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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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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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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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Are there “partially explosive” logics?

Roughly speaking, I'm wondering if it's possible to meaningfully grade different systems on how explosion-tolerant they are. In classical sentential logic and intuitionistic sentential logic, a ...
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Where can I learn about the philosophy behind mathematical and logical proofs?

I'm looking for something that dives into the philosophical idea of a "proof," and explains how the subjects of mathematics and logic deal with it. Does anyone have any book or article recommendations ...
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Is there a natural example of a non-self-referential semantic paradox in philosophy?

A commonly studied paradox is the liar's paradox. The liar's paradox is to determine whether "this statement is false". The usual resolution is to state this the sentence is not actually a statement ...
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Name of Principle Giving Precedence to a More General Hypothesis

As far as I know, there is a principle that gives precedence to a theory that is more general than a more specific one, i.e the more general one is more acceptable. What is the name of that principle?
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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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Why does Hume believe that ought brings a new relation?

If means-end reasoning, where we can say that one is ought to do X in order to get Y, does not bring a new relation, then in order to tell that ought brings a new relation, we ought to assert that ...
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On Putnam's belief that we can choose a logic system based on the task at hand

I was reading "A Graphic Guide to Logic" and a little speech bubble from Hilary Putnam says that "I still believe that there are facts in the world that determine which logic it is appropriate to use ...
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168 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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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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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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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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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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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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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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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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Alternate form of “all x are y”

It's typically correct to say something like "all cats are beautiful" as ∀x(CAT(x)->BEAUTIFUL(x)). It is incorrect to say ∀x(CAT(x) & BEAUTIFUL(x)) because you're effectively saying "everything ...
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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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159 views

The sea battle paradox and the soundness criterion

Again a short look at Aristotle's resolution (one of many) of the sea battle paradox: In one famous example about a hypothetical sea battle, [Aristotle] observes that the necessary truth of a mere ...
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82 views

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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123 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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114 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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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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108 views

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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265 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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128 views

Semantic expressiveness of modal logic

I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself: P1 ◇ ∀a, ∃x // GNB(x, a) ∧ ...
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Can the conclusion of an inductive argument be that there is only one exception to the list of evidentiary claims?

Can this be an example of an inductive argument? Premise 1: Country A rejected idea Z. Premise 2: Country B rejected idea Z. Premise 3: Country C rejected idea Z. Premise 4: Country D rejected ...
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48 views

Informally explain the proof of the diagonal lemma

I am reading this proof of the diagonal lemma and I do not understand what is happening here. Could you informally explain what is the strategy here? I would appreciate it if you went step by step. I ...
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Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
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What criteria does Frank Jackson give in order to assert the negation of a conditional?

In Frank Jackson's paper, On Assertion and Indicative Conditionals he gives a criteria for when one should assert a conditional (material conditional). This criteria is given in terms of conditional ...
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Recommendation: Second Order Logic textbook

I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...