There
Are Lots of Ordinary Things (And They Aren't Made of Matter)
I.
Introduction
In this paper, I will first
present the problem of vagueness in general and show how it leads to
the sorites paradox. I will thus initially give a fairly standard
version of the paradox as a set-up for the sections that follow.
Second, I will examine the views of Peter K Unger, who holds that the
paradox has correct premisses, correct reasoning, and a correct
conclusion. Particularly, Unger argues that the correctness of the
sorites paradox implies that vague concepts are incoherent, even
something so simple as an “ordinary thing”. In the final section,
I take issue with Unger's treatment of these implications and argue
that, given the correctness of the conclusion of the sorites paradox,
there are still numerous avenues open to us that do not end in
Unger's extreme skepticism. Particularly, I will argue that a
flexible and functional-pragmatic approach to concepts is needed, and
that the nature of the concept is very different than what is assumed
by Unger.
Importantly, Unger's conclusions
are only attractive if no other solution to the paradox is to be
found. I focus on him, and his specific versions of the sorites, in
order to present an alternative outcome to the acceptance of the
conclusion of the paradox.
II.
Vagueness & The Sorites Paradox
The phenomenon of vagueness has
several related but not identical components according to Rosanna
Keefe: borderline cases, lack of precise boundaries, and
susceptibility to the sorites paradox. Since the sorites paradox
makes reference, in many of its forms, to on one or both of the other
two components, I will focus on it. An example of the sorites runs as
follows. There are two premisses:
(P1) – A collection with x
grains of rice is a heap
(P2) – If a collection with x
grains of rice is a heap, so is a collection with x-1 grains
If we give the initial x a
sufficiently large value, say 1000, we get an uncontroversial claim,
namely that a 1000-grain collection is a heap. Now if we apply modus
ponens using P1 and our conditional P2, we get that a collection with
999 grains is a heap; continuing this procedure, we are led
inevitably into a borderline region, where for example 25 grains is
heap; finally, we get the end-result that 1 grain of rice is a heap,
or even that 0 grains constitute a heap! It is easy to generalize
this result so that wherever we have a predicate that either admits
of borderline cases or lacks precise boundaries is susceptible—this
is because, as Keefe notes, the lack of precise boundaries is nothing
but the possibility for there
to be borderline cases (7).
As Sainsbury notes, there are
three primary strategies for dealing with the sorites: accept it as
valid and deal with the implications, reject one of the premises, or
reject the reasoning. Perhaps the most radical suggestion is the
first, advanced by Unger. It is to this we now turn.
III.
Accepting The Conclusion: Peter Unger
Rather than attempt to find
fault with the apparently commonsense reasoning of the sorites, Unger
looks elsewhere to explain the problems generated thereby. First, he
uses various versions of the “sorites of decomposition” to draw
the absurd conclusion that a stone (or object in general) with 0
atoms is still a stone (or other object). There are several methods
to get to this result: removing atom by atom, cutting into various
fractions, &c. This argument he calls “indirect”, because it
presupposes the concept (stone, object, &c.) that it sets out to
prove incoherent—it is a reduction ad absurdum.
In
contrast to this, Unger also posits a “direct” argument from the
“sorites of accumulation”. This time, instead of starting with
the concept/object, we start with nothing and slowly and
imperceptibly (at first) add atoms or dust until we have accumulated
what common sense would tell us is an object. The thing is, however,
that we cannot say it is an object because of the sorites paradox—for
that, it was gradual and fuzzy enough. This reasoning, combined with
the indirect sorites of decomposition, leads to such absurdities as
that everything
is a stone and that nothing
is
a stone. Or
against this, if we insist there must be an “obliteration point”
in decomposition, so that, for example, a pizza ceases to be a pizza
when it has less than a certain vague amount of materiality,
certainly an atom
more
would not change that designation. Reasoning up with our sorites of
accumulation, we conclude that removing one
atom
or even none
at all
is equivalent to the obliteration point! Thus, removing one atom from
our pizza results in us having a pizza (by our assumption that one
atom does not matter) and
in
us not having a pizza (by our current sorites reasoning). We see now
that the two types of sorites, direct and indirect, are two sides of
a potent and maddening phenomenon.
