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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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Self determination in non atomistic time?

I am reading the book " perspective in whiteheads metaphysics" by Stephen David Ross. On page 182 he says" whiteheads theory of events is atomistic-primarily to allow for self determination, but the ...
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Hume's argument for the subjectivity of morality

I am trying to analyze the following argument by Hume in his Treatise of Human Nature: But can there be any difficulty in proving, that vice and virtue are not matters of fact, whose existence we ...
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How do disjunctive antecedents work in Marc Lange's stability concept of laws of nature?

I'm an ecology student who's dabbling into philosophy of science. I'm currently writing a term paper on laws of nature (with a focus on ecology as a special science) and try to wrap my mind around ...
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Given the principle of innocence, how shall we explain logic's usefulness?

I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60: ...two fundamental assumptions (the other one being the principle ...
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What argument styles have only recently been labelled fallacies?

While reading Douglas Walton's "Historical Origins of Argumentum ad Consequentiam", I realized there is at least one argument style that appears reasonable but which has been labelled as a logical ...
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Do α and β entail each other?

Show whether the following is true or false: α |= β or β |= α, for any two formulas α and β I'm assuming here that α and β are formulas, not a set of formulas. My thought is that I can prove that ...
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What are the consequences of rejecting identity of indiscernibles

What kind of system are we in if we explicitly take its negation as an axiom? Here's the identity of indiscernibles. (1) ( ∀P.P(x)↔P(y) ) → x = y Here it is written in prenex normal form (2) ∀x∀y.∃...
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Are there degrees of rationality/plausibility to assumptions?

There are many kinds of premises, in every possible field. I'll limit this question to metaphysics, although it can definitely be applied to each and every scientific/philosophical study. For example,...
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170 views

Connections between concepts

How can it be possible that two concepts have a connection between them? Even when we admit that every such connection is empirical, we have a necessary connection between the concept "connection" and ...
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168 views

Why isn't humanistic logic taught in schools any more?

Specifically, I'm curious about the loci or categories that Agricola and later Ramus used extensively. Were they found to be problematic at a later time? If not, why not use them? They're so helpful ...
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Is a Thomist possible modal proposition a non-judicative proposition?

According to Thomist philosophy and logic, is a possible modal proposition (either divisive or compound) a non-judicative proposition? It would seem to me that the other three modal propositions (...
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What are some of the best books for a robust introduction to Logic and Critical Thinking?

As the question states: What are some of the best books for a robust introduction to Logic and Critical Thinking? My background: I'm 24, graduating with two degrees in Political Science and ...
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What questions or areas in the foundations of mathematics remain active research fields?

By foundations of mathematics I am referring to the mathematical, logical, and philosophical foundations of the subject. I'm interested in seeing which of these have active research going on within ...
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which problem Russell is focusing on while providing a solution, in his introduction to the Tractatus?

In the final part of his introduction to the Tractatus Logico-philosophicus, Russell provides a possible solution to the problem of the impossibility of self-reference of logic: There is one ...
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are Wittgensteins propositions analytic or synthetic?

Wittgenstein provides a logical analysis of propositions in the Tractatus; does he there admit the Kantian distinctions between analytic/synthetic and a priori/a postereroi divisions; or does his ...
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Please what do we call this type of hypothetical statement?:

"It is certain you have a nose when you can smell but not everyone with a nose can smell". Or "It is certain you have a brain when you can think. But not everyone with a brain can think" Note: As I ...
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Prove that if the tree method determines that a set of sentences T implies a sentence A, then T does in fact imply A

Having trouble wrapping my head around how to prove this. My first question about this is what it means for the tree method to determine that the set of sentences implies A. I'm taking it to mean that ...
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Why don't two equivalent propositions contribute to the same semantics?

We often have 2 propositions that have the same truth table, in that they are true and false given the same conditions. Nevertheless, we still feel as though there different semantics (i.e meaning..),...
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Grice: Comparing Natural Meaning, Non-Natural Meaning, Conventional Implicature and Generalized Conversational Implicature

I am currently reading "Meaning" and "Logic and Conversation" by Paul Grice. I find it a little difficult to differentiate clearly between his concepts "natural meaning", "non-natural meaning", "...
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201 views

Does Reflective Set Theory “RfST” fulfill the requirements of founding Category Theory and Mathematics?

On mathoverflow I've posed the question in the title in connection to Muller's 2001 criteria for a founding theory of mathematics, which largely raised in connection to Category theory [see here]. ...
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Why can't existence be expressed in linear temporal logic?

In some circumstances, existence cannot be expressed in linear temporal logic. I don't understand why it can't be constructed with negations and global quantifiers. For example, the wikipedia page (...
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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 such a thing as unary logic?

Is there such a thing as unary (as opposed to binary, ternary, …, n-ary) logic? cf. Is there any reason for the heavy focus on binary relations in formal logic?
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Is there a connection between argument diagramming and formal logic systems such as propositional/ predicate logic?

