Questions tagged [logic]

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

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38 views

Is there such a thing as ωth-order infinitary logic?

I've seen references to ωth-order logic sprinkled (sparsely) throughout my studies, though what properties this has compared to and contrasted with nth-order logics I wouldn't be able to tell you (I'm ...
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Is this a reasonable argument? Dr. Fauci on Face Masks

In a recent interview, Dr. Anthony Fauci (Chief Medical Advisor to the President of the U.S.) was asked why he advised the public against wearing masks in early 2020. One of Dr. Fauci's arguments was ...
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3answers
125 views

How to model “forget about” in first order logic?

The other day, my housemate said "Don't forget to not leave the spoon at the bottom of the container". I understood what he meant: "Do not leave the spoon at the bottom of the ...
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The relationship between Rationalism and logic

Here is an excerpt from the book An Introduction to Philosophy by Russ W. Payne (2015) which is causing me some confusion. Mathematics had long served as the rationalist’s paradigm case of knowledge ...
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11answers
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Is Yoda committing a fallacy?

I've been debating with a hard core Star Wars friend who loves repeating Yoda's "Do or do not, there is no try" knowledge. I tried to explain that the DO (B) and DO NOT (C), are end results, ...
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778 views

Why fallacy of amphiboly exists in this sentence?

I am reading Essentials of Logic, 2e by Irving M. Copi. And I do not understand this exercise from page 87. Identify the fallacy of ambiguity that best characterizes each passage. ... Being ...
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32 views

Summary of philosophical positions on how belief revision proceeds in mathematics?

Since mathematicians have embraced classical logic, as e.g. MacFarlane points out in his 2021 intro book to philosophical logic (§ 7.4), one needs to distinguish between [meta-]reasoning and argument/...
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2answers
67 views

Question about Kenny’s critiques on Mill’s logic

Recently, I have read a book called New History of Western Philosophy by Anthony Kenny. In this book, he starts chapter 4 Logic with a section called Mill’s Empiricist Logic, which contains an ...
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logical truth and additional sentences [closed]

If an atomic sentence A is a logical truth(for example, a = a), can we determine whether any additional sentences are logically necessary based on this information? And if A is a logically false ...
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How to prove ∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy) using natural deduction? [closed]

∀x∃y(Fx→Gy) ⊢ ∃y∀x(Fx→Gy) I tried to use reductio ad absurdum by assuming ¬∃y∀x(Fx→Gy) and then using quantifier negation to simplify it further, but it got very messy when I had to use ∃-elimination ...
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I'm having trouble constructing a truth trees for these questions? Could someone do a step-by-step answer for this? [closed]

Construct truth-trees for the following sets of sentences. For each, note whether the tree you construct has a completed open branch or is closed. 
 (a){(∀y)(F y ⊃ Gy), ∼(∀y)∼F y, (∀x)∼Gx} (10 marks) (...
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What is the name of this fallacy (if it is indeed a fallacy)?

What is the name of this fallacy (if it is indeed a fallacy): Drinking alcohol makes me laugh Laughing is good for me Therefore drinking alcohol is good for me Assuming the premises are true then ...
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Combining the knower with other paradoxes

The knower paradox concerns a sentence such as, "This sentence is unknown." Now liar sentences can be paired with honest sentences, e.g. "This sentence is true." So suppose there ...
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Proving using natural deduction ~(AvB) v (~A&B) with premise ~A [closed]

Been stuck at this for a little... I tried proof by contradiction but got literally stuck at the first step... So hypotheses is ~A and to derive is: ~(AvB) v (~A&B). Would appreciate any help.
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How can one formalize that an argument composed of a true and a false statement is “partly true”?

In classical logic if either A or B is false then "A and B" is false. But in natural language it's often the case to hear someone say "that's only partially true" or "that's ...
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Making inferences from a counterfactual conditional statement about consistency

Please take a look at a passage from an LSAT: The economy is doing badly. First, the real estate slump has been with us for some time. Second, car sales are at their lowest in years. Of course, had ...
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Question about proving a set that is quantificationally inconsistent in PD+ (Finished the proof but want it to be checked)

Does ∃x(Nx & ~Nx) contradiction itself? Is there an error in my proof? Thank you
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Prove (-A=-A) = [-(-A => A) = (A=>-A)]

This is not homework I do this for fun. I tried using prover. The result is quite confusing. I use the Logic Book This is the last problem I want to do in this section. I have to it mostly in SD+ . |- ...
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2answers
58 views

Fitch Proof help please

I think I got it, could you take a look, please.
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1answer
55 views

Is there a weaker/general version of Incompleteness Theorem which holds for every formal axiomatic system?

Is there a general version of Godel's Incompleteness Theorem which holds for any formal axiomatic system (and not just those capable of modelling basic arithmetic)? If no, is it absurd to ask why such ...
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75 views

Questions About Complete Truth Tables

Why do you need a complete truth table to prove that a sentence is a tautology when you can just make a partial truth table starting with labeling the sentence as false and if it's impossible, the ...
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Analysis of Liar-like sentences in fuzzy logic

Let t0 = FALSE and t1 = TRUE. In fuzzy logic, 0 or 1 can be switched out for any real number in the interval [0,1]. This lets us construct all manner of liar/honest-like sentences, ranging from, "...
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4answers
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I don't see the problem caused by the following entailment

From Forall X (p.74): (3) ‘It’s not the case that, if God exists, She answers malevolent prayers.’ Symbolizing this in TFL, we would offer something like ‘¬(G → M )’. Now, ‘¬(G → M )’ entails ‘G’ (...
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What is the most basic reasoning that creates all kinds of reasoning?

