GAMMA (III) METAPHYSICS, chaps. i and ii
"Being"
I am going to take up now chapters one and two together as a
coherent unit, alloting two weeks for the reading of them. For a
change the Greek is not difficult, for those who are reading the
Greek text. It is fairly fluent. But what it all means, Greek or
English, is another matter. There are a number of technicalities in
the text that may offer some puzzlement. So this week I will
endeavor to outline the text in a way to make it as clear as
possible, and to explain it. I am going to intersperse comments in
brackets as I go along. Next week I will post a somewhat redundant
treatment for those who would like to address some of the
technicalities in an alternate manner. Skip it, if you wish.
1. The first chapter is very short and straightforward: there is a
science [namely, metaphysics] that investigates being by itself,
just plain being, being qua being, on hE on. It is different from
all the particular sciences, 1003a21-32. [Short and simple as it is
this chapter is of utmost importance, establishing on hE on, being
qua being, an unquestionable abstraction in our terms, as the
object of the Metaphysics.]
2. BUT - and this is a big but! - to de on legetai pollachOs, being
means many things, 1003a33-a34 [and thus arises the problem of
ambiguity that will plague us throughout the Metaphysics, unless we
are very, very attentive to it. It will not just be "being" that
means many things, but several other words and concepts as well.
But here we are concerned with "being", and the remainder of
chapter ii will explore some of the many meanings of "being." It is
still part of the introductory, or propaedeutic section of the
Metaphysics, A through E, i (I - VI, i). We are dealing with
language here, with "being" as a word, or term. At least that seems
to be the side on which the emphasis lies. Otherwise the analyses
of Book Z (VII) and later books might seem redundant, where as they
are the featured ontology of the Metaphysics.]
The many meanings of "being:"
a. some examples of a"pros hen" meanings, or paronyms [words
with slightly differing spelling or name, and a different
definition, but with a common derivation. It is these terms,
paronym, synonym, homonym and polynym that I am going to
analyze in more detail next week]: health and healthy,
medical and medicine, etc., 1003a34-b4
b. Thus "being" is meant many ways, but all looking to one
origin, b5-b6: as substances (ousiai), as states (pathE) of
substance, as "ways to substance" (hodos eis ousian), or
"ceasings to be" (phthorai), or privations (sterEseis), or
makings or being made or productive of substance or things
having to do with it, and their negations. Thus we even say
that not-being IS not-being, b5-b10
c. [generalizing:] just as there is one science of health, so it
is with others. It is not the business of one science to
investigate only the nature of synonymous (kath' hen), but
also of paronymous (pros hen) [modes of being]. Even these
[paronyms] are in a sense kath' hen [i.e. point to a single
derivation]. Clearly it is the business of one science to
investigate beings as being. It is absolutely properly the
the science of the first [entity] on which the others depend
and through which they are understood, b11-b17
d. if this is ousia, the philosopher should have a hold on the
principles and causes of beings (ousiOn). One impression and
one science of [each and] every kind, like one grammar
investigates all sounds. Thus one science investigates being
qua being as a kind, however many species there are, and the
[special] sciences investigate the species, b17-b22
e. [Aristotle now turns to the special consideration of being
and unity, the pair of co-ordinate highest genera that we
have met before in the seventh and eleventh problems of Book
B (III), and will meet again. This traditional problem was of
special importance to him and his contemporaries] if being
and one are the same and one nature in their following each
other as principle and cause, although not the same in
definition (whether we suppose this or not, it is indeed what
happens), since one man and man are the same . . . [etc.],
it is the same with one; it is clear that the addition [of
one] in these means the same, and one is nothing different
from being. The ousia of each thing is one, not by accident,
and so it is with any being whatever, b22-b33
f. As many as are the kinds of unity, so many are the kinds of
being. About which it is the business of same science to
investigate. I mean about the same and the like and the other
such, legO d'hoion peri tautou kai homoiou kai tOn allOn tOn
toioutOn. [Now what's going on here! These some of our
friends the tanantia of Plato's Parmenides. More will appear
below.] Similarly all the contraries (tanantia) lead back to
the same principle [to hen]. We have looked into this in our
treatise on contraries [there is some speculation about just
what he is referring to there], b33-1004a2.
