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The Stuff of Thought
Q: How did you start out in music?
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The Metaphysics of Sentences
One of the weirdest things about your brain is the fact that sentences, born as a product of thought, emerge from you as real things in so far as they all have real properties of structure and content. That is to say, they exist in a realm somewhere between disembodied ideas and those strings of words we all produce on sound waves in the air or as marks on paper or as circuits on a chip. And yet, how these "things" are created eludes our understanding. We just seem to have some sort of magic filter somewhere in our brain that picks out real sentences from jumbles of words and casts the non-sentence material onto the junk heap of the incomplete or unintelligible. Single words (or names) are often proposed to be the basic blocks of language, but I think the sentence has the greater claim for this distinction. (Appanrently, Ludwig Wittgenstein thought so too, but he may have gotten that idea from Gotlieb Frege.)
We know a sentence when we see or hear (or even think) one, even as infants. No one taught us this. And no one has successfully explained how or even why this happens. It might as well have come from outer space. This is important – important, at least, to the peculiar little world of this website. Because it helps to realize that you are playing with this weird gift every time you utter a sentence.
There are two ways of grasping the idea of a sentence. Both are more or less theoretical depending on one’s perspective. Let me try to get at these two approaches to a sentence through the well-established terrain of mathematics. To do this you will have to, at least to begin with, force yourself to see a sentence, for convenience sake, as just a collection of numbers. There are an infinite number of numbers (1+1+2+3+4 . . . .) and there are an infinite number of sentences.
UNDER CONSTRUCTION
Mathmeticians deal with all kinds of numbers – real numbers, whole numbers, negative numbers, imaginary number, surds, etc. But there is another distinction that is going to be useful here. And that is the difference between a number and a numeral. I could explain this, but I think I’d rather you hear it from a mathematician – or two.
So with credit to Ernest Nagel and James R. Newman, I quote from their now-legendary little book Godel’s Proof:
(p. 82 footnote)
We know a sentence when we see or hear (or even think) one, even as infants. No one taught us this. And no one has successfully explained how or even why this happens. It might as well have come from outer space. This is important – important, at least, to the peculiar little world of this website. Because it helps to realize that you are playing with this weird gift every time you utter a sentence.
There are two ways of grasping the idea of a sentence. Both are more or less theoretical depending on one’s perspective. Let me try to get at these two approaches to a sentence through the well-established terrain of mathematics. To do this you will have to, at least to begin with, force yourself to see a sentence, for convenience sake, as just a collection of numbers. There are an infinite number of numbers (1+1+2+3+4 . . . .) and there are an infinite number of sentences.
UNDER CONSTRUCTION
Mathmeticians deal with all kinds of numbers – real numbers, whole numbers, negative numbers, imaginary number, surds, etc. But there is another distinction that is going to be useful here. And that is the difference between a number and a numeral. I could explain this, but I think I’d rather you hear it from a mathematician – or two.
So with credit to Ernest Nagel and James R. Newman, I quote from their now-legendary little book Godel’s Proof:
(p. 82 footnote)