Re: Infinity can not exist

From: Ross A. Finlayson (raf_at_tiki-lounge.com)
Date: 07/09/04 

Date: Thu, 08 Jul 2004 19:44:19 -0700

What's the idea of mathematics anyways?

I guess it's a science about being able to communicate the meaning, and embodiment, of a mathematical
construct. In that sense it the language to describe itself and the language in which that is contained.

Mathematics has its own symbology, that is about succinctness, and the ability to represent with a symbol
that is basically divorced from the script that it was taken, or itself often as not a letter or glyph,
instead a stylized representation of the concept, for example the arrow representing vector. Many times a
symbol is a glyph representing the letter of the word of that symbol. Sometimes it is an inventor's
initial. Other times glyphs in order enumerate the independent variables of a system.

Anyways I had another thought about equating the empty set and the universal set. It was about everything
that a symbol could represent, and how in the most minimal conceptualization of the least possible concept
that it was as well a statement of everything. It was just another one of those plain language statements
with two true and opposite meanings.

In another sense, I want to advance the concept of the models where the two true yet opposite meanings, or
rather, one obviously true and the other indirectly, are simultaneously true. Perhaps in a way that is an
enabling metastatement, the statement acknowledging its own abstraction from the particular domain, but
then again perhaps its is just a statement that lends itself to interpretation in terms of these really
quite fundamental, simple, and mundane, even, ruminations on the most primitive, and only, containers of
mathematical set theory: sets.

So the statement was something along the lines of "all a symbol can represent is just that", with "all"
interpreted as "anything" or "everything".

That's kind of like the difference, or lack thereof, between "for each", "for any", and "for every." For
example, with a basket of apples, there is perhaps difference in coring the apples: "for each apple, core
it", "for an apple, core it." In that sense for each/every/all is different than for any, unless the
interpretation is that "for any" that it is "for every".

Think of it this way, "for each" means to then sequentially "do", "for all" to simultaneously do, and "for
every" to sequentially do depending on another implied predicate, and "for any" to depend on another
implied predicate to do.

I hope that's not simply diversion, although I am trying to figure out ways to divert logicians into
considering some of my plain language logical statements, particularly those that are easily and simply
reduced to two glyphs: "this exists" and "and it equals itself", for their silhouettes, "where something
else doesn't" and "as it wouldn't", or something along those lines, for the ability to represent
continuous logic in binary logic, with or without an infinite binary word, and the concept of the binary
complement of any binary word.

There has been some recent discussion about the continuous vis-a-vis the discrete, what with wonder about
the nature and existence of infinity and what meaning it has to an ant, or you or me. In fact "recent" in
this sense means "in the time of recorded history".

I was reading Rudy Rucker's "Infinity and the Mind", it's pretty good reading, 70's state-of-the-art. He
mentions for example that the Dedekind construction of the real number is the post-Aristotlean (actual
infinities allowed) Eudoxus construction. Infinity or its specter was apparent to the early
theoreticians, it is still today, and then and now is by definition an unbounded playground of the
imagination.

Regards,

Ross F.

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