Early in most logic textbooks you find what I see as a very useful tool for understanding arguments called "argument diagramming." This is where you find the premises and conclusions, give them ...
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journal for mathematics of philosophy/mythology

I have been working on research involving the use of mathematical formulas and reasoning in order to philosophical concepts, specifically concepts concerning mythology, the Jungian model of the psyche,...
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What does this formal sentence mean for the given interpretation?

screenshot of question If the domain is the natural numbers and R(x,y) is interpreted as ("x is the square of y"), I would interpret ∀X∃yR(y,x) as meaning "the square of any natural number is a ...
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216 views

How can I explain the distribution of an O proposition's predicate?

A student raised a tough question while I was teaching formal fallacies: couldn't the statement that "some cats are not tabbies" be made with confidence upon seeing a single cat that is not a tabby? ...
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Some questions on Graham Priest's remarks about Russell's solution of paradoxes

In his book Beyond the Limits of Thought while talking about Russell's solution of paradoxes Graham Priest writes (text made bold, footnotes and references omitted), Russell solved these problems ...
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How to define identity of intension?

In philosophy, there is much mention of the intension/extension distinction. Two properties can be extensionally equal but not intensionally equal. It is very easy to define when two properties are ...
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127 views

How do you have to rate the probability of an existential claim?

If the prior probability of every universal hypothesis is zero how would you have to rate the probability of the statement that unicorns (at least one) exist? Probability of an event = number of ...
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151 views

Why is Psychologism invalid according to Husserl?

I am having a difficult time understanding the critique of psychologism. From Dan Zahavi's book Husserl's Phenomonology: Logic (as well as, for instance, mathematics and formal ontology) is not ...
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What is the difference between Herbrand Logic and Relational Logic or Predicate Logic?

I am learning a course from Stanford University, and it introduces the notion of Herbrand Logic. However in Wikipedia I cannot find a definition specifically for "Herbrand Logic", only for Herbrand ...
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Boolean equation Indexing exercise

By the method of indexing, prove the following Boolean equation to be valid: (A ∪ B)′ ∩ C = (C ∩ A′) ∪ (C ∩ B′) What I tried to do - but somehow it doesn't go right, where did I made a mistake, ...
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Formalize “Buffalo buffalo buffalo buffalo buffalo”

Source: p 145. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. "Buffalo" sentences (pp. 73, 101, and 139) can be formalized if we establish two conventions. ...
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Can the material conditional be used in other situations?

Can the material conditional in classical logic (e.g. propositional logic or predicate logic like first-order logic) be used to reason about propositions that are not factual? E.g., using a ...
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Nominalist views and contradictions

Given a flavor of nominalism which denies that simple sentences and existential quantifiers referring to mathematical objects are literally true (pretense theory, fictionalism, figuralism, etc.), ...
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Where can I find logical fallacies in action?

I'm looking for a website that gives logical fallacies in action. Not a video that explains logical fallacies, but a video, say a debate between two people where one of the debators uses a logical ...
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What are some alternatives to Mill's induction methods?

I have been taught that Mill's methods for identification of causes (agreement, difference, etc.) only apply when we can define our universe of possible causes very strictly (i.e., when we know all ...
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Does Every Logic Have the Potential for Violent Measurement?

Measurement, in the broad sense, involves useful abstractions and logical applicability that allow us to survey environmental data with extreme precision and prediction. The tools or instruments used ...
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Can Kant's antinomies be translated into formal logic?

Kant proves the limits of human reason by providing 4 antinomies, pairs of rational but contradictory statements, which he claims pure reason can never help us decide which one of the pair is correct. ...
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Infinitary logic and algebra

After identification of equivalent formulas, is the algebra of formulas of a two-valued propositional calculus with infinitely long expressions a (free) sigma-complete Boolean algebra?
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Does anyone know of any essays on Adam's Thesis and Deontic Conditionals?

I'm curious if anyone knows of any essays which concerns how deontic conditionals fit with Adam's Thesis. (Adam's Thesis is the idea that the probability of an indicative conditional A > C is equal ...
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Testing the validity of syllogism argument

I came across a validation method for testing the validity of a syllogistic argument which seems quite easier to grasp: For example: To test the argument: no P is B some C is B Therefore, some ...
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278 views

Are numbers universal in Set Theory and nominalist in Category Theory?

The number 3, when considered as a universal, abstracts the property of 3'ness from all groups of 3 objects. One supposes that this universal, by conceptual neccessity of what is understood by the ...
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What is a good history of logic book that covers all logic?

Including inductive, formal and mathematical. I find them separated a lot and I don't know if I have the ability to sit through all the Handbook of the History of Logic series.
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Is it there any trivialist model in physics (like in quantum mechanics)?

Trivialism is a system that proposes that literally every proposition is true and false at the same time blatantly breaking the principle of no contradiction and triggering the principle of explosion (...
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Can hypercomputation compute the impossible?

There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
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Logic-related note-taking question

I have been thinking about note taking from a logical perspective recently. It started when I realized that note-taking is basically a process of extracting "statements" or "arguments" from a piece of ...
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Why is a square circle metaphysically impossible?

We have definitions for both a square and a circle. By definition, I understand that it's impossible to have a square circle. However, why does the word 'square' have to necessarily mean 'a plane ...
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If logical propositions aren't tautologies (a la Wittgenstein), then what could they be?

This is a historical question about philosophical views. I believe I understand the claim made by Wittgenstein and others that logical propositions are tautologies. I'd like to know what other views ...