Re: Universal grammar

In article <1xtufwa9zmj5e$.1qlsp5bsv9f86.dlg@xxxxxxxxxx>, Joachim Pense
<snob@xxxxxxxxxxxxxx> wrote:

Hans> When developing a metamathematical theory, notational
Hans> problems do not occur, because one just skips over them! :-)
Hans> For example, Shoenfield, "Mathematical Logic", defines his
Hans> formal system in Lukasiewicz style prefix notation, thus
Hans> writing "A B =>", but as this becomes unreadable to humans,

Unreadable to you maybe. But I guess the Japanese would find this
notation very user-friendly and perfectly readable.

Isn't he just reporting what Shoenfield writes?


Hans> he later just says let "A => B" be a different notation for
Hans> "A B =>". This way of glossing over details is typical for
Hans> human written mathematics. You can't do that when working
Hans> with a computer.

Why not? Heard of reverse-Polish notation or postfix notation? All
of prefix, infix and postfix notations are employed in computing.


I think you are missing his point. As I understood it, he is not
saying that infix notation is less formally definable than postfix
notation, but rather that S. introduces postfix notation formally, and
at a certain point switches to infix notation (because S. considers it
more readable), but fails to give a formal definition of it. This
certainly won't work when you are working with a computer rather than
a human reader.

You are right here - I pointed this out in another post.

There are more examples like this. For example, the propositional calculus
defined by Mendelson uses only the operator "=>" (implication) and "~"
(not). Then, when one defines operators like "and", "or", "<=>", and says
that these are not part of the object theory itself, but are
symbols extraneous to it, and expressions containing those symbols
should first be rewritten into the theory one is developing.

--
Hans Aberg
.

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