Questions tagged [logic]

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

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15
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8answers
8k views

If a person claims to know anything could it be disproven by saying 'prove that we are not in a simulation'?

Everyone starts out at 0 and if anyone wants to say that they know something they have to prove that claim. Is the counter to this person claiming that they know something logically correct? Person ...
0
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2answers
75 views

How does one tell if logical expressions are equivalent?

How do I check if these expressions are equivalent? ∀a,b [P(a) ∧ ¬R(a) ∧ S(b)] → G(a,b) ∀a [(P(a) ∧ ¬R(a)) → (∀b [S(b) → G(a,b)])]
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2answers
89 views

Problem with existential import in syllogisms (Barbara)

For a syllogism in Barbara, why is it the case that All men are mortal. James’ son is a man. Therefore James’ son is mortal. assumes that James has a son but in the case of saying All ...
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0answers
128 views

Things can exist even if it is impossible to provide concrete examples of it?

In mathematics, there are many things that can be rigorously proven to exist, but at the same time rigorously proven that no concrete examples of it can be given. This is a crazy idea for non-...
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2answers
81 views

Help with an existential natural deduction proof

From the assumption ∃x∃y R(x, y) I need to derive the conclusion ∃y∃x R(x, y) From the comments: I tried to use Existential Elimination but I can't figure out how to do it properly.
0
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1answer
30 views

How does one go about this natural deduction proof?

From no assumptions derive the conclusion ∃x t = x (where t can be any term).
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2answers
163 views

Confused about the answers to two logic problems

True or False? If monkeys can fly, then 1 + 1 = 3. What is logically equivalent to all x (p(x) + ~q(x))? For the first one I think it is False.
0
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2answers
189 views

All philosophers are nerds. So, no squares are circles [duplicate]

Can the above argument be valid? If it can, I want to know why, as far as I see, even though the conclusion (no squares are circles.) is true, it doesn't seem to be following the premises (not a ...
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4answers
141 views

Definition vs Logic

Logical consequence means that, if, P implies Q, then Q is True not because (or when) we interpret (or find) it to be True, but it is set to True as soon as P is set to True. This means that Q is ...
0
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5answers
189 views

In an argument: why True P and False C is invalid, but False P and True C is valid?

P= premises; C= conclusion. Some Americans are women (True). Brad Pitt is an American (True). Therefore, Brad Pitt is a woman (false)-- invalid. All dogs are ants (False). All ants are mammals(False)...
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7answers
589 views

Could an argument with false Premises and a true Conclusion be logically valid?

Am unsure (leaning more towards no): true P and true C is valid, false P and false C is valid, True P and false C is invalid, how about false P and true C? P= Premises; C= Conclusion. People who ...
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1answer
66 views

Solve using rules of inference

If the ghost is in our imagination, then it is immortal. But if it is not in our imagination, then it is mortal and animal. If the ghost is either immortal or animal, then it is carnivorous. A ghost ...
4
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1answer
74 views

Decidability of predicate logic

In the language of predicate logic with only identity and no predicates, function symbols, or constants, is it possible to construct infinitely many non-equivalent formulas?
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3answers
107 views

Presenting an example, then claiming the other person needs more information before using the same example - is either of us making a fallacy?

I recently had a conversation with someone in which they used an example to illustrate a point: "For example, if you tell me something [which isn't scientifically proven to be effective] works ...
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3answers
389 views

Do Gödel's First Incompleteness Theorem imply the inconsistency of Platonic Infinity?

According to Modern Mathematics (where the majority of mathematicians agree about the notion of actual infinite sets, as established mostly by George Cantor) an inductive set (as given by ZF(C) Axiom ...
2
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1answer
328 views

What is the difference between “logical equivalence” and “material equivalence”?

Wikipedia offers this as the difference between "logical equivalence" and "material equivalence": Logical equivalence is different from material equivalence. Formulas p and q are logically ...
2
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2answers
68 views

Is argument from need a valid type of reasoning, even in some cases?