g. There are as many parts of philosophy as there are ousiai. So
there must be some first and containing them. Being falls at
once into genera [cf. Liddell & Scott, p. 716]; the sciences
follow these. There is philosophy and mathematics [for
example], and even this has parts, and there is primary and
secondary science and others in order in mathematics, a2-a9
[this section of the text may belong with d. above]
h. [this seems to pick up where f. above left off] it is for one
science to investigate opposites, and the oppsite of unity is
many-ness. Negation and privation are [also] for one science
to investigate, since both look at the one which is denied,
etc. (either simply or in some kind; in the latter case
difference is implied in the denial; plain denial is its
absence; in the case of privation there is some underlying
basis for the privation), a9-a17
i. So the opposites of the above [f., line 36, the same and the
like, etc.], the other and the unlike and the unequal and
such others as are listed according to these and to many and
the one [the tanantia of the Parmenides] are the business of
the aforementioned science. They are contrary; contrariety is
difference; difference is otherness. So since one is meant
many ways, and these will be meant many ways, it is for one
science to know them all, because the meanings do not differ
because they are many but only if they are not synonyms or
paronyms (ei mEte kath' hen mEte pros hen). As they all refer
to the first, as when one is meant as a paronym of the first
one, it must be held likewise about the same and the other
and [the rest of] the tanantia. As each is meant many ways,
it must be related somehow to the first of each kind, by
state or action or other such categories, a17-a31
j. it is clear that it is for one [science] to think about these
and about ousia (this was one of our problems [#5]), and it
is up to the philosopher to be able to investigate them all.
If not the philosopher, who will ask whether Socrates is the
same as Socrates seated, or if there is [only] one contrary,
or what IS the contrary, or how many ways stated? Likewise
with other such [questions]. Inasmuch as these [tanantia] are
necessary attributes of the one qua one and being qua being,
not like numbers or lines or fire, it is clear that it is of
this science to know what they are and their properties. And
those who look into numbers, etc. do not err in that they are
not philosophizing, but they are not investigating ousia,
which is primary. Just as number qua number has its own
attributes, like oddness and evenness, commensurability and
equality, excess and defect, and these belong to the numbers
themselves and related to others (same as a solid in motion
or motionless or weightles or having weight, each its own),
likewise being qua being has its own and these are what it is
a philosophers job to examine, a31-b17
k. for example, dialecticians and sophists are in the same line
as the philosopher, but sophistry is merely apparent wisdom,
and the dialecticians argue about everything, although being
is a common topic for all, yet clearly these [matters] are
proper to philosophy . . . , b17-b26
l. [recap] the other [right] side of the list of opposites is
negation [of the left side, and I disagree emphatically with
Ross here: it is the tanantia of the Parmenides that he is
referring to here, not his own list of the Pythagorean in
Book A (I) 986a22-a26, although it is possible that these
were all mixed up in contemporary tradition] and [the two
sides] lead to being and not-being, and to one and many,
rest to the one and motion to the many. Beings and being (ta
d'onta kai tEn ousian), they agree, are nearly all compounded
of contraries. [The old boys] call all the archai contraries,
some odd and even, some hot and cold, some limit and
unlimited, some love and hate. And all the others appear
derivable from the one and the many (I referred to this [in
the third problem]); the principles and by and large the rest
come together as one class. It appears from these that it is
[the business] of one science to investigate being qua being.
Everything is contraries or from contraries, and the origin
of contraries is the one and the many. These are [matter] of
one science, whether synonymous or not, as truth has it. But
all the same if the one means many things (pollachOs legetai
to hen) the others are read in light of the first, and the
contraries [are] too, and if there is no being and one,
universal, overall and separate (chOriston), equally there is
nothing else whether paronyms or the rest. Thus it is not the
geometer's job to speculate about what the contraries are, or
purpose or one or being or same or other; he just uses them.
so it is clear that it is for one science to investigate
being qua being and what belongs to it qua being, and it is
the same science of beings and of what belongs to them, [all]
the things we have mentioned, and prior and posterior, and
genera and species, and whole and part, and other such,
1004b24-1005a18.
* * *
I see that I have given a fairly close line by line translation of
most of chapter ii there. It is an important chapter, deserving our
close attention. The technicalities of Aristotle's linguistic
terminology (paronyms, synonyms, homonyms) plays an important part
of his endeavor to point out the relations of the different
meanings of the words, "being" and "one." I will return to these
next week. So does the peculiar relation in which Aristotle and his
contemporaries seem to have held being and unity (one). This is in
part inherited from Parmenides and Plato, although I would suspect
that it had wider currency than we know, that in Parmenides, in
Plato's Parmenides, and here we see only the tip of the iceberg, so
to speak.
This chapter is a discussion of language, of words, of terms. To be
sure, words are related closely to things, but here the emphasis
seems to be on the side of language. Signs of this are his use of
linguistic terms, the context of "pollachOs legetai," the devotion
of the remainder of the Book to matters logical, and the following
presence of Book D (V), a sort of short dictionary of terms. These
all cohere as introductory materials. There is latent here an issue
of great importance, which had better be faced squarely: what is
the object of metaphysics, of Aristotle's Metaphysics? Several
times in this chapter he says explicitly that it is all these
meanings of "being." This is so, in the sense that "being" covers
all these meanings, and that being "resides in" all beings, etc.
But he prefaces that observation here, with the emphatic statement
of the first chapter that metaphysics is concerned with being qua
being, on hE on. And he will repeat this later on. Thus the
ambiguity that metaphysics, this Metaphysics, is in one sense
concerned with all beings, while in another, for us more pertinent
sense, it is concerned with being qua being, being itself, being
(as we would now say) in the abstract.
