Questions tagged [logic]

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

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5answers
604 views

A Question Regarding Russell's Paradox

Consider the 'set' behind Russell's Paradox: R = { x | x is a set and x ∉ x } in light of Cantor's definition of set ("aggregate"/Menge) in his CONTRIBUTIONS TO ...
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3answers
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Why is the darapti syllogism invalid?

I found the following exposition of darapti on wikipedia: All squares are rectangles. (MaP) All squares are rhombuses. (MaS) ∴ Some rhombuses are rectangles. (SiP) As far as I can see, this is ...
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399 views

What logical systems categorize A->~A as a contradiction.?

In the basic propositional logic I learned in school A->~A is not a contradiction because it is not false when ~A is true. What logical systems would hold this statement to always be false?
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Are “If P then Q” and “Q only if P” equivalent?

My textbook says "If P then Q" and "Q only if P" are logically equivalent, but consider this: "If it's green, it's poisonous." "It's poisonous only if it's green." Now say there's a purple ...
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What's the word for anything is true if the antecedent is false?

(1) If A then B. (2) A is false. Then B can be anything (true or false) and (1) remains true. So B is true by __. What's the word or words in the blank?
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1answer
591 views

What is the origin of the truth table in logic?

Specifically for the material implication if possible. Who was the first to use a truth table for this and justify its validity?
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4answers
347 views

Is there any reason for the heavy focus on binary relations in formal logic?

As a fan of C. S. Peirce, I'm surprised that, at least triadic relations, aren't investigated as much as binary relations are. What I mean is that with binary relations, they have already been ...
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What is the difference between the “is” of predication and the “is” of identity?

What is the difference between these, the "is" of predication and the "is" of identity? For example, when I say, "my pet is a cat", am I using "is" as an identity or as a predicate?
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1answer
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Is Belnap's four-valued logic technically a relevance logic?

Belnap, the American Logician, constructed a four-valued logic which is a form of relavance logic; interestingly the truth-values it takes are: true false both true & false neither ...
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1answer
304 views

Why is a predicate of 0-arity considered as a sentence letter?

I often find that nullary functions are considered constants and 0-arity predicates are considered sentence letters. What is the intuition behind that notation?
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906 views

Inference rules for quantifiers in logic

I have come across an inference rule that if I had statements like: Not all are birds which translates to ~(x)Bx, is equivalent to, Some are not birds which translates to (∃x)~Bx. According to this ...
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Does epistemology = logic?

Is epistemology—the study of knowledge, how knowledge is acquired—really the same as logic? If not, what are the differences between epistemology and logic? By logic, I mean the art by which we order ...
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769 views

How could the concept of 'evidence' be defined, and how significant is it?

What is evidence, and how much of it means that a proposition is true? Does a partial / total lack of evidence mean that a proposition should be ignored? Is the concept evidence more important to ...
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If the premises of an argument CANNOT all be true, then said argument is valid

Based on the fact that a deductive argument is said to be valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false, I am ...
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290 views

References for the Realism/Anti-Realism debate in Logic

The concept of anti-realism in logic seems to be an interesting and growing idea. I'm looking for references (papers, books, authors...) regarding the debate between realism and anti-realism but ...
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531 views

What is the logic in the Tractatus-Logico Philosophicus in modern terms?

In the SEP entry on Wittgenstein, the description of the logic utilised in the Tractatus Logico-Philosophicus to describe his logical atomism appears to be at least formally classical propositional ...
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How do mathematical objects relate to the real world?

I am just going to give an example of what I mean using Skolem's Paradox. I DO NOT want to get into Skolem's Paradox itself or its "resolution." Skolem's showed that countability is relative in ...
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378 views

Step by step natural deduction: (T > E) ^ (A > L) /… (T v A) > (E v L)

I'm having trouble proving the following using natural deduction: (T > E) ^ (A > L) /... (T v A) > (E v L) I checked the answer but I didn't quite understanding the reason why the proof progressed ...
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Does Wittgensteins own solution to Russells Paradox actually work?

In the Tractatus, Wittgenstein attempts a solution of Russells paradox 3.333 A function cannot be its own argument, because the functional sign already contains the prototype of its own argument ...
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Can something be nothing?

I am confused about this question. It may have a simple answer of which I have overlooked. Can something be nothing? Because I believe nothing must be something, like a fact or idea of no thing ...
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5answers
683 views

Why is this set {CqCpq, CCpCqrCCpqCpr, CCNpNqCqp} the most common set of axioms for propositional calculus?

If you look, you can find many "equivalent", sufficient axiom sets for classical propositional calculus. The set {CqCpq, CCpCqrCCpqCpr, CCNpNqCqp} seems like the axiom set most commonly used. There ...
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How are rules of inference established as valid?

I'm curious as to how rules of inference are established. Is this an empirical act? For example if I know the premises "If I jump, then I fall" and "I jump" is it truly valid to conclude that "I fall"?...
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1answer
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Wittgenstein criticizes Coffey's work 'The Science of Logic' in its assumption that every proposition requires a subject and a predicate. Why?

Why does Wittgenstein believe there can be propositions that lack a subject or predicate? What examples does Wittgenstein give in support of this belief?
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Is “I cannot imagine a mechanism for X to happen, so X can never happen” a named logical fallacy?

I have encountered this reasoning quite frequently: Somebody posits the hypothesis that an event X can happpen. A recent example I encountered was "vinegar and salt in the boiling water make eggs ...
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What's the name of the logical fallacy where a debater extends a statement far beyond the original statement to make it true?