To begin with, I know that if I need X , does not necessarily mean that X exists. But in some cases, it seems very convincing that if I need X then X exists. These are some examples : If I am ...
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0answers
84 views

Do nominalists predicate everything equivocally?

Do nominalists predicate everything equivocally? Equivocal predication is when only the name is common between two things, for example: "bark" in tree bark and dog's bark.
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1answer
71 views

Are there rules for the following in the Open Logic Project's proof checker?

I'm using http://proofs.openlogicproject.org/ but can't find out what the translation of the rules are. I'm new at this, so when I try to make proofs, I know what I want the justification to be (which ...
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2answers
72 views

How to solve this natural deduction problem?

This one is driving me crazy. I don't understand most keys for de morgan, modus ponens, etc, so please abbreviate if possible? EX: DM, MP, SIMP, HS, Conj, Imp (material Implication). Thank you anybody ...
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2answers
57 views

major/minor term of a syllogism when order of conclusion can be reversed

Consider: All ‘A’s are ‘B’s No ‘B’s are ‘C’s Is it not the case that the conclusion to this could either be: No ‘A’s are ‘C’s or No ‘C’s are ‘A’s ? Is it not also the case that the minor term ...
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1answer
52 views

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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1answer
139 views

What if Euthyphro gave the opposite answer?

As part of a course I am taking, I was asked to continue the dialogue Euthyphro as if Euthyphro had given the opposite response to Plato's famous question: Is the pious loved by the gods because it ...
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0answers
45 views

What is the name of the fallacy where acknowledging an issue is confused with actually addressing the issue?

A few days ago an artist came to present his work to our class. At the beginning of his presentation he said "I know cultural appropriation is a very loaded topic, and it occupies my mind often" as ...
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2answers
39 views

How to use use the Fitch System to prove (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q) ⇒ p)?

I'm getting a bit stuck in a tailspin on this one. I'm quite new to logic. I'm not sure how or when we use negation to get P. How then does that connect to (¬p ⇒ q) ⇒ ((¬p ⇒ ¬q)?
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1answer
151 views

I don't understand Parmenides's argument for why we can't think about what doesn't exist

I have been learning about Parmenides, and I don't think I am correctly understanding his argument for why we can't think/speak about things that don't exist. I tried to apply his logic to a ...
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2answers
76 views

Given premise ~(P↔Q) how can one derive (~P↔Q) using Fitch?

Given premise ~(P↔Q) derive (~P↔Q) using Fitch-style natural deduction. I thought of simplifying the premise but I am still not able to find an answer. Can someone please help me?
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1answer
90 views

Honestly have no Idea how to prove A v ¬¬B from A v B (LPL Q. 6.18)

Premise A v B Goal A v ¬¬B Please help. It seems so self evident but I don't know how to get there.
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2answers
35 views

In First-Order Logic, can you deduce an existential quantifier purely from other existential quantifiers?

Let's say we have: ∃x(Fx → Gx) and ∃xFx can we deduce ∃xGx? I've been throwing myself at this problem for days and every time it just seems like the entire enterprise is flawed. Existential ...
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1answer
33 views

How do you prove (p => q => r) => (p => q) => p => r using the Fitch system?

I'm quite new to logic. Thank you for taking the time to review this post. I tried the following and got to the conclusion I wanted but I was never able to prove the statement.
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1answer
44 views

Cogito corollaries and meaning [closed]

Doubt implies thought. I'm doubting. So I'm thinking. [(d→t) ∧ d]→t Thought implies existence. I'm thinking. So I exist. [(t→e) ∧ t]→e d→t; ¬t→¬d; [¬t ∧ (d→t)]→¬d t→e; ¬e→¬t; [¬e ∧ (t→e)]→¬t [(d→...
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2answers
81 views

Trouble with cookies [closed]

Matter cannot be created. Cookies are matter. So cookies cannot be created. I know this seems absurd but I'm using this to make an important point about arguments. The argument appears to be valid ...
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2answers
157 views

Does the Universe make sense? [closed]

When faced with a paradox, we say: well this can't be because it doesn't make sense. p = "x doesn't make sense" q = "x doesn't exist" The contrapositive preserves validity: p implies q (not q) ...
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0answers
70 views

The enunciation clause (Lyotard & Levinas)

As kind of introductory remark, let me state that I'm not academically-trained in philosophy, so my apologies if this comes up as a rather simple question. I was reading Logique de Levinas by JF ...
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17answers
12k views

Why doesn't philosophy have higher standards for its arguments?

