Questions tagged [logic]

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

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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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268 views

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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48 views

De Re, Counterfactuals, and rigidity

This is going to come off as vague or obscure; but, I hope the idea is performatively expressed: Two questions: Do you think that Kripke would argue that the impossibility of de re counterfactuals ...
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48 views

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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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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171 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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324 views

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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70 views

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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120 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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ELI5 - Abduction vs. Inference to Best Explanation (IBE)

How can you explain to a 5 y.o. how abductive reasoning differs from IBE? I don't understand even though I read SPE and these papers: Campos, Daniel G. On the Distinction between Peirce’s Abduction ...
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Can a Rigid Designator still exist if there is only one possible world?

According to Kripke, a rigid designator is a pronoun (but not all pronouns are rigid designators) and they pick out the same unique individual in each possible world. I understand this, however, if ...
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57 views

Language confusion; necessary/nomological/true in all worlds

I got confused by the way different people use language in the context of physicalism. In particular, Kripke seems to equate "necessary truths" with something that is true in all possible worlds. Is ...
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108 views

Modal logics - philosophical paradoxes using modeling by possible worlds

I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) ...
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45 views

Circularity between truth and meaning?

These two common claims are equally appealing: (1) the meaning of a ( declarative) sentence consists in its truth conditions (2) the truth of a sentence depends on its meaning But are we moving ...
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70 views

Is there an Abstract/Concrete Gray Area?

In natural language and daily life, it has become prevalent there is a class of entities which do not follow the abstract concrete distinction. Many people refer to abstractions that exist in time. (...
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How did Aristotelian logic view this?

I am very interested in the logical aspect of Aristotelian philosophy, especially how it was used by al Farabi and Ibn Sina in explaining understanding and breaking this complicated process down ...
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126 views

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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51 views

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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101 views

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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203 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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47 views

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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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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Syntactic and semantic eliminability/conservativeness

Let L be a ground language, and L+ the extension of L with additional signature terms and axioms. We say L+ is syntactically conservative over L if every sentence in L that is provable in L+ is ...
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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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185 views

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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46 views

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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177 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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264 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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223 views

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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110 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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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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Is double negation deconstruction applied to all branches of a truth tree?

If I am making a truth tree and already working on two branches when I come across a double negation (eg. ~~A), do I just decompose it to A right where it is, or do I add A to all branches? Hope I'm ...
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165 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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130 views

compactness theorem failure in English

In this link they show how the compactness theorem fails in english: (first page with the starbucs example): https://ocw.mit.edu/courses/linguistics-and-philosophy/24-241-logic-i-fall-2005/readings/...
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Names for most popular taxonomies of informal fallacies?

Informal fallacies are not formal, so as might be expected, there exists no prevailing standard taxonomy. Various books on logic and logical fallacies organize fallacies differently, (see chapter ...
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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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370 views

What is the difference between relational logic and predicate logic?

I am studying the Introduction to logic course from Stanford University and I begin learning about relational logic. However when I search on google for the terms there I end up often with results ...
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143 views

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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48 views

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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52 views

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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81 views

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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90 views

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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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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Which philosophers proposed theories containing the performative contradiction?

Socrates was blamed of this by being wrongly interpreted of saying: "I know that I don't Know." or other variants. What he really said was: "I neither know nor think that I know." Source: https://en....
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Did Wheeler's “It from Bit” allow inconsistencies to exist?

Physicist John Wheeler proposed a model of the universe based on "It from Bit" asserting that the world is fundamentally information. I've been told both that Wheeler's It from Bit is compatible with ...