betsy@dartvax.UUCP (Betsy Hanes Perry) (09/30/85)
"There is another [error] which is the opposite of this:
we may deny the reality of differences because there is continuous
variation between the different things. A very old example
illustrates this error. One may throw doubt on the reality of
a beard by a process beginning by asking whether a man with
one hair on his chin has a beard. The answer is clearly "No."
Then one may ask whether with to hairs on his chin a man has a beard.
Again the answer must be "No." So again with "three," "four,"
etc. At no point can our opponent say "Yes," for if he has
answered "No" for, let us say, twenty-nine hairs, and "Yes"
for thirty, it is easy to pour scorn on the suggestion that the
difference between twenty-nine and thirty hairs is the difference
between not having and having a beard. Yet by the process of adding
one hair at a time we can reach a number of hairs which would
undoubtedly make up a beard. The trouble lies in the fact that
the difference between a beard and no beard is like the
difference between white and gray in the fact that one
can pass by continuous steps from one to the other.
In this argument, the fact of continuous variation has
been used to undermine the reality of the difference. Because
there is no sharp dividing line, it has been suggested that
there is no difference. This is clearly a piece of crooked
argument which would take in no reasonable person, so long, at
any rate, as it was used about beards and not about anything
which engaged our emotions more strongly.
From "How To Think Straight," Robert H. Thouless, Simon and Schuster,
1939, pp. 127-128.
--
Elizabeth Hanes Perry
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