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Comments on "Understanding Natural Kinds: Part I" by Benjamin Cohen draft
of March 1981

1. I find myself more in agreement with what you actually say in the paper
than what your lecture seemed to be saying (as far as you were allowed to
get) and with what the abstract promises.  In particular your footnote
interprets the efforts at non-monotonic reasoning as an attempt to treat
typicality within a logical framework.  You don't discuss the prospects for
success of such attempts, but what you say doesn't directly argue against
prospects for such success.

2. As a part of a philosophy dissertation, the paper makes a
presupposition common to philosophers.  Namely, it presupposes that
counterexamples kill a formalism dead.  AI has to be more modest and take
a positive view of formalisms, asking what can be done with it rather than
immediately looking for something it can't do and letting that kill it.
Unfortunately, much AI work, especially AI dissertations, tend to sweep
under the rug everything a particular formalism won't do.

In the present case, a proper treatment of the "formal semantics" paradigm
would identify the class of problems for which it is likely to succeed in
formalizing some common sense knowledge well enough to be used.

3. Your point that Montague semantics doesn't even begin to express the
real world facts important for understanding sentences is well taken.  I
hadn't realized how little interest philosophers had in such questions
till I attended Barwise's lectures on perception, and he eventually told
me that no specific features of vision were to be treated.

4. Bob Moore is right that definability isn't a very live issue.  The
"formal semantics" approach will content itself with axiomatizing concepts
without demanding that they be eliminable by definitions.

Of course, ever since I started working on non-monotonic reasoning about
1975, I have agreed that axiomatization itself isn't enough to express our
common sense knowledge without non-monotonic rules of reasoning.  Even in
"Some Philosophical Problems from the Standpoint of Artificial
Intelligence" which appeared in 1969, Pat Hayes and I recognized that
there were serious difficulties in trying to get correct axiomatizations
of common sense.  We called the difficulties the "qualification problem".
The current non-monotonic reasoning formalisms are probably still
inadequate.

5. The problem of compositionality has to be redefined to become
meaningful, because it is always possible to give any system a
compositional semantics if one is willing to use suitable function domains
for the domains of meanings of expressions.  Thus suppose you have some
rule for assigning meanings to sentences as a whole.  Then I can define
the meaning of an arbitrary segment of a sentence as a map from the
Cartesian product of possible preceding segments with the space of
possible following segments to meanings for the sentences.
Compositionality can be made a meaningful restriction of semantic rules
only if we restrict the domain that can serve as meanings.  Thus modal
logic is non-compositional if wffs must have truth values as meanings but
becomes compositional if we use suitable functions from possible worlds as
meanings.

6. From the AI point of view the reformulation on page 2 of the problem of
natural kinds as a linguistic problem is dubious.  Natural kinds like
biological species are a fact about the world and the ability of men and
machines to acquire information about it.  These facts have linguistic
consequences, but they aren't basically linguistic facts.

I don't think that natural kinds occur only in nature, and moreover I
think the concept is a relative one.  A small child treats almost all
words as denoting natural kinds, i.e. as having meanings that aren't
merely matters of definition and which depend on facts that he doesn't
know.  Discovering that some words have extensions whose boundaries aren't
definite comes at an age of perhaps ten.

The word "hill" should be compared to the word "horse".  No-one supposes
that there is something that science will tell us about which eminences
are to be counted as hills.  Nor will science tell us which animals are to
be regarded as domestic.

It doesn't seem to me that the notion of "natural kind" should be used to
revive (Aristotelian or Platonic ?) essences.

7. Grumbles and misprints

Using Chang and Keisler as a reference muddles what is important about
Tarskian semantics for philosophy with what is of purely mathematical
interest.  Isn't the little bit in Rogers' "Mathematical Logic and
Formalized Theories" enough for your purposes.

Corrected spellings: wierd → weird, curousity → curiosity, a-typical →
atypical, , proto-typical → prototypical, quadraped → quadruped.

8. I hope you will sometime switch to putting your main efforts into
making a formalism you consider adequate.  My experience is that one
cannot win methodological arguments against formalisms without having a
competitor and examples that the competitor does better.

∂13-Apr-81  1404	COHEN at PARC-MAXC 	Reply to Comments   
Date: 13 Apr 1981 14:00 PST
From: COHEN at PARC-MAXC
Subject: Reply to Comments
To: John McCarthy <JMC at SU-AI>
cc: cohen

Professor McCarthy,

0. Let me first tell you how pleased and flattered I am to receive your
very kind and perceptive comments.  Your work has always made a very
strong impression on me including your recent work on Circumscription and
if you'll pardon the paraphrase, the topic of Part I is an AI problem from
the standpoint of philosophy of language !!

1. Although my philosophizing certainly gives the impression that I take
counter-examples to be critical I regard them more as thought experiments
and certainly would never suggest that people scrap the predicate calculus
because horse is non-definable !!! Clearly the formalism works in certain
domains like expert systems and data-bases. The counter-examples are
intended to make a meta-theoretical point and to focus new attention on
problems which I know the AI community is already well aware of.

2. I am going to spend a considerable amount of time discussing
non-monotonic logic. I have not made up my mind yet but I suspect that I
will argue that better theories of content and better representation
schemes are what is ultimately needed though the problems encountered in
both enterprises may turn out to be equivalent.

3. I agree with your comments on the qualification problem and the
difficulty of axiomatizing common sense -- something I used to believe was
feasible . Your welcome comments on compositionality amplify the points I
am making. The argument against unrestricted compositionality then begins
to sound like the arguments linguists make against unconstrained
transformational grammars -- they're too general and powerful to say
anything specific about human language.

4. I think there is some misunderstanding of my position in your point 6.
I don't believe there are any purely "linguistic" problems because with
Quine I don't believe one can objectively separate the problem of meaning
from the problem of knowledge. So the linguistic "reformulation" is
misleading at that point. I agree with your comments about hills and
horses and I am strongly against the revival of essences of any kind. It
is this revival which quantified modal logic is committed to (as Quine has
proved) and I believe it is part of the meaning postulate approach.  I may
not have indicated this as well as I wished in my lecture.

5.  Your grumbles and misprints are much appreciated. 

6.  I am working on a more adequate knowledge representation scheme and
hope that an alternative view that is not a mere notational variant will
be the result.


Ben