All Questions
Tagged with symbolic-logic set-theory
5
questions
4
votes
4
answers
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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 ...
10
votes
7
answers
3k
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What did Russell mean when he wrote that the null-class, the class having no members, did not exist?
I am not quite sure I interpret the following sentence correctly in Bertrand Russell's paper on existential import:
and among classes there is just one which does not exist, namely, the class having ...
- 8,363
3
votes
3
answers
357
views
How do we arrive at stronger theories in mathematics/logic?
A reasonable aim of formal mathematics/logic is to build systems which can "interpret" many things. As an example, ZFC can interpret a number of things. Incompleteness Theorems provide us ...
- 1,139
4
votes
1
answer
148
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Prove ∀w(∀v((v=w∧φ(v))⇔φ(w)))
In this math question of mine, an answer pointed me to this theorem:
∀w(∀v((v=w∧φ(v))⇔φ(w)))
which in turn, the answerer stated, implies another theorem:
∃v(v=t∧φ(v))⇔φ(t)
which was the fact I ...
- 817
4
votes
2
answers
672
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Subformulas of the WFF (∀x) ((∀y) ((x ∈ y) ∨ (y ∈ x )))
Consider the well-formed formula in set theory (∀x) ((∀y) ((x ∈ y) ∨ (y ∈ x ))). I believe there are 5 subformulas:
(x ∈ y)
(y ∈ x)
((x ∈ y)∨(y ∈ x))
(∀y) ((x ∈ y)∨(y ∈ x))
(∀x) ((∀y) ((x ∈ y)∨(y ∈ x)...
- 817