Questions tagged [logic]

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

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Structure of “affirming the consequent fallacy”

The formal structure of affirming the consequent fallacy is, P1 - If A is true, then B is true P2 - B is true --------------------------------- C - Therefore, A is true Now if I transform like that, (...
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33 views

Does a proposition have to have a true conclusion?

“...understand that a belief is propositional, which means it can be expressed in a declarative sentence—a sentence that is either true or false...Recall that in logic, a proposition has been ...
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What the Preface paradox tells us about the principle of explosion

The Preface paradox (adopted on a classical logician): Imagine that a classical logician has just written a textbook (on classical logic). He has included many assertions in it and has thoroughly ...
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Can I lie saying an affirmation onto something that doesn't exists

If someone asks me where I live, and I give an addres I know doesn't exists, for example, "Sunset Boulevard 1600", being the address number 1600 inexistent, ¿Am I lying? If I am lying, then ...
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4answers
87 views

Let P does not imply Q, and Q does not imply P. Are P and Q independent?

Let P does not imply Q, and Q does not imply P (P → Q and Q → P are both false). Would it correct that P and Q are independent? Is it possible to have R that can imply both P and Q?
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Ontology - How do we describe actions/scenarios in relation to objects?

Does anyone know how actions to do with objects are represented in ontology or first order logic? Example: the cat sits on the mat. I think the cat and mat have properties that relate them to each ...
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2answers
77 views

Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?

Is there a difference between rejection of a belief, and withholding judgement? Does rejection of a belief B, mean ¬B or does it mean a lack of B?
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121 views

Generating the simplest sort of Cosmological Argument

First, I am not a philosopher, but rather an applied mathematician. However, the Cosmological Argument has always intrigued me. At times I feel that all attempts are necessarily hopeless, at other ...
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175 views

How do we arrive at stronger theories in mathematics/logic?

A reasonable aim of formal mathematics/logic is to build systems which can "interpret" many things. As an example, ZFC can interpret a number of things. Incompleteness Theorems provide us ...
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2answers
83 views

Can a logical statement be meaningless?

Can a logical statement be meaningless? If a statement is logical, then it can be proven mathematically, but if logical statements can be meaningless still doesn't that prove that mathematical proofs ...
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Why is the use of the ND rule ∃E not correct in this proof?

Is there anyone who could explain to me why these errors occur? It seems to me the rule was used properly.
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Does the definition of “mutually exclusive” include the case where neither A nor B happen?

Does the definition of "mutually exclusive" include the case where neither A nor B happen? I ask this because I remember in logic, "xor" has to be A or B and doesn't include the ...
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Why are variables logical symbols, but predicates non-logical symbols in predicate logic?

I was reading this wikipedia page on first order logic: https://en.wikipedia.org/wiki/First-order_logic And it says variables are logical symbols and predicate symbols are non-logical. It also says ...
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1answer
75 views

Is the statement “no form of human knowledge can justify metaphysical absolutes” self defeating?

A common objection to the statement "no form of human knowledge can justify metaphysical absolutes" is that the statement itself is a metaphysical claim. One response is that the statement ...
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Putnam and Skolem Paradox

Why, according to Putnam in "Models and Reality", is moderate realism more affected by the so-called Löwenheim-Skolem Paradox than extreme realism? I understand the gist of Putnam's grip ...
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How is logical form semantic?

According to Wikipedia: In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system How can something be a semantic version of another thing? ...
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Justification logic and set theory

I was reading the SEP article on justification logic and the question arose for me, whether the difference between intrinsic and extrinsic justifications of set-theoretic axioms (a difference that has ...
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1answer
81 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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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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191 views

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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4answers
792 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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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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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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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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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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1answer
59 views

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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1answer
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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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174 views

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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1answer
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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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1answer
47 views

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
63 views

Fitch Proof help please

I think I got it, could you take a look, please.
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1answer
59 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
90 views

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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3answers
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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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271 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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2answers
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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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1answer
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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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174 views

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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1answer
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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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2answers
36 views

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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1answer
60 views

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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