- §6. Category Theory
- The multivocity of "being" at the end of §5 is important
for Aristotle's category theory.
Of things said without
combination,
each signifies either: (i) a substance (ousia); (ii) a quantity;
(iii)
a quality; (iv) a relative; (v) where; (vi) when; (vii) being in a
position; (viii) having; (ix) acting upon; or (x) a being
affected.
(Cat. 1b25–27)
- what does the philosophical category theorist categorize?
- his examples make reasonably clear that he means to
categorize
the basic kinds of beings there may be.
- he starts the Categories
speaking of things said "in combination" and things said
"without
combination": it looks as if he is talking about language:
- A thing said "in combination":
- things said ‘without combination’:
- But he is not speaking about language (at least so I think,
pretty strongly)
- ‘Man runs’ is truth-evaluable, whereas neither ‘man’ nor
‘runs’
is.
- Things said without combination signify entities:
- sufficiently complex to be what makes the sentence ‘Man
runs’
true, that is a man and is running
- below the level of truth-making, so, e.g., an entity man,
taken by itself, and an action running, taken by itself, are
not true or false by themselves
- If that is correct, the entities categorized by the
categories are the sorts of basic beings that fall below the
level of
truth-makers, or facts.
- Such beings evidently contribute, so to speak, to the
facticity of facts, just as, in their linguistic analogues,
nouns and
verbs, things said ‘without combination’, contribute to the
truth-evaluability of simple assertions.
- If it is a fact that Socrates is pale, then the basic
beings in view are Socrates and being pale.
- the first is a substance
and the second is a quality,
says Aristotle.
- these beings may be basic without being absolutely simple.
After all, Socrates is made up of all manner of parts—arms
and legs,
organs and bones, molecules and atoms, and so on down. He is
not absolutely simple.
- The theory of categories in total recognizes ten sorts of
extra-linguistic basic beings:
-
Category
|
Illustration |
Substance |
man,
horse |
Quality |
white,
grammatical |
Quantity |
two-feet long |
Relative |
double,
slave |
Place |
in
the
market |
Time |
yesterday, tomorrow |
Position |
lying,
sitting |
Having |
has
shoes on |
Acting Upon |
cutting, burning |
Being Affected
|
being cut,
being burnt |
- Surely meant to be exhaustive and irreducible:
- exhaustive: there are no further sorts of basic entities
- irreducible: none of these can be eliminated as being
simply
part of another
- BUT Aristotle offers no discussion of whether they really
are
exhaustive and irreducible
- Aristotle has slightly different lists of what look like
categories here and there outside of the Categories.
- Kant praised A. for category theory, but criticized him
for
essentially brain-storming it instead of building and
defending it
systematically (Critique of Pure Reason, A81/B107).
According to Kant,
Aristotle's categories are groundless.
- Aristotle himself mainly tends to justify the theory of
categories by putting it to work in his various
philosophical
investigations. It is not so much explicitly defended as
functionally defended: it works...
- Example: time:
- Aristotle poses a simple question: does time exist?
- Yes, ‘time is the measure of motion with respect to
the
before and after’ (Phys. 219b1–2).
- time does exist, because it is an entity in the
category of quantity
- like all items in any non-substance category, it
exists
in a dependent sort of way:
- just as if there were no lines there would be no
length,
- so if there were no change there would be no time.
- questions of existence are, at root, questions
about category membership.
- If we ask whether qualities or quantities exist,
Aristotle will answer in the affirmative, but then
point out also that
as dependent entities they do not exist in the
independent manner of
substances.
- Aristotle contends that all other things are either
said-of
primary substances, which
are their subjects, or are in
them as subjects.
- If there were no primary substances, it would be
impossible for anything else to exist. (Cat. 2b5–6)
- the theory of categories spans his entire career and serves
as
a kind of scaffolding for much of his philosophical
theorizing, ranging
from metaphysics and philosophy of nature to psychology and
value
theory.
- but it is not entirely in harmony with everything he says:
he may have developed his ideas over time. Categories
is often considered early, with no great basis.
- §7. The Four Causal Account of Explanatory Adequacy
- Aristotle expects the explanations he seeks to meet certain
criteria of adequacy. He takes care to state his criteria
One way in which cause is
spoken of
is that out of which a thing comes to be and which persists, e.g.
the
bronze of the statue, the silver of the bowl, and the genera of
which
the bronze and the silver are species.
In another way cause is spoken of
as
the form or the pattern, i.e. what is mentioned in the account
(logos)
belonging to the essence and its genera, e.g. the cause of an
octave is
a ratio of 2:1, or number more generally, as well as the parts
mentioned in the account (logos).
Further, the primary source of the
change and rest is spoken of as a cause, e.g. the man who
deliberated
is a cause, the father is the cause of the child, and generally
the
maker is the cause of what is made and what brings about change is
a
cause of what is changed.
