From: Thomas Walker Lynch Date: Sat, 22 Aug 2026 15:27:56 +0000 (+0000) Subject: . X-Git-Url: https://git.reasoningtechnology.com/%28%5B%5E?a=commitdiff_plain;h=730dbabb2809c4d248cfe60c35a69bdda108fd60;p=TM-2026 . --- diff --git a/document/book/TM-2026.html b/document/book/TM-2026.html index dbc4cc9..154be16 100644 --- a/document/book/TM-2026.html +++ b/document/book/TM-2026.html @@ -409,18 +409,17 @@

When a geometer erases his drawing the theorem is untouched. He draws it again badly and the theorem is untouched. Every square that has ever been drawn could be wiped away and the theorem would still hold, and it held before any of them were drawn. Such is the non-temporal nature of Forms.

- The definition of a symbol given in section is Platonic in its structure. It begins with an unnamed math object that has required properties. The definition then states that we do not write down a symbol directly. A representation convention is chosen for example, a Greek letter say, and what appears on a page is an instance of that representation. Here the symbol is the Form of a symbol, the representation is the shape drawn in the sand, and there can of course be many instances drawn. + The definition of a symbol given in section is Platonic in its structure. It begins with an unnamed math object that has required properties. The definition then states that we do not write the symbol directly, as it remains abstract. A representation convention is chosen for example, a Greek letter say, and what appears on a page is an instance of that representation. Here the symbol is the Form of a symbol, the representation is the shape drawn in the sand, and there can of course be many instances drawn.

- If we were to rephrase the explanation of the geometers drawing squares in the sane, we would say there exists a math object called a square, what the geometers are attempting to draw in the sane is a representation of the square that they all agree on, and what is scratched into the sand is an instance of that representation. Furthermore, whether the geometers decide to instead do something else on that day, and now instances of squares are drawn in the sane, the math object remains unchanged. + If we were to rephrase the explanation of the geometers drawing squares in the sane, we would say there exists a math object called a square and that it is described by properties, but we can not write it down directly, so it remains as an abstraction. What the geometers are using as a guide an agreed upon representation of the square that they all can recognize instances of. What is scratched into the sand and is under discussion is an such an instance. Furthermore, whether the geometers decide to instead do something else on that day, and no instances of squares are drawn in the sand, the math object known as a square remains unchanged.

- There is subtle difference between a Symbol, being a form, and the symbol described in the section , namely that symbol of section is a math object, and the Platonic Symbol has no such limitation. This might be significant, as the section is being separated out of a defined set, where as a Platonic Symbol consists only of the required properties placed on a Symbol. + There is subtle difference between a Symbol, being a form, and the symbol described in the section , namely that symbol of section is said to be a math object, whereas the Platonic Symbol is a Form. This might be significant, as the section is being separated out of a defined set.

-