Topic: | Re:Correct application of categorical logic does not cause misuse of the either/or distinction. |
Posted by: | nj |
Date/Time: | 01/11/2003 04:13:09 |
Hello. I made two mistakes, (1) and (2), in my post about the application of categorical logic. If you read my first post to this thread, then please read this post. (1) I made vague use of the terms "valid" and "form" in my first post. (2) I made innaccurate use of the term "standardized" in my first post. I'll address points (1) and (2) by correcting the misuse of terms in quotes (3) and (4). (3) "My attempting at formulating a falsely dichotomous argument failed to produce a valid syllogism. Conclusion (16.3) is not a valid conclusion to draw from premises (16.2) and (16.1). The syllogism is not in valid form." (4) "I can expand upon my point (1) using example (16), an example of a standardized categorical logic syllogism. (16.1) Some men are ugly men. (16.1.1) Some M are U. (16.2) Some men are nonugly men. (16.2.1) Some M are not_U. (16.3) Some men are handsome men. (16.3.1) Some M are H. In the case that the the negation of the symbol U, not_U, is identical with the symbol H, the conclusion of syllogism (16) is true for reason (17), that is: (17) All nonugly men are handsome men. (17.1) All not_U are H." In quote (3), I wrote that the quoted syllogism (16) was not in valid form. Well, I meant to write that the syllogism was not in standardized form. I knew that the syllogism was not in standardized form. My use of the terms "valid form", was meant to avoid a discussion of standardizing arguments, but, by my writing of quote (4), I brought my ignorance of categorical logic into plain view. In quote (4), I wrote that the quoted syllogism (16) was a standardized categorical logic syllogism. In fact, I knew, at the time I wrote my first post, that my standardization of quoted syllogism (16) was not adequate. (5) I lacked full knowledge of standardization criteria applicable to quoted argument (16), so I wasn't sure how to formally standardize it according to classical rules of syllogistic logic. (6) I already knew that quoted argument (16) was an invalid syllogism and an incorrect interpretation of a natural language argument. I wanted to write an example that made clear that the natural language version of quoted argument (16) was invalid. (7) So I did not present a standardized form of the unsound quoted argument (16). Reason (5) lead to my result (7). But, if I had not written that quoted syllogism (16) was in standardized form, I might not be writing this post right now. Anyway, here are some revisions, starting with revision (8), revisions that I will make to the first post of this thread. My revision (8) would substitute for quote (4), replacing the content of quote (4) in my previous post. (8) " I can expand upon my point (1) using example (16), an example of a standardized categorical logic syllogism. (16.1) All nonugly men are handsome men. (16.1.1) All not_U are H. (16.2) Some men are nonugly men. (16.2.1) Some M are not_U. (16.3) Some men are handsome men. (16.3.1) Some M are H. Syllogism (16) is valid, but the conclusion of syllogism (16) is sound only if proposition (17) is true, that is: (17) All nonugly men are handsome men. (17.1) All not_U are H. proposition (17) is premise (16.1), in syllogism (16). Premise (16.1) is false. Premise (16.1) falsely implies that the complementary relationship: (34) ugly/nonugly is equivalent to the contrary relationship: (35) ugly/handsome. Syllogism (16) is valid, but not sound. " The quoted syllogism (16), the quoted syllogism in revision (8), is STANDARDIZED, according to criterion (9). (9) The first premise of the standardized categorical syllogism has the middle term as its subject term, and the conclusion's minor term as it's predicate term, while the second premise has the middle term as its predicate term, and the conclusion's major term as its subject term. I need to make another revision, (10), to my first post, as well. (10) "Consider syllogism example (29). (29.1) All forum guests are NLPers. (29.1.1) All G are N. (29.2) Some people nonhappy with the forum are forum guests. (29.2.1) Some not_H are G. (29.3) Some people nonhappy with the forum are NLPers. (29.3.1) Some not_H are N. In the case of syllogism (29), statement (30) is true: (30) Some people nonhappy with the forum are NLPers. But what is the answer (33) to the question: (32) Is it true, from syllogism premises (29.1) and (29.2), that some people unhappy with the forum are NLPers? The answer (33) is: (33) No, it's not true. You don't know if the nonhappy people are unhappy people. The nonhappy people could be ecstatic, or indifferent, or disappointed." I made revision (10) by substantizing the adjectival predicate, the adjectival predicate that appears in my first post as part of the first post's syllogism (29): (11) nonhappy with the forum to make it a subject term noun phrase: (12) people nonhappy with the forum. Changing predicate (11) to predicate (12) brought some clarity to the categorical syllogism quoted in revision (10), and also put that categorical syllogism into standardized form (I hope!). If I were to rewrite my post completely, I might follow two additional steps, (13) and (14). (13) write each example syllogism using an explicit equivalent parameter for each term used in a single syllogism and (14) translate the parameterized syllogism statements back into readable english. I could make an attempt to integrate revisions (8) and (10) back into my earlier post, along with the further changes that result from my following steps (13) and (14). I have two requests for any reader who made it to the bottom of this post by reading the post. My request is: (15) If you spot an inadequacy or other error in the syllogism standardization criterion I give in item (9) of this post, could you please reply back to this post? I will also appreciate any reply that alerts me to other errors in this post. -nj ps: if you're interested in how to parameterize subject and predicate terms in a syllogism, reply to this post, and I'll explain what I think it is to parameterize subject and predicate terms. I didn't explain what I meant by parametrization of terms in this post, but I can in a reply post. If you're upset that I didn't explain what I meant, but you know what I meant, you could still tell me why you're upset, in a reply to this post. pps: if you're upset that you read this far, but you had difficulty reading the writing, read: "Re:Re:Re:Re:andrea's new book and WITW 27/10/2003 22:44:58 nj", particularly item (2) in that post. |