Topic: | Categorical Logic & Either/Or. Topic: Epistemology. |
Posted by: | nj |
Date/Time: | 03/11/2003 08:26:05 |
Hello. I got my earlier questions answered. Yes, I was still lacking in knowledge of categorical logic. I didn't know about figures in categorical logic, but was relying on categorical syllogism validity tests that checked syllogism statements for combinations of term distribution and mood, rather than combinations of figure and mood. This led to my confusion when I encountered a discussion of standard form syllogisms of figure 1. I thought figure 1 syllogisms were the only standard form of categorical syllogism. My mistake. Below is a substantial revision of my post, my post about the either/or distinction. ------------------------------------------------- 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) 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 between the terms "ugly" and "nonugly" is equivalent to the contrary relationship between the terms "ugly" and "handsome". Some nonugly men can look other than handsome, instead having a look that is: (18) funny (19) gorgeous (20) boring (21) plain (22) strange (23) dark. 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) Your natural language intuitions are satisfied by the writing of the categorical syllogism. (25) The syllogism is valid, or, the conclusion logically follows from the premises. YOu can confirm criterion (24)'s satisfaction if the syllogism says what the author meant it to say. You can confirm criterion (25)'s satisfaction if the argument is logically correct. Categorical logic prescribes reliable rules to determine if a categorical syllogism is logically correct (valid). You can use those rules, or you can use your own mathematical sense, to determine whether a syllogism is valid. 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, validity in virtue of its form, is correctly determined by the rules of the categorical syllogism. Categorical logic does not force you to construct false dichotomies. So 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 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 (32) to the question: (31) Does it logically follow that, from syllogism premises (29.1) and (29.2), some people unhappy with the forum are NLPers? The answer (32) is: (32) No, it does not logically follow. The nonhappy people might not be unhappy people. The nonhappy people could be ecstatic, indifferent, and disappointed people who are NLPers. So, when confronting a seeming failure of reasoning, a failure like dichotomous thinking represents, check if the logician equated a complementary relationship to a contrary relationship, when he formalized his categorical logic syllogism. -nj |