# Mathematical Logic

Craven, Jim jcraven at clark.edu
Tue Jul 8 08:16:39 MDT 2003

```Here is an exercise I do in class to show the tautological nature of formal
mathematical logic and "proof".

I show them a TV program in which the supposed "magician" asks for three
different single-digit integers from 0 to 9. E.g. 3, 2, 6, On the show he
then reverses them to 6, 2, 3 and sets it up to subtract 326 from 623.

623
-326
-----
297

He then asks the audience to add across the individual integers of the
result 2 + 9 + 7 = 18 But he already has 18 prewritten. He then makes the
claim that "no one can figure out how this works" (always 18)

So we set it up as follows:  X1 X2 X3  Rule 1: Must be three DIFFERENT
integers; Rule 2: X1 > X3
-X3 X2 X1
----------

Given the set-up and the rules: If X1 > X3, then X3 - X1 must = X3 + 10 -
X1;
Then X2 -1 - X2 must = X2 - 1 + 10 - X2;
Then X1 - X3 must = X1 -1 -X3

Then adding the individual integers of the result across we get:

X1 - 1 - X3 + X2 - 1 + 10 - X2 + X3 + 10 - X1 = y

Since the + and - X1s, X2s and X3s cancel out, we get 10 + 10 -1 -1 = 18

Once we get you to accept the two basic rules and step inside the box of the
game the result will be predictable if you can do basic arithmetic. I use
this to illustrate how the powers-that-be can get people to accept the basic
rules and premises of "the game"--capitalism--and then the "predictions"
become automatic and contrived; I also use this to challenge some of the
tenets of philosophical positivism--prediction is the only test of
"validity" and the basis for "testing" the appropriateness of the
assumptions of the syllogisms without any need for independent empirical
support for the premises of the deductive process.

Jim C.

```