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Topic: | Re:IQ and Cognitive Development |
Posted by: | Ann Olivier |
Date/Time: | 2009/4/24 21:40:18 |
I would like to suggest that perhaps one of the difficulties some students have in taking tests which test their intellectual development might be that they do not recognize the logical vocabulary of ordinary language.?They do not realize, for instance, that "nevertheless" does not mean approximately the same thing as "therefore", nor that "it follows that" *does* mean the same thing as "therefore". Years ago when teaching undergraduate philosophy, it became apparent to me that many students had little idea of how to tell a premise from a conclusion, a lack that made reading, for instance, Parmenides' argument against motion or St. Anselm's ontological proof for the existence of God, very difficult if not impossible. As I saw it, the main problem for many of them was inability to recognize?the logical operations imbedded in ordinary language.?So I tried to teach them that vocabulary.?Ordinary language is replete with the language of logical operations including conjunction (and),? implication (if... then) premise indicators (because), conclusion indicators (therefore), and negation (no, not).?(Interestingly, there seems to be only one way to express disjunction in English, "either . . . or".?Hmmm.?Wonder why.) These logical operations are often expressed not only by means of grammatical "conjunctions" and prepositions but also by verbs and other grammatical parts of speech,?as well as being presented by whole phrases.?Furthermore, the logical meanings are often presented by expressions whose meanings are very complex, imbedding as they do not only logical meaning but non-logical meaning as well.?For instance, "to the contrary notwithstanding" means "A is true, and B is true, and A is *most emphatically* not B", and "supposing" means not only "if" but also "think of this thought as a possibility".?(The complexity of ordinary language is truly astonishing!) At any rate, to help the students find the logical structure of texts I had them learn some vocabulary which conveys logical operations.?Here are a few examples: Conjunction indicators:?and, also, too, in addition, besides, furthermore Negations:?no, not, un-, im-, in-, a- Disjunction indicators:?either ... or Premise indicators:?because, owing to,?whenever. supposing,?on account of, from (non-standard English) (Notice especially that sometimes premises are expressed *after* their conclusions.) Conclusion indicators:?therefore, so, it follows that, consequently, Q. E. D. Opposition indicators (these have complex meanings which include two conjunctions and one negation):?but, however, yet, nevertheless, as contrasted with,?(Piaget noted somewhere that "however" includes "and".?Did he talk about this general subject anywhere??I'd like to know his thinking on the subject.) Implication indicators:?if . . . then, implies Conclusion indicators:?therefore, so, it follows that, accordingly Notice that some logical indicators are single words, that they include other parts of speech besides prepositions, and that many of these expressions include much, much more meaning than the simple logical content.?And notice that some are whole phrases. while others are only parts of words.?Further, not all of them are standard English.?Last, be aware that these expressions do not always mean the same thing in different sentences. How to tell what these expressions mean in any given sentence??I'm afraid there is no rule.?Just look at the context and ask yourself the classic question of Wittgenstein: what does this MEAN?? I might add that I also taught the students to mark some little symbols above the expressions in the texts they were reading so that the logical structure of the whole text would be more apparent.?A dot above an "and" meant "and", while a triangle meant a conclusion;?arrows were used to point towords premises, "Y" meant opposition, and a tilde (a squiggly symbol I can't reproduce here) meant negation. Some time ago I mentioned this little method on this list, and several people were interested in my unit that explains it in more deetail.?However, I couldn't find a copy of it at that time.?I've since found it,?and I'll gladly send it to you if you send me your email address again, and if I can figure out how to attach an attachment.?Sigh. |