Further, the end (telos) is spoken
of
as a cause. This is that for the sake of which (hou heneka) a
thing is
done, e.g. health is the cause of walking about. ‘Why is he
walking
about?’ We say: ‘To be healthy’— and, having said that, we think
we
have indicated the cause.
(Phys. 194b23–35)
- example he proposes in Physics ii 3:
- A bronze statue:
- what is it?
- what is it made of?
- what brought it about?
- what is it for?
- in asking these questions we are seeking knowledge of
the
statue's four causes (aitia):
- formal
- material
- efficient
- final
- when we have identified these four causes, we have
satisfied a reasonable demand for explanatory adequacy.
- In Physics ii 3, Aristotle makes twin claims about this
four-causal schema: (i) that citing all four causes is
necessary for
adequacy in explanation; and (ii) that these four causes are
sufficient
for adequacy in explanation.
- Why necessary?
- not all phenomena admit of all four causes.
- coincidences lack final causes
- If a debtor is on his way to the market to buy milk
and
she runs into her creditor, who is on his way to the
same market to buy
bread, then she may agree to pay the money owed
immediately. Although
resulting in a wanted outcome, their meeting was not
for the sake of
settling the debt; nor indeed was their meeting for
the sake of anything at all.
It was a simple co-incidence. Hence, it lacks a final
cause.
- mathematical abstractions lack material causes
- a triangle existing as an object of thought
independent
of any material realization will trivially lack a
material cause.
- thus all four are not always necessary, but ordinarily,
leaving one out leaves out a necessary part of an adequate
explanation:
so it's a sort of default to have all 4 rather than really
being
necessary.
- The sufficiency claim is exceptionless
- But one might specify the material cause more or less
proximately, by specifying the character of the matter
more or less
precisely.
- my arm is flesh and bone and sinew, but it is also
carbon and hydrogen, but it is also electrons and
protons: the flesh and bones and sinews are more
proximately my arm.
- Not just any level of generality suffices.
- He means to insist that there is no fifth kind of cause:
he
challenges his readers to identify a kind of cause which
qualifies as a
sort distinct from the four mentioned. (Phys. 195a4–5).
- He thinks he can argue forcefully for the four causes as
real
explanatory factors, that is, as features which must be
cited not
merely because they make for satisfying explanations, but
because they
are genuinely operative causal factors, the omission of
which renders
any putative explanation objectively incomplete and so
inadequate.
- some scholars have come to understand them more as
becauses
than as causes—that is, as explanations rather than as
causes narrowly
construed
- such judgments reflect an antecedent commitment to one
or
another view of causation and explanation—that causation
relates events
rather than propositions; that explanations are
inquiry-relative; that
causation is extensional and explanation intensional; that
explanations
must adhere to some manner of nomic-deductive model,
whereas causes
need not; or that causes must be prior in time to their
effects, while
explanations, especially intentional explanations, may
appeal to states
of affairs posterior in time to the actions they explain.
- Generally, Aristotle does not respect these sorts of
commitments: his approach to aitia may be regarded as
blurring the
canons of causation and explanation. It is not clear how
aware he is of that, whether he would consider it a
problem, or how he would respond.
- §8. Hylomorphism
- matter (hulê) and form (eidos or morphê).
- Hylomorphism =df
ordinary objects are composites
of matter and form.
- "=df" means "is defined as"
- "ordinary objects" refers to such things as statues and
houses, horses and humans.
- Hylomorphism holds that no such object is metaphysically
simple, but rather comprises two distinct metaphysical
elements, one
formal and one material.
- formulated originally to handle various puzzles about
change.
- A. insists all change involves at least two factors:
something persisting and something gained or lost.
- Thus, when Socrates goes to the beach and comes away
sun-tanned, something continues to exist, namely
Socrates, even while
something is lost, his pallor, and something else
gained, his tan.
- This is a change in the category of quality, whence
the
common locution ‘qualitative change’.
- in whatever category a change occurs, something is
lost
and something gained within that category, even while
something else, a
substance, remains in existence, as the subject of that
change.
- substances too can come into or go out of existence;
and
these are changes in the category of substance.
- in the case of the generation of a statue, the
bronze
persists, but it comes to acquire a new form, a
substantial rather than
accidental form.
- matter and form come to be paired by Aristotle with another
fundamental
distinction, that between potentiality
and actuality.
- the bronze is potentially a statue, but it is an actual
statue when and only when it is informed with the form of a
statue.
- before being made into a statue, the bronze was
potentially
many things, but it was not potentially butter or a beach
ball.
- form =df that which makes some matter which is potentially
F
actually F
- matter =df that which persists and which is, for some
range
of Fs, potentially F
- in Physics i 7 and 8, we have the following simple argument
for
matter and form:
- (1) a necessary condition of there being change is the
existence of matter and form;
- (2) there is change;
- hence (3) there are matter and form.
