Questions tagged [symbolic-logic]
For questions related to symbolic logic, also known as mathematical logic. Topics might range from philosophical implications of metamathematical results to technical questions.
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What is a definition, written in symbolic logic, for a person living nearby?
Students often need some axioms and/or definitions to play with in order to learn formal logic.
What is a definition of a neighbor written in the style of symbolic logic?
By neighbor, we mean a person ...
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Would an erotetic operator be equivalent to its own demi-operator?
"Recap": demi-operations are e.g. "the square root of negation" in experimental(?) logic. (The association of demi-negation with using imaginary numbers as truth values is a little ...
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Is Russell's Paradox a semantic paradox or a syntactic paradox?
Is Russell's Paradox a semantic paradox or a syntactic paradox? I ask because of the following:
Let P be a predicate
Let SEP be the property of being a set of things that satisfies P
Let SP be the ...
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If X is a statement, is the collection of all interpretations of X a set?
Let X be a statement
Let SI be the predicate set of interpretations of X
Let IX be the predicate interpretation of X
Let NA be the predicate not contained in A
∃A∃B(SI(A)∧IX(B)∧NA(B))→∀A∃B(SI(A)→...
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Importance of Logical Notation
Does better notation lead to ease of abstraction and shorter proofs? I ask because I tried translating the following from Euclid’s Elements into my own idiosyncratic notation: Prime numbers are more ...
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What is the significance of the Coincidence Lemma?
There is not a Wikipedia article about the coincidence lemma.
I will try to explain the proof and then ask why it is important.
The coincidence lemma is meant to show that the satisfaction relation ...
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Which is correct, "the implication A → B" or "the implication ‘A → B’"?
Which is correct?
The true (or false) implication A → B.
The true (or false) implication ‘A → B’.
What are the arguments for saying that it is wrong to say:
the implication A → B
and the we should ...
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What difference between the truth of a conditional* and its logical validity?
I am confused . . . Here is a remark on the "classical analysis" of the implication:
On the classical analysis, logical implication is the same, not as the truth of a conditional statement, ...
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Can assumption in Hilbert style proof system be contradictory?
⊢（¬A→A）→A
I don't know how to solve this proof with the Axiom, Theorem and Inference rule in Hilbert-style proof system so I ask my classmate and he show me his answer. After viewing his proof, I was ...
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Did Russell had something like the notion of domain in the sense defined now by mathematics textbooks?
The expression ∀x(ϕx → ψx) is supposed to mean that, in Russell's parlance, ϕx → ψx is true "for all values of x". However, what are those values that Russell is referring to?
At some point ...
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Why not just give up on the idea of truth-functionality?
I understand that today only a minority of academics who are specialised in formal logic accept the horseshoe (aka "Classical Logic" or "First-Order Logic") as an accurate, or even ...
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stuck! first order logic - identities (specifically "only")
Please correct me on why these may be wrong(identities). I've tried many times but it seems I'm missing something.
for they key: M(x) = is a moon, O(x,y) = x orbits y, and m = mars, e = earth
Only ...
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At what point in the history of mathematics, and why, did mathematicians come to say "A implies B" to mean "not A or B"?
Here is what one respondent to my previous question says:
A big part of the problem here lies with interpreting the word ‘implies’, which is ambiguous in English. Unfortunately, mathematicians get ...
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What does Tarski mean when he says "variables do not posses any meaning by themselves"?
This is an excerpt from Alfred Tarski's Introduction to Logic and the Methodology of Deductive Sciences:
As variables we employ, as a rule, selected letters, e.g. in arithmetic the small letters of ...
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How is this logic valid?
An excerpt from Logic 2010:
In particular, what is confusing is that it permits assuming the conditional but then reaching a contradiction to prove the conditional. In my experience, that is not a ...
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