I have been thinking a lot. I am considering (and inclined toward) the view that we must restrict ourselves to a first-order language. As I recall, Quine believed this. I think it destroys most of math. But science can, I think, get along with just rational numbers. It is possible to do math as just manipulation of symbols, which have no meaning – except in our imaginations. Also, it seems to destroy my ideas about belief.<\/p>\n
After more thought: I am not sure it affects my philosophy of belief. I quantify over symbols for properties and relations – not properties and relations themselves!<\/p>\n
Note: (later yet). There could be many properties and relations foe which there are no symbols.<\/p>\n
Another Note (Still later). Could you permit quantifying over names of properties and relations of properties and relations and so forth (without quantifying over the properties and relations themselves?<\/p>\n
Another Note (Still later) I read in Goble – _The Blackwell Guide to Philosophical Logic_ (page 34)\u00a0 that thhere cannot be adequate descriptions of natural (hence rational) numbers in first-order languages. I had forgotten that — there is so much to remember. I need to work out axioms for my idea – which is not either exactly first-order or higher-order. (at least as I understand these).<\/p>\n
Another Note (7\/28) I should have known 1st order logic was inadequate to arithmetic – as Goedel’s theorem proves any logic adequate to arithmetic is incomplete, and he also proved st order logic was complete. (At least if my foggy memory & reasoning are correct).<\/p>\n
<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
I have been thinking a lot. I am considering (and inclined toward) the view that we must restrict ourselves to a first-order language. As I recall, Quine believed this. I think it destroys most of math. But science can, I think, get along with just rational numbers. It is possible… Continue reading