The foundations of arithmetic

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1. IxiausMay 2011
   For quite a long time I hated Math and was horrible at it - I remember being up until 2AM in the morning with my father during 7th and 8th grade trying to do my math homework, taking tests and feeling confident about all of it then receiving my grade that said I failed. After I dropped out of high school and did some self-discovery (involved India, a commune, and a few other journeys) I began a self-study curriculum (created by me). I didn't bring math into the curriculum until about three years ago, I've been fond of logic and the methods of logic for quite some time and ended up finding "The Foundations of Arithmetic" by Gottlieb Frege - a treatise attempting to provide a purely logical framework for number (he influenced set theory) and the operations on number; but, reading it really fired me up, I was absorbed and interested, Frege showed me a completely different side if mathematics that no one in my education had cared to show me or even hint at.

   With that new found interest in Mathematics I set about to find a book that I could use to teach myself. I won't say how I came across it, but I ended up coming across "Practical Mathematics" by C.I Palmer - the 1919 publication, very old. The book is intended for working adults in mechanical trades; the problems in the book were often given using real-world problems in the technical trades. The author also used much more technical language! It was refreshing! Even my high school math textbooks felt like the authors were trying to teach kids and regarded their audience as nothing more than insufferable immatures. This book has been immeasurably valuable to me, I now feel less "darkness" and confusion when I see a math problem, I'm finally seeing the utility in my everyday life of the things I'm learning (my gf had a wedge table and was selling it on Craigslist and needed to know the length of the arc, for example). I actually know how to add and subtract fractions, it's no longer a mystical act of numbers disappearing here and showing up there.

   The greatest thing about that book? Certain operations that most schools only ever taught me as a mechanical process were taught to me and explained to me with the underlying fundamentals in "Practical Mathematics". In 1919 there were no calculators, it had to all be done by hand, even square roots, and you couldn't really survive without knowing why or how certain mechanical operations are used the way they are in Math.

   I'm not sure if college or higher mathematics gets into that stuff, but, it was a revelation for me and I'm well on my way through the Algebras and Trig now - I didn't even make it out of pre-algebra in the traditional educational system. I can also see the beauty of mathematics too, something I never thought I would understand about mathematicians when I used to hate the subject.

   There will never be any "killing" of math. But our educational system has a long way to go.

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2. williamcottonFeb 2023
   In Frege's The Foundations of Arithmetic he disagrees with Kant that a proposition like "2 + 12 = 14" is synthetic (and Kant used large numbers as an example of how analysis would fail!!!). However, once we have a large language model we can experimentally show that math computations are indeed synthetic. Kant was right!
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3. vehemenzSep 2022
   I read The Foundations of Arithmetic and On Sense and Reference for my analytic philosophy course. This was in the U.S. fifteen years ago. I agree that he was not treated as obscure at all. We wouldn't have Carnap (the analytic philosopher) without Frege.
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4. mchannonApr 2019
   Such as Frege's Foundations of Arithmetic?
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