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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How does 'use-mention' apply to formulas?
When we use 'terms' such as words it is generally clear however, if we have a formula:
And I write:
'x+1=2 is true for x=1' is this 'using' or 'mentioning'?
If a formula contains variables, it has no ...
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What is the 'meaning' of an unassigned formula with free variables?
What does a variable refer to in a formula? If it is a free variable, it has no reference, yet it exists as an element of the formula.
In an unassigned formula, what is the semantic meaning of a ...
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How can sequences/expressions occur in other sequences/expressions?
I know I specifically wrote a question about Wetzel, however I do not want to invalidate previous answers.
In Quine's 'Mathematical Logic' he discusses occurences of 'expressions' in other '...
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Wetzel's 'occurences'
I was reading this often quoted article by Linda Wetzel (1993) where she discusses the 'occurence' of expressions in others and Quine's issues with the idea, she describes an expression as a sequence ...
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Is '=' a relationship between the objects or their expressions?
The Wikipedia definiton of equality gives it as a 'relationship between two expressions'
This confuses me as when we define mathematical expressions like 2+2=4 it makes no sense to say that '=' or '...
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Is a variable simply a symbol?
If a 'variable assignment' function maps from a set of symbols, would it be correct to formulate a variable as simply a particular symbol that performs the role of a variable in my language? So when ...
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Are there only two levels in languages, meaning and symbols?
Say in my language I have a 'variable x', in my language the symbol x represents a (variable) number, so at a level of meaning it is an object, and at a level of symbols 'x' is simply a set of lines ...
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Need help with this Symbolic Logic Proof please
I am having trouble solving this proof. Line 5 is wrong, I know it's Demorgan's Law, but the proof machine doesn't accept that as an answer. I think it only accepts ~Elim, vElim, vIntro, ~Intro, &...
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First use of exportation/importation in formal logic?
Who is the logician who first used exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r))?
Gödel used it in his 1939 Logic lecture, but it doesn’t seem to have been known from the Aristotelian ...
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Is there a proof of exportation/importation from more obviously true implications such as Modus ponens?
Is there a proof of exportation/importation, namely, ((p ∧ q) → r) ⇔ (p → (q → r)), from more obviously true implications such as the Modus ponens, Transposition, de Morgan etc.
I don’t believe that ...
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Phrases such as 'x is an unspecified object' [closed]
Would a phrase like 'x is an unspecified object' be part of my meta-language? As x is a variable, such an expression is not meaningful in relation to any object in my interpretation, however we ...
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Has anyone ever really constructed a countable model of set theory that falls in the trap of the Skolem's Paradox? [closed]
In an article named 'Skolem’s Paradox' on SEP, there is a description of the Paradox I'm asking about here:
Skolem's Paradox arises when we notice that the standard axioms of set theory can ...
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Why does this conversion rule need ∃xT?
In the wiki page of Prenex normal form, there is a rule for conjunction as follows:
(∀xφ)∧ψ is equivalent to ∀x(φ∧ψ) under (mild) additional condition ∃xT or, equivalently, ¬∀x⊥(meaning that at least ...
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Why are undefined references and variables not specifically differentiated?
In my opinion, this topic is more philosophical than mathematical, but if it is not, I will ask it on another forum.
My understanding
I'm talking about non-reserved symbols here. Not about 0, 1 or π.
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Is Norman Megill's view of Gödel's incompleteness theorem compatible with what philosophers have said about it?
Here is one recent and seemingly expert appreciation on the consequences of Gödel’s incompleteness theorem for mathematics:
Gödel’s incompleteness theorem showed that it is impossible to achieve ...
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