Dear Ben, lists - Thank you for good illustrations of the issue. I discuss the example with suicide and banrkuptcy from "An Improvement of the Gamma graphs" towards the end of ch. 8. Here Peirce denies the rule of passage - the "strange rule" as he has it - granting the equivalence between your graph 1 and your graphs 2 and 3. Thereby, P insists that "There is a man, and if he goes bankrupt, a man commits suicide" is different from "There is a man, and if he goes bankrupt, he commits suicide". There are at least two difficulties here - one that we tend to read these claims as causal, temporal claims while they must be read as purely logical - the other is that a claim about (at least) one person having two properties (2,3) is identified with (1) a claim about two persons having one property each (but the two may be identical, we do not know). It is the second of these difficulties which P addresses, and the reason for his doubts, leading him to deny the "strange rule" seems to be that he wants to be able to read the implication in 2) and 3) as saying that having one property entails having the other.
Best F Den 18/01/2015 kl. 00.20 skrev Benjamin Udell <bud...@nyc.rr.com<mailto:bud...@nyc.rr.com>>: Jim, list, Expository examples in everyday language are usually open to logical criticism. If 'these beans' lack reference, then Peirce's examples of inference modes don't work any more than my examples with 'John'. As to the rules of passage in terms of graphs, here are some examples. Note that 'Z' plays the same role as 'bankrupt'. <Postbilag.png> See "An Improvement on the Gamma graphs" (1906), CP 4.573-580, see 580 http://www.existentialgraphs.com/peirceoneg/improvement_on_the_gamma_Graphs.htm . There you'll see the graph equivalences that bothered Peirce. Best, Ben On 1/17/2015 5:41 PM, Jim Willgoose wrote: Curious. The formula "S is P" or "S is not P" do not seem to carry enough information to decide the question. On the other hand, if "John" lacks reference, the statements "John is blue " and John is not blue" are consistent. (trivial empty) Further, one may tempted to treat these as Universals; (or singleton classes). But then, the existent singleton class inclusive of "every John" doesn't seem to obey the rule of contrary, namely, "may both be false," unless there are two Johns. Aristotle's definition of a contradiction seems to me to exclude this. The square of opposition is always fun to play with. I sometimes like to consider that "everything exists" so it works alright. BTW, waiting to see how you use the "rules of passage" in terms of graphs. Jim W
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