Questions tagged [logic]

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

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Mechanics of Perception

How is perception formed? By perception I mean 'thought' or 'idea' of the World. What I see by itself does not contribute anything to thought. Only an acknowledgement can contribute to structuring of ...
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45 views

Reasoning for Inductive inference?

Just out of curiosity, if I should replace the deductive inference related questions to inductive inference, then which are true? Inductive inferences rearrange current knowledge in such a way that ...
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2answers
61 views

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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Question about conjunctions

Would this principle be true for conjunctions: For any proposition p, if p is a conjunction with at least three conjuncts, then there are more distinct conjunctions that can be created out of the ...
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172 views

Do Most Philosophers Ignore the Rules of Dialectical Logic?

In metaphysics it is well known that all selective conclusions about the world as a whole are undecidable. Most philosophers infer from this that metaphysics is incomprehensible. I believe this is a ...
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4answers
109 views

Russel's paradoxical set from a different view

Suppose naïve set theory, let's do a tought experiment: Informally, let's define a set € such that € contains all the sets that don't contain themselves.(yes, all but not necessarily only those), ...
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62 views

Would this be an invalid or valid argument? [closed]

All mathematical truths are knowable. All mathematical truths are eternal. So All that is knowable is eternal.
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3answers
95 views

A deontic premise that leads to a necessity from a permission

I wanted to devise some rules for myself, then formulate those rules using formal symbolic logic, and one of the rules that I have set for myself is : "Do not say what is unnecessary", in other words :...
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144 views

Why is it argued that an argument has one and only one conclusion?

Why can't an argument have more than just one conclusion? If we assume some premises and we assume them to be true, then by some inference rules we are sometimes able to deduce more than just one true ...
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45 views

What are some key differences between an argument in logic and a theory in mathematics?

Both are composed from rules and assumptions which enable us to deduce other inevitable truths that results from these rules and assumptions, right?
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6answers
130 views

Is it true in some sense that the only “truth” people are capable of knowing is the “truth” that they assume to be true?

What are some viewpoints on the following assertion in philosophy and logic? Anything people argue to be true is only their assertion based on some axioms or premises which they assume to be true (...
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Does Barrow and Tipler's “anthropic principle-multiverse” entail the existence of all logically possible universes?

I've read several texts that indicate that the anthropic principle (applied to cosmology, and more specifically, to the multiverse) yields the existence of all logically possible universes (most like ...
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156 views

How do you measure circular reasoning? [closed]

How do you measure circular reasoning?
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What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results?

What are some popular theories/opinions in philosophy against the certainty placed on the laws of logic and its results? You would think philosophers wouldn't ever criticize or try to debunk logic ...
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What is the difference between a premise and an assumption in logic?

It seems to me that an assumption is an untold premise in my argument. Is it right?
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29 views

Why there is no suberogation function?

Going off the definition of logical validity that depends on true premises going to true conclusions, there is no imperative logic. However, it seems that some "imperative arguments" look regular ...
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50 views

An erotetic argument about the liar paradox

I noticed something about the liar paradox, when the liar sentences are taken as questions. Let’s start with the liar index, “This sentence is false.” Allow this to be questioned: “Is this sentence ...
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1answer
69 views

What is the difference in logic between strong and weak negation?

My main concern is to separate different forms of logic. I am hoping to use negation as a way to do that. In the abstract to "Web Rules Need Two Kinds of Negation", Gerd Wagner writes ... there ...
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2answers
135 views

Does the existential quantifier express existence?

Does the existential quantifier express existence? The existential quantifier is a symbol of symbolic logic which expresses that the statements within its scope are true for at least one ...
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8answers
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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 ...
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2answers
74 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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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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127 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.
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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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162 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.
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186 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 ...
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5answers
187 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
444 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 ...
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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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105 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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386 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 ...
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256 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 ...
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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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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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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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65 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
54 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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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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137 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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44 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
38 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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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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75 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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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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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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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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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→...