Cf: Animated Logical Graphs • 17 https://inquiryintoinquiry.com/2019/07/09/animated-logical-graphs-17/
All, Note. There were a few clumsy and potentially misleading constructions in my last email. I've fixed them in the blog post linked above and in the transcript below. ⁂ To get a clearer view of the relation between primary arithmetic and primary algebra consider the following extremely simple algebraic expression. Figure 1. Cactus Graph (a) https://inquiryintoinquiry.files.wordpress.com/2019/07/box-a.jpg In this expression the variable name “a” appears as an operand name. In functional terms, “a” is 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, and of which values we know but two. Putting it all together, the algebraic expression “(a)” varies between the following two choices. Figure 2. Cactus Graph Set () , (()) https://inquiryintoinquiry.files.wordpress.com/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
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