Re: Cum Hoc, Ergo Propter Hoc

From: Daniel Ryan (danielmryan_at_sprint.ca)
Date: 08/30/04 

Date: Sun, 29 Aug 2004 23:19:23 -0400

> So are the following also examples of the same logical fallacy?

As far as the first one, no. It broaches a different fallacy.

> (a) I can demonstrate a one-to-one correspondence between
> complex numbers and points in the (x,y) plane. There are two
> real numbers that correspond to every complex number, and
> there are two real numbers that correspond to every point in
> the (x,y) plane. Given a point in the (x,y) plane, I can
> use the SAME TWO NUMBERS to define a complex value, and
> vice versa.

This taps into a subtle issue relating to the reals vs. the rationals:

The rationals (aleph-0) are nestled within the real number line in terms of
numerical value; the intuitive implication from this is that any real number
can be accurately mapped by a rational, including a rational expressed in
decimal form which terminates at a finite value.

Pi = 3.141592653.............

This intuitive implication has been proven to be false, by (at least)
Whitehead and Russell. A number has to belong to aleph-0 or aleph-1 but not
both. (Formally: the interestion of the set of numbers in aleph-0 and the
set of numbers in aleph-1 is the empty set.)

A statement such as "Numbers in Aleph-0 are nestled into Aleph-1 in terms of
value; therefore, Aleph-0 is a subset of Aleph-1" is not an example of cum
hoc, ergo propter hoc but a diferent fallacy: non sequitur - "it does not
follow".

Let me be clear about something. This post is essentially digressionary: I
have no evidence that Prof. Wiles paper contains either the cum hoc, ergo
propter hoc fallacy or the non sequitur fallacy, as I have not read it. This
is posted for information's sake only.