Seeking General Advice on Non Standard Analysis
I would be eternally indebted if anyone could provide me with some helpful info on the following issue.....I will try not to bore too much here.
Okay, so I'm a postgrad philosophy student in London. I usually work on topics in philosophical logic, logical metaphysics and set theoretic issues in possible worlds theories, but I have decided I'm newly a bit interested in philosophy of maths, and have decided to do a thesis on a topic in the history of philosophy of maths. It will be on Berkeley and his objections to the use of infinitesimals in 17th century calculus. (I can provide more info if it would help someone recommend a course of action to me, but I should probably stop if that's not necessary...)
What I'm interested in is whether Robinson's non-standard analysis would have solved some of the consistency issues Berkeley had with the use of infinitesimals. Now, I'm not dreadful at maths, (but since this is an advanced topics forum, I'm probably, given the likely inhabitants of a place like this, comparatively pretty dreadful really) but I'm finding it very difficult to get my teeth into non-standard analysis. Nothing I've found is very accessible to someone not pretty up on their maths.... Also, being a logician, I'm getting the idea that some of the notation is used somewhat differently in maths, so I'll have to brush up on that too.
So, anyway, if anyone could recommend a text or series of lectures, or indeed any approach that they thought might be helpful, I would really appreciate it, because it would be pretty embarrassing to hand in the thesis to my superstar logician supervisor, and have him say, 'You don't get maths do you Clare?'
Now- to the pub...
Thanks so much!
Re: Seeking General Advice on Non Standard Analysis
I were you, I would go to this website and download the first chapter of Keisler's textbook. Now there is next to nothing about philosophy there. But it gives a rather good idea about the foundations of non-standard analysis.
The book Infinitesimal Calculus by Henle and Kleinberg does have bits and pieces of some philosophy in it.