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 can one prove ∃𝑥(𝐹(𝑥)→𝐺(𝑥)) given the premise ∃𝑥𝐹(𝑥)→∃𝑥𝐺(𝑥)?

Premise: ∃𝑥𝐹(𝑥)→∃𝑥𝐺(𝑥) Desired Conclusion: ∃𝑥(𝐹(𝑥)→𝐺(𝑥))
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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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Brain question, Need help solving for class. Logic Philosophy [closed]

LOGIC and PHILOSOPHY A reasonable believer is one whose beliefs include Q if they also include both P and (If P, then Q), and who trusts the results of her reasoning while remaining introspective ...
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An addict's argument [closed]

An addict argues that he or she would rather die "happy" than struggle with quitting... is this a logical fallacy? And if they consider their existence to be meaningful, is it ethical to insist that ...
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Are Pathos, Logos, and Ethos equally valid?

The three main ways of reasoning are Pathos, Ethos, and Logos. I have tended to see Pathos as inferior to Ethos and Logos because it appears to rely more on emotions than on facts. But does it really ?...
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Is there a sentence of this form? [closed]

Is there a set of sentences Γ with no predicates besides "=" with the property that an interpretation is a model of Γ iff the size of the domain is a finite multiple of three?
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Was there any 20th century physicist that proposed the existence of a multiverse and at the same time accepted Birkhoff's/von Neumann's quantum logic?

Was there any well renowned and Nobel laureate physicist from the last century who believed that multiple universes/realities existed and at the same time liked Birkhoff's/von Neumann's quantum logic ...
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Which of common rules of inference are rejected on some philosophical grounds?

My question is: is there a mathematical or philosophical basis for rejecting any of the following rules of inference? If yes, then what is the argument for rejecting any of them? I am asking this ...
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1answer
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Question about v-variants of variable assignments

In Full Predicate Calculus, some variable assignment q satisfies a disjunction under interpretation U if q satisfies one or both disjuncts under U, it satisfies a conjunction under interpretation U if ...
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Is it true that an argument cannot be both inductive and cogent?

I have been asked a question in class where we would need to pick out the false statement from a given set of options. The problem is that I am not really sure why my answer was wrong? Here is the ...
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Is Kant's transcendental logic a kind of erotetic logic?

In the first Critique, Kant presents a "problematical" concept of the ideation of reason, e.g. he talks about a focus imaginarium or something at one point. And his discourse on noumena as not "...
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How can the mere observation of race (without an assertion of equivalence) logically be considered racism?

During a social situation in which one observes the race of a person, I have heard the argument that it is racist to refer to that person by his or her race. Let's say that I have "hypothetically" ...
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How does supervaluationism resolve the Sorites paradox? Are there any problems with this resolution?

So I was reading about resolutions to the Sorites paradox, and I got most of them, but I didn't understand the one labelled supervaluationism. Would someone explain it to me in very basic terms please?...
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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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The nature of truth and logical connectives

I think most would agree that: P or !P !(P and !P) are always true. This allows us to have certainty no matter what we're talking about. Does that make the logical connectives the most fundamental ...
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The truth of statements which do not capture everything about the object [closed]

Logically it could be true to say: "All human beings are mortal (and therefore Peter is mortal because Peter is a human being)." But the above statement could be false in a sense, because mortality ...
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Are there implicit premises in propositional logic or formal systems generally?

We have an example of syllogism: "All men are mortal. Socrates is a man. Therefore, Socrates is mortal." This is a valid argument. Yet there are implicit premises which should be said in order for ...
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Impeachment Hearing [closed]

The law professor made an argument if x is not y, y is a null set. In statistics you can not prove the null is correct, you can only fail to reject the null. How does logic / level philosophy handle ...
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2answers
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Use-mention distinction

Is it 1+1 or “1+1” that is a formula of addition? To my intuition, it is the former, and the latter seems to be a name of the formula. The reason why I ask this question is that provided my intuition ...
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3answers
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What is the purpose of logical division for classification?

It's my understanding that we use division to classify things in the world so that we can define them, say, with a genus-species tag. However, in the introductory books I've read, they mention that ...
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Did logicists use mathematical entities (in their attempt) to reduce mathematics to logic?

Two concepts F,G are equinumerous if there exists a one-to-one correspondence between the objects that fall under F and G. Equinumerosity is one the most fundamental building blocks of Gottlob ...
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Logic and critical thinking [duplicate]

To what extent is it necessary for human beings to understand and use logic in order to be critical, logical, and rational, and to what extent is it necessary to adapt argumention to different ...
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Having trouble with a proof

I have been working on this proof and can't seem to figure out how to do a critical step. I am trying to derive the universal quantifier @x and @y. I have derived @z already. Any help is appreciated ...
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1answer
63 views

Existential Import

How is it that universal propositions (from the Boolean standpoint) don't commit us to the existence of the subject term while particular propositions actually do? Also, why particularly take or focus ...
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Truth Value of Definite Descriptions

I'm currently studying definite descriptions in logic. My textbook postulates Bertrand Russell's view of definite descriptions, but I'm curious about other views as well (in the context of classical 2-...
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why are ∀x(P(x)→ ∃y(Q(y)∧R(x,y))) and ∃y(Q(y)∧∀x(P(x)→(R(x,y))) not logically equivalent?

been sitting here for hours and still can't figure this out. is the order of ∀x and ∃y important in this case? all I can think of now is "all P is R of some Q", but I don't think this is right.
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What are the eventual purposes of symbolic logic?

