Re: Cantorian pseudomathematics

Han de Bruijn wrote:
> The "Universal Quantifier" is only an abbreviation for "for all"; the
> "existential quantifier" is an abbreviation for "there is a." If we
> merely write our statements in plain English, we are using automatically
> all of the predicate calculus that we need for our purposes, and doing
> it more intelligibly. [ Huh? Why then _any_ formalization of logic? ]

No, you don't do it more intelligbly, since natural language
expressions are too often syntactically ambiguous. The formalization
allows that a computer can determine exactly the syntax of any
statement, and along with this, the rules of semantics are also
recursive: given some determination of the truth of the atomic
sentences, we can strictly calculate the truth of any sentence built up
from the atomic sentences (granted, we do not always have a
determination of the truth of the atomic sentences, but that is not a
deficiency of the formalization itself.)

MoeBlee

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