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Questions tagged [logic]

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

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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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1answer
205 views

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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53 views

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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1answer
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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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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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2answers
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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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Fitch Arrow Proofs [on hold]

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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35 views

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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How might I notate that an entity either cannot have a quality or has all of it?

I have two friends, Charles and Louis. I want to state that given one of the following conditions then Charles and Louis are identical: Charles does nothing. Louis does nothing. Charles does ...
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What is a predicate according to Aristotle's Organon?

There is of course predicate as in predicate logic; but I'm asking about the notion in Aristotle's Organon. Consider the proposition: Socrates is a man. Man is a universal, Socrates is a ...
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Does the Fallacy Fallacy make logic useless?

I should add that I'm not a formal student of philosophy and haven't studied it in any serious depth. I just like logic, and logical fallacies. I like to spot them, and I like to debate using them, ...
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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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8answers
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Is there a name for an argument like “A implies B; B implies A; therefore A”?

Is there a name for the following false syllogism? A implies B and B implies A therefore A For example: If unicorns exist then they have horns, by the definition of a unicorn. But in order for ...
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4answers
226 views

Help with a proof in Classical Sentence Logic

Premise: (A implies B) implies C Conclusion: (C implies A) implies A I had a logic exam a few hours ago and this was one of the problems, but I really didn't know where to start. Since the main ...
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4answers
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How does one prove De Morgan's laws for quantifiers?

One of De Morgan's laws state that ¬∃x P(x) is equivalent to ∀x ¬P(x), but how would one go about formally proving this? Numerous attempts to find a solution have been futile, even proofwiki.org ...
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1answer
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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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Are Wittgenstein's propositions analytic or synthetic?

Wittgenstein provides a logical analysis of propositions in the Tractatus. Does he there admit the Kantian distinctions between analytic/synthetic and a priori/a posteriori divisions; or does his ...
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1answer
64 views

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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1answer
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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1answer
417 views

How is Wittgenstein’s “notorious paragraph” about the Gödel's Theorem not obviously correct?

Timm Lampert quotes from Wittgenstein's "notorious paragraph" (§8 of Remarks on the Foundations of Mathematics, Appendix 3) in http://wab.uib.no/agora/tools/alws/collection-6-issue-1-article-6....
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2answers
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Is there an Informal Fallacy for misusing/overidentifying Informal Fallacies in an argument?

I frequently find myself reading discussions where people use Informal Fallacies as if they are invincible battering rams that destroy any argument they encounter. For example, somebody might say "...
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2answers
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Why do we need Aristotle's theory of predication?

My question is about Aristotle's theory of predication. Why do we need it at all? I know it's intuitive to pick up something and say something about it like "S is P", but doesn't this lead us to ...
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1answer
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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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3answers
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How do I apply existential elimination to the following Fitch proof?

I am trying to prove ∀x.∀y.loves(x,y) from Relational Proofs using the Fitch system from Barwise and Etchemendy. I can get as far as line 5, but I cannot figure out how to apply Existential ...
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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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1answer
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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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0answers
124 views

Why is a square circle metaphysically impossible?

We have definitions for both a square and a circle. By definition, I understand that it's impossible to have a square circle. However, why does the word 'square' have to necessarily mean 'a plane ...
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1answer
51 views

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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1answer
160 views

Where can I find logical fallacies in action?

I'm looking for a website that gives logical fallacies in action. Not a video that explains logical fallacies, but a video, say a debate between two people where one of the debators uses a logical ...
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1answer
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Proof from tree to steps

I'm able to get the proof in a tree form (it's invalid). Is there a method where I can transform it to steps method indicating the rules of inference and replacement?
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2answers
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Derivation using inference rules

Suppose I have the premise: ~(AvB).(Negation A or B) How can I get to the conclusion: A<=>B (A if and only if B) using inference rules like introduction or elimination and also ...
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How do we get science interested in formal logic as a model of logic? [closed]

To the extent that deductive logic is thought of as a capacity of the human brain, and to the extent that formal logic is meant to be a model of it, I believe a scientific approach is badly needed. ...
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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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Is the “omniscient-omnipotent-omnipresent” definition of God consistent?

God is commonly defined as an omniscient (infinite knowledge), omnipotent (unlimited power), omnipresent (present everywhere) entity. Is there any logical inconsistency in this definition? I have ...
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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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Which problem is Russell focusing on while providing a solution, in his introduction to the Tractatus?

In the final part of his introduction to the Tractatus Logico-philosophicus, Russell provides a possible solution to the problem of the impossibility of self-reference of logic: There is one ...
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2answers
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Existential quantifier proof help

I know I have to use the existential elimination rule twice but I'm still having troubles. ∃x∀y((Kyf ↔ x = y) ∧ Bx), ∃x(Kxf ∧ ¬Bx) ⊢ Fa ∧ ¬Fa
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272 views

What does this table regarding the 'connectives' '&' and '~' mean?

I'm a modern philosophy student and I'm reading content on the truth-value of sentences in logical structure, but I had trouble underatanding how connectives contribute to the truth-values of say ...
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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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666 views

How to find redundant premises?

Suppose I have this simple argument: ( P ⊃ Q ) R P Therefore, Q Here's the truth table I made in an excel worksheet: As you can see this comes out valid but in reality it isn't valid ...
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How soon could a student study the main branches of philosophy and be expected to understand the concepts as well as they understand other concepts? [closed]

With main branches I mean formal logic, mainly rules of inference, axiology, as in ethics and aesthetics, phenomenology and epistemology. Even if students do not appreciate the deepest meanings at ...
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1answer
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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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Logic. Having problems with interpretations

My question asks me to specify a true and a false interpretation over the domain {1,2,3} of (∃x¬Fx → ¬∃xFx) So I have said that the extensions of a,b,c are 1,2,3 Do I just need to find extensions ...
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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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Why can some arguments be proven only through Conditional or Indirect Proof?

For brevity, abbreviate as CP 'Conditional Proof', as DM 'Direct Method, and as IP 'Indirect Proof'. Source: p 445, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Indirect 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) ...