# Questions tagged [philosophy-of-logic]

Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.

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### Do Gödel's incompleteness theorems and Tarski's theorem of indefinability of truth show we can never discover and prove every truth?

I thought I had a grasp on this. Do Gödel's apply to just math; logic, too; or more, and what does its applicability entail? If it applies to math, does it apply to physics? Similarly with Tarski: can ...
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### How universal is logic? [closed]

There is what seems to me an inconclusive debate in the academic literature concerning the idea that logic is universal, but in what sense exactly would logic be universal? One example of a claim that ...
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### Is Fermat's last theorem a logical necessity or a different kind of necessary truth?

Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. The question was, is this a logically necessary ...
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### Question about a presentation on substructural logic (negation modulo two kinds of residuation)

I've been reading through this slide-based presentation on substructural logic and I'm delightfully perplexed by the following section: What is the use to which the two given flavors of negation can ...
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### Missing two syntactical expressions of rules of inference in sentential logic

I have a table of the rules of inference in propositional logic. Among the entries are an Associative and a Commutative. The Associative rule is expressed with disjunction, but the commutative is ...
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### Does logical pluralism imply conceptual pluralism?

By "conceptual pluralism," I mean something like, "Multiple conceptual analyses of the same concept are true." The example for the sake of which this question occurred to me is the ...
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### Has anyone studied the beings of logic from Heidegger's "Time & being" perspective?

The nature of the word 'logic' differs according to the context where it is used (i.e., Aristotle and Socrates, boolean algebra, symbolic logic, propositional logic, etc.) Has any philosopher focussed ...
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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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### Is the Law of Excluded Middle an allowed argument in court?

Is the Law of Excluded Middle a valid deduction rule in court? If not, is it reasonable to say that all arguments in court must be "constructive in nature"? As an example, consider this ...
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### Is mathematics based on formal logic, or vice versa?

Math is obviously based on logic in a heirarchical sense, but what about the historical sense? Is there any historical evidence of a "transition" from first order logic to mathematics? All ...
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### Who ever argued that natural languages have an exact logic?

Peter F. Strawson famously concluded his 1950 critique of Bertrand Russell's theory of descriptions by the somewhat irrelevant remark that ordinary language has "no exact logic". Russell, in ...
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### Could a quantum computer simulate any system based on different types of logic?

Quantum computing is based on quantum mechanics (obviously) which has different logical rules than classical/Boolean logic. However, does this mean that a quantum computer could simulate or process ...
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### Trivialism vs Alethic Nihlism

What are the similiarities and differences between the two theories (as well as arguments for and counterarguments against). From what I know, trivialism states that everything is true (and I believe ...
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### What is logic in the context of Classical Logic?

How mathematicians define the concept of logic for the purposes of Classical Logic? Also, how do philosophers and mathematicians at different period in history defined the word "logic", if ...
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### Conjunction with questions: an issue more of logic or of language (if not both)?

Assume that questions can be conjoined with other questions, e.g.: Who is Shawn Balt? What is prawn salt? Who is Shawn Balt and what is prawn salt? Assume that wh-terms are (plurally) agglomerative ...
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### How is the completeness of first order logic reconciled with the incompleteness of set theory?

First Order Logic (FOL) is complete in the sense that: there is a proof procedure for FOL such that just the statements(/wffs) of FOL that are true and remain true under any re-interpretation of their ...
1 vote
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### What does it mean "to provide semantics" in the context of formal logic?

When reading some SEP articles, this is a phrase I commonly came across, "this provides a semantics for this logic". But what does it mean?
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### What logics/philosophies deny the law of excluded middle (LEM)?

What logics/philosophies deny LEM, the law of excluded middle (tertium non datur)? This law is expressed as Philosophical Axiom 4.2: Tertium non datur (Non est medium inter esse et non esse. ‑ ...
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### Is there a system of logic which denies DNI?

From what I know, the law of double negation is often simplified as p <=> ~~p. Intuitionist logic splits the biconditional into DNI and DNE. DNI: p -> ~~p DNE: ~~p -> p and denies DNE ...
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### Were there any logicians in the past who argued that the Liar was logical, and so either true or false?

The Liar seems to have been universally regarded as paradoxical from the moment philosophers started to discuss its logic. Is that really the case, though? My question is as follows: Outside ...
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### Logic and math as a study of possibilities and not so much about human reasoning

Most of what I've come across about the "hierarchy of disciplines" seem to say that logic/math is more fundamental than physics, physics more fundamental than chemistry ... biology more ...
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### What are the arguments of philosophers against the reasoning which justifies the horseshoe from truth-functionality?

There is a reasoning in mathematical logic which is meant to prove that the horseshoe is the only logical operation which fits our notion of conditional. The reasoning starts from the idea that the ...
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### Is Rule-Based Machine Learning an Example of Inductive Logic in the Philosophical Sense?

Human beings are capable of deciding upon rules based on intuitions and observations their neurons presumably provide (certainly metaphysical presumptuous). According to WP, this is inductive ...
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### Do computers use logic?

I know we refer to computers as using logic, logic gates and the like, but is this just us ascribing human capacities to the machines? It sounds like a case of us giving more meaning to the machines ...
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### Natural Language and Implication

I understand that relevant logic deals with a natural-language interpretation of implication, but it seems too restrictive. It does seem a bit of a reach to say that there is a conceptual link between ...
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### What is the meaning of Coherence by Whitehead?

