QUALITATIVE MEASURE IS NOT
OBJECTIVE

*Anil mitra PHD, COPYRIGHT © 2000, REFORMATTED **June
25, 2003*

This topic concerns an invalid form
of argument that commonly enters thought – perhaps in a careless way. Here is
an example of the argument:

In what
follows is assumed that a *pinch* is very small in comparison to a *heap*

If a pinch
of salt is added to a *small* heap of salt the result remains a *small*
heap [A]

But [A]
implies that any number of pinches added to a small heap results in a small
heap [B]

But this contradicts common sense
according to which:

A
sufficient number of pinches added to a small heap results in a heap that is
not small. [C]

The paradox is well known. It could
be approached by “fuzzy” and many-valued logic. But the following is the
essence. Consider:

Every heap
is either small or not small [D]

[D] and [A] are contradictory [E]

But the truth of [D] follows by tautology – since ~ [D] is a contradiction. Therefore [A] is not true – given a fixed size of pinch, there is some small heap which is not small when a pinch is added to it

ANIL MITRA
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