- The second premise is a phainomenon accepted without
further
defense.
- The first premise is justified by the thought that since
there is no generation ex nihilo, in every instance of
change something
persists while something else is gained or lost. In
substantial
generation or destruction, a substantial form is gained or
lost; in
mere accidental change, the form gained or lost is itself
accidental.
Since these two ways of changing exhaust the kinds of change
there are,
in every instance of change there are two factors present.
These are
matter and form.
- matter and form are mind-independent features of the world
and
must, therefore, be mentioned in any full explanation of its
workings.
- §9. Aristotelian Teleology
- "teleology" is the idea that things have purposes, goals,
ends that they are moving towards unless blocked
- The efficient cause requires a word or two first: Aristotle
observes
that nothing potential can bring itself into actuality without
the
agency of an actually operative efficient cause. Since what is
potential is always in potentiality relative to some range of
actualities, and nothing becomes actual of its own accord—no
pile of
bricks, for instance, spontaneously organizes itself into a
house or a
wall—an actually operative agent is required for every
instance of
change. This is the efficient cause. These sorts of
considerations also
incline Aristotle to speak of the priority of actuality over
potentiality: potentialities are made actual by actualities,
and indeed
are always potentialities for some actuality or other. The
operation of
some actuality upon some potentiality is an instance of
efficient
causation.
- The final cause, the one that is invoked by "teleology," is
quite controversial and difficult.
- easy cases: computers and can-openers are devices
dedicated
to the execution of certain tasks, and both their formal and
material
features will be explained by appeal to their
functions. we give
them their functions. their functions are their purposes.
they exist and are what they are only if they perform their
function. All tools are functionally defined.
- more difficult: nature exhibits teleology without design.
living organisms not only have parts which require
teleological
explanation— for instance, kidneys are for purifying the
blood and
teeth are for tearing and chewing food—but whole organisms,
human
beings and other animals, also have final causes.
- organisms have final causes, but were not designed. He
thus
denies that a necessary condition of x's having a final
cause is x's
being designed.
- most (not all) objections to Aristotle's final cause are
stupid: any
number of mind-numbing examples exist
- in the 19th century, German scholar Zeller was able to say
with perfect accuracy that ‘The most important feature of
the
Aristotelian teleology is the fact that it is neither
anthropocentric
nor is it due to the actions of a creator existing outside
the world or
even of a mere arranger of the world, but is always thought
of as
immanent in nature’ (1883, §48).
- Aristotle offers two sorts of defenses of non-intentional
teleology in nature, the first of which is replete with
difficulty. He
claims in Physics ii 8:
For these [viz. teeth and all
other
parts of natural beings] and all other natural things come about
as
they do either always or for the most part, whereas nothing which
comes
about due to chance or spontaneity comes about always or for the
most
part. … If, then, these are either the result of coincidence or
for the
sake of something, and they cannot be the result of coincidence or
spontaneity, it follows that they must be for the sake of
something.
Moreover, even those making these sorts of claims [viz. that
everything
comes to be by necessity] will agree that such things are natural.
Therefore, that for the sake of which is present among things
which
come to be and exist by nature. (Phys. 198b32–199a8)
- The argument here seems problematic.
- Aristotle seems to introduce as a phainomenon that
nature
exhibits regularity: humans tend to have teeth arranged in
a
predictable sort of way, with incisors in the front and
molars in the
back.
- He then seems to contend, as an exhaustive and
exclusive
disjunction, that things happen either by chance or for
the sake of
something
- Aristotle is himself aware of one sort of counterexample
to
this view and is indeed keen to point it out himself:
- bile is regularly and predictably yellow, its being
yellow is neither due simply to chance nor for the sake
of anything.
Aristotle in fact mentions many such counterexamples
(Part. An.
676b16–677b10, Gen. An. 778a29-b6).
- It seems to follow, then, short of ascribing a straight
contradiction to him, either that he is not correctly
represented as we
have interpreted this argument or that he simply changed
his mind about
the grounds of teleology. Taking up the first alternative,
one
possibility is that Aristotle is not really trying to
argue for
teleology from the ground up in Physics ii 8, but is
taking it as
already established that there are teleological causes,
and restricting
himself to observing that many natural phenomena, namely
those which
occur always or for the most part, are good candidates for
admitting of
teleological explanation.
- this is a bit more detailed than is usual at this
stage in our exploration of Aristotle, but it is useful,
because it illustrates that Aristotle often needs our
charity. We can catch him out in an apparent mistake,
but if we think about it, and help him a little, he may
have a very good point that is not a mistake at all...
