"Logic is to the philosopher what the telescope is to the astronomer." Suzanne K Langer
Suzanne K. Langer's "Introduction to Symbolic Logic" was one of my first favorite mathematics books. I thought it revealed all secrets to the origin and nature of mathematics. Her book shows how to derive symbolic logic from language alone. This i hoped was the key tools to being a mathematician. I started rereading it recently since 1) it's been a long time, and 2) i've made connections between James Burke's connections and Jacob Bronowski's "Origin of Knowledge and Imagination." Suzanne's book is unique amongst Symbolic Logic books; and despite her coming close, she doesn't have Jacob Bronowski's ideas to see that even her book doesn't encompass all the secrets to mathematical creativity(it's not her fault; Jacob Bronowski's ideas comes later in the twentieth century).
Still, in rereading, I've found much to review and rethink. I also found perhaps a possible proof of Jacob Bronowski's ideas. Like the way you won't find a number two, or an imaginary number, or even a set of zero dimensional points all aligned as a straight line lying around on the ground, you won't find a relation lying around on the ground. Nature comes at you as a whole; we make the dividing lines. For instance, the sun; there's no dividing line between the matter and the energy of the sun. Yes, there's some things that seem to have hard dividing lines like the tree from the air; but, this is a perception of scale. On other scales, you can see the thermodynamic energy flowing between me, the air, and the tree. I noted this when rereading chapter 2.1 of Suzanne's book.
I assumed that those who've read my ideas about the origin and nature of mathematical concepts(2nd or 3rd post of this blog); you should see the logical connections of what I'm suggeting as a proof of my and Jacob Bronowski's ideas. If Jacob Bronowski's ideas are wrong, then why don't you find bare relations on the ground?(much less negative numbers, the square root of two, one dimensional lines composed of zero dimensional points and so on and so forth)
just found a pretty good image of her youth days. She was born in 1895 and lived to 1985!