Questions tagged [philosophy-of-logic]
Philosophy of logic is a branch of philosophy concerned with investigating the nature, scope and role of logic.
47
questions with no upvoted or accepted answers
4
votes
0
answers
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 ...
- 23.1k
4
votes
0
answers
92
views
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 ...
3
votes
0
answers
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 ...
- 12.3k
3
votes
0
answers
112
views
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 ...
- 292
3
votes
0
answers
72
views
How do dialetheists determine which contradiction is true?
I have been reading a lot about dialetheism lately. I know for a fact that dialetheists do not believe that every contradiction is true. (Surely there is a difference between asserting that Liar is ...
3
votes
0
answers
380
views
Which rational thinkers (theologians, philosophers, scientists, mathematicians etc.), prior to 1850, disagreed with Aristotle's logic?
Did any intellectual luminary ever articulate any major disagreement with Aristotle's logic prior to the inception of modern mathematical "classical" logic?
Which rational thinkers, such as ...
- 6,248
3
votes
1
answer
129
views
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 ...
3
votes
1
answer
109
views
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 ...
- 131
2
votes
0
answers
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 ...
2
votes
0
answers
60
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 ...
- 481
2
votes
0
answers
65
views
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 ...
- 107
2
votes
4
answers
178
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 ...
- 1,073
1
vote
0
answers
33
views
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 ...
- 23.1k
1
vote
0
answers
140
views
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 ...
user63990
1
vote
0
answers
26
views
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 ...
- 12.3k
1
vote
0
answers
131
views
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 ...
- 51
1
vote
0
answers
76
views
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, ...
1
vote
0
answers
70
views
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 {...
- 559
1
vote
0
answers
57
views
Yablo's condition on "Truth about a subject matter"
In section 2.4 of "Aboutness" Yablo offers the following analysis of what does it mean that a statament is true about a certain subject matter/topic:
So, what is the proposition we are ...
- 395
1
vote
0
answers
63
views
Arguing that English does not satisfy the Tarski condition by appealing to truth value gap
I am reading Graham Priest's In Contradiction (P.12), where he is asserting that English satisfies the Tarski condition (a variant of semantic closure) and thus contains true contradiction.
He ...
1
vote
0
answers
215
views
What are the eventual purposes of symbolic logic?
What is the teleology of logic? Every body of knowledge has to have a teleology for which it's designed. The body of knowledge in logic doesn't clearly have any teleology or any purpose to which it ...
- 47
1
vote
0
answers
35
views
Aristotle's Categories and Linguistics
I have actually two questions:
What he calls substances or non-substances seem to me as, now what we call a matter of language. So what he calls substances could be seen as concrete nouns, and non-...
- 11
1
vote
0
answers
96
views
What paradoxes arise from quantifying over EVERYTHING?
This question is in context of the umbrella view of objects, that there exists a general category that everything falls under. Here are the quote and link that peaked my curiosity.
Finally, note ...
- 567
1
vote
0
answers
167
views
Semantic expressiveness of modal logic
I am wondering how much of the semantic of basic philosophical questions can be expressed by formal arguments in modal logic. Here is one argument I formalised myself:
P1 ◇ ∀a, ∃x // GNB(x, a) ∧ C(a)...
- 6,248
1
vote
0
answers
62
views
Recommendation: Second Order Logic textbook
I'm looking into Universalist Realism, Nominalism, Trope theory and the application of Second Order logic to each of them, however I have little/no experience with Second Order logic. Please let me ...
1
vote
0
answers
169
views
What is the relation between expressive completeness and semantic completeness
A formal system is expressively complete if and only if it is capable of expressing, as a formula, everything that is the subject of that formal system.
A deductive system is semantically complete if ...
1
vote
0
answers
43
views
Why do we seek to "limit" our scope for the search after truth?
In philosophy and science, we quite often make systematic approaches that limits our thoughts to be as accurate as possible.
Examples are endless - basically every logical system, every ...
- 3,846
1
vote
0
answers
163
views
What are the differences (if any) between classical and modern predicativity
I am researching Predicativity and I've encounterd defenition for classical predicativity and for modern predicativity but I can't understand the differences between them.
Thanks
- 261
0
votes
0
answers
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 ...
- 559
0
votes
1
answer
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 ...
- 151
0
votes
0
answers
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 ...
- 6,248
0
votes
0
answers
47
views
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....
- 139
0
votes
0
answers
25
views
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 ...
- 111
0
votes
0
answers
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 ...
- 12.3k
0
votes
0
answers
28
views
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 ...
- 12.3k
0
votes
0
answers
193
views
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 ...
- 5,648
0
votes
0
answers
76
views
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 ...
- 478
0
votes
0
answers
60
views
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 ...
- 101
0
votes
0
answers
48
views
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?
...
- 1
0
votes
0
answers
615
views
Baconian Logical Fallacy
I have been reading about logical fallacies lately, and I saw the Baconian fallacy listed here (of course on everyone's favorite site, Wikipedia). The description provided reads:
"using pieces of ...
- 1
0
votes
0
answers
84
views
Are axioms more important than definitions?
To prove a theorem in mathematics we usually use our axioms, definitions and other already proved theorems. Suppose we wante to prove a specific theorem and we haven't prove any other theorem and also ...
- 691
0
votes
0
answers
34
views
Possible Models
A model consists in one or more possible worlds. Necessity in a world is determined by its associated set of possible worlds.
I am curious whether there is any work that involves an account of ...
- 159
0
votes
0
answers
128
views
Bibliography about non-mathematical applications of logic:
I have been recently playing with modal and temporal modal logics in the context of "organisms" (mostly after some study of entelechy in Aristotle and relatedly, some ideas of current biology). I have ...
- 1
0
votes
0
answers
189
views
Can hypercomputation compute the impossible?
There are things which are illogical/logically impossible (like saying that 2+2=4 and 2+2=5. Without changing anything in the axioms of mathematics or logic, this would be a contradiction and would be ...
- 387
0
votes
0
answers
279
views
The sea battle paradox and the soundness criterion
Again a short look at Aristotle's resolution (one of many) of the sea battle paradox:
In one famous example about a hypothetical sea battle, [Aristotle] observes that the necessary truth of a mere ...
- 4,580
0
votes
1
answer
70
views
What counts as a logically necessarily true statement and what is not?
"If an existing population contains both mortal and immortal beings, some members of that population are not subject to death."
Is this statement considered logically necessarily true?
I personally ...
- 9
-4
votes
2
answers
287
views
Is Classical Logic the proper model of the deductive logic of human reasoning?
Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it?
The expression "Classical ...
- 6,248