# Questions tagged [logic]

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

403 questions with no upvoted or accepted answers
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### The enunciation clause (Lyotard & Levinas)

As kind of introductory remark, let me state that I'm not academically-trained in philosophy, so my apologies if this comes up as a rather simple question. I was reading Logique de Levinas by JF ...
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### What is an explanation really?

Let's consider a hypothetical 'Church of the Moon' on a distant planet with a huge moon. The members of this church base all their beliefs about the moon and their religious practices on their holy ...
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### Is an argument with contradictory premises valid?

I have hard time determining whether the below argument is valid: (P1) Nobody ever plays with a bear. (P2) Bob plays with a bear. (C) Therefore, bears are friendly. I think this argument is valid. ...
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### Philosophical meaning of the Curry Howard Correspondence

At a technical level, I understand the Curry-Howard correspondence in various settings, and its usefulness as a technical tool. What I'm looking for is a fairly rigorous discussion of genuinely ...
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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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### Is Tarski's derivation of the Liar paradox valid?

First a link to his derivation: http://www.jfsowa.com/logic/tarski.htm Its a famous essay so you really should read all of it but at the moment its enough if you read section 7 where Tarski derives ...
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### Is there a Formal discipline of tying Logic Puzzles to Mathematical Equations?

I am attempting to find the answer to a long standing question in mathematics, known as the Collatz Conjecture. In this attempt, I’ve figured for myself, in a way that I haven’t seen produced anywhere ...
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### What are some ways of understanding plural predication (and what are some academic resources on the matter)?

The particular case I'm thinking about has to do with existence. Peter Van Inwagen writes: 'When I say that affirmation of existence is denial of the number zero, I mean only that to say that Fs exist ...
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### Entry points from philosophy into mathematics at higher levels?

Everytime I look up of the link between philosophy and mathematics, I see the topics only of the most foundational levels discussed. As in logic, and stuff. When I study higher mathematics theories, ...
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### How does logic deal with objects that change?

Say I have an object that is currently red, but in one day will be painted green. If I put it in my formal language with a constant symbol 's' and define the colours green and red using 'g' and 'r' ...
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### Is the assertion of a moral imperative in complying with a person's self-attested "gender" consistent with broader principles of declared attributes?

The Wikipedia style guide discusses how if a person states that they consider themselves a particular gender, selects a name for themselves in conjunction with a change in gender, and asserts ...
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### How could second-order logic satisfy (neo) Fregean's epistemic goal?

Recently I've been reading Shapiro's Higher Order Logic in The Oxford Handbook of Philosophy of Mathematics and Logic, Chapter 25. There are some paragraphs confusing me:  One traditional goal of ...
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### First-order semantics for plural logic

There are commonly thought to be two kinds of set-theoretic semantics for second-order logic: the standard one, where relation (and function) variables range over the entire power set of a model ...
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### Is there a "for dummies" construction of the valuation model of the relevance logic R from a De Morgan monoid?

I am confused how one gets the anti-chain preserving negation in Belnap-Dunn's FOUR, which by all accounts underlies their R (which adds implication), when R's valuation model is constructed from a De ...
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### What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
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Semantic Anti-Realists hold that a claim has a (constructive) proof if the claim is true. I wonder whether this position runs into a version of Yablo's supposedly non-circular version of the liar ...
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### Rewriting a set of propositions that includes a circular proposition

"For any proposition P, if I believe that P then this paragraph (everything that is written between the quotes) entails that I believe that P. I believe that I exist. For any proposition P, if I ...
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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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### 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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### What to read for an introduction on the epistemology of logic?

I would like to read about the epistemology of logic, preferably at a undergraduate level (not being a philosopher myself). What (text)book should I read for a good introduction on these topics? The ...
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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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### 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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### Why can some arguments be proven only through Conditional or Indirect Proof?

For brevity, abbreviate as CP 'Conditional Proof', as DM 'Direct Method, and as IP 'Indirect Proof'. Source: p 445, A Concise Introduction to Logic (12 Ed, 2014) by Patrick Hurley Indirect proof ...
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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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### Can a variable in FOL be bound by two quantifiers if they are the same

∀x∀y((P(m) /\ Z(a,x)) > ∀xW(x,c)) Something like this. I don't think it is a sentence because the variable x is bound twice and the nested quantifier is still within the scope of the original ...
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### Is Logic Pre-Human?

