[FOM] dx's and dy's versus epsilon-delta

Neil Tennant neilt at mercutio.cohums.ohio-state.edu
Wed May 20 16:58:48 EDT 2009

A brief observation about dx' and dy's versus epsilon-delta treatments:

Modern "rigorous" textbooks provide epsilon-delta definitions. But they
hardly ever actually use those definitions when proving theorems of the
differential calculus. I was surprised by this when I sought to regiment,
in natural deduction, the small amount of real differential calculus used
in Newton's derivation of Kepler's laws of planetary motion. In
re-deriving everything as a logician, I found I had to put in completely
different reasoning for the main theorems and lemmas than that which is to
be found in the textbooks (even Apostol).

Anyone interested in the results of this escapade is welcome to send me a
private email for the two papers concerned:

1. The Logical Structure of Scientific Explanation and Prediction:
Planetary Orbits in a Sun's Gravitational Field

2. Natural Logicist Foundations for Functions of Reals and their

Neil Tennant

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