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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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Fitch Biconditional Proof Help?

Hi, I'm starting to learn formal proofs using Fitch, but I'm having a bit of trouble figuring out my arguments. I've generally mapped out the subproofs I was considering to use, but I'm unsure how to ...
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1answer
158 views

Does following logic necessarily require one to conclude that they are objective and have no bias?

In social psychology, naïve realism is the human tendency to believe that we see the world around us objectively, and that people who disagree with us must be uninformed, irrational, or biased. It is ...
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Is there a concept that relates to the idea of a “snuck premise”?

In this video around 6:00 into it, Charisma on Command channel, "7 Reasons Ben Shapiro Is So Dominant in Debates" https://www.youtube.com/watch?v=JY5t6iUzajk the concept of a "snuck premise" is ...
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Can something proved by contradiction always be proved without a proof by contradiction?

Proof by contradictions work by assuming that something is true, and then using logic (along with other assumptions which you know are true) to show that that leads to a contradiction, thus proving ...
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557 views

How to prove : (( P → Q ) ∨ ( Q → R )) by natural deduction

Here's another of Tomassi's exercises I can't solve (Logic, page 106): : (( P → Q ) ∨ ( Q → R )) I have to use natural deduction and the only rules I know are: • assumptions, • modus ponendo ...
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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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102 views

Do mathematicians use logic when adding things up?

I asked a similar question recently, and it was closed. So, bear with me. When two things are materially equivalent we don't add anything to work out how much we have of both together, right? If ...
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1answer
63 views

How to solve the derivation?

Derive the following without assumptions: ¬∃xFx↔∀x¬Fx How do I solve this derivation?
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Is there a summary of Russell’s Principia Mathematica?

Perhaps better, is there an accessible version of the Principia? I am looking for a summary that would summarize and clarify Russell’s reasoning behind his famous conclusion that 1 + 1 = 2.
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1answer
66 views

Is this an Affirming the Consequent fallacy?

If a Company doctor is competent, then he or she has completed the Company's "Fitness-for-Duty Examiner" certification training. [If P then Q] Company doctors are all Certified Fitness-for-Duty ...
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1answer
62 views

Is logic a consequence of structure of language i.e. syntax?

I was reading the paper An elucidatory reading of the Tractatus and in page-3 section- Ineffabilist Readings, it was written "The order in our propositions, which renders them capable of thus ...
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Are there “partially explosive” logics?

Roughly speaking, I'm wondering if it's possible to meaningfully grade different systems on how explosion-tolerant they are. In classical sentential logic and intuitionistic sentential logic, a ...
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How do you prove law of excluded middle using tertium non datur?

I’m in my second year of an undergraduate philosophy degree. Last year we did classical logic (TFL and FOL truth tables and fitch style natural deductions). This year, one of the topics we are ...
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66 views

Can “free will is an illusion” be proven logically? [closed]

What is your view or argument?
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1answer
176 views

What is the subject of Tractatus by Wittgenstein?

Is Tractatus about the Philosophy of language or Philosophy of logic. I was hearing John Searle's lecture and he said there are two strands in Philosophy of language :- 1. Logical theory of language 2....
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Completeness/Soundess of Second Order Logic

I recently read that Gödel's incompleteness theorem entails that second order logic cannot simultaneously hold the traits of: (i) completeness, (ii) soundness, and (iii) effectiveness. However, I saw ...
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What criteria does Frank Jackson give in order to assert the negation of a conditional?

In Frank Jackson's paper, On Assertion and Indicative Conditionals he gives a criteria for when one should assert a conditional (material conditional). This criteria is given in terms of conditional ...
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2answers
176 views

Can we define this set?

Given an infinite set S in some universe U, construct the set of complementary pairs C: {{A,Ac}} where A,Ac∈P(U), the power set of U, and A or Ac is contained in S, not necessarily a proper subset ...
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136 views

What is compactness?

The proof, formal definition and academic explanations are easy to find but hard to understand. Can you please explain it in ordinary language with clear examples? See the following references: ...
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108 views

How does one prove ‘(B→C)→¬A’ from ‘(A→B)∨C’ and ‘(A→¬C)’ in Fitch?

I am trying to work my way through this Fitch proof, and I am not sure what I am doing wrong, but I keep getting stuck no matter what I try. First attempt: Second attempt:
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289 views

Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Tegmark's mathematical multiverse hypothesis assumes that all mathematical structures exist as universes But do you know whether his hypothesis also allows/accept universes described by other types ...
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1answer
101 views

How are the assumptions underlying logic chosen?

Logic works based on certain assumptions about its rules. How are these axiomatic assumptions selected in the first place, given that a system of logic does not exist prior to the point of selection? ...
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Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
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1answer
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Is complete isolation possible?

Imagine an ideal box, whose contents are perfectly isolated. Whatever is inside it, it has not, has had or will have any relations with the rest of the universe. We could say that its content does not ...
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How do the premises support the conclusion in this argument?

The argument below is from the book "A concise introduction to logic". The condition under which many food animals are raised are unhealthy for humans. To keep these animals alive, large quantities ...
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1answer
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Logic vs Deity: does one supersede the other? [closed]

Note: This isn't a question asking for an explanation, that would be a debate, more one asking for clarification. I don't want this turning into a debate about the existence of deities. Whenever ...
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257 views

How to get proof using proof editor and checker

How can I use http://proofs.openlogicproject.org/ or http://logic.tamu.edu/daemon.html to derive the given conclusion from the given premise: (∃x) ( Fx ∙ (y) (Fy → y = x) ) / (∃x) (y) (Fy ≡ y =...
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Is this argument valid?