As an aid in tracking the "many meanings of `being'" I append here
a chart of the various paronyms, synonyms, and so forth that you
have encountered here in this Book Gamma (IV), chapter ii, and
will, by the way, encounter again in its "shadow" in K, iii.
on
..................................
. . .
. . .
on hE on onta hen - plEthos
. . . .
. . . .
ousia . pathos . tanantia (the
. .(K, iii). . rest of the list)
. . . . . . .
. . . . .
. . . . .
hexis diathesis kinEsis poiotEtes .
(these are all found in K, iii) .
.
.
.
onta
.
.........................................
. . . .
. . . .
ousiai pathE ousias hodoi (ex hE) ta pros tEn
. eis ousian ousian
. . legomena
. . (catch all)
. .
. .
ta sumbebEkota .
(K, iii only) .
.
.
...............................
. . . .
phthorai sterEsis poiEtika gennEtika
EFL, 3/7/96
GAMMA (IV) METAPHYSICS, chap. ii
Some Terms
Chapter two is devoted to the many meanings of being. to de on
legetai pollachOs. In the course of arranging those meanings, this
chapter makes use of a number of technical terms, which have been
variously interpreted and which may be the cause of confusion.
These terms are: synonym, homonym, pros hen, kath' hen, and so
forth. The use and meaning here of some of them is sometimes
different from their common use in English in our time, and that is
far from helpful. Their use by and meaning for Aristotle may be
found in many places aside from Gamma, ii, Metaphysics. The first
chapter of Aristotle's Categories, and the commentary of Alexander
Aphrodisias on the present chapter (In Metaph. Arist., ed.
Michael Hayduk, Berlin, 1891, p. 241) are most helpful. Ross'
commentary, vol. I, p. 256-57 and 269 may also be consulted, as
well as Bonitz, Index, and Liddell, Scott, Jones. Using these
references, we summarize the technical terms as follows:
Term word definition root or
or genus derivation
synonym same same not applicable
(= kath' hen)
homonym same different not applicable
paronym different different same
(= aph' henos kai pros hen)
For the sake of symmetry and completeness, we might add:
polynym different same not applicable
Aristotle rarely uses such a term as polynym, and only then in a
different context (Historia animalium, 489a2; De mundo, 401a12).
Nevertheless, he seems to use it in such a manner, i.e. a
different name for the same thing (heis On ho theos poluOnumos
estin), even though Alexander Aphrodisias (280, 19) equates it
with synonymy. It would fit here the situation of on and hen as
different names for the same (ei dE to on kai to hen tauton, etc.,
1003b23). (See also Speusippus, fr. 32, ed. Lang.)
The term, paronym, Aristotle does not use here, although he did
use it in Categories, I, i. Paronyms differ in their flexion
(case, gender, tense, etc.), but they "have an address to a name"
(diapheronta tE ptOsei tEn kata tounoma prosEgorian echei), i.e. a
common root or derivation. Instead he uses here the equivalent term
pros hen, as our table above shows.
Before considering what Aristotle says in detail, let us look again
at the texts of Gamma, ii, and its paraphrase, K, iii, as wholes,
and ask ourselves, what is Aristotle trying to do in these two
texts? One can see that
(1) there are some theoretical comments,
(2) there are some illustrative analogous examples, and
(3) there are the many meanings of being, the pollachOs
legetai to on, so to speak.
Let us inspect the texts in terms of these three activities:
(1) The theoretical comments. The many meanings of being are, in
Gamma, ii:
pros hen kai mian tina phusin, to one and some one nature,
ouk homOnumOs, not homonymously,
pros mian archEn, to one principle (or beginning),
kath' hen (dist. from pros hen) = synonymous,
pros mian phusin, to one nature,
kai tropon tina kath' hen (see above),
(ou gar ei pollachOs, heteras, all' ei mEte kath' hen
mEte pros hen, see above),
(pros to prOton, to the first)
These are the phrases used wherever the question of meaning is
raised by use of the word legetai or a paronym thereof. All but
the last two are near the beginning of chapter ii of Gamma. The
last two actually refer not to "being," but to other terms, and
thus are parenthesized in the list above. So far these main points
are made: (a) the meanings of being seem to point toward one
primary meaning, nature or principle; (b) they are not homonymous;
(c) they can have both a pros hen (paronymous) and a kath' hen
(synonymous) relation to the one primary meaning.
In K, iii, they are:
ei homOnumOs ouk hupo mian epistEmEn, if homonymous,
not of one science,
ei kata ti koinon hupo mian epistEmEn, if with
something in common, of one science,
kath' hen ti kai koinon, after some one and common thing,
These restate the main points made above, excepting the lack of
mention of pros hen, which however is used plentifully in the
examples to be studied below.
