Topic: | Correct application of categorical logic does not cause misuse of the either/or distinction. |
Posted by: | nj |
Date/Time: | 31/10/2003 00:59:20 |
Hello. I wanted to make three claims, numbered (1) through (3), about the either/or distinction, and about the false idea that correct application of categorical logic causes misuse of the either/or distinction. (1) Categorical logic does not force a falsely dichotomous interpretation of the either/or distinction, the either/or distinction used in natural language. (2) Two types of predicate relationships can be involved in understanding an either/or distinction. (3) False dichotomies, binary thinking, and polarized thinking, can stem from a failure to distinguish complementary predicates from contrary predicates (antonyms). Statement (2) identifies predicate relationships (4) and (5), which are explicitly mentioned in statement (3). (4) the complementation or complementarity predicate relationship. (5) the contradiction or contrariness predicate relationship. Examples of complementary predicates are listed in predicate pairs (6) through (10). (6) caucasian/noncaucasian (7) healthy/nonhealthy (8) excellent/nonexcellent (9) capitalist/noncapitalist (10) friend/nonfriend Examples of contrary predicates are listed in predicate pairs (11) through (15). (11) good/evil (12) divine/satanic (13) strong/weak (14) beautiful/ugly (15) love/hate 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. But, some nonugly men look other than handsome, instead having a look that might be: (18) funny (19) gorgeous (20) boring (21) plain (22) strange (23) dark. 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. My statement (1) is true, though. The burden is on you, the author or interpretor of a categorical syllogism, to write or interpret the categorical syllogism so that the syllogism is accurately tested against criteria (24) and (25). (24) Are your natural language intuitions are satisfied by the writing of the categorical syllogism? (25) Is the syllogism in valid categorical syllogism form? Syllogism (16) represents a false dichotomy, and is not a valid form of categorical syllogism. To associate the rules of categorical logic, with a personal failure to distinguish complementary and contrary predicate relationships, is to make an error of type (26). (26) The error is one of blaming the instrument for the user's fault in her use of it. or, to put error (26) nonmetaphorically: (27) The error is one of confusing a complementary predicate relationship with a contrary predicate relationship, when you are determining the validity of a categorical syllogism. A categorical syllogism's validity can always be correctly determined by the rules of the categorical syllogism. Categorical logic does not force you to construct false dichotomies. What might force you to construct a false dichotomy? Maybe: (28) the limits of your vocabulary, its limits to correctly express complementary relationships between predicates, determine if you can translate accurately from a categorical syllogism to its natural language equivalent. Consider syllogism example (29). (29.1) All forum guests are NLPers. (29.1.1) All G are N. (29.2) Some forum guests are nonhappy with the forum. (29.2.1) Some G are not_H. (29.3) Some NLPers are nonhappy with the forum. (29.3.1) Some N are not_H. In the case of syllogism (29), statement (30) is true: (30) Some NLPers are nonhappy with the forum. But what is the answer (32) to the question: (31) Is it true, from syllogism premises (29.1) and (29.2), that some NLPers are unhappy with the forum? The answer (32) is: (32) No, it's not true. You don't know if the nonhappy NLPers are unhappy NLPers. The nonhappy NLPers could be ecstatic NLPers, for example. Or indifferent NLPers. In case you're interested, a valid form of syllogism (16) is given by syllogism (33). (33.1) Some men are nonugly men. (33.1.1) Some M are not_U. (33.2) All nonugly men are handsome men. (33.2.1) All not_U are H. (33.3) Some men are handsome men. (33.3.1) Some M are H. Premise (33.2) is false. Premise (33.2) falsely states that the complementary relationship: (34) ugly/nonugly is equivalent to the contrary relationship: (35) ugly/handsome. Syllogism (33) is valid, but not sound. So, when confronting a seeming failure of reasoning, a failure like dichotomous thinking represents, you can always blame the logician, even if the logician gave a valid argument. -nj |