Questions tagged [logic]

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

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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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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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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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Does it hold that everything exists necessarily?

In Quantified modal logic, "constancy’s defenders can point to certain powerful arguments in its favor. Here’s a quick sketch of one such argument. First, the following seems to be a logical truth: ...
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How does Consequentialism handle uncertainty?

E.g. Suppose you are a Consequentialist faced with a variation of the trolley car problem. Your options are to save five people with a 20% likelihood or one person with a 100% likelihood. Which option,...
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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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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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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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Is double negation always applicable to commitments?

If I commit to X, am I always committing to not ~X? In classical propositional logic, double negation always the same as not negating at all. I'm curious if this principle applies to commitments. ...
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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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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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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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Having trouble paraphrasing sentence

F: French wins gold medal G: Germans win gold medal D: Danish win gold medal I have to use truth connectives to paraphrase: They will not all win gold medals I am thinking when paraphrasing it , one ...
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What is the definition of intension?

I have read in philosophy books about intension. But no one has defined it rigorously. What does it actually mean? I asked in a previous question about identity of intension. If this question is ...
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About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
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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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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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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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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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Can a lack of knowledge or understanding invalidate a positive claim?

Consider the example of causal determinism. It can be phrased in many ways, all with identical meaning: - The idea that "every event, including human cognition and behavior, decision and action, is ...
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Question on the “Property of an Object” and the “Action of an Object” (+the “State of an Object”)

I have confronted a philosophical problem related to the definition of the "property of an object." What I believe is: The capability of an object (the capability to desire) is the property of an ...
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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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1answer
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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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Axioms for modal logics based upon counterfactuals

Suppose we have a logic for counterfactuals as with David Lewis. I here use ⇛ for the counterfactual conditional. So suppose we have: Rules: (1) If A and A→B are theorems, then B is a theorem. (2)...
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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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6answers
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How would someone go about proving every known fact about the universe?

I will tell my wife known facts about the universe, and she will then tell me “well that could be fake how do we really know”. Even after explaining all the telescopes and other tools we have to find ...
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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 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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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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Does Godel's second incompleteness theorem mean it's impossible to know whether a proven statement cannot also be disproven?

I am trying to understand Godel's Second Incompleteness Theorem which says that any formal system cannot prove itself consistent. In math, we have axiomatic systems like ZFC, which could ultimately ...
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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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LPL Predicate Logic Translations Exercise 11.20.7

I have this one question (Part 7) in exercise 11.20 that I can't seem to get the answer from. I tried ∀x∀y ((x ≠ y ∧ Larger(x,y)) → Dodec(x)) and ∀x∀y (Larger(x,y) → Dodec(x)), as well as many other ...
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Is Kurt Gödel's Incompleteness Theorem a “cheap trick”?

I found a throw-away critique of Kurt Gödel's Incompleteness Theorem in an essay about Deconstruction: The basic enterprise of contemporary literary criticism is actually quite simple. It is based on ...
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Is the sentence, 'God exists', a logical statement?

According to wikipedia a statement is either (a) a meaningful declarative sentence that is either true or false, or (b) that which a true or false declarative sentence asserts. Is the sentence God ...
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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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If-then statement and time between antecedent and consequent

Suppose the following statement. "If I kick the ball then the ball will hit the wall." Can this sentence have a truth value? I mean the time that I kick the ball, it hasn't reached the wall so the ...
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Is the material implication the correct model of conditional reasoning in mathematics?

Question: Do you believe that the material implication correctly models the kind of conditional reasoning necessary in mathematics to prove a theorem? Example: If x > y and y > 0, then x > ...
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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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Could the axiom of infinity be in itself inconsistent?

I've seen several threads discussing the axiom of infinity but I wasn't able to find a discussion on this particular aspect. And recent conversations with some people have led me to wonder if it is ...
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What are some benefits of a second order logic?

I have read that a second-order logic can help one define equality by quantifying over all predicates such as what is done in the following definition: (x=y):⟺[∀P:P(x)⟺P(y)] By contrast a first-...
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Is having “skin in the game” always beneficial in “thought and action” as Taleb seems to think?

I was skimming through the tweets about Taleb when I saw one from one of his former [friends][1] which was about Taleb's "skin of the game" saying that it is neither necessary nor sufficient ...
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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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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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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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Deductive reasoning & conditionals

What would be a good example of explicit deductive reasoning that doesn't seem to be possibly interpreted correctly as a conditional (If A, then B)?
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Lists and predicates on lists in classical first order logic

I have to express some basic Prolog code in classical first order logic (FOL). In Prolog i use lists, together with member/2 and append/3 a lot. Could you give me some tips for writing clauses like ...
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How does abduction differ from inductive reasoning?

Consider this statement: Abductive reasoning typically begins with an incomplete set of observations and proceeds to the likeliest possible explanation for the set. But couldn't the same ...
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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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