All Questions
Tagged with symbolic-logic philosophy-of-logic
34
questions
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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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-1
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2
answers
79
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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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2
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0
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139
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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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1
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2
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108
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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 ...
- 613
5
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3
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What did Bertrand Russell mean exactly when he said that *such that*, while fundamental both to formal logic and to mathematics, is "undefinable"?
Bertrand Russell in Principles of mathematics (1903) presents the notion of such that as fundamental to logic and mathematics, and states that it is “undefinable”:
The Indefinables of Mathematics
...
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0
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2
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100
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Treating truth as a predicate
It is interesting to me that in some conventions of logic I have seen (generally, common ones), the form of logical language is designed to make “truth” implicit. For example, merely to write:
P(x)
is ...
- 2,431
3
votes
1
answer
136
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What are the arguments of philosophers against the reasoning which justifies the horseshoe from truth-functionality?
There is a reasoning in mathematical logic which is meant to prove that the horseshoe is the only logical operation which fits our notion of conditional.
The reasoning starts from the idea that the ...
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2
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0
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72
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Questions about Feature Placing Languages/Predicate Functor Logic
About a year and nine months ago, I poses a question here about Quine's predicate functor logic and ontological nihilism. I'm still having trouble wrapping my head around these ideas. I hope someone ...
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2
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328
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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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0
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1
answer
223
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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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8
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2
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850
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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 ...
- 193
0
votes
1
answer
243
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an argument that is clearly valid but invalid in a sentence logic
I was reading these paper(dont really remember the title) it stated that there are simple arguments that are clearly valid but would be counted as invalid in the sentence logic system it was using. i ...
-3
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3
answers
300
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How to reconcile the fact that mathematical proofs are logical implications with the lack of a formal calculus equivalent to the logical implication? [closed]
Theorems follow from axioms. That is, theorems are the logical consequence of axioms. Thus, mathematical proofs are essentially deductive. Proofs are all essentially logical implications. There is ...
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0
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1
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209
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Equivalence Thesis
What is, if any, the canonical justification accepted in mathematical logic for the Equivalence Thesis, asserting (1) that indicative conditionals are truth-functional logical expressions and (2) that ...
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-4
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2
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299
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Is Classical Logic the proper model of the deductive logic of human reasoning?
Which mathematicians and philosophers unambiguously claimed that Classical Logic was the proper model of the deductive logic of human reasoning, and when did they say it?
The expression "Classical ...
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