(2) The examples which Aristotle gives of multiplicity of meaning
(pollachOs legesthai) are, in Gamma, ii:
healthy, meaning protective of
healthy, meaning productive of health
healthy, meaning signifying (pros hugieian)
healthy, meaning receptive to
medical, meaning having
medical, meaning naturally suited for (pros) medicine
medical, meaning the work of
In K, iii, they are:
medical, referring to (pros) medicine
medical science, meaning knowledge of medicine
medical knife, meaning useful for medicine
healthy, referring to (pros) health
healthy, meaning signifying health
healthy, meaning productive of health
The effect of these examples is the same in both chapters. The
reference to one primary meaning, nature or principle is clear. The
precise kind of linguistic relationship depends on the definitions
of the linguistic relations. Since these can vary even in
Aristotle's own definitions and usages, there is where much of the
difference in interpretation seems to have lain. Little can be
added with any certainty to points (b) and (c) in (1) above, i.e.
whether these are homonyms or not, or paronyms, or synonyms, or
pros hen equivocals, or something else. And little need be added.
What we want to know is not Aristotle's linguistic theory of
multiplicity of meaning here, but his theory of the multiplicity of
the MEANING OF BEING, i.e., his linguistic theory OF BEING. We want
to know this only to help us understand later his theory of being
itself. Being means many things, to on legetai pollachOs, chiefly
because of its synonyms and polynyms, of which then proceeds to
give us abundant examples:
(3) the many meanings of being (pollachOs legesthai to on) in
Gamma, ii, are, in order of appearance:
on hE on, being qua being,
ousiai, substances,
pathE ousias, properties or states of substance,
hodos eis ousian, coming into being,
phthorai, passings out of being,
sterEsis, privation,
poiotEtes, qualities
poilEtika productives,
gennEtika ousias, generatives,
ta pros tEn ousian legomena, things stated
in relation to substance,
onta, beings,
ousia, substance,
on, being,
hen, one,
tanantia, the contraries (several are named
under this collective appellation);
in K, iii, in order of appearance, they are:
pathos ontos hE on, property of being qua being,
hexis, state, or condition,
diathesis, disposition,
kinEsis, motion,
tanantia, the contraries,
ta sumbebEkota kath' hoson estin on, attributes
(contingent, or necessary).
These lists hardly seem presented in a systematic fashion at
first sight. Nevertheless they illuminate the multiplicity of the
meanings of being, even if without any apparent order. It is not
difficult to derive some order from them. Mind you, in doing so
we are moving a step away from what is explicit in the texts, but
I don't think we are moving very far away. Something like the
following order seems capable of being derived easily, even
though it may admit of some possible variation in detail (this is
the same chart as furnished last week):
on
..................................
. . .
. . .
on hE on onta hen - plEthos
. . . .
. . . .
ousia . pathos . tanantia (the
. .(K, iii). . rest of the list)
. . . . . . .
. . . . .
. . . . .
hexis diathesis kinEsis poiotEtes .
(these are all found in K, iii) .
.
.
.
onta
.
.........................................
. . . .
. . . .
ousiai pathE ousias hodoi (ex hE) ta pros tEn
. eis ousian ousian
. . legomena
. . (catch all)
. .
. .
ta sumbebEkota .
(K, iii only) .
.
.
...............................
. . . .
phthorai sterEsis poiEtika gennEtika
Even if it is possible to vary the details of this arrangement,
the main features are apparent anyway. We use the word "being"
first to denominate pure being, and individual beings; and
Aristotle also investigated it in a special sense: the one. These
are the three most general classes of meaning. Then there are the
subdivisions of each of these, and subdivisions of the
subdivisions, more or less as shown (not completely, to be sure).
These are enough to indicate the many kinds of being, universal
and individual, substantial and accidental, and others. Now it
can be said with some clarity of meaning that our first science,
the science we are seeking, deals with all being, but that means
(1) pure being (on hE on, (2) being as one (hen) and its
derivative contraries, and (3) individual beings, yes, but only as
they represent being generally (onta hE onta), not qua individuals.
Thus it deals with being, its polynyms and paronyms.
This is in fact what the Metaphysics deals with in Books E - I.
But it does so according to what at first sight looks like a
different division of being. Only the very initial division into on
hE on and on ti bears any resemblance to the above. For a very
simple reason: there (E - I) the investigation is ontological; here
(G, ii) it is linguistic. Gamma, ii, is still an introductory sort
of investigation, putting us on our guard about our language, or
giving us a taste of what is to come. Being means many things.
There are many ways we speak of it, and it has many kinds itself.
Here Aristotle only addresses the ways we speak of it; there the
ways it is. And he adopts the scheme of the categories.
