[CG] Re: Theme One Program • Exposition

Cf: Theme One Program • Exposition 8 http://inquiryintoinquiry.com/2022/10/08/theme-one-program-exposition-8/ All, Logical Cacti (cont.) The abstract character of the cactus language relative to its logical interpretations makes it possible to give abstract rules of equivalence for transforming cacti among themselves which partition the space of cacti into formal equivalence classes. The transformation rules and equivalence classes are “purely formal” in the sense of being indifferent to the logical interpretation, entitative or existential, one happens to choose. Two definitions are useful here: • A “reduction” is an equivalence transformation which applies in the direction of decreasing graphical complexity. • A “basic reduction” is a reduction which applies to a basic connective, either a node connective or a lobe connective. The two kinds of basic reductions are described as follows. • A “node reduction” is permitted if and only if every component cactus joined to a node itself reduces to a node. Node Reduction https://inquiryintoinquiry.files.wordpress.com/2018/04/cactus-graph-e280a2-… • A “lobe reduction” is permitted if and only if exactly one component cactus listed in a lobe reduces to an edge. Lobe Reduction https://inquiryintoinquiry.files.wordpress.com/2018/04/cactus-graph-e280a2-… That is roughly the gist of the rules. More formal definitions can wait for the day when we have to explain all this to a computer. Regards, Jon