## A Isn’t a

Posted by vlorbik on November 12, 2009

**Symbolic Logic as Beginning Algebra**

We’re {\it reasoning}

already as soon as we’re doing math

of {\it any} kind… and {\it algebraic}

reasoning is going to involve looking

at certain (so-called) strings of symbols.

What better symbols to {\it start} on,

then, in Beginning a course of study of

Algebra, than the symbols created for

discussions of {\it reasoning itself}:

the language of {\bf Symbolic Logic}?

The “usual” way of introducing Algebra

of course uses the symbolism of

Real Number Arithmetic.

This frequently leads to considerable

difficulties due to the astonishingly

rich structure of the Real Number

field.

Working with an {\it un}familiar

symbolism is a tremendous

advantage if it were only for

the ability to wipe out

forest-and-trees issues

like “is multiplication

really repeated addition?”

at a stroke. This is to say

nothing of having “routed

around” such commonplace

anxieties as “I’ve never

been very good at fractions“.

Already these are very good

reasons to at least experiment

with “logic as introductory algebra”.

But… best of all!… there are {\it two values}

in our base set—{\sc t} and {\sc f} typically, or

0 and 1—as opposed to, well,

infinitely or even continuously many.

We will be able to display

{\it complete} “addition” and

“multiplication” tables:

the results of {\it every possible

calculation} of certain kinds. This clears the mind

wonderfully… for what else but

{\it other} kinds of calculating!

## vlorbik said

update on the repeated additon flap

by the ever-awesome #-warrior (jason dyer):

http://numberwarrior.wordpress.com/2010/02/26/multiplication-is-not-repeated-addition-revisited/

see also (hat-tip):

http://mathmamawrites.blogspot.com/2010/02/what-is-multiplication.html

sue v.