Questions tagged [logic]

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

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What is the CLASSICAL account of deductive validity?

I am just wondering what is the classical account of deductive validity and if there are other accounts.
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Looking to prove that my knowledge bases leads to empty clause

Using the resolution method, I want show that the following knowledge leads to the empty clause. ∃x (q(f(x))∧s(f(x),A)) ∀x∀y¬∃z (p(x, y)∧s(x,z)) ∀x (q(x)∧ ∃y s(x, y)) ⇒ (∃z (r(z)∧ p(x,z))) What I ...
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Measuring a Person's Aesthetic Sense

Can we measure or evaluate the aesthetic sense of a person? Like, can we statistically say that Person A has a superior aesthetic sense to Person B? Since beauty is relative, can we truly 'grade' ...
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How do we separate rules of logic from non-logical constraints?

I think that very often the idea of 'constraint' appears in mathematics. For example, when a triangle is considered, 3 points are constrained not to be co-linear, and then we try to discover the ...
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What is an argument with necessarily true conclusion?

I cannot understand what an argument is with a necessarily true conclusion. Could you explain to me what it is and write here some examples? Moreover, what is the meaning of “necessarily true” and “...
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Language Proof and Logic 15.16 [duplicate]

This problem concerns the practice problem 15.16 of the textbook Language, Proof and Logic. So I saw a similar post here, which gave most of the correct answer (Language proof and logic Chapter 15 ...
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Is an argument valid if one of the premises don't affect the conclusion?

Let's say I have an argument with premises P, Q and R, with a conclusion S. But let's also say that Q and R are sufficient to conclude S. But having P as a premise doesn't affect the argument in any ...
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Which philosophers proposed theories containing a performative contradiction?

Socrates was blamed of this by being wrongly interpreted of saying: "I know that I don't Know." or other variants. What he really said was: "I neither know nor think that I know." Source: https://en....
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Book Introduction to Logic. Patrick Suppes-Section 2.1-Excercise 4

Anybody can help me with the solution of this exercise? Construct a (non valid) rule of inference which by itself will satisfy Criterion II but violates Criterion I? Thank you in advance. Diego.
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What falls under Hegel's concept of “absolute knowledge”: does that include deductive logic and scientific explanation?

In the wikipedia page for Hegel's Science of Logic, it states: According to Hegel, logic is the form taken by the science of thinking in general. He thought that, as it had hitherto been ...
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What is the meaning of free variables?

In some books I see something like: phi(x1,...,xn) with free variables among x1,...,xn. An example of this is on 2nd paragraph, page 25 of the book Knowledge in Action. I have included a snapshot of ...
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Could the link between virtues and pleasures and pains in the third chapter of Nicomachean Ethics' book II be considered a hypothetical syllogism?

In the chapter 3 of Nicomachean Ethics' book II, Aristotle says: Again, if the virtues are concerned with actions and passions, and every passion and every action is accompanied by pleasure and ...
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Is is logically inconsistent to say that male on female violence is wrong? (Compared to vice versa)

I have always believed that the reason it is more wrong for a man to hit a woman than vice versa is mainly because women tend to be physically weaker then men, and that even if a women initiated ...
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Logical, semantic and self-referential paradoxes: The Truth teller and the Liar (draft) can an expert on the matter give feedback?

Title: Logical semantic and self-referential paradoxes: The Truthteller and the Liar (draft, informal) (major) assumption: A statement is either true or not true (law of excluded middle, classical ...
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Fitch Novice! Need help [closed]

hello everyone! I'm not too experienced with fitch and I was wondering what I'm doing wrong. Any help is appreciated! Premises are ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) ∀x∀y∀z((StrongPref(x,y)∧...
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Fitch Proof - Arrow's logic of preferences

I've been stumped on this one question in particular for several days now and I'm hoping to get some help on where I'm going wrong. Given the following premises: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,...
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Can anyone tell which one of these sentences are materially implies(implication) and logically implies(implication)?

these are the contexts: 1): If the number 0 has a certain property, and any natural number a has the property implies that a +1 also has the property, then every natural number has the ...
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Why does one need to specify that the language is “well-orderable” for first order logic to be complete?

While reading Wikipedia I noticed the phrase "well-ordered language" in the following related to Gödel's completeness theorem: The completeness theorem then says that for any first-order theory T ...
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What are the types of non-deductive arguments?

I've been looking for it, but Google leads the search to multiple sort of pages that, although they talk about logic, explain the subject very differently from each other and they don't fix a list ...
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What are the conditions needed for a good argument in the field of informal logic?

I'm trying to get the difference between the concept of argument in the field of formal and informal logic and I'm still a little bit confused by how. Are true premises and non-false conclusions ...
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Is the doomsday argument flawed?

Through the doomsday argument people try to calculate the number of humans that will ever live based only on the number of humans that have lived until now. To me this arguments seems very flawed, but ...
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Fitch Arrow Proofs [closed]

Using the FITCH program and the FITCH derivation rules you should make a proof or derivation of C10 from P5 through P11. P5: ∀x∀y(StrongPref(x,y)→ ¬StrongPref(y,x)) P6: ∀x∀y∀z((StrongPref(x,y)∧...
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A question about material implication

I have a question about reading material implications. I know this read as "if p then q". like: if the moon is made of green cheese then the earth is round. but I can't read it in this sentence: ...
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Which solution is better for this predicate?