Gamma, ii, and K, iii, are also a response to the third and fifth
problems of the list at the beginning of B. "Since, speaking of
being in many ways, we speak of all being [but] after one common
[aspect], and in the same way of contraries, and those can all be
subjects of one science, our problem is solved which we posed at
the beginning; I mean the one[s] in which we asked how there
could be one science of many and different kinds of being." Thus
ends K, iii. "It is clear that it is [the task] of one science to
investigate being qua being, and the subsistents in it qua being,
and not only substances but subsistents of the kind mentioned and
prior and posterior (i.e. the contraries?) and genus and species
and whole and part and all other such things." Thus ends Gamma, ii.
Book Gamma plays an important part in the total scheme of the
Metaphysics. Before launching into his main ontological
investigation (E - I), Aristotle endeavors to clear up some
difficulties that might stand in our way, that might arise from
the varieties of the word, "being." If metaphysics deals with any
being or all beings, it does so only in the qualified sense that
they are parts of being.
The other technical (and to us perhaps unusual) aspect of Book
Gamma is the equivalence of the polynyms, Being and One, to on and
to hen. Although this at first may seem strange to you, it cannot
be emphasized how central a tradition this was in ancient Greek
philosophy. We have already met with it in Book B (III), in the
eleventh problem. I have also pointed out in my outline of the
Metaphysics as a whole, how it shapes the organization of the same
by its inclusion as the subject of a whole Book, Book I (X), as a
third and odd-man-out ontology. Such was the importance of this
tradition that Aristotle could not ignore it. We can trace it in
Parmenides, in Plato's Parmenides, and no doubt elsewhere as well.
In Book I (X) he dispenses with it, at least to his satisfaction,
but it seems to have come back to life and then some with
neoplatonism, where the One is elevated so far that it is even
beyond Being! It does not pay to underestimate the importance of
the One in those old days, not in the least here.
EFL, 3/14/96
GAMMA (IV) METAPHYSICS, chapter iii
The principles of knowledge, and the Law of Contradiction
[With this third chapter, Book Gamma takes off in a new direction.
Although it is short, the chapter deserves close study, and I
propose to do a bit of translation from the Greek at some spots (1.
and 4. below) to elucidate what seems to me to be their meaning,
and to point up certain issues.]
1. one must state whether it is for one science or different
sciences to study about the so-called axioms of knowledge
(mathEmata), and about being. [Recognize this as the second problem
in Book Beta (III)?]. It is for one inquiry, the philosopher's
[about being], and about these [principles of knowledge], because
it applies to all beings, not just some separate kind. All use
them, because they are of being qua being, being every kind [of
being]. They use them to the extent that they are fitting; that is
the extent to which they apply to the kind [of being] they are
being used for. So it is clear that they apply to all [kinds of
being] qua beings, hE onta, (this is common to them all). The
investigation (theOria) is about learning about being qua being, on
hE on, and about these [principles of knowledge], 1005a19-a29.
[I have translated the above lines carefully, because of a
particular issue they concern. We mentioned it two weeks ago, and
we will have reason again later to question the extent to which the
Law of Contradiction applies to being qua being, on hE on. There is
no question that it applies to beings. But to being itself, on hE
on? Being means many things, as we saw in chapter ii. Two of those
meanings are (1) pure being qua being, and (2) all beings. These
two meanings are confounded here in Gamma, in chapter ii and in the
present passage. There is a sense in which pure being qua being is
found parcelled out, as it were, if such a thing is possible, in
all beings. In a sense it is, and in a sense it isn't. This is
another one of the ambiguities and paradoxes we will face. In close
proximity here, in lines a28-29, Aristotle uses hE onta and on hE
on, "as beings" and "as being." Believe me: here is going to be one
of the main difficulties of the Metaphysics. It has ALWAYS been the
main difficulty of all metaphysics: distinguishing particulars and
abstractions. They are so different and yet so entangled.]
[[Special note: may I call the attention of those of you who are
reading or consulting the Greek text to an good example of one of
the technical difficulties attendant upon our enterprise. I mean
the possible confusion of substantive and procedural uses of a word
or synonym, or what in the computer programmer's world is sometimes
referred to as the confusion of calculation and address arithmetic.
Look carefully at the lines 1005a24-25, hoti tou ontos estin hE on,
hekaston de to genos on. ontos hE on is the subject here of the
discussion, but estin and the second on are predicative existential
uses of the verb, einai. Or in plain language, what is being talked
about, and what is being said about it, use two different modes of
the word, being. I pause to point this out only because it is such
a good and concentrated example of one of the difficulties of this
ontology. This kind of thing is not uncommon. En garde!]]