Is this argument valid? No one under 18 is permitted to vote. No faculty member is under 18. The philosophy chairperson is a faculty member. Conclusion: The philosophy ...
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1answer
154 views

Universe as a container; Critique of the Kalam Cosmological Argument?

I was introduced to the Kalam Cosmological Argumant the other day (I know, late to the party), and it struck me that there seems to be a rather simple critique that I couldn't find an accounting of. ...
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1answer
355 views

Can possible-but-non-actual objects have accidental properties?

The modal logic I am considering is the "Simplest Quantified Modal Logic" which combines first-order predicate logic with identity, with S5 in the most straightforward way, described here and slightly ...
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256 views

A question on logical positivism and pragmatism with regards to meaning of a statement

‘Despite all its weaknesses, democracy is still the best form of government compared with all other forms of government that have been tried in human history.’ Which of the following is False ...
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170 views

How does one go about proving (A&B)⊃C |- A⊃(B⊃C)?

I am relatively new to logic and deductive reasoning, so this problem has been giving me some trouble. I want to start with an assumption of (A&B) and try to isolate a subproof where I can then ...
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2answers
158 views

How do you prove B v A |- A v B?

I am having trouble with how to use the assumption, which I feel that I will need for this proof. If any one can demonstrate or give hints for this proof, I would greatly appreciate it.
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Does rejecting the law of the excluded middle mean rejecting it for all propositions or only for those one cannot derive?

Wikipedia describes the law of the excluded middle as such: In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is ...
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Logic related to Cantor's argument [closed]

Suppose we construct a choice function that separates R/{0} in the interval (0,1) (viewed in base 2) into two sets A and B each consisting of an arbitrary element chosen from every pair of complements....
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1answer
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How to translate classical logic to basic Kripkean logic?

I'm trying to semantically prove the following argument (sorry about the formatting - I'm new to stackexchange): if P ⊨c Q then ⊨k 򪪪(P → Q) However, I don't know how to translate or relate the ...
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85 views

McGee's Counterexample to Modus Ponens

I'd like to start off by saying that I have read the other posts in the Math StackExchange and here about this paper, but I think my question is a bit different from those although it does stem from ...
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3answers
188 views

if only one thing exists, nothing exists?

If one thing does not differ from any other, it has no identity (it has no properties, features, limits...). If something has no identity, it's not a thing. So only one thing can't exist. i.e.: I ...
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111 views

Are analogies logical arguments?

I have heard several analogies that attempt to give people a better understanding of the Christian trinity. Some compare it to H2O and how water can be solid, liquid, or gas. However, this is a form ...
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How to derive (∃x)(y)(Ax ⊃ By) from (x)Ax ⊃ (y)By?

Upon multiple attempts, I keep arriving at the same conclusion, but I believe this is not right. How shall one proceed with this one? I've exhausted the resources I have at my reach.
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Can we ask an infinite amount of questions or is there a limit to how many questions we can ask? [closed]

I've been thinking about the nature of questions and answers to questions. Can I ask people opinions on whether they think it is possible to ask an infinite amount of questions or do we as human ...
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Is there any worth—other than historical—to reading Aristotle's works on logic?

What I mean is that presumably a topic such as logic would have, at this point, been so advanced that the ancestral works are unnecessary. I would read it for pleasure, but have they been ultimately ...
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What's a Good Introduction/Summary to Probabilistic Logic?

I hadn't even heard of Probabilistic Logic before today. My world view was already leaning in this direction as I never really put much stock in either the law of the excluded middle or the principal ...
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1answer
52 views

What does predicative mean?

I'm reading this page https://plato.stanford.edu/entries/type-theory/ where the words predicative and impredicative are used in this context: Notice that for defining the predicate R, we have ...
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4answers
117 views

How to denote physical (not logical) impossibility in modal logic?

Say I want to note that in this world, it's physically impossible to jump over the Eiffel Tower. I can just write ¬◇x, but this seems to say that in all possible worlds x is impossible, and I want to ...
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126 views

Can a reason cost 5 dollars?

Imagine a school where no one can wear a red hat. John goes to school with a red hat costing 5 dollars. Someone says John's red hat "is" the reason why he can't get into the school. What is the ...
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‘The claim that I had an affair with Miss A and that I didn’t father her child is false’

The prosecutor asks, ‘Did you father the child of the murdered victim Miss A?’. Mr. N replies, ‘The claim that I had an affair with Miss A and that I didn’t father her child is false’. In response ...
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Is there a rigorous definition of ‘everything’?

Is there a rigorous definition for this concept? ‘The collection of every individual thing’? If an ‘individual thing’ is something that is different from something else, ‘everything’ could be the ...
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Why do we think objects and beings are real? [closed]

How can we tell if we are real and not a simulation that we perceive to be real. Given we know not what the universe is except what we perceive it to be. What if galaxies are just but other ...
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Why do humans make infants? [closed]

Considering that humans are the most intelligent species on earth, why do humans make infants? I cannot understand the reason why humans make infants, when humans can't predict whether the ...