[EM] Richard's frontrunners example (fwd)

[Forest Simmons]

The following email from me to Tony came back to me as undeliverable, so
I'm hoping he can get it in the [EM] list. Others can read, too.

Forest

---------- Forwarded message ----------
Date: Fri, 23 Feb 2001 14:38:05 -0800 (PST)
From: Forest Simmons <fsimmons at pcc.edu>
To: Anthony Simmons <krl at yahoo.com>
Subject: RE: [EM] Richard's frontrunners example (fwd)

I liked your response so much that I cut short the following response that
I was preparing. But I thought you might be interested in another Simmons
version of the same answer. 

Forest

---------- Forwarded message ----------
Date: Fri, 23 Feb 2001 14:29:23 -0800 (PST)
From: Forest Simmons <fsimmons at pcc.edu>
To: MIKE OSSIPOFF <nkklrp at hotmail.com>
Cc: election-methods-list at eskimo.com
Subject: RE: [EM] Richard's frontrunners example

Here's one way of looking at it:

I tell my kids that if they clean their rooms, then they can have a treat.

If they clean their rooms, then I must come through with the treat, or
"Dad's a liar."

If they don't clean their rooms, then I cannot be accused of having lied, 
whether or not I decide to give them the treat.

The convention is "If A then B" means "B or not A".  A convention is a
definition, so it is actually a fact of technical language (among those
who make or accept the agreement).  If a definition confuses people, then
it can be said to be in poor taste, and if it contradicts itself or some
other important element of the technical language, then you could say it
was wrong.  But a definition, per se, has no natural correctness or
incorrectness; in mathematics it is just an abbreviation (however ill
advised) of some other combination of the previously defined terms, or of
the undefined terms.

It is not possible to define all of the terms in a language without
circular paths among the definitions.

Mathematicians try to get multiple use out of colloquial words and phrases
when their colloquial meaning approximates the technical meaning, but
often the result is more confusing than helpful.

Logical implication is a borderline case in this regard.  What makes it
worse is that "If A Then B Else C" statements for program flow in computer
science are another (related but not identical) usage of the same
language.

In this case, A is a statement to be tested as true or false, but B and C
are commands or jumps, etc. to be carried out, not to be tested for truth
or falsity. In the computer science usage, if A is false, then B will be
definitely skipped, or the flow is wrong.  In logic, if A is false, then B
may or may not be true without contradicting the implication.

Logical OR is another borderline case.  In colloquial usage, "or" is often
intended to be what we call "exclusive or" (XOR).  So in colloquial
English usage, if someone says, "You can have fries or toast..." it would
probably mean one or the other but not both.  In math when I say n is
either even or a multiple of three, the possibility of both is not
excluded.


Forest


On Thu, 22 Feb 2001, MIKE OSSIPOFF wrote:

> 
> >If A then B, is commonly understood to mean that A causes B.  In mathmatics
> >this isn't the case.  An if...then statement is a truth functional
> >statement, saying that whenever A is true, B is true.  If we have
> >established the truth of 'if A then B' (or we are positing the truth of 
> >that
> >statement), the following is true;
> >- if A is true, B is true
> >- if B is false, A is false
> 
> So far so good, I didn't doubt those things.
> 
> >
> >Because it is a truth functional statement, if A is false, the statement A
> >then B will be true (irrespective of the truth of B).
> 
> That's the part I didn't understand.
> 
> 
> >This is the tricky
> >bit - if A is false, it is an impossible contradiction for A to be true.  
> >As
> >a result; if A is true then anything is true.  The statement 'if A then...'
> >will always hold. eg. if water can talk then I'm a banana - a true &
> >logically valid statement.
> 
> I understand what you're saying, but, supposing that water actually
> can talk, and, because that's impossible then we can suppose everything
> that's impossible--that sounds a bit weak, doesn't it? Wouldn't it
> make much more sense to just say that, since water can't talk, then
> the statement that you're a banana if water can talk isn't saying
> you're a banana? Can it be true or false to not say that you're a
> banana? The statement would be true if it said that you aren't a banana.
> But it doesn't. It merely doesn't say that you are one.
> 
> Now we're talking about conventions of logicians & mathematicians.
> But conventions aren't the same as facts.
> 
> Mike Ossipoff
> 
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