Re: definitions

Tibor Benke (benke@SFU.CA)
Thu, 23 Jun 1994 02:20:57 -0700

Hi Dwight,

Sorry for the delayed reply. You say:
>Benke writes:
>"also something from one of Rev. Dogeson's (Sp)[Dodgson is the correct
>spelling] books), and what any word means is what I say it means and I will
>define it in a way which suits my purposes. This approach seems a bit
>arrogant to me"
>Dodgson was referring (if memory serves me correctly) to the fact that
>mathematicians DEFINE words to have meaning in an axiomatic system and when
>that is done whatever usual meaning associated with the word is suspended;
>e.g., the Theory of Groups has nothing whatsoever to do with groups as
>ordinarily understood. Since an axiomatic system is a purely mental
>construct, it is necessary to either use this device (or to use nonsense
>words!) to avoid introduction of properties via the normal meaning of the
>word which are not, in fact, part of the axiomatic system. In this context
>it is not arrogant, but necessary; outside of defining terms for use in
>axiomatic systems. I would agree that it can become arrogant--but it can also
>help clarify that the ordinary meanings words have may include meanings that
>are not appropriate for the context in question.

Of course, you are perfectly right, the great logician knew what he was
talking about, and I would not presume to criticize it or, worse, accuse
him of arrogance.

It was the dogmatic advocacy of nominalism, and its cavalier application
that I was protesting..

Many great scholars take advantage of the potential to create
misunderstanding. For example, look at Karl Popper's definition of
'historicism' in his _Poverty of..._ and compare it to Karl Mannheim's
treatment of the subject in his essay "Historicism". While Popper uses his
own abstract concept, which enables him to include Plato, J.S.Mill, and
Marx in the ranks of historicists, Mannheim speaks of a definite tendency
in German scholarship, best characterized by Ranke, Dilthey, and maybe
Troeltsch - a point of view growing out of the consideration of actual
problems raised by the 'scientific' (wissenschaft) study of history and
giving rise to a method of grasping social phenomena in a certain way.

It seems to me that we must be careful that we neither rigidly adhere to
the ready made definitions of concepts, nor loose sight of the fact that we
make the concepts ourselves. But above all, we should not base a theory on
a definition, since definitions are inherently tautological, which is why
they are useful.

>@> Tibor Benke /