2. they [the principles of knowledge] are not the business of any
of the partial sciences. Recap. a29-b8
3. it [the Law] is the most certain, the best-known and the
unconditional principle, that the philosopher must have, b8-b18
4. [follows now the famous Law of Contradiction, b18-b27]
to gar auto hama huparchein te kai mE huparchein adunaton tOi
autOi kai kata tO autO, it is impossible for the same thing at
the same time to be predicated and not to be predicated of the
same thing in the same respect [or belong to and not to belong
to the same, etc.], b19-b20
[This is followed by variations, stated in terms of being and of
contraries. Mutatis mutandis they amount to the same.]
adunaton gar hontinoun tauton hupolambanein einai kai mE
einai, it is impossible to suppose any same thing to be and
not to be, b23-b24
ei mE endechetai hama huparchein tOi autOi tanantia, if
contraries cannot be attributed to the same, b26-b27
[Here is the big problem: the Law states that it is impossible for
the same thing at the same time to be predicated of, or attributed
to, the same . . . , etc. Being qua being, on hE on, however has no
predicates or attributes, as we shall see in due course. In so far
as "the science we seek," metaphysics, has to do with on hE on, and
not its derivatives indicated by "the many meanings of being," it
would seem as though the Law has nothing to do with it. Being qua
being is above all that. I plan to return to this point and an
associated one again, but before doing so let us continue with the
text. The remainder of this Book Gamma (IV) is about the Law.]
5. the man who denies this would contradict himself, b30-b34
[literally, "would have opposite opinions," hama gar an echoi tas
enantias doxas ho diepseusmenos peri touto, but diapseudO is a very
strong word, and reminds us of Eubulides' Liar, ho pseudomenos,
recorded by Diogenes Laertius, II, 108. More on this later.]
[I am not inclined to say much about the Law of Contradiction at
this present time, other than what I have already intimated above,
namely that it may have certain limits. I prefer to see first what
Aristotle has to say about it in the ensuing chapters of this Book
Gamma (IV), before further comment. For those of you who wish, it
is not difficult to find extensive discussion of it. One example is
J. Lukasiewiez article (1910) translated by V. Wedin in The Review
of Metaphysics, 24 (1970-71), p. 485-509; and again by Jonathan
Barnes in Articles on Aristotle, 3. Metaphysics, London, Duckworth,
1979 (Lukasiewiez was one of our century's eminent logicians).
There are many others. I do deplore a tendency to complicate this
with a host of technicalities, mathematization and symbolization
(with the best of intentions) that render it opaque to the
generality of men and women. The need is to simplify and clarify
problems that are meaningful to all of us. I will call this the
humanist approach. We are all of us human beings with some
experience of life and its problems, which philosophy (indeed all
the humanities) must reflect, answer to, help us with. If it does
not, then bye, bye philosophy.]
EFL, 3/21/96
GAMMA(IV) METAPHYSICS, chapter iv
Refutations of denial of the Law of Contradiction
1. there are those who think otherwise, but we think it impossible,
and that this is the most certain of all principles, 1005b35-1006a5
2. it is not a matter for proof, a5-a11
3. there is an elenchic proof: it is impossible for the
contradictor to even speak. He refutes himself with his lack of
stable definition, and things must mean something, if one is going
to speak, a11-a28.
a. names mean something is or is not, a28-a31
b. some one thing, essentially one, a31-a34
c. paronyms give no trouble, if only limited in number, a34-b7
d. names must mean some one thing [The technical terms here seem
to get a bit confused, but the thrust of the argument is
clear enough], b7-b18
e. to be and not be [something] can only be the same in the case
of homonyms [different thing with same name], b18-b28
f. necessity implied in definition, b28-b34
g. difference in essence is more different that difference in
attributes; if there were no differences, all is one, b34-a10
h. don't confuse attributes with essences, one subject with many
predicates is still one subject, 1007a10-a20
i. distinction of subjects and predicates. Accidents must be
predicated of a subject, and this must be definite, a20-b18
4. there must be affirmation and denial, or everything is mixed up;
against the followers of Protagoras and Anaxagoras, b18-1008a2
5. if affirmation is compromised, denial is compromised, a2-a7
6. if it turns out [responding to several dilemmas] that there is
something that can be denied, the opposite affirmation is even
more sure; if one can't distinguish the truth, one can't say
these things, and there is nothing [distinct]; all is one, a7-34
7. no affirmation and denial of same thing at same time, a34-b2
8. truth and falsity must be distinguished, or there is no speech;
speech doesn't mean anything, b2-b13
9. actions are distinguished as good or bad. Why do we do anything?
Value judgements and choices, b13-b31
10. differences in degree, b13-1009a5
Although this is a long and rambling chapter, sometimes seeming
repetitive, there are some main themes in it. But first of all,
what does he mean by an elenchic proof? It is used for refutation,
of course, but how does it differ from a regular proof? He is
explicit about this here, 1006a15-a18: in a regular proof you look
for the premiss, but you use some other premiss in a refutation not
a regular proof, to d'elegtikOs apodeixai legO diapherein kai to
apodeixai, hoti apodeiknuOn men an doxeien aiteisthai to en archEi,
allou de tou toioutou aitiou ontos elegchos an eiE kai ouk
apodeixis.
