32 Unphilosophical Introduction

2 Unphilosophical Introduction
that the agreed beliefs aren’t literally shared (viz. that they are only
required to be similar), then his account of content similarity begs the
very question it was supposed to answer: his way of saying what it is for
concepts to have similar but not identical contents presupposes a prior
notion of beliefs with similar but not identical contents.
The trouble, in a nutshell, is that all the obvious construals of similarity
of beliefs (in fact, all the construals that I’ve heard of) take it to involve
partial overlap of beliefs.5 But this treatment breaks down if the beliefs
that are in the overlap are themselves construed as similar but not
identical. It looks as though a robust notion of content similarity can’t
but presuppose a correspondingly robust notion of content identity.
Notice that this situation is not symmetrical; the notion of content identity
doesn’t require a prior notion of content similarity. Leibniz’s Law tells us
what it is for the contents of concepts to be identical; Leibniz’s Law tells
us what it is for anythings to be identical.
As I remarked above, different theorists find different rugs to sweep this
problem under; but, as far as I can tell, none of them manages to avoid it.
I propose to harp on this a bit because confusion about it is rife, not just
in philosophy but in the cognitive science community at large. Not getting
it straight is one of the main things that obscures how very hard it is to
construct a theory of concepts that works, and how very much cognitive
science has thus far failed to do so.
Suppose, for example, it’s assumed that your concept PRESIDENT is
similar to my concept PRESIDENT in so far as we assign similar
subjective probabilities to propositions that contain the concept. There
are plenty of reasons for rejecting this sort of model; we’ll discuss its main
problems in Chapter 5. Our present concern is only whether constructing
a probabilistic account of concept similarity would be a way to avoid
having to postulate a robust notion of content identity.
Perhaps, in a typical case, you and I agree that p is very high for ‘FDR
is/was President’ and for ‘The President is the Commander-in-Chief of
the Armed Forces’ and for ‘Presidents have to be of voting age’, etc.; but,
whereas you rate ‘Millard Fillmore is/was President’ as having a
probability close to 1, I, being less well informed, take it to be around
p = 0.07 (Millard Fillmore???). This gives us an (arguably) workable
construal of the idea that we have similar but not identical PRESIDENT
concepts. But it does so only by helping itself to a prior notion of belief
identity, and to the assumption that there are lots of thoughts of which
5 ‘Why not take content similarity as primitive and stop trying to construe it?’ Sure; but
then why not take content identity as primitive and stop trying to construe it? In which
case, what is semantics for?
What Concepts Have To Be 33
our respective PRESIDENTs are constituents that we literally share. Thus,
you and I are, by assumption, both belief-related to the thoughts that
Millard Fillmore was President, that Presidents are Commanders-in-Chief,
etc. The difference between us is in the strengths of our beliefs, not in their
contents.6 And, as usual, it really does seem to be identity of belief content
that’s needed here. If our respective beliefs about Presidents having to be
of voting age were supposed to be merely similar, circularity would ensue:
since content similarity is the notion we are trying to explicate, it mustn’t
be among the notions that the explication presupposes. (I think I may have
mentioned that before.)
The same sort of point holds, though even more obviously, for other
standard ways of construing conceptual similarity. For example, if
concepts are sets of features, similarity of concepts will presumably be
measured by some function that is sensitive to the amount of overlap of
the sets. But then, the atomic feature assignments must themselves be
construed as literal. If the similarity between your concept CAT and mine
depends (inter alia) on our agreement that ‘+ has a tail’ is in both of our
feature bundles, then the assignment of that feature to these bundles must
express a literal consensus; it must literally be the property of having a tail
that we both literally think that cats literally have. (As usual, nothing
relevant changes if feature assignments are assumed to be probabilistic or
weighted; or if the feature assigned are supposed to be “subsemantic”,
though these red herrings are familiar from the Connectionist literature.)
Or, suppose that concepts are thought of as positions in a “multidimensional
vector space” (see e.g. Churchland 1995) so that the similarity
between your concepts and mine is expressed by the similarity of their
positions in our respective spaces. Suppose, in particular, that it is
constitutive of the difference between our NIXON concepts that you think
Nixon was even more of a crook than I do. Once again, a robust notion
of content identity is presupposed since each of our spaces is required to
have a dimension that expresses crookedness; a fortiori, both are required
6 Alternatively, a similarity theory might suppose that what we share when our
PRESIDENT concepts are similar are similar beliefs about the probabilities of certain
propositions: you believe that p(presidents are CICs) = 0.98; I believe that p(presidents are
CICs) = 0.95; Bill believes that p(Presidents are CICs) = 0.7; so, all else equal, your
PRESIDENT concept is more like mine than Bill’s is.
But this construal does nothing to discharge the basic dependence of the notion of
content similarity on the notion of content identity since what it says makes our beliefs
similar is that they make similar estimates of the probability of the very same proposition;
e.g. of the proposition that presidents are CICs. If, by contrast, the propositions to which
our various probability estimates relate us are themselves supposed to be merely similar, then
it does not follow from these premisses that ceteris paribus your PRESIDENT concept is
more like mine than like Bill’s.
to have dimensions which express degrees of the very same property. That
should seem entirely unsurprising. Vector space models identify the
dimensions of a vector space semantically (viz. by stipulating what the
location of a concept along that dimension is to mean), and it’s just a
truism that the positions along dimension D can represent degrees of Dness
only in a mind that possesses the concept of being D. You and I can
argue about whether Nixon was merely crooked or very crooked only if the
concept of being crooked is one that we have in common.
It may seem to you that I am going on about such truisms longer than
necessity demands. It often seems that to me, too. There are, however, at
least a zillion places in the cognitive science literature, and at least half a
zillion in the philosophy literature, where the reader is assured that some
or all of his semantical troubles will vanish quite away if only he will
abandon the rigid and reactionary notion of content identity in favour of
the liberal and laid-back notion of content similarity. But in none of these
places is one ever told how to do so. That’s because nobody has the
slightest idea how. In fact, it’s all just loose talk, and it causes me to grind
my teeth.
Please note that none of this is intended to claim that notions like belief
similarity, content similarity, concept similarity, etc. play less than a central
role in the psychology of cognition. On the contrary, for all I know
(certainly for all I am prepared non-negotiably to assume) it may be that
every powerful intentional generalization is of the form “If x has a belief
similar to P, then . . .” rather than the form “If x believes P, then . . .”. If
that is so, then so be it. My point is just that assuming that it is so doesn’t
exempt one’s theory of concepts from the Publicity constraint. To repeat
one last time: all the theories of content that offer a robust construal of
conceptual similarity do so by presupposing a correspondingly robust
notion of concept identity. As far as I can see, this is unavoidable. If I’m
right that it is, then the Publicity constraint is ipso facto non-negotiable.
OK, so those are my five untendentious constraints on theories of
concepts. In succeeding chapters, I’ll consider three stories about what
concepts are; viz. that they are definitions; that they are prototypes/
stereotypes; and (briefly) something called the ‘theory theory’ which says,
as far as I can make out, that concepts are abstractions from belief
systems. I’ll argue that each of these theories violates at least one of the
non-negotiable constraints; and that it does so, so to speak, not a little bit
around the edges but egregiously and down the middle.We will then have
to consider what, if any, options remain for developing a theory of
concepts suitable to the purposes of an RTM.
Before we settle down to this, however, there are a last couple of preliminary
points that I want to put in place.