We have this predicate: Prime(x) ≡ x>1 ∧(∀y)(Divide(y,x) → (y=1 ∨ y=x)). Now I have to turn this into an English sentence. I've come up with three answers: x is a prime number if x is greater ...
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Can I use some software method to solve and derive logic proofs?

For example, suppose I have this problem: T (T ⊃ (B ∨ M)) (M ⊃ H) ~H I heard there's a programming language called Prolog which can verify whether the conclusion was true or false. I would like to ...
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What exactly is a first-order logic?

Can someone explain in simple terms what exactly is a first-order logic? From my amateur standpoint, I think that first-order logic is a some kind of a system of symbols and general logical rules and ...
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ELI5 - Abduction vs. Inference to Best Explanation (IBE)

How can you explain to a 5 y.o. how abductive reasoning differs from IBE? I don't understand even though I read SPE and these papers: Campos, Daniel G. On the Distinction between Peirce’s Abduction ...
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Do computer languages instantiate only predicate calculus?

All the computer languages I'm familiar with, be they imperative or declarative have the same core mechanics (arithmetic and logic).They have the same loops, conditionals etc. Whatever the language it ...
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What are good sources on vivid designators?

Wikipedia lists a vivid designator as the following: Vivid designator: In modal logic and the philosophy of language, a vivid designator is a term which is believed to designate the same ...
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What's illogical in Justice Kagan's hypothetical with law clerks writing and editing memos?

Is Kagan's slipup one of formal or informal logic? Can you please unravel in high-school terms, but more broadly, how Alito's counterargument rebuffed Kagan's argument? I have music degrees, but ...
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A question about possibility

1) If A, then B 2) ~ A 3) So, possible that B Valid or not? My take: Not valid. Reason: Valid means if all premises true, conc. must be true That means adding new information should not alter ...
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What is the Barcan Formula?

can someone please help explain this Barcan formula to me? (In English translation and maybe with an example?) (◊ ∃x Fx) ↔ (∃x ◊ Fx) And if there is only one possible state of the world, would it ...
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Can a Rigid Designator still exist if there is only one possible world?

According to Kripke, a rigid designator is a pronoun (but not all pronouns are rigid designators) and they pick out the same unique individual in each possible world. I understand this, however, if ...
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Did Wheeler's “It from Bit” allow inconsistencies to exist?

Physicist John Wheeler proposed a model of the universe based on "It from Bit" asserting that the world is fundamentally information. I've been told both that Wheeler's It from Bit is compatible with ...
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Language confusion; necessary/nomological/true in all worlds

I got confused by the way different people use language in the context of physicalism. In particular, Kripke seems to equate "necessary truths" with something that is true in all possible worlds. Is ...
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How and why Aristotelian essentialism is a problem for Quine?

I cannot understand how and why the Aristotelian essentialism is problematic for Quine. I have tried to read articles on the theme but probably I am not smart enough to understand them. Could you ...
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Can a solipsist doubt?

I've been thinking about epistemological solipsism, which seemingly necessarily follows from metaphysical solipsism. Namely, that the "world" of the solipsist is one and the same with the self of the ...
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Analogy between an unknown in an argument, and a contradiction in the principle of explosion

Context I like to argue that, since we do not know what consciousness is, we can not specify what it can not do. Therefore we can not state we can't do something now, nor in the future. Up to the ...
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Proof Tree to Fitch Proof

I was wondering if anyone could help me on a proof I've been working on: I was able to check that it is valid with a proof tree generator (prooftools): However, I still haven't figured out the proof....
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Modal logics - philosophical paradoxes using modeling by possible worlds

I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) ...
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Does the Münchhausen trilemma negate its validity?

https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the ...
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Logical Necessity

Logical necessity is that which is necessary by definition. Otherwise it is sometimes considered to be that which cannot possibly be false, or cannot be otherwise metaphysically. The usual example is ...
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Another logic proof problem I'm stuck on :(

sigh stuck on another problem Premises P Conclusion (( ~(Q → R) → ~P) → (~R → ~Q)) I am allowed to use Modus Ponens, Modus Tollens, Hypothetical Syllogism, Simplification, Conjunctions, Addition, ...
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Having trouble starting a proof

I am given the following premise: ( Q --> R ) and the following conclusion (( ~ Q --> ~ P ) --> ( P --> R )) I am allowed to use Modus Pollens, Modus Tollens, Hypothetical Syllogism, ...
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Fitch Question Please Help Me [closed]

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : [![enter image description here][1]][1] How do I reach this goal? Which rules do I use and with which ...
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Is marxist dialetic according to Aristotle classical logic?

Is a static binary logic compatible with one based on dynamic evolution by overcoming?
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Fitch Questions Please Help Me

I'm having trouble understanding writing out a proof. The proof I'm trying to work with is : How do I reach this goal? Which rules do I use and with which support steps to each rule (proofs to prove ...
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Why are non-logical predicates of 0-arity treated as logical variables?

In the "Non-logical symbols" section of Wikipedia, it states: A predicate symbol (or relation symbol) with some valence (or arity, number of arguments) greater than or equal to 0. These are ...
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Interpreting conditional statements

If we have the conditional statement: a -> b -> c Do we interpret it as "if a, then b, if b, then c" or "if a, then if b then c"? In other words, which of the arguments would be valid: 1) a -...
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Fitch Proof Help

I'm having some trouble solving this proof in Fitch. How do the universals switch place from the premise to the goal? There is no negation in the goal so negation introduction is not the way to go, I ...