Page 12 - Logical and Spiritual Reflections
P. 12


8 LOGICAL REFLECTIONS



This might all seem credible, were we not to notice some glaring errors in Hume’s
5
understanding of generalization, and more broadly of induction .
Hume’s error was to concentrate on the positive aspect of generalization and totally ignore
the negative aspect of particularization. Since he unconsciously equated inductive
6
reasoning solely with generalization from past regularity, he naturally viewed the fact that
some breach of regularity might indeed (as often happens) occur in the future as evidence
that generalization as such is flawed. But this is just a misapprehension of the nature of
induction on his part.
He should have known better, since Francis Bacon had (some 80 years before, in his
Novum Organon) , already clarified the all-importance of the “negative instance” as a
7
check and balance against excessive generalization and in other forms of induction.
Because Hume failed to grasp this crucial insight, we can say that his understanding of
induction was fragmentary and inadequate.

All generalization is conditional; we may infer a generality from similar particulars,
provided we have sought for and not found evidence to the contrary. To generalize to “All
X are Y” we need to know two things, not just one: (a) that some X are Y, and (b) that no
X to date seem not to be Y. Though the latter condition is usually left tacit, it is absolutely
8
essential .
If we did find such contrary evidence early, before we generalized, we would simply not
generalize. If we find it later, after we generalized, we are then logically required to
particularize. Synthetic generalities are not meant as static absolutes, but as the best
available assumptions in the given context of knowledge. Generalization is a dynamic
process, closely allied with particularization; it is not a once and for all time process.
The same logic applies to other forms of induction , notably adduction. The latter refers to
9
a broader concept of induction, from any evidence to any derived hypothesis (which may
contain different terms than the evidence). The hypothesis is not merely confirmed by the
evidence it explains, but equally by the absence of contrary evidence and by the absence of
better alternative hypotheses.

Note this well: the data that confirm a hypothesis do not suffice to make us believe it. The
simple proof of this is that when a hypothesis is rejected for some reason, the data that in
the past confirmed it continue to logically confirm it, yet the hypothesis is thrown out in
spite of that. There are essential additional conditions, which make our inductive
conclusion unassailable thus far, namely (to repeat) that we have to date no data that belies
it and no more fitting hypothesis.
10



5
I here refer the reader to Future Logic, Part VI, for a fuller understanding of the issues.
Read at least chapters 50 and 55.
6 This error has, I have read, already been spotted by Karl Popper.
7
England, 1561-1626. The full text (1620) is posted on the Internet at
http://etext.library.adelaide.edu.au/b/bacon/francis/organon/complete.html.
8
Still today, many writers, philosophers and teachers fail to realize and mention this
essential condition when they define or discuss generalization. It should nevermore be left tacit, to
avoid the perpetuation of Hume’s error.
9
Indeed, in the very act of concept formation, we do not merely include certain cases into it,
but also (if only tacitly) exclude other cases from it. There is always both a positive and a negative
aspect to thought, though the latter is often less manifest. Integration is always coupled with
differentiation.
10
The logical calculus involved is thus not a simple dependence on “confirmation”, but a
much more complex and global set of considerations, including “non-rejection” and
   7   8   9   10   11   12   13   14   15   16   17