- Perhaps he has a broader sort of motivation for teleology
- animals other than man make things using neither craft
nor
on the basis of inquiry nor by deliberation. This is in
fact a source
of puzzlement for those who wonder whether it is by reason
or by some
other faculty that these creatures work—spiders, ants and
the like.
Advancing bit by bit in this same direction it becomes
apparent that
even in plants features conducive to an end occur—leaves,
for example,
grow in order to provide shade for the fruit. If then it
is both by
nature and for an end that the swallow makes its nest and
the spider
its web, and plants grow leaves for the sake of the fruit
and send
their roots down rather than up for the sake of
nourishment, it is
plain that this kind of cause is operative in things which
come to be
and are by nature.
- Since nature is twofold, as matter and as form, the form
is
the end, and since all other things are for sake of the
end, the form
must be the cause in the sense of that for the sake of
which. (Phys.
199a20–32)
- But perhaps all that talk of spiders and ants and plants
doing things for some end is just imprecise and lax. We
might yet
demand that all such language be assiduously reduced to
some
non-teleological idiom when we are being scientifically
strict and
empirically serious
- we would first need to survey the explanatory costs and
benefits of our attempting to do so. Aristotle considers
and rejects
some views hostile to teleology in Physics ii 8 and
Generation and
Corruption i.[22]
- §10. Substance
- Aristotle insists upon the primacy of primary substance in
his
Categories.
- star instances of primary substance are familiar living
beings
like Socrates or an individual horse (Cat. 2a11014).
- with the advent of hylomorphism, these primary substances
are
revealed to be metaphysical complexes
- now we have three potential candidates for primary
substance:
form, matter, and the compound of matter and form.
- which is the primary substance?
- The compound: we say that Socrates lives in Athens, not
that
his matter lives in Athens.
- The matter: it underlies the compound and in this way
seems a
more basic subject than the compound, at least in the sense
that it can
exist before and after it does.
- The form: the matter is nothing definite at all until
enformed; so, perhaps form, as determining what the compound
is, has
the best claim on substantiality.
- Aristotle settles on form (Met. vii 17).
- He expects a substance to be, as he says, some particular
thing (tode ti), but also to be something knowable,
some essence or
other.
- These criteria seem to pull in different directions:
- the first in favor of particular substances, as the
primary
substances of the Categories had been particulars
- the second in favor of universals as substances, because
they alone are knowable.
- many scholars have concluded that Aristotle adopts a
third
way forward: form is both knowable and particular. This
matter,
however, remains very acutely disputed.
- Aristotle prefers form in virtue of its role in generation
and diachronic persistence.
- When a statue is generated, or when a new animal comes
into
being, something persists, namely the matter, which comes
to realize
the substantial form in question.
- But the matter does not by itself provide the identity
conditions for the new substance.
- the matter is merely potentially some F until such
time
as it is made actually F by the presence of an F form.
- the matter can be replenished, and is replenished in
the
case of all organisms, and so seems to be form-dependent
for its own
diachronic identity conditions.
- For these reasons, Aristotle thinks of the form as
prior
to the matter, and thus more fundamental.
- Further, in Metaphysics vii 17 Aristotle offers a
suggestive
argument to the effect that matter alone cannot be
substance.
- Let the various bits of matter belonging to Socrates be
labeled as a, b, c, …, n.
- Consistent with the non-existence of Socrates is the
existence of a, b, c, …, n, since these elements exist
when they are
spread from here to Alpha Centauri,
- but if that happens, of course, Socrates no longer
exists.
- Heading in the other direction, Socrates can exist
without
just these elements, since he may exist when some one of
a, b, c, …, n
is replaced or goes out of existence.
- So, in addition to his material elements, insists
Aristotle, Socrates is also something else, something
more (heteron ti;
Met. 1041b19–20).
- This something more is form, which is ‘not an
element…but
a primary cause of a thing's being what it is’ (Met.
1041b28–30).
- The cause of a thing's being the actual thing it is,
as
we have seen, is form.
- Hence, concludes Aristotle, as the source of being and
unity, form is substance.
- Feel free to entertain the following question: suppose
your form is made up of formal parts A, B, C, ..., N:
would you exist without some of them? Maybe: in that
case, form as the cause of a thing's being a thing (in
this case you being you) is vulnerable to the same
objections as matter. So Aristotle needs to explain why
parts of a form are not like material parts, or somehow
meet this objection in another way.
- many questions remain. For example, is form best
understood
as universal or particular? (that is, is there a form of you
that is peculiar to you and shared by no other human, or is
your human form the same as every other human's form)
However that issue is to be resolved, what
is the relation of form to the compound and to matter? If
form is
substance, then what is the fate of these other two
candidates? Are
they also substances, to a lesser degree? It seems odd
to conclude
that they are nothing at all, or that the compound in
particular is
nothing in actuality; yet it is difficult to contend that
they might
belong to some category other than substance.