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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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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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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Jackson's simplification of Lewis' triviality result
I'm reading chapter 11 of The Blackwell Guide to the Philosophy of Language by Frank Jackson, and once he touched upon Lewis' triviality results he writes:
However, this definitely doesn't look that ...
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Why do equivalent propositions sometimes differ in apparency?
I study maths, and I have found that a useful way of thinking about two propositions A and B being equivalent is to regard them as being two different ways of saying the same thing, or equivalently, ...
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Question on Godel's Remark on Algorithmic Nature of Mind
Gödel claimed that what the Theorems do entail (specifically, the Second Theorem) is that mathematics is inexhaustible:
It is this theorem [i.e., the Second Theorem] which makes the
incompletability ...
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Is Tarski's theory of truth widely accepted
Tarski's truth theorem asserts that a truth definition for a (reasonably strong) theory cannot be formalized within that theory.
It seems that Tarski's theory of truth has met with a lot of criticism. ...
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Tarski's sufficient conditions for the Liar paradox and self-reference
Tarski gave three sufficient conditions in his 1944 paper The Semantic Conception of Truth for the Liar paradox to occur:
The language in which the Liar sentence is stated in is semantically closed, ...
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Is logic about a priori mind?
What is logic?
One can imagine Turing, Godel or Post writing a paper on logic. What provides the "validity" to the content they write? One proper answer to this question is the a priori &...
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In the context of philosophical logic, what does 'extra-logical' mean?
I am having trouble understanding what 'extra-logical' actually means in the context of philosophical logic.
Case in point: Bueno and Colyvan argues in their paper Logical Non-Apriorism and the ‘Law’ ...
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Does Quine's Predicate Functorese maintain the existence of relations?
Quine's predicate functorese has been proposed as a "feature-placing" language for ontological nihilism (Strawson, Azzouni, Dasgupta, Diehl). This is often used to eliminate objects and ...
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Is it there a "completely expressive" formal system / logic language?
I wonder whether it exists a formal system such that all (or a considerable number of) the others can be considered as a subsets or fragments of it.
I would say that, for instance, First-Order logic ...
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Stephen Yablo's Aboutness and logical subtraction
I was finishing reading Aboutness by Yablo, but there is an intuitive definition that I do not get:
He says on page 148 that:
What is this relation of adding falsity, or being additionally false, or
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Confidence margin for logical verification
I'm starting to read Wittgenstein and I keep circling around a problem, which I'll lay out with the following ideas:
a. Logical space is the totality of external reality.
b. A proposition is logical ...
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Formal logic - a priori or a posteriori
I am aware of the classical classification of logical calculus as apriori. I have also read pretty much anything I could get my hands on regarding "logic", including "New Essays on the ...
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Do not understand Truth value gap theorists' response to the Strengthened Liar
Truth value gap theorists assert that the Liar sentence is neither true nor false - it has no truth value. But here comes my first question:
If we take a sentence's meaning to be its truth condition, ...
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Is the distinction between fact and opinion, and objectivity and subjectivity universal or cultural? [closed]
I noticed in certain cultures that I interact with here in Malaysia, it seems that the distinction between fact-opinion and objectivity-subjectivity is non-existent. Whereas in STEM and the scientific ...
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What is the exact form of law of non-contradiction that dialetheism rejects?
Dialetheism asserts that there are sentences that are both true and false, e.g. the Liar. This seems to, quite obviously, go against the law of non-contradiction (LNC), and indeed Priest seems to ...
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Is deductive logic, and more specifically propositional logic, ultimately derived from induction?
Is the system of propositional logic itself induced, beyond its manipulated assumptions? It seems to be the case that we use propositional logic on the basis of two facts - firstly that it seems to ...
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Infinite Regress in Language and Logic?
I had this idea, and it seems novel to me, but I'm wondering if there is a philosopher that addresses this issue already because I think it's kind of interesting.
When making a logical statement, you ...
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Why are some things considered "impossible" even in other universes?
For example, I often hear that life could not develop in a universe where the fundamental constants were even slightly changed, or where certain physical laws were different. But if we're dealing with ...
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an argument that is clearly valid but invalid in a sentence logic
I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...
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Can we make statements for persons/objects that cease to exist?
I am asking this question because I thought what truth value would have a have a quantifier over a set that contains persons that are dead. For example suppose I state:
"For every x that is ...
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Is there some non-classical logic where the van der Waerden theorem does not apply?
The van der Waerden theorem is a theorem in the branch of mathematics called Ramsey theory which states that for any given positive integers r and k, there is some number N such that if the integers {...
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Hegel's counter proof of the old Logic
In his book on Logic,Hegel makes a counter proof of the old way of defining Logic. I have trouble understanding in which way Aristotle or Descartes were wrong according to him.
Could someone explain?
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Fail to understand Tarski's substitution argument for logic apriorism and a rebuttal against it
I have been reading Bueno and Colyvan's Logical Non-apriorism and they mentioned that Tarski has the following argument for logic apriorism:
If, in the sentences of the class K and in the sentence X, ...