I am just started reading the book Process and Reality. On page 5, He talked about what is the accentual thing we have to keep in mind while building a speculative philosophy. Pints are Rational side....
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### How to proof that Classic propositional logica and Logic of paradox have the same logical truths

As far as I understand it, in Priest's "Logic of paradox" there is a proof to the effect that $\phi$ is classically valid IFF $\phi$ is valid in the Logic of Paradox (LP), that is: \$\vDash_C ...
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### Did Aristotle used the term *contradiction* or the term *contradictory* in his discussions of *reductio ad impossibile*?

Did Aristotle used the term contradiction or the term contradictory in his discussions of reductio ad impossibile? Two translators who disagree: For all those which come to a conclusion through an ...
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### The massive problem with regarding string manipulations as the foundation of mathematics

Formalists believe that mathematics is just a game of string manipulation, not much different from other games like Ludo or chess. I think string manipulation is an extremely useful way to think about ...
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### How does pluralism about doxastic logic work?

If person M has a concept of belief, and a logic for that concept, B1, but some other person N has concept B2, with different inference rules over the operator, then on the first-order level, does M ...
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### Is probabilistic modus tollens a fallacy?

Modus tollens takes the form of "If P, then Q. Not Q. Therefore, not P." A probabilistic version of Modus Tollens says "If P, then Q is very improbable. Q. Therefore, P is very ...
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### Which philosophers have considered irrational conviction

It seems a characteristic of humans to be convinced about a matter in the absence of overwhelming evidence, even where logic suggests that are other valid alternative positions to take. We see this in ...
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### The discursive nature of a concept [closed]

Concepts are universal, insofar as they are not individuated, and they are abstractions. What does it really mean to say concepts are discursive?
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### On what basis do we derive logic? [duplicate]

I find that using logic is purely pragmatic.We use many forms of logic to conclude various things about our "world" which is through epistemology.But yet, the fallacy I find here is that we ...
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### A question on the belief operator in Doxastic Logic

Let Bp be the statement "it is believed that p". Why is ~Bp not equivalent to B~p? in words it amounts of saying that: "it's not believed that p" equivalent to "it's believed ...
1 vote
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### What is a convincing explanation of how Russell's "golden mountains" argument is logically fallacious?

Here is the now famous passage in his book on Western philosophy where Bertrand Russell explains why Aristotle's position that the universal affirmative "All Greeks are men" implies the ...
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### If it is not possible that p is not possible in K, does it follow that p is possible in K?

I have the following question. If it is not possible that p is not possible in K, does it follow that p is possible in K? Thanks in advance!
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### Can computer science be used to "test" theories of logic?

I feel like this might be a stupid question, like I think I've read at least one major text according to which, "Of course logics can be tested in a computer-science context, not necessarily in ...
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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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### Point in infinite regress where a 'why' question can no longer be answered

Example: Q1: If I collected one apple, and I collected another apple, why do I have two apples now? A1: Because 1 + 1 = 2 Q2: Why is 1 + 1 = 2? Another example: Q1: If gravity pulls us downwards, ...
1 vote
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### Why is "appeal to nature" a fallacy?

Appeal to nature states that just because something is natural doesn't mean it is right (ethical). Morality is not objective but the existence of this fallacy attempts to objectively define morality ...
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### Is there some formal system of "first-person logic"?

The SEP article on indexicals mentions a lot of the seemingly logical complications that arise in connection with them. Indexicals are also comparable to variables and hence objects of schematism, so ...
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### If platonism was correct, would everything be real despite everything being formal?

In one of his recent essays (https://writings.stephenwolfram.com/2021/04/why-does-the-universe-exist-some-perspectives-from-our-physics-project/) the scientist Stephen Wolfram says (at the end of it, ...
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### Logical relativism ≠ logical pluralism = logical inclusivism?

Logical pluralism, in an attempted slogan, is, "There is no One True Logic, but a plurality of 'true' logics." But so on this site I have seen the phrase "logical pluralism" ...
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### Paraconsistent logic for daily life

In everyday life, there can be evidence to support both a proposition and the negation of it. I guess paraconsistent logic is an appropriate way to model this. Is there any research in that direction?
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### Is logical possibility the same as mathematical possibility? [closed]

Is everything that is logically possible also mathematically possible, and vice versa? Note, I am not suggesting that logic and mathematics are identical. I am merely asking whether logical ...
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### How to solve "impossible" problems?

In mathematics and philosophy there are some unsolvable problems like Russell's paradox or the liar's paradox that are usually said to be undecidable... There are also other "impossibilities"...
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### How does society decide what styles of argument are valid or invalid for practical purposes?

I know that type of inferences you can make from a given system of axioms depend on what background logic you choose. For example, in some systems of logic, we can do a proof of contradiction but in ...
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### Which logicians before the 19th century adopted the logical operation ¬P ∨ Q as best model of the truth conditions of the conditional?

Which logicians (outside 19th century mathematical logic) adopted, explicitly or implicitly, Philo's idea that the truth conditions of the conditional "If P, then Q" were best expressed as &...
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