No
matter how discerning we think we are, our concepts of objects are
not sensitive enough to respond to the addition or subtraction of a
single atom. It is simply not plausible that concepts track changes
that minute. Such an occurrence would be a “miracle of conceptual
comprehension”, which Unger takes as less plausible than his own
view. Importantly, the fact of common-sense conceptual focus (it is
ordinary
things
that are being attacked, not things in general) leaves open the
question of scientific or more precise concepts, and indeed Unger
seems (relatively) optimistic about such an enterprise: the proper
use of mathematics in the argument is to “aid
in the development of better, precise ideas with which those concepts
may be replaced” (128). Unfortunately,
Unger does not adequately pursue these “better” concepts for the
remainder of the paper, only
saying that they reference physical objects of such and such a size
and shape.
IV.
Implications: Against Unger
From
all
this
Unger
concludes that the problem lies within the concept of “stone” or
“object”, that the “ordinary object” as our everyday common
sense perceives it is incoherent: “The
most rational way of responding to the contradictions, I submit, is
to deny application for the ordinary concepts...” (145).
Perhaps stated more
radically:
Thus,
it
appears quite obvious to us now that there will be no application to
things for such nouns as 'stone' and 'rock', 'twig' and 'log',
'planet' and 'sun', 'mountain' and 'lake', 'sweater' and 'cardigan',
'telescope' and 'microscope', and so on, and so forth. Simple
positive sentences containing these terms will never, given their
current meanings, express anything true, correct, accurate, etc., or
even anything which is anywhere close to being any of those things.
(148).
It is not only that our concepts
are incoherent in that they may lead to contradiction, rather they
are absolutely useless as far
as truth, correctness, accuracy, &c. are concerned. These
sorts of concepts simply fail to apply,
they are empty.
A
first
possible objection is that our concepts of ordinary objects are not
“based on” the matter that makes them up at all, but on their
function or some other condition. For example, it's not clear that my
concept of “hammer” has much to do with the atoms that make up a
hammer, or even with the material with which it has been constructed.
Perhaps a hammer is for hammering, and a table for putting things on,
and when these functions can no longer be fulfilled (due to the
removal of matter, for example), they cease to be hammers or tables.
Because
there is
a hard limit for when a tool cannot be used for its function, for
example when the table cleaves in half. In responding to this
functional definition, Unger writes:
The
intuitive correctness of this reasoning makes vividly clear the
futility in the thought that certain ordinary things, because they
are 'functionally defined', will withstand a sorites attack. But, of
course, this Aristotelian approach gets ordinary thinking wrong at
the start. A fake rake is not a rake (which is fake) but, supposing
there to be any rakes at all, a broken rake is a rake which is
broken. Further, a rake This
may
be first made in a lucite cube, and in such a way that the rake will
shatter if the cube does. Thus, it will never be much good for
raking, and so on, and so forth. (139-140)
With
these cryptic remarks, Unger deposes of what I would consider the
commonsense view of ordinary things. To respond, and to strengthen
our argument, we could add notions of appearance
to our functional theory, so that we might consider something that
looks
like
a rake to be a rake, for
a certain purpose.
In other words, in different contexts we might consider a different
criterion for what makes a rake—we still call a “fake” rake
used as a prop in a stage play a rake, but if we were actually raking
leaves we wouldn't want anything less than a good sturdy “real”
rake. Thus
our concept of “rake” is stretchy, and may or may not contain,
for different purposes, Unger's rake “made in a lucite cube”.
To
use Unger's example, if we cut a table in half we do not have a
proper table left, in the same sense as when we had a
functionally-working table (whatever we think those functions might
be, it is clear that probably at least one has changed). We have, I
would say, two halves of a table. The incoherence is said to come in
when we take this to the extreme, by pulverizing the table into dust.
