Re: The meaning of set?

Rupert wrote:
Aatu Koskensilta wrote:
Rupert wrote:
The good thing about ZFC is that we have an algorithm for generating
all the sentences we accept as theorems.
Really? What is that algorithm?

What I have in mind is an algorithm for listing every theorem of ZFC.
Such an algorithm exists because this set is recursively enumerable.

Sure.

I'm not sure what your concern is. Perhaps you find my use of the
phrase "the sentences we accept as theorems" to be imprecise.

That was my concern. The recursive enumerability of the set of theorems of ZFC gives us no clue as to what algorithm it is, if any, that generates all the sentences we accept as theorems (in general, or of ZFC), unless "we accept as theorems" is intended to be read as "for which formal derivations exist in ZFC". So I wonder what the relevance of your observation was, if it was just that the set of theorems of ZFC is recursively enumerable?

Zuhair's "different approach to sets and analysis based on them" might well be pure waffle, as the case appears to be, but not because he doesn't present an algorithm for generating everything that he would accept as a theorem - whatever sense of accepting is meant here. We might just as well object that set theory is unacceptable because we can't given an explicit algorithm listing all the theorems acceptable on basis of the informal principles. What Zuhair needs to do is to present a coherent and interesting account of sets - he can worry about precise axiomatization, let alone formalization, later. I'll be holding my breath.

--
Aatu Koskensilta (aatu.koskensilta@xxxxxxxxx)

"Wovon man nicht sprechen kann, daruber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
.

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