FOM: R: Questions about Polya's "Plausible Reasoning"

[Luigi Borzacchini]

-----Messaggio Originale-----
Da: "D. E. (Steve) Stevenson" <steve at cs.clemson.edu>
A: <fom at math.psu.edu>
Data invio: sabato 13 gennaio 2001 17.14
Oggetto: FOM: Questions about Polya's "Plausible Reasoning"


> Happy New Year to all:
>
> George Polya in [1] makes two statements that are not attributed. I am
> interested in knowing the references.
>
> 1. He has a long quote from Aristotle "A syllogism is a discourse in
which,
> certain things being stated, something other than that what is stated
> follows of necessity from their being so."
>

It can be found in Analytica Priora I, 1. 24 b 19-21 and in Topica I, 1.
100a 25-27


> 2. He lists four attributes of syllogisms as impersonal, universal,
> self-sufficient, and definitive. I assume this is standard, but where do
> these properties come from? What alternatives might be considered
standard?
>

These features are substantially resulting from the Aristotelean distinction
of his syllogism with respect to eristic, rhetoric and paralogisms.
These kinds of argumentation were different from perfect syllogisms for the
absence of some of the above features.
Eristic was substantially dialectic, and was characterized by opinion-based
premisses and hence was not definitive.
Rhetoric was characterized by the role of the audience, which required ad
personam arguments, and hence was not universal and impersonal.
Paralogisms were sustantially wrong, as in sophisteries or wrong geometric
constructions.
Imperfect syllogisms required the addition of other, external to the
premisses, facts, and hence were not self-sufficient (probably many correct
geometric proofs required implicit graphical arguments).
These aspects can be found in the first sections of Analytica Priora, Topica
and Rhetorica.

It is important to underline that Aristotle's writings represent the true
'emergence' of these distinctions, and that in different works or even in
different parts of the same work the borders between those forms of
argumentation can be different.

Best wishes
                                       Luigi Borzacchini