What is the teleology of logic? Every body of knowledge has to have a teleology for which it's designed. The body of knowledge in logic doesn't clearly have any teleology or any purpose to which it ...
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2answers
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(p->q) v (q->p) with Natural Deduction

Well, indeed I have the answer to this exercise but I don't understand some steps. From 6 to 17 are OK for me but from 2 to 5 and then when step 5 is again called in step 10 is something I don't get ...
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1answer
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Language, Proof and Logic Exercise 14.13 (Fitch)

Having trouble proving this. I know how to prove the first conjunct of the conclusion, but not the second one. Picture shown is the attempt proof of the second conjunct (rules haven't been added yet). ...
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Inductive reasoning and probability: probability of the conclusion versus probability of the supporting relation?

It is often admitted that inductive reasoning has something to do with probability. While in a ( valid) deduction the premises necessarily imply the conclusion, in an inductive reasoning the premises ...
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With or without opposition between A and B, how many ways are there for A not to be B?

I'm looking for references and "loci" regarding the concepts of opposition, distinction, diversity, and negation. I'm not certain if one must distinguish the case in which A and B stand for concepts ...
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Can Hegel's theory of logic be formalized?

In paraconsistent logic, we have dialecticism. So is it possible to formalize the logic of Hegel, like Anton Friedrich Koch in "Hegel's on the logical big bang and the evolution of logical space", and ...
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Language, Proof, and Logic 14.11 Fitch Proof

Been stuck on this question for awhile now and I just don't know how to get Cube(x) so that I can use ^ intro with Cube(x) and ∀y (Cube(y) → y = a) and then use ∃ intro to get the conclusion. This is ...
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3answers
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Can the word “probably” be used in a proposition? (logic)

I'm interested in applying logic to day-to-day reasoning. The problem is that formal logic seems really restrictive to limit inductive arguments to be only universal ("all swans are white"). Few ...
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'this statement is true' , 'this statement is not not true' [duplicate]

Given the following self-referential sentences a. this statement is true b. this statement is not not true are (a) and (b) intersubstitutable, given classical logic can one eliminate the double ...
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how to prove ‘¬∃xP(x)→(P(a)→Q(a))’ from no premises? fitch

I am totally lost on how to do this... can anyone help? What does it mean? I tried to understand what it means before proof but am totally clueless
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LPL Predicate Logic Translations Exercise 11.20.7

I have this one question (Part 7) in exercise 11.20 that I can't seem to get the answer from. I tried ∀x∀y ((x ≠ y ∧ Larger(x,y)) → Dodec(x)) and ∀x∀y (Larger(x,y) → Dodec(x)), as well as many other ...
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Translation to language P

I am taking an intro class in philosophy and I have having trouble with some assignment questions. I need to translate into the language P. Here's the translation keys: Fx: x is a firefighter Dx: x ...
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4answers
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Liars paradox towards a solution?

This statement is not true 2.This statement is true only if true and not true. (1) and (2) are clearly different sentences, but do they express the same proposition? If yes, then it becomes clear ...
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Fitch Proof Final Step

I've been able to get this far, but I don't know how to finish it off. This setup was given to us as an something that can be proved as a proof without premises in the form ((P → R) ∨ (Q → R)) → ((P ∧ ...
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Proof With No Premise

How would I prove this in Fitch? ((P ->R) ^ (Q->notR)) -> (Q->notP) More generally, what is a strategy I can use to tackle these types of problems in general? I tried working backwards, breaking ...
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Using logic to do metalogical proofs? Is there a circularity problem here?

(1) If modus tollens were not correct, then I could have (P-->Q), ~Q and P. (2) But I cannot have (P--> Q) , ~Q and P. For, in that case, I would have (~P v Q) and ~Q and P; which means I would have ...
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What is the name of the fallacy involving white and black swans?

If one argues: I have seen only white swans, therefore there are no black swans. What would this fallacy be called?
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Is it possible to make decisions without some kind of belief system? [closed]

Normally when we talk about belief, we mean religious beliefs. But even the criticizers of religions have some kind of belief system. They base all their decisions on the premise of logic. Thats why I ...
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Is there a form of set theory involving imperatives and interrogatives?

I finally read the article Is there a Logic of Imperatives? Conifold showed me and it elicited the question, for me, whether imperative programming is a form of imperative logic at all? The essay took ...
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Existential Elimination in Fitch (Barber of Seville)

To be clear, I'm just struggling to understand why Fitch won't let me use EE. From other examples I've seen, I've set it up correctly for EE. I've also tried using BotE and EE on the desired sentence, ...
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Are we sinners because we sin or do we sin because we are sinners?

This question arose after I read a sentence like this : We are not sinners because we sin We sin because we are sinners. So "because it's carnivore then it eats meat" --vs-- "because it eats meat ...
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Equivalences in Sentence Translation with Quantificational Logic

Consider the sentence "If all the birds in my house are peacocks, then Charlie is a peacock," and let the provided symbols be denoted as B for bird, H for house, P for peacock, and c for Charlie. ...
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What is the fundamental axiom of reasoning?

Is it true that a fundamental axiom of logical reasoning is that reality doesn't contradict? Can someone explain why this assumption is a reasonable starting point if true or what a more accurate ...
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Is this a logical fallacy or simply a bad argument?

In my English class today, we were talking about thesis statements. One of the students said that one of the thesis statements didn't sound right; its syntax sounded odd. However, my teacher said that ...