Mathematical systems are an excellent model for organizing and conducting thought: In the mathematics community, any argument in support of a conjecture, that deviates from "sound argument" never ...
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2answers
259 views

Can someone explain this logical statement?

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced ...
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3answers
85 views

Why is there an O type conclusion in modus celaront

Modus celaront is type logical syllogism. No reptiles have fur. (MeP) All snakes are reptiles. (SaM) ∴ Some snakes have no fur. (SoP) The conclusion is of a O type(Some .. are not ...). Why is ...
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3answers
1k views

When is pointing out a person's hypocrisy not considered to be a logical fallacy?

People keep using the word "whataboutism" and it seems people don't really know what it means, and I don't see how it's a logical fallacy if it's a very good argument. For instance, if the U.S. says ...
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1answer
123 views

Did anyone argue against the possibility of a perfect prediction from within a system?

Did anyone offer an argument against the possibility of a perfect and complete prediction about a system from within that system along the following lines: Let's imagine a machine (like a desktop ...
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4answers
546 views

What is the difference between logical consistency and logical entailment in deductive logic?

I am having a little trouble sorting out two definitions from the first chapter in my logic textbook, The Logic Book by Bergmann, Moor and Nelson. I am under the impression that a set in a sentence ...
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2answers
91 views

Incorrect statement in Suppes' Introduction to Logic

Chapter 2 of Suppes' develops the notion of sentential inference and how to construct rules of inference. However, there is one part in his development that seems incorrect no matter how I look at it. ...
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2answers
64 views

Negation of a relational quantified term?

Formally, when you negate a quantified term which is attached to a relation, is a distributed term always made undistributed and vice-versa? For example, consider this statement : Anyone who assists ...
2
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2answers
135 views

Wittgenstein's solipsist, from Tractatus?

According to the early Wittgenstein of the Tractatus, the solipsist is one and one and the same with the world. He then makes the claim that solipsism coincides with realism. 5.64, Wittgenstein ...
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0answers
68 views

Using solipsism's incoherence with doubt as proof of the external world?

I have the following rough outline of utilizing solipsism as a proof by contradiction to the goal of asserting an epistemological proof of the external world. A solipsist (Wittgenstian) lives in a ...
2
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1answer
257 views

Does this argument make sense?

Consider the following argument: (A) Either sales or expenses will go up. (B) If sales go up, then the boss will be happy. (C) If expenses go up, then the boss will be unhappy. (D) ...
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2answers
173 views

Who first studied asymmetric relations qua relation?

Who first asymmetric relations qua relation, viz., the fact that A relates to B by some relation does not always/necessarily imply that B relates to A by the same relation. ?
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1answer
110 views

Who first studied “logical (ir)reversibility”?

Who first studied "logical (ir)reversibility" philosophically? By "logical (ir)reversibility" I mean questions like:Why is it easier to multiply large numbers than to factorize them? understand a ...
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1answer
60 views

Quick question on validity of arguments across propositional and predicate logic

Could someone clarify a quick question regarding the following please? From the text: Assume Γ ⊭ ϕ. Then there is an L2-structure A such that all members of Γ are true in A and ϕ is false in A. ...
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1answer
37 views

Quick question on discharging assumptions

Could someone explain conceptually what the consequences are of assumptions NOT being discharged in a natural deduction ? Suppose the objective is to establish a claim of the form : 'If A,then B.' ...
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1answer
36 views

What should be the correct form for this particular argument?

Thank you for reading my concern and providing your precious time. I am writing this question to highlight the difficulty in solving the problem due to wrong punctuation and sentence construction. ...