Questions tagged [mathematical-logic]
15 questions
7
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2 answers
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 frames strike me as very algebraic in flavour, even if they…
jdonland
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6
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1 answer
Is the overlap between Yoneda's lemma and Peirce's pragmatic maxim known?
In philosophy, particularly in ethics, the pragmatic maxim (WP) states that an object may be considered solely in terms of its effects on the surrounding context. In the special case of ethics, the maxim states that the ethical ramifications of an…
Corbin
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4
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3 answers
Does logic give us a single definitive and universal answer for comparing the odds of unlikely events?
As an amateur who has interest in logic and mathematics I've been reading about the concept of different probability perceptions. I'd like to have your opinions over the subject below.
When it comes to probability assessment/comparison of two…
Geerts
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4
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1 answer
Questions Regarding Tarski's Semantical Formalization of the Colloquial Usage of Truth
My question is in regard to a problem (albeit a simple one) that I ran into reading Tarski's paper "Concept of Truth in Formalized Languages".
On page 159 Tarski states:
(5) for all p, ‘p' is a true sentence if and only if p.
From what I…
Max Maxman
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3
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4 answers
Prerequistes for mathematical logic
I have a working knowledge of calculus and linear algebra. But when I pick up books on mathematical logic (for example the ones listed in the logic study guide by Peter Smith), they often use mathematics I am not familiar with. Is it possible for a…
user56417
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2
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1 answer
Does every mathematical question have an unambiguous answer?
Does every mathematical question have an unambiguous answer?
For example, suppose I were to assert "In the decimal expansion of pi, does there occur in at least one location a billion 1's in a row?" Now, that is a purely mathematical question, so…
user107952
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2
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Per Mathematical Structuralism, can a pure mathematical theory have semantics that is not closed on isomorphism?
This question is the philosophical side of a question that I've recently posted to MathOverflow. Here, I'm specifically asking about the output of Mathematical Structuralism on that question that I'll re-post here. However, I'll include the brief…
Zuhair
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How does understanding of fragments differ from understanding of the whole?
Consider a person reading a mathematical proof, then each syllogism from it's antecedent maybe understood by that person, yet they may find it difficult to understand the whole proof. At times however, a person maybe able to understand the proof as…
Reine Abstraktion
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How does Barthes' ideas of Metalanguage differ from simple propositional logic?
On the wikipedia for post structuralism,
In Elements of Semiology (1967), Barthes advances the concept of the metalanguage, a systematized way of talking about concepts like meaning and grammar beyond the constraints of a traditional (first-order)…
Reine Abstraktion
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0
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Are brains geometrically equivalent to three-dimensional Venn diagrams?
I had a coworker who was kind of obsessed with Christopher Langan's supposed "theory of everything," and one article of evidence he introduced was his thought that the way our eyes are circular and they cross their information to produce our…
Kristian Berry
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0
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Philosophy books for mathematicians
Are there any books on philosophy that make relatively heavy use of math? I'm not looking for anything on formal epistemology, logic, or philosophy of math. Two examples of books that fall in the category I'm interested in are Infinity Causation and…
user236343
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0
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is there such a thing as non-constructive computational “proof”?
For the problems which can’t modified into a constructive proof, is there some useful notion of proving them to some computational approximation?
I’m referencing:
“Interpretations come at a cost: for example, when we pass from our initial, natural…
J Kusin
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Why is conjunction interposed with intersection instead of union?
My philosophical background going into set theory was heavily laden with Kantian and neo-Kantian elements, so one of my essential premises was read off the following passage from the first Critique [2nd ed., Meiklejohn translation]:
The same…
Kristian Berry
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0
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5 answers
Why do many philosophers state their arguments without using mathematics or formal language?
I am an amateur lover of philosophy and a researcher in physics and computer science. When reading a book of philosophy, I always find it frustrating that philosophers are so polysemous and ambiguous in their arguments.
Of course, I believe that…
Light Yagmi
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Can we logically derive a value for 0÷0?
I have a "proof" that 0÷0 = 2:
0÷0 = (100 - 100) ÷ (100 - 100)
= (10⋅10 - 10⋅10) ÷ (10⋅10 - 10⋅10)
= (10² - 10²) ÷ 10(10 - 10)
= (10 + 10)(10 - 10) ÷ 10(10 - 10)
= (10 + 10) ÷ 10
= 20 ÷ 10
= 2
It's obviously wrong mathematically (0÷0 is…
Wenura
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