From: gavan@UCT_elc.mth.uct.ac.za (Gavan Tredoux)
Subject: Logic and the South African Defence Act
Date: Sun, 26 Jul 92 16:39:04 GMT
Organization: University of Cape Town
X-Newsreader: Tin 1.1 PL4

scott@concave.cs.wits.ac.za (Scott Hazelhurst) writes:

[SA Defence Act definition of 'white' for purposes of conscription]

: "1. 'White person' means a person who (a) in appearance obviously
: is a white person and who is not generally accepted as a
: coloured person; or (b) is generally accepted as a white person
: and is not in appearance obviously not a white person,
: but does not include any person who for the purpose of the
: repealed Population Registration Act freely and voluntarily [admits?]
: that he is by descent a Black or coloured person unless it is
: proved that the admission is not based on fact.
: "2. The above definition of a 'white person' must be read with
: the following definitions: (a) 'coloured person' means a person
: who is not a white person or a Black; (b) 'Black' means
: a person who is, or is generally accepted as, a member of any
: aboriginal race or tribe of Africa"


This is actually very amusing, an exercise in logic worth pursuing.
(Preliminary question: is this classical logic?) We use the symbols

not  		~
or  		\/
and  		/\
implies  	==> 
equality	=

with the obvious bindings and parentheses

0.  black = indigenous.

1.  (appears white) /\ (~ coloured) ==> white 

2.  (~~(appears white)) /\ (~(black \/ coloured)) ==> white 

3.  coloured = ~(white \/ black) ? Ambiguous, might be parsed as
3.' coloured = (~white) \/ black

So the only independent test we have is for blackness. Leaving aside
its vagueness, a little substitution produces

4. (appears white) /\ (~~(white \/ black)) ==> white, or
4' (appears white) /\ (~((~white) \/ black)) ==> white

Are we in classical logic? That is, do we have (~~p) = p? Or are
the legislators of the august parliament INTUITIONISTS? Assume they aren't,
which is reasonable to say the least. Consider either 3 or 3':

----------------------------------------------------------------------------------
a. (Assuming 3 is intended)
----------------------------------------------------------------------------------

By substitution and cancelling the ~~ in 1

5. (appears white) /\ (white \/ black) ==> white

By distribution laws

6. (((appears white) /\ white) ==> white) /\ (((appears white) /\ black) ==> white)


So if you're black and appear white, then you're white. Notice the presence
of the "or" between (a) and (b) in the text of the act, which is why we get
both 1 and 2 as valid implications.

By substitution in 2 and more manipulation we get

7. (appears white) /\ (~black) /\ white ==> white

Notice that this is a logical tautology, as is the first clause of 6, and is
thus redundant. It appears that our parliament now LEGISLATES tautologies.
Nice to be reassured ... 

----------------------------------------------------------------------------------
b. (Assuming 3' is intended)
----------------------------------------------------------------------------------

By substitution in 1, distribution and cancellation

5' (appears white) /\  (~black) /\ white => white

Which is more reasonable, although obviously redundant, another
legislated tautology. 

But 3' is clearly unreasonable,
for one is then coloured if one is black, but for the purposes
of the act that's fine - they want to identify whites rather more
urgently. How would this affect the status of the House 
of Representatives, the coloured House of Parliament? Intriguing.

But once could argue very convincingly in law that this
is so unreasonable that Parliament could not possibly have intended
it. This forces 3 and then the act is again patently unreasonable.
Perhaps the rush to get it through clouded their minds?

Again by substitution in 2 we get

6'  (appears white) /\ (~black) /\ white => white

Another legislated tautology.

----------------------------------------------------------------------------------

I think the above forms an excellent basis for disputing the validity of
the Defence Act as currently ammended, at least those *crucial* clauses,
and is conclusive proof of the stupidity of our legislators.

Maybe the ECC should get on to this ...

Gavan Tredoux
Dept Math / Dept Philosophy
University of Cape Town


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