It was German philosopher Martin Heidegger (1889-1976) who famously said, "animals are poor in world." Although this may be true, I do not see them as being poor in logic. Paleontologists have ...
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### What part of a universal propositions is the antecedent?

The wiki article on vacuous truth says: a vacuous truth is a conditional or universal statement that is only true because the antecedent cannot be satisfied. I'm familiar with identifying the ...
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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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### Looking for references for some remark of Quine's

I'm looking for a comment I think I remember Quine having made. He's talking about our understanding of proofs. I think he says something along the following lines... If you understand many different ...
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### Is there a detailed doxastic logic with a doubt operator?

I was "experimenting" with a doxastic logic with a doubt operator D besides the belief operator B, trying to come up with intuitive equivalences of interleavings (e.g. DBA = BDA, perhaps), ...
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### Where do presuppositions fit into Grice's theory of meaning?

To clarify, by "Grice's theory of meaning" I am referring to the view that the informational content or meaning of an utterance is made up of three components: what is said - the actual ...
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### States-of-affairs as zero-place analogues of properties and relations?

I've been going slow through the SEP article on intrinsic properties, and came across this intriguing gem: (The locution ‘state of affairs’ is used differently by different philosophers. Here it is ...
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### Propositions vs sentence types and tokens and the context insensitivity of PL

I came across the following explanation for the context insensitivity of the language of propositiional logic (PL) on page 34 of The Laws of Truth by Nicholas Smith: Because glossary entries pair ...
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### A question on quantified modal logic

I originally posted this on math.stackexchange.com, but I’m cross-posting it since I know there are good modal logicians on here too. Also, I already asked a similar question here: Identity in ...
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### Existential vs. universal alternation

Is there a difference between trivial and nontrivial negation? It occurred to me that we could think of the following series of negation operations/relations: Empty negation = primordial double-...
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### Natural language into logic and proof

I'm working through Logic by Paul Tomassi, and there is one particular problem I'm stumped with. The problem is on pg 186 and involves representing an argument in English as a sequent and then ...
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### Is this a problem with verisimilitude talk, many-valued-logic talk, or something/nothing else?

A perhaps naive characterization of verisimilitude is "closeness to truth," the proximity coming from the similarity. At least, the SEP article uses, "The number of planets is 9," ...
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### Bias type based on achievement of goals

What type of bias is it if I favour an idea because the implementation of the idea will benefit me? Example: I favour limited gun control despite reading contrary arguments because my livelihood is ...
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### How to prove that: ⊢/k ◻p v ◻¬p

My though it that we can refer to completeness. So just argue that ◻p v ◻¬p does not have a corresponding model. But I am not sure...
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### Substructural logic and the Continuum

The SEP article on change and inconsistency goes over a theory of continuous motion that involves true contradictions. So arguably, the dialethic/paraconsistent Continuum is one way to logically frame ...
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### Questions about Feature Placing Languages/Predicate Functor Logic

About a year and nine months ago, I poses a question here about Quine's predicate functor logic and ontological nihilism. I'm still having trouble wrapping my head around these ideas. I hope someone ...
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### When does a conditional statement hold true according to Dialetheists?

I understand that for the consequent to really follow from the antecedent, it (the consequent) must be both relevant and necessary given the antecedent. So my question is: which types of conditional ...
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### Are logical truths a subset of facts which in turn is a subset of possible truths?

Are logical truths (those that are true in all possible interpretations) a subset of facts (known via observation in our reality)? Are facts a subset of possible truths(satisfiable)? Where do axioms ...
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### Logic vs Metalogic

In Hunter's "Metalogic," the author defines metalogic as a theory of sentences used to express truths of logic, and goes onto explain model theory and proof theory. When reading books ...
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### Can the logic used by continental philosophers like Hegel be formalized by mathematicians?

Can the logic used by continental philosophers like Hegel be formalized by mathematicians? I heard the logic used by Hegel and Heidegger is different from the logic used by analytical philosophers ...
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### Examples of, or counterexamples to, the concept of erotetic inference?

Suppose that the generality-particularity ordering is the comprehensive ordering on inference. Compare: What is the first integer after 2? What is the first prime integer after 2? (2) would seem ...
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### Are questions truth-apt; what is the use of assigning questions a truth-value?

Is John black (or white)? Yes he is black. No he is not (black). I don’t see how can the question be truth-apt and what use is there in assigning (or even being able to assign) a truth-value to the ...