Hypothetico-deductive method, abductive reasoning, induction, deduction, reduction to absurdity, dialectic.... There's reasoning in mathematics, too. What is the fundamental reasoning that creates all ...
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264 views

What makes an argument objectively more “compelling”?

If person A gives an argument to person B in order to convince them about the truth of claim X, how can B determine how compelling A's argument is in a way that is as objective as possible (i.e. in a ...
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Can 'All S is P' ever be false if S is empty?

I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"? In the boolean interpretation 'All S ...
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Help with Fitch formal proof?

I'm having trouble solving this formal proof in Fitch. I've put together most of it, but I think I need to use disjunction elim(?) at some point and am having trouble doing that.
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1answer
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Show the following is valid in SD+: How to solve this derivation

This is not Homework.l do this for fun and expand my learning. I am obviously having difficulties with SD+,thus l post many problems. I am using the Logic Book Problem has be done in SD+ Using goal ...
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2answers
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Non catastrophic presupposition failure

In a previous question, I asked something similar but without explicitely referring to the source material of my doubt. Now I try to state it here with more precision: In "Non-catastrophic ...
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3answers
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Is rational to logical as rectangle is to square?

That is, if X is logical, is it necessarily rational? What's an example of something that is rational, but not logical. If logical does not necessarily imply rational, what's an example of something ...
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Is the concept of a “model” in logic grounded?

The concept of a "model" in logic has always seemed a little suspicious to me - as it implies statements that are not deducible from the axioms, yet are true anyway. What could "true&...
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Some minimal insightful example for the distinction between internal vs external logic of a Gentzen system?

I've read the following: Definition (Internal logic) An argument from premises to conclusions is valid in the internal logic of a sequent system iff the sequent G ⇒ D is derivable in that system. ...
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I need help with with to do this derivation

This is not homework I do this fun and to expand my knowledge. I am using the Logic Book I am having trouble obviously doing SD+ derivations as I post several of them. I have to show this derivation ...
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How do I symbolise this statement with a definite description in first order logic?

"If there is exactly one present King of France, then the present King of France is a present King of France" The part I am confused about is the consequent of the conditional which equals ...
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Although only half of a dish is red, can I call it ‘red dish’?

Although only half of a dish is red, can I call it ‘red dish’? Or only when an entire dish is red, can I call it ‘red dish’?
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Need help to show the following is valid in SD+

I have to rely only on SD+ rules I use the Logic Book. Show that the following is valid in SD+ Derive Y=Z 1.~Y-> ~Z. Assume 2.~Z->~X. Assume 3~X->~Y. Assume I got Z->Y but am stumped on ...
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Has there been any philosophical interpretation (or application) of Stone lattices?

Stone lattices/algebras are Heyting (i.e. intuitionistic) lattices in which both laws of De Morgan hold, or equivalently, Heyting lattices in which also ~p \/ ~~p = 1. While these have been studied a ...
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I am stuck on SD+ style proof and need to know how to do it

I am using SD+. Most of the derivation has to be done using it I am finding this one tricky I request help or hints to solve it Derive L => H 1.~L v (~Z v ~U). Assume 2.(U & G) v H Assume 3.Z. ...
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Name for the concept where gluts are not (necessarily) a filter? (Or do gluts have to be a filter?)

In the following proof (which you'll excuse me, I hope, for giving only as slides/images), it is shown that (the relevance logic) R enriched with (A->B)\/(B->A) --enrichment which the authors ...
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Is there a “for dummies” construction of the valuation model of the relevance logic R from a De Morgan monoid?

I am confused how one gets the anti-chain preserving negation in Belnap-Dunn's FOUR, which by all accounts underlies their R (which adds implication), when R's valuation model is constructed from a De ...
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91 views

Is it there a “completely expressive” formal system / logic language?

I wonder whether it exists a formal system such that all (or a considerable number of) the others can be considered as a subsets or fragments of it. I would say that, for instance, First-Order logic ...
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If I am unsure about the existence of morality, Am I morally obligated to find out the answer?

Since we do not know if morality has an independent existence, are we morally obligated to know if it exists?
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If A is true then B must also be true

What if in the statement, "If A is true then B must also be true," A & B are related but, "B must also be true," is not necessarily true because other possibilities exist? In ...
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Need to check to if my SL is correct for following problem

This is not homework . l do this for fun. I am 58. I graduated Concordia University in 1993 Problem comes from the Logic Book by Bergman pg 217 (17)c I want to see if my SL is correct. If civil ...
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Confidence margin for logical verification

I'm starting to read Wittgenstein and I keep circling around a problem, which I'll lay out with the following ideas: a. Logical space is the totality of external reality. b. A proposition is logical ...
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67 views

Could someone please write this argument's form

"No rock is sentient. Some mammals are sentient. Hence, no mammal is a rock." I wrote a form and it's apparently wrong, but I don't get how.
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How do you reduce repeated modality in S5?

Kenneth Konyndyk's Introductory Modal Logic claims (p. 55) that all formulas in S5 with a modal degree greater than 1 can be reduced to degree 1. By degree, he means the maximum number of modal ...
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I need help to Derive F & G

Derive F & G F=G. Assump. F v G. Assump. ? G. F & G. & I 1-? Should l use disjunction elimination or biconditional elim. next? I am flubbered Help
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138 views

Formal logic - a priori or a posteriori

I am aware of the classical classification of logical calculus as apriori. I have also read pretty much anything I could get my hands on regarding "logic", including "New Essays on the ...
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4answers
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What's the logical basis for Dunne suggesting that there need to be several dimensions of time in order to measure the speed of one's progress?

As a solution to the problem of the subjective passage of time, J. W. Dunne proposed an infinite hierarchy of time dimensions, inhabited by a similar hierarchy of levels of consciousness. Dunne ...

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