# 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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### 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 ...
915 views

### 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 ...
177 views

### What is an object's properties?

What can we consider an object's properties, for example, when can we consider an object's properties as 'changing'? For example, if I move an object from my desk to my table, has it changed? If I ...
59 views

### 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 ...
1 vote
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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 ...
101 views

### 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 ...
48 views

### 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 ...
2k views

### 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 ...
59 views

### 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 ...
169 views

### 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 ...
1k views

### 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 ...
29 views

### 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 ...
56 views

### 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 ...
20k views

### What is the difference between Law of Excluded Middle and Principle of Bivalence?

Law of Excluded Middle: In logic, the law of excluded middle (or the principle of excluded middle) is the third of the so-called three classic laws of thought. It states that for any proposition, ...
94 views

### 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 ...
1 vote
41 views

### 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 ...
2k views

### 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 ...
1 vote
332 views

### 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. ‑ ...
51 views

### 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 ...
483 views

### 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 ...
100 views

### 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 ...
6k views

### 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 ...
88 views

### 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 ...
139 views

### 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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### Where is the fallacy in Seth Yalcin's counterexample to the modus tollens?

Where is the fallacy, do you think, in Seth Yalcin’s argument (2012) that the Modus Tollens is not a generally valid form of argument? Seth Yalcin’s counterexample to the Modus Tollens (MT) https://...
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### potential violation of law of excluded middle

Consider the following sentence: "Either Santa Claus is hungry or Santa Claus is not hungry." This seems to be a straightforward application of the law of excluded middle. However, it also ...
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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 ...
1 vote
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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 ...
280 views

### 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 ...
32 views

### 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 ...
148 views

### 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, ...
232 views

### Using logic to do metalogical proofs? Is there a circularity problem here?

(1) If modus tollens were not correct, then I could have (P-->Q), ~Q and P. (2) But I cannot have (P--> Q) , ~Q and P. For, in that case, I would have (~P v Q) and ~Q and P; which means I would have ...
245 views

### 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 ...
971 views

### What is the difference in logic between strong and weak negation?

My main concern is to separate different forms of logic. I am hoping to use negation as a way to do that. In the abstract to "Web Rules Need Two Kinds of Negation", Gerd Wagner writes ... there ...
579 views

### 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 ...
1 vote
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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?
1 vote
306 views

### 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 ...
90 views

### 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 ...
1 vote
63 views

### 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 ...
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### Why did the mid-19th century and earlier thinkers fixate on one-place predicates?

A book I'm reading mentions the following: A major barrier to the development of first-order logic had been the concentration on one-place predicates to the exclusion of many-place relational ...
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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!
166 views

### 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 ...
2k views

### Does the Fallacy Fallacy make logic useless?

I should note that I'm not a formal student of philosophy and haven't studied it in any serious depth. I just like logic, and logical fallacies. I like to spot them, and I like to debate using them, ...
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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