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 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 ...
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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, ...
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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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Can the laws of mathematics and even logic change over time?
Can the laws of mathematics and even logic change over time? Like, maybe at one time there were finitely many prime numbers and now there are infinitely many? Or maybe at one time the laws of ...
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Is there a proof of exportation/importation from more obviously true implications such as Modus ponens?
Is there a proof of exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r)), from more obviously true implications such as the Modus ponens, Transposition, de Morgan etc.
I don’t believe that ...
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Is there stance that every logical and mathematical derivation exists/is contructable but we only care about a proper subset?
I'm thinking every logical derivation as something like all the derivations in the Principle of Explosion - really everything.
It could just be a helpful interpretation, not trying to get super deep ...
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What is the difference between philosophical logic and the philosophy of logic?
Is there a difference between philosophical logic and the philosophy of logic? If so, can someone elucidate the distinction between the two? Also, what are some references on the philosophy of logic?
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Can even the laws of logic vary from one possible world to another?
In my previous question, here: Can truths about the natural numbers vary across possible worlds?, I started off by saying that "The truths of logic are the same in all possible worlds". But ...
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Has anyone ever really constructed a countable model of set theory that falls in the trap of the Skolem's Paradox? [closed]
In an article named 'Skolem’s Paradox' on SEP, there is a description of the Paradox I'm asking about here:
Skolem's Paradox arises when we notice that the standard axioms of set theory can ...
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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 ...
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Reasoning and Randomness
What is the relation between reasoning and randomness or more specifically finding any relation between logic and stochastic processes? Why does it work so well, I wonder. For instance, prices in ...
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What is logic, and can logic itself be true or false?
In my understanding, logic is the process by which we can determine whether a conclusion is true or false, starting from a bunch of premises.
What kinds of logic are there, then, and what would it ...
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Transconsistency operators and degrees of logical explosivity?
So I noticed in an article I was reading that they talked about consistency and/or inconsistency or otherwise transconsistency operators. I don't recall the details, but they sound like propositional ...
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Is there a term that means "soft validity?"
By "soft validity" I mean this: The formal definition of validity is that if the premises are true, the conclusion must be true. I will call this "hard validity." "Soft ...
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Why do we call logical concepts abstract when logic is specific to the situation?
Things like propositions and predicates, which are specific to certain logics.
Example:
If only classical logic applied, not everything would be possible. (LEM, etc).
Many logicians say classical ...
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Fallacy of division in an old book
I have identified a fallacy of division in an old book written in Spanish and I would like you to confirm if it is indeed a logical fallacy. The underlined part of the image contains the argument that ...
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Finding the laws of logic logically
Consider the statement ''The laws of classical logic compraised of Identity, Excluding middle and Non-contradiction'', In which type of knowledge the above statement comes under? Is it purely ...
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What is the difference between spoken language and logical language?
To my understanding, we talk about things like propositional, predicate and higher order logic because spoken language is not fully logical. But, how exactly is it not logical? Usually the ambiguity ...
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According to Classical Theists, is God limited by the laws of logic?
I was pondering this question while writing on whether or not God had the ability to create a best of all possible worlds. I hold that God is not limited by anything (a view among classical theists ...
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Why was Russell discontent with Wittgenstein's view on "logic as tautologies"?
While reading Logicomix, I came across a scene that I don't quite understand.
Russell: ...Logicians are creating elaborate ways to "say the same things in different words"...this "...
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What, if anything, is the difference between studying logic mathematically and studying it philosophically?
There seems to be a distinction between studying logic mathematically and studying it philosophically and, in practice, it is reasonably clear which framework one is using when one studies logic.
I've ...
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Why should universal generalization work for abstract objects?
I am reading a logic book in my free time and usually the inference rule of universal generalization is motivated by real-life examples: Imagine having the statement that all people with brown hair ...
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How did Descartes made a logical skeptic argument against logic, without falling into a paradox, in his Metaphysical Meditations? Is it actually valid
René Descartes seems to have made some arguments against logic and mathematics in his Metaphysical Meditations, however it seems that these arguments are still logical, and the problem is whether that ...
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Why aren't Kripke semantics "syntax in disguise"?
The Wikipedia article on Kripke semantics suggests that they were considered a major breakthrough in part because algebraic semantics were seen as merely "syntax in disguise". But Kripke ...
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Laws of logic literature recommendations
What are some books/papers/articles I could read to develop an informed perspective on questions like "where do the laws of logic come from? Do they have a deep connection with the structure of ...
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What did Godel mean by intensional paradoxes?
I have read recently a chapter in Hao Wang: A logical journey: From Godel to Philosophy , where Wang mentions his discussions with Godel on intensional paradoxes, but I have no clue what exactly they ...
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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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A proposal for the meaning of life [closed]
I propose that the meaning of something is "all of the information related to it", and thus that the meaning of life is "all of the information related to life" - all of the causes ...
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What is mathematics? What are some of the most predominant philosophical definitions of mathematics?
Philosophers have given the nature of mathematics a lot of thought. As a beginner exploring philosophy, one of the questions which presents itself is 'what is X', and in this case, X is mathematics.
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can S5 be the weakest logic?
If we were to prove that an argument is a logical truth only in S5 logic out of (K, T, S4, and S5). does that make S5 the weakest of these four logics in which the argument is a logical truth?
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