Questions tagged [logic]

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

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5
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7answers
3k views

Is it nonsense to say B -> [A -> B]?

Is it nonsense to say B → [A → B]? I would have thought so, it seems to say that every fact deductively follows from every other. But I was looking at a recent closed question, on natural deduction, ...
2
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0answers
21 views

This statement is in a disjunction with itself

Are the following listed statements equivalent? 1: (1) is in a disjunction with (1) 1: (1) is in a disjunction with (1) OR 1: (1) is in a disjunction with (1) (the intended meaning of (1) is '...
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3answers
107 views

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 ...
3
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1answer
159 views

Formal logic to describe causation?

I'm looking for any formal work that has been done on describing causation the way people understand it. I am not looking for logical implication, more a way to talk about "Why?" questions. Basically, ...
0
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1answer
49 views

Can supervaluationism relate to the abortion debate? If so, how?

So I'm writing an essay on the Sorites paradox and how it relates to the abortion debate. One resolution to the paradox I was reading about came from supervaluationism, but I'm not entirely sure if or ...
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2answers
102 views

Infinity - Sizes vs Types

Suppose there is a line, infinitely long in both directions. Make arbitrarily "uniform" cuts or "integers". Obviously there are infinitely many of these. And there are arbitrary "lengths" BETWEEN ...
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1answer
44 views

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))
1
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1answer
229 views

Omnipotence Paradox Defense and Meinongianism/Neo-Meinongianism

I was considering a solution to the omnipotence paradox in which excluding logical impossibilities from the definition of omnipotence is justified as follows. Consider the proposition, "God could ...
4
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1answer
87 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 ...
2
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1answer
51 views

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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2answers
87 views

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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0answers
33 views

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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1answer
37 views

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 ...
2
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1answer
192 views

What is an example of a predictive conditional?

Can someone explain to me with an example what a predictive conditional is? Does this type of conditional have necessary and sufficient conditions?
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0answers
34 views

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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3answers
90 views

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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0answers
33 views

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?
9
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4answers
821 views

Logical consequence and material conditional - Are they the same?

I'm taking basic discrete math course which includes basic intuitive introduction to logic (only things like statements, tautology truth tables, etc.). During the learning, I've wondered what is the ...
2
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1answer
54 views

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 ...
3
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1answer
64 views

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 ...
3
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1answer
27 views

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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0answers
450 views

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? [closed]

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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9answers
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How to prove (A v B), (A → C), (B → D) therefore (C v D)

Obviously since A → C and B → D then if A v B one of C or D must be true. My only idea is v must be introduced, but how would I use subproofs to show one of A /\ C or B /\ D is never false if A v B?
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0answers
49 views

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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1answer
23 views

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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4answers
65 views

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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0answers
60 views

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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0answers
41 views

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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0answers
35 views

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 ...
2
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7answers
7k views

If everything is possible, is it possible for something to be impossible?

If everything is possible, is it possible for something to be impossible? Possibility and impossibility are modal notions; and are dual in the usual formulation; the SEP remarks: It would seem to ...
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3answers
60 views

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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2answers
37 views

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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2answers
106 views

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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1answer
253 views

If metaphysical grounding of beliefs is not necessary what is to logically compel one to believe anything?

'Grounding' is the notion that 'because of X, Y', X being the reason one can accept Y beyond pragmatic considerations. In this way, X and Y are analogous to cause and effect respectively. If it is ...
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0answers
20 views

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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0answers
36 views

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 ...
0
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1answer
119 views

How to prove rigorously that “ necessarily ( A OR ~A) ” does not imply “ necessarily A OR necessarily ~A”?

In De Interpretatione , Aristotle criticizes logical fatalism ( a metaphysical doctrine professed in the Megarian School, in particular by Diodorus Cronus). Aristotle reconstructs the reasoning of ...
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4answers
137 views

Language Proof & Logic 8.31 Fitch Proof

Been working on this one question for the past hours and I can't ever seem to get the last step working. Any help would be appreciated!
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1answer
46 views

How can I prove the law of excluded third (p ∨ ¬p)) using Fitch?

Good day. I do not quite understand how I can get ~~p after the 11th line. According to the proof of the law itself (and all reasonable logic) I should get it, and then simplify the expression - but ...
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1answer
64 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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2answers
52 views

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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2answers
62 views

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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1answer
109 views

How do you prove A <-> C given the following premises?

Using the 20-rule proof system (replacement rules, rules of inference, conditional proof, and reductio ad absurdum) and given these 3 premises: A -> ~B ~C -> B ~A -> ~C I know that since I'm ...
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6answers
1k views

What does it take to answer a philosophical question?

I apologize in advance if my question should be discussed on Philosophy Meta, but when thinking about the question I couldn't decide whether it would be appropriate there. Thinking about the ...
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10answers
11k views

Which fallacy: “If white privilege exists, why did Elizabeth Warren pretend to be an Indian?”

I recently came across this meme. It's clearly a logical fallacy (the existence of one use of a socioeconomic tool other than white privilege does not preclude the existence of white privilege), but I'...
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1answer
162 views

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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2answers
43 views

(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
1k views

How to prove ¬(p→q) ⊢ p &¬q

This is the first time I have posted anything on this forum. I am using Tomassi's Logic. Unfortunately I have been unable to solve some of the problems. One I can't solve is this one: ¬(p → q) ⊢ p &...
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0answers
36 views

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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8answers
1k views

How does abduction differ from inductive reasoning?

Consider this statement: Abductive reasoning typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set. But couldn't the same ...