependent phenomena in philosophy and to what extent such heuristic discourse features in more precise mathematical settings. In order to model ...
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162 views

Informal fallacies and their fallacious nature

What imparts to informal fallacies their fallacious nature? I have been reading Wikipedia because of the ease of access, as well as some references listed there, like https://www.humanities.mcmaster....
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What type of fallacy does the phrase “I don't live to eat, I eat to live” fall into?

It's typically used in an attempt to convince people to switch to a healthy diet but in my opinion it does a very poor job because: no-one literally lives to eat, but it's one of the many small ...
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1answer
126 views

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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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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222 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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115 views

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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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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217 views

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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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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129 views

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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1answer
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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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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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177 views

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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115 views

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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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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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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Does anyone have an example where a sufficient condition comes first?

Example: Sufficient Condition of A+ MUST MEAN Necessary Condition of Studying occurred Temporally speaking, either condition can occur first, or the two conditions can occur at the same time. In our ...
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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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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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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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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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258 views

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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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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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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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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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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Why is the material conditional a thing? [duplicate]

If people have a problem with conditionals with false antecedents and with true consequents always being true, why not just change it according to what is found to be more intuitive? Regarding ...
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118 views

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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Does denying the Limit Assumption in counterfactual logic lead to contradiction?

According to the similarity semantics for counterfactuals, a counterfactual A > C is true iff on the most similar class of worlds to the actual world (or any given world the counterfactual's truth ...
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Can/Do there exist any quantifiers other than “there exists” and “for all”?

I'm curious about why there are only the two logical quantifiers there exists and for all. Intuition and human language support the idea that these quantifiers make sense, but otherwise it seems ...

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