I have supplied the word, "regular," there only for our
clarification. You may do away with it, if you wish. But what are
his "other premisses?" There seem to be two of them: first that
when one speaks one must mean something, something definite and
distinct, or one is not saying anything; and second, that one who
denies the Law of Contradiction is in danger of denying himself. He
rings, as you noticed, several variations on the former theme. The
latter, which I sometimes call the "turnabout" argument, in that it
throws the objector's argument back in his own face, is lightly,
but surely touched on: adunaton, an monon ti legEi ho amphisbEtOn,
it is impossible if the objector so much as says a thing. Why? In
faulting the Law, he lays himself open to contradiction.
Aristotle has been disturbed by all the talk of hoi polloi in the
Agora and round about, talk of what we would perhaps today call a
relativistic sort, and caused probably by proposals of Protagoras
and Anaxagoras and others, not to mention talk of the sort Plato
gives us a sample in the Euthydemus. His specific objections to the
doctrines of particular physicists are reserved for the next
chapter (v). Here he raises all the common sense arguments he can
think of to bolster his refutations, refutations indeed not
sophistical but of followers of the sophists. The need for
definition and the possibility of self-contradiction are the "other
premisses."
Are we justified in being cynical about all the chatter in the
streets and houses of ancient Athens? Was it all "sophistry?" Are
Protagoras and Anaxagoras to be written off as charlatans? I don't
think so. The tentativeness of the time is manifest. And look
around ourselves, at the fakes and the climbers mixed with the
genuine seekers and scholars. Are those old Greeks so different
from ourselves, except perhaps for being perhaps more curious and
talkative? Consider also that many things you and I take for
granted were still puzzles to them.
Let me call your attention to a couple of technical phrases in this
chapter. Aristotle uses them frequently elswhere too. (1) the
phrase to ______ einai, in which any noun in the dative case fills
in that blank, means the essence of whatever it is. Thus to
anthrOpOi einai means the essence of man, and so forth. (2) to
hoper ______, as in to hoper on, means just that thing itself, as
in being (by) itself. Bonitz has some extended remarks on this on
p. 533 of his Index. So do Liddell, Scott, Jones on p. 562 of their
dictionary.
EFL, 3/28/96
GAMMA (IV) METAPHYSICS, chapter v
The Presocratic philosophers
[In the last chapter (iv) Aristotle seemed to be defending the Law
of Contradiction against the sort of contention that sounded like
it might have come from the plain man about town who had been
listening to sophistic philosophers. Although a couple of
philosophers were named, the argument seems directed against their
followers more than against themselves. This chapter seems
differently oriented, as if against the ideas of serious
philosophers, well known to us by name, who proposed doctrines that
Aristotle thought to undermine the Law. Several are named, along
with their doctrines. In Aristotle's view, they wrongly put their
faith in appearances, in ta dokounta kai ta phainomena.]
1. Protagoras' doctrine [that "man is the measure of all things"]
compared to the prior opinion [the denial]: if all appearances are
true, they must also be false, since there are contrary appearances
[an ambiguity here: does not this also imply self-contradiction? If
they contradict each other, they cancel each other], 1009a6-a16
2. reply to the truly perplexed is easier than reply to those who
merely play with words and require an elenchic refutation [last
week's crowd], a16-a22
3. the truly perplexed get their opinions from sensibles, in which
are opposites. A thing that changes must be both what is and what
is not. Anaxagoras' mixture, and Democritus' void and full, are
being and not being, 22-30
4. in a sense they are right, in a sense not: being means two
things, to on legetai dichOs, and there is another kind of being,
allE tina ousia tOn ontOn, that doesn't change, which we expect
them to recognize [implication is that their "sensationalism" may
apply to beings, but not to substrate being itself. This fits the
observation of the first two chapters of this Book, the doctrine of
the many meanings of being. Passing mention of potentiality and
actuality, not brought up again until Book Theta (IX)], a30-a38
5. the perceptions of the majority are no criterion, a38-b6
6. opposites appear differently to us and to animals, and to the
single individual at different times, and it isn't clear, which
opinion is right, b6-b11
7. opinions of several Presocratics, Democritus, Empedocles,
Parmenides, Anaxagoras, Homer, who identify thought with sensation,
hupolambanein phronEsin men tEn aisthEsin, b11-b33
8. the perplexity of these philosophers is discouraging, but it is
because, seeking the truth about beings, they suppose that beings
are only the sensibles, b33-1010a7
9. Cratylus and the Heracliteans opine that, if everything moves
and nothing remains still, nothing can be proved true, a7-a15
10. Aristotle's replies to the Heracliteans, a15-b17
a. there is a substrate remaining through change, a18-a22
b. quantities change, but it is by form that we know
everything, a22-a25
c. limitation of the world we know, a25-a32
d. rest more likely than change, a32-b1
e. appearance is not the same as perception, b1-b3
f. difference of perspective, b3-b11
g. opinions about the future, b11-b14
h. different reports of different senses, etc., b14-b26
11. Recap, b26-1011a2
a. These theories do away with essence and necessity, b26-b30
b. that there are not substances which cause the sensation,
even without sensation, is impossible, b30-1011a2
[Whereas in the last chapter (iv) the emphasis was on meaning, the
main theme of this chapter is the error of reliance on aisthEta. It
is where these philosophers go wrong. What is the context of these
remarks? What is the other-than-aisthEta they overlook? It is not
the Cartesian res cogitans or cogitata, or Kantian transcendantals
or twelfth century universals. All these may be derivatives of what
Aristotle suggests here but they belong to other ages, other
contexts. Aristotle's other-than-aisthEta is his allE tina ousia
tOn ontOn "that doesn't change" (1009a37) the on huparchontOn of
1010a20. esti ti kai heteron para tEn aisthEsin, ho anagkE proteron
einai tEs aisthEseOs, there is something else beside sensation
which must be prior to it. That is his "other meaning of being,"
the on hE on. It is out of such an ontology that the later ones
will derive, but they are in the future. One reason for mentioning
this is that there is a line here, outhen an eiE mE ontOn tOn
empsuchOn (1010b30) "there would be nothing, were there no animate
being," that sounds like George Berkeley's "esse est percipi." But
the context here is strictly Aristotle's own ontology, which we are
going to see develop before our eyes, indeed have already seen
suggested: onta versus on hE on.
