From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: Names and types of bad reasonings?
Date: 19 Aug 1999 01:41:59 -0400
Newsgroups: sci.math
Keywords: Quaternio terminorum and other logical fallacies

In article <01bee9eb$7eee85e0$439508d1@thebluewizard>,
The Blue Wizard <TheBlueWizard@pressroom.com> wrote:
>Got a question:
>
>I know of "reductio ad absurdum" reasoning, which is a legitimate tool in
>mainstream mathematics.
>However I am not interested in *these* sort of valid reasonings.
>
>I just want to know the names and types of other kind of "reasonings",
>which are quite erroneous.
>One example I know of is "ad hominen" reasoning.

Three books come to mind:

(1)
The Book of the Fallacy (A training manual for intellectual sunbersives)
by Madsen Pirie; Routledge & Kegan Paul, London and Henley, 1985
ISBN 0-7102-0521-X

It starts with Abusive Analogy and ends with Wishful Thinking, and yes,
discusses the classics such as Quaternio terminorum, Ignoratio elenchi and
Petitio principii. 

(2) How to Lie with statistics, by Darrell Huff (41st printing), W.W.
Norton & Company, New York-London 1982 (1st printing 1954),
ISBN 0-393-09426-X

The title says it all.

(2) The Art of Controversy, by Arthur Schopenhauer; you will have to scan
Schopenhauer's collected or selected works in you library. My copy comes
as the last chapter of "The Will to Live", Selected Writings of A.S.,
Frederick Ungar Publ. Co. New York 1967
ISBN 0-8044-6847-8

Surprisingly entertaining, considering the reputation of last century's
German philosophers (Schopenhauer was born in 1788, lived for 72 years.)

Have fun, ZVK(Slavek).
==============================================================================

From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: Names and types of bad reasonings?
Date: 19 Aug 1999 13:21:05 -0400
Newsgroups: sci.math

In article <37BC235D.9B0C2C2A@hut.fi>,
Pertti Lounesto  <Pertti.Lounesto@hut.fi> wrote:
[...]
>> kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) writes:
>>
>> >(1)
>> >The Book of the Fallacy (A training manual for intellectual sunbersives)

Correct the spelling, of course: subversive (look at the keyboard and you
will find the origin of the typo)

>> >by Madsen Pirie; Routledge & Kegan Paul, London and Henley, 1985
>> >ISBN 0-7102-0521-X
>> >
>> >It starts with Abusive Analogy and ends with Wishful Thinking, and yes,
>> >discusses the classics such as Quaternio terminorum, Ignoratio elenchi and
>> >Petitio principii.

>Maybe there are no counterexamples against
>"Quaternions" or "terminorii"?

[a welcome list of counterexample books deleted]

"Quaternio terminorum" is a frequently observed fallacious application of
the classical syllogism:

Men are animals;
Animals are mute;
 hence
Men are mute

Here "animals" is used in two meanings: first, including humans, but
second, excluding humans. So, the scheme

A are B
B are C
 hence
A are C

was violated because it was applied as a non-syllogism - where B1 and B2
may sound misleadingly similar:

A are B1
B2 are C
 hence
(what?)

The terms A, B1, B2, C are the "four terms" (quaternio terminorum) of this
fallacy.

By extension, quaternio terminorum is a fallacy coming from assuming
transitivity of a relation which is not transitive:

From  the assumptions

x is perpendicular to y
y is perpendicular to z

if you expect that x should be perpendicular to z, you are committing the
(extended) quaternio terminorum fallacy.

Cheers, ZVK(Slavek).
==============================================================================
[Relevant website: --djr]
	http://www.nizkor.org/features/fallacies/
	http://www.rhetor.com/compete/fallacies.htm