Article #182
Subject: Pascal on mathematical proof and definition
Author: Andrew W. Harrell
Posted: 7/30/2012 11:33:19 AM

Pascal on Mathematical Proof and definition


In his essay “On Geometrical Demonstration (on the Geometrical Mind) included
later in the Great Books volume Pascal explains his ideas about some
fascinating theories of mathematical proof and definition. It is interesting
to compare this essay on Pascal’s mathematical method of discovery and proof
with Descartes, and later Poincare’s. But, that is a more difficult
discussion. I will just mention some of his aphorisms and assertions here:
“We must give definition to the defined. [in order to discovery new truths]”
Rules for definition:
1) do not attempt to define any of those things so well known in themselves
that we have no clearer terms to explain them by.
2) Do not leave undefined any terms that are at all obscure or ambiguous
3) Use in the definitions of terms only words perfectly well known or
already explained.
Rules for axioms:
1) Do not fail to ask that each of the necessary principles be granted,
however clear and evident it may be.
2) Ask only that perfectly self-evident things be granted as axioms 3) “Time
is [defined as] the motion of a created thing”

“The three fundamental concepts of science and mathematics are:
1) motion
2) number *
3) space

*in relation to understand how to define number you might want to see our
discussions on “How do we define the number one?” that are posted on the
http://www.yhwhschofchrist.org/discussionboard Sciene and Religion directory.
It focuses on the German Logician and Mathematician Gottfried Frege’s ideas
of this, the history of the development of the modern computer, and how this
question relates to epistemology and the question “What is the Concept of a
Concept”.