Suppose that someone initially states that "fossil fuel consumption due to mobile phone usage is similar to that of private transportation, so if you think we should switch to electric/bike to fight ...
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435 views

What are the dialetheist semantics for logical negation?

This question is in a sense a follow-up, or elaboration, of the question "What are the motivations for Dialetheism?". Reflecting on the way I phrased that question, and the way I remarked on answers, ...
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486 views

Is the notion in Hume that you cannot deduce an “ought” from “is” related to his assertion that reason must be the servant of the passions?

I hear it asserted that David Hume said one cannot deduce an "ought" from an "is". I also find it asserted that he said reason must be only the servant of the passions. I had long uncritically ...
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1answer
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What is the axiom of reducibility? And what philosophical controversies did it incite?

Trying to come to terms with basics concerning philosophy of logic, and wish to ask about some particular issue: What is in simple words the axiom of reducibility put forward by Russell? And what is ...
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Are there rules for dealing with self-reference “paradoxes” in logic?

My favorite paradox that leads to an endless regress, and also leads to a question: The sentence after this is true. The sentence before this is false. When contradictions appear in proofs, ...
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2answers
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Does fictional discourse pose special difficulties for logic?

Natural language is context-dependent, like the statement “My uncle is a plumber”, which is true or false depending on who asserts it. There has been lots of discussion about fictional entities and ...
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779 views

Modal Logic: a question concerning accessibility

I’m reading a lot about modal logic lately, right now Lewis “On the Plurality of Worlds” and Priests “Introduction to Non-classical Logics”. It is postulated that the different worlds have nothing to ...
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395 views

Asymmetries in two opposite arguments from ignorance

Joe claims: "There is no proof that unicorns exist, therefore unicorns do not exist". Alice claims: "There is no proof that unicorns do not exist, therefore unicorns exist". Bob claims: "There is no ...
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Is there such a thing as a 'necessary truth'?

Wikipedia (note the redirect) defines 'necessary truth' as statements which "could not be untrue", and I assume that this is how the term is usually used. A search through the SEP shows that while ...
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5answers
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Can an argument be formally valid with sound premises and still be informally fallacious?

Consider the following two assumptions: Validity Assumption: Assume an argument is valid. It follows all the formal logical rules of inference. The inference contains no formal logical fallacy. ...
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Is finding truth possible?

Consider the following argument: If want to know that something is true, I need to first know what is truth. If I need to know what is true, I need to find the truth. (Is there ...
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1answer
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The difference between argument, inference, deduction and proof?

I am trying to distinguish argument, inference, deduction and proof. First, let's look at the distinction between argument and inference (if there is one). This online source states: An argument ...
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3answers
152 views

Do limits of human nature suggest that it could be principally understood?

Human nature is limited, so is our thinking. We are limited by our bodies, and power of thoughts is limited by the number of cortical and other neurons, number and speed of their connections, which ...
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1answer
385 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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0answers
319 views

Rigid designators, equality and functions in many-valued logic and (simple) quantified modal logic [closed]

After reading "In Defense of the Simplest Quantified Modal Logic", I wonder how to add functions to the language of the simplest quantified modal logic (QML for short). The simplest model of QML has a ...
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2answers
653 views

Is Gödel's incompleteness theorem still valid if one uses a higher-order logic?

Gödel's incompleteness theorem is wholly formal (in my understanding), and relies on a proof system that I assume is first-order. Does it make any difference to the theorem if higher-order logic is ...
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8answers
327 views

Does believing in a Christian God logically imply believing in miracles?

Assume you are a Christian and you believe that the descriptions of the life of Jesus are facts. Things like turning water into wine magically, walking on water and other miracles seem to be ...
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What is a good first textbook for self-learning logic?

I would like to begin studying logic on my own. The problem: with the quantity of books available, I have no idea on how to distinguish the good ones from the bad ones. Please suggest to me some good ...
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Is it an informal fallacy to call an argument ridiculous without pointing out the flaw?

I think it is one kind of informal fallacy to dismiss a logical argument by just calling it ridiculous without actually showing how the argument is invalid. At first, I thought it to be ad hominem as ...
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1answer
415 views

Does one have to become a Platonist to refuse to be a Platonist?

I believe the answer is no, but Scott Aaronson on his blog just gave in interesting argument to the contrary. This is in connection with the now famous paper Undecidability of the Spectral Gap, and ...
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Philosophical justifications for the assumption of a non-empty domain in classical first-order logic?

Are there any "canonical" (or at least, quite good) papers that attempt to justify the supposition made in the model theory for classical first-order logic that the domain in non-empty? I know that ...
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706 views

What are the “undefinable numbers” in real analysis and philosophy?

What if any important results in real analysis make use of the notion of an "undefinable" real number? (Whatever "important" may mean to the reader.) Or is it used more in the philosophy of ...
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Is there any coherent argument in support of consciousness being an illusion?

Whenever, I hear someone like, say, Daniel Denett say conscious is an "illusion", I'm always left pretty stumped. Firstly, both the terms "consciousness" and "illusion" are generally left undefined, ...
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137 views

Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...
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Question on learning type in Plato Cave Allegory

My question is based on the Cave of Plato. In this myth I see two types of learning. The first type of learning is the person that is released from the cave and climbs up to the light. The second ...
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Is syllogism an inference rule?

I was reading Anthony Andres' article, "ARISTOTLE AND THE CONVENTIONAL LOGICIANS ON THE FOURTH FIGURE". The author explains why according to him the introduction of the fourth figure by his ...

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