Re: inverse/obverse


Ken Pledger wrote:
-big snips-

Ken,

Thank you. I appreciate the references to Euclid. The Dover editions -
Heath's translations - and a good drafting compass was my first real
glimpse of the beauty of mathematics. Its funny... since I picked
geometry up on my own, out of Euclid , I had to eventually be told that
it wasn't necessary to draw out the whole circles in my
constructions. They looked much cleaner after I had this information.
Anyhow, what I was able to see in Euclid was axiomatic structure. I
don't think math would have meant anything to me otherwise. Kneal and
Kneal in The Development of Logic believe that, although Aristotle
wasn't a mathematician per se, the origins of greek logic,
Aristotle's included, most likely arose from consideration of the
type of reasoning found in geometry at the time. (I've only read
sections here and there from this title.) My next major influence came
in the form of Frege's Foundations of Arithmetic. I read this book
six times over the last summer. I'd have to say that it is one of the
most profound things I have ever read. I enjoy Boole's Laws of
Thought. I visualize Boole as trying to shove a square logical block
into a round algebraic hole. I can almost see it... good, good is good
squared...shove, shove... and yet, somehow things begin to work. It
almost fits. Dedekind's terminology was very difficult and I'll
have to go back to him when I have the time. (I'm beginning to see some
of these terms pop up in discrete math... mappings etc.) I wish that
more of Cantor's work was in English. Trying to read papers that
reference other papers that you cannot read doesn't do a thing.

I suppose I'm at the point where I cannot be self taught anymore.
Hence, the classes. I do however prefer reading the primary sources for
these things.

Thanks again,

-Mike

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