On 8/7/2011 2:23 PM, Christopher Menzel wrote:
> Seems to me that that example only shows that there is more
> to the definition of*bachelor* than "unmarried man" -- perhaps
> something like "unmarried man who is not prevented from marrying
> by civil or religious law". It doesn't show that there is anything
> "problematic" about the notion of analyticity. (01)
I agree that the definition of 'analytic truth' is OK. And I agree
that it applies to any term that can be defined by necessary and
sufficient conditions. (02)
But philosophers as early as Aristotle noticed that finding necessary
and sufficient conditions for biological species is not easy --
especially when you first discover a new one. (03)
Long before Wittgenstein talked about family resemblances or Rosch
proposed prototypes for definitions, Whewell (1858) wrote (04)
> Natural groups are given by Type, not by Definition. And this consideration
> accounts for that indefiniteness and indecision which we frequently find
> in the descriptions of such groups, and which must appear so strange and
> inconsistent to anyone who does not suppose these descriptions to assume
> any deeper ground of connection than an arbitrary choice of the botanist.
> Thus in the family of the rose tree, we are told that the ovules are very
> rarely erect, the stigmata usually simple. Of what use, it might be asked,
> can such loose accounts be? To which the answer is, that they are not
> inserted to distinguish the species, but in order to describe the family,
> and the total relations of the ovules and the stigmata of the family are
> better known by this general statement....
>
> Though in a Natural group of objects a definition can no longer be of any
> use as a regulative principle, classes are not therefore left quite loose,
> without any certain standard or guide. The class is steadily fixed, though
> not precisely limited; it is given, though not circumscribed; it is
>determined,
> not by a boundary line without, but by a central point within; not by what it
> strictly excludes, but by what it eminently includes; by an example, not by
> a precept; in short, instead of a Definition we have a Type for our director.
> (vol. 2, pp. 120-122) (05)
Following is what Kant said on the subject: (06)
> Since the synthesis of empirical concepts is not arbitrary but based on
> experience, and as such can never be complete (for in experience ever new
> characteristics of the concept can be discovered), empirical concepts
> cannot be defined.
>
> Thus only arbitrarily made concepts can be defined synthetically. Such
> definitions... could also be called declarations, since in them one
> declares one's thoughts or renders account of what one understands by
> a word. This is the case with mathematicians. (07)
Source: (08)
Kant, Immanuel (1800) _Logik: Ein Handbuch zu Vorlesungen_, translated
as _Logic_ by R. S. Hartmann & W. Schwarz, Dover, New York, 1988. (09)
You can add Wittgenstein, Waismann, Quine, and many others to those
who have cited problematical issues in defining empirical concepts by
necessary and sufficient conditions. (010)
John (011)
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