[CG] Re: Operator Variables in Logical Graphs

Operator Variables in Logical Graphs • 3 • https://inquiryintoinquiry.com/2024/04/10/operator-variables-in-logical-gra… ❝And if he is told that something is the way it is, then he thinks: Well, it could probably just as easily be some other way. So the sense of possibility might be defined outright as the capacity to think how everything could “just as easily” be, and to attach no more importance to what is than to what is not.❞ — Robert Musil • “The Man Without Qualities” All, To get a clearer view of the relation between primary arithmetic and primary algebra consider the following extremely simple algebraic expression. Figure 4. Cactus Graph (a) • https://inquiryintoinquiry.com/wp-content/uploads/2019/07/box-a.jpg Here we see the variable name ‘a’ appearing as an “operand name” in the expression ‘(a)’. In functional terms, generally speaking, an operand name like ‘a’ might also be called an “argument name” but it's best to avoid the potentially confusing connotations of the word “argument” here, since it also refers in logical discussions to a more or less specific pattern of reasoning. In effect, the algebraic variable name indicates the contemplated absence or presence of any arithmetic expression taking its place in the surrounding template, which expression is proxied well enough by its formal value, of which values we know but two. Putting it all together, the algebraic expression ‘(a)’ varies between the following two choices. Figure 5. Cactus Graph Set () , (()) • https://inquiryintoinquiry.com/wp-content/uploads/2019/07/box-.jpg The above selection of arithmetic expressions is what it means to contemplate the absence or presence of the arithmetic constant ‘( )’ in the place of the operand ‘a’ in the algebraic expression ‘(a)’. But what would it mean to contemplate the absence or presence of the operator ‘( )’ in the algebraic expression ‘(a)’? That is the question I'll take up next. Regards, Jon cc: https://www.academia.edu/community/lOa9mp cc: https://mathstodon.xyz/@Inquiry/112225263055943815