Is it still a table? No, it doesn't have any of the functions I would
associate with the concept “table”. It might be objected that
this posits a sharp boundary whereafter a
certain function appears or disappears. Indeed, in everyday usage,
there is
such a boundary, but contra the epistemicists, it lies within the
mind, with our application of the concept to an object. For example,
at some point I will get irritated sitting around testing a hammer
and removing atom by atom! Then I will arbitrarily say that the
object is no longer useful as a hammer!
Note
that this line of argument does not refute Unger's reasoning,
and thus leaves intact the logical problems associated with concepts
of ordinary things that are somehow “based on” the matter that
makes them up.
Another
objection
I would raise is
a
version of one
Unger himself raises, that these operations are not everywhere
carried out to the extremity of paradox. There may
indeed be
certain limit-points at which our concepts break down, certain
extreme cases that dissolve meaning—the conclusions of Unger's
sorites paradoxes are of this type. Here,
by “concepts” I mean those that may be based on material
composition, though I tentatively suggest that no concept is entirely
free from break-down points.
However, such points are simply
not
often encountered
(in my life only in philosophy papers!).
The problem with Unger's version of this objection is that he frames
it in terms of intensionality: “And,
it might be urged, it is only an extensional sentence which makes any
proper sense, and which should be used in the formulation of any
worthwhile sorites argument” (135). Instead of
intensional-nonmeaning vs extensional-meaning, it ought to be framed
in terms of the actual application of the relevant concepts. Thus, we
can reason with and about incoherent concepts without problem most of
the time, and this includes non-formal reasoning (or just plain
playing around) as well. Put another way, Unger is absolutely right
that our concepts do not always track truth, correctness, or
accuracy—But so much the worse for truth, correctness, and
accuracy!
It
is only the desire that our concepts be purely “coherent” that
leads us to the conclusion that “incoherent” concepts fail to
apply. Rather, I think we should conclude that concepts need not be
bounded by formal logic—and indeed in practice, they are not.
What's wrong with incoherent concepts? This includes incoherence due
to the sorites paradoxes as well as liar paradoxes and whatever else.
Put another way, it seems to me far more rational to use and apply
incoherent concepts (in pragmatically- and socially-determined ways,
of course) than to deny that these concepts apply at all.
V.
Conclusion
Given the above arguments, I
suggest that Unger's arguments ought to be taken seriously within the
context of conceptual formalization, but that they really pose little
to no problem for ordinary things, which are not concepts of the sort
Unger supposes. Thus, the sorites is a real paradox and should be
dealt with as such—but its implications are not those presented by
Unger. Particularly, concepts such as “heap” are perhaps left
open by the above reasoning. As Unger admits,
“It
may be much harder than one might first suppose, I would suggest, to
achieve coherence while adequately serving anything much like our
everyday concerns.” (150).
I
suggest that it it seems very
very
difficult, and probably not even advisable.
When
thinking of an ordinary thing, Unger says, “At
best, we are thinking of something, but only in much the way we do
when thinking of a fictional entity” (149). I
would here suggest that our pragmatic or functional view of concepts
is, while not fictional, perhaps not resting on an absolute fact of
the matter. Concepts
are, I suggest, a cultural hodge-podge, and there may be more hodge
or more podge at different times. In
any case, atoms and specks of matter have never entered my concepts
of ordinary things, and I don't see why they ought to. Unger
confuses this non-issue with a “miracle of conceptual
comprehension”, assuming our concepts must
make reference to amounts of matter.
Works
Cited
Keefe,
Rosanna. Theories
of Vagueness.
Cambridge, UK ;New York: Cambridge University Press, 2000. Print.
Sainsbury,
R. Paradoxes.
3rd ed. Cambridge: Cambridge University Press, 2009. Print.
Unger,
Peter. “There Are No Ordinary Things.” Synthese, Vol.
41, No. 2 (Jun., 1979), pp. 117- 154. Electronic.
