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Showing posts with the label rationalism

Final Thoughts on Cowie

In recent weeks, I've given my reactions to Fiona Cowie's 1999 book, What's Within. Today I'll conclude that line of posts. Cowie only briefly discusses Chomsky's famous reply to Skinner, and so far as I can tell her discussion accepts the idea that Skinner got outside of the range of his competence by writing VERBAL BEHAVIOR, and that Chomsky was right to rebuke him. Her view on language development, then, is not "forget all this subsequent nonsense, go back to Skinnerian 'positive conditioning' as a model, and try again." Her view, rather is that if there is to be a tenable empiricism with regard to language it will have to be an "enlightened empiricism," a post-Skinnerian sort. And she seems to hope such an enlightened empiricism will develop as a school of thought, though she does not explicitly align herself with it. If I understand her, she is saying that a minimalist nativism as to language ability may be necessary to expla...

Still Thinking About Numbers

As I mentioned in a blog entry last week, the value of pi slips away from you if you try to state it as a simple fraction, even in a good try such as 22/7.  If we represent numbers in decimal rather than fractional form we can express the strangeness of pi, its irrationality, in a different way. We can turn any simple fraction into one of three sorts of number: a simple integer, an integer followed by a string of decimals that comes to a definite end, or an integer followed by the string of decimals that doesn’t come to an end but that settles down into satisfyingly dull repetition.        Here are some simple fractions: 9/3, 11/4, and the aforementioned 22/7. The first, 9/3, resolves itself into the integer 3. 11/4 is 2 ¾, or in decimal form 2.75. That is where it terminates. 22/7 is 3 1/7 or in decimal form 3.142857142857.... It is a repeating decimal. That is: the sequence "142857" will continue repeating for as long as you have the patience to ...