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.
327
questions
4
votes
1
answer
237
views
Was Tarski the first to discuss the logically of the truth predicate?
Tarski famously discussed, formally, the logically of the truth predicate, in The Concept of Truth in Formalised Languages (1935).
Was he the first to do so?
Thank you for any scholarly reference.
- 37.8k
0
votes
0
answers
39
views
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 ...
1
vote
2
answers
108
views
Is it possible to stick to one of these viewpoints of variables?
It has been a struggle to find a precise account of the concept of variables. There are however two viewpoints that I've seen authors convey in several logic textbooks.
Variables as placeholders for ...
- 14.7k
4
votes
0
answers
43
views
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 ...
- 16.7k
4
votes
4
answers
2k
views
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 ...
- 135
0
votes
0
answers
41
views
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)→...
2
votes
1
answer
75
views
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 ...
- 16.7k
2
votes
1
answer
103
views
Why doesn't one assert in metamathematics that a sentence S is a logical consequence of the conjunction of a set of sentences?
In other words, why isn't there -- at least in standard textbook presentations of things like the deduction theorem and the compactness theorem -- a conjunction connective that is applied to sets of ...
- 250
0
votes
0
answers
56
views
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 ...
- 2,431
1
vote
1
answer
101
views
How can I formalize the argument that morality cannot exist, in FOL?
I am trying to formalize the following argument:
Every moral theory is equally valid.
One can always get a new moral theory from another one.
For something to be metaphysically real or to exist, it ...
- 2,431
0
votes
0
answers
65
views
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 ...
- 8,363
-1
votes
2
answers
79
views
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, ...
1
vote
1
answer
59
views
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 ...
- 37.8k
4
votes
1
answer
61
views
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 ...
- 27.2k
4
votes
1
answer
89
views
Unusual change of meaning of word "any" in negative sentences form "for all" to "there exists". Predicate logic
Question. Why does the word "any" in negative sentences changes its meaning from "for all" to "there exists"?
Origin of the question. I have a question about translating ...
CommunityBot
- 1