[Ross (p. 275) has a good comment here: "Bonitz argues that
Aristotle attaches too much importance to isolated phrases of the
early thinkers. Certainly neither Empedocles nor Democritus nor
Parmenides nor Anaxagoras can fairly be charged with consistent
sensationalism . . . " Perhaps not. Perhaps Aristotle may be a
little "quick on the trigger," using those "old boys," palaioi, for
his own purposes. But the implications seem to be there, and the
simplicity of the earlier accounts just would not do for him. What
he adds is worth adding.]
EFL, 4/4/96
GAMMA (IV) METAPHYSICS, chap. vi
Aristotle's rebuttals (cont.)
This short chapter finishes, in effect, the discussion of the
preceding chapters, repeating points made in both iv and v.
1. the truly puzzled may be persuaded that there is no proof of
everything (i.e. there are first principles) 1011a3-a14
2. the others, seeking a knock-out argument, appeal to contraries,
but they contradict themselves out of their own mouths, hoi d' en
tOi logOi tEn bian monon zEtountes adunaton zEtousin, enantia gar
eipein axiousin, euthus enantia legontes [Ross in his comment here
cites six different readings, but they all but one agree that self-
contradiction is involved. Also, "knock out" is a bit of a steal
from Ross, p. 279. I like it. It reminds us of Euthydemus and
Dionysodorus], a15-a16
3. if not everything is relative (pros ti), but there are some
absolutes (auta kath' hauta), then all appearance is not true.
Appearance is relative to someone, a17-a20
4. so those who are trying to use the knockout argument, tEn bian
en tOi logOi, had better take care, and specify to whom and when
and how it applies. If they don't, the contraries, tanantia, will
immediately be applied to them, sumbEsetai hautois tanantia tachu
legein, a21-a25 [Notice variant reading hautois/autois (line 25).
Smyth-Messing, Greek Grammar, paragraph 328, Note (p. 93) justifies
Ross' choice, hautois. Tredennick chooses autois, but translates as
a reflexive (hautois). This point is not without significance.]
5. examples of illusory phenomena, and Aristotle's reply: opposite
appearances are not in the same respect, the same time . . . a25-b1
6. they [the logic choppers] must say not that this is true, but
true to someone. Everything [according to them] must be relative to
opinion and sensation, so nothing would happen, no one having a
prior opinion, hOste oute gegonen out' estai outhen methenos
prodoxasantos, b1-b7
7. unity and definiteness are necessary, b7-b12
8. restatement of the Law of Contradiction in two modes, (1) it
is impossible to affirm what is denied about the same thing at the
same time. Thus (2) contraries cannot subsist in, or be predicated
of, the same thing at the same time, unless in different respects,
pEi . . . pEi, b13-b22
Notice in passing the appeal again in 2. and 4. above to self-
contradiction (already suggested in v, 1009a6-a16): obviously, if
they hold that contraries are true, then the contrary of what they
say is true; they contradict themselves. Self-contradictory
statements were a matter of interest to Aristotle and his
contemporaries. Witness Eubulides' reference to "The Liar"
argument, and Plato's use of "turnabout", according to Diogenes
Laertius, ii, 108 and iii, 35 (Loeb ed., I, 236 and 308). Self-
contradictory statements, here a strong argument in Aristotle's
hands, were at times a puzzle to the ancients, and indeed
throughout history up to the present century. In a separate
addendum I repeat with some revision the bibliography and comment
on the Liar, posted a year ago on the Parmenides list, inasmuch as
it provides a larger context for our understanding of its use here.
Aristotle's use of it as a rebuttal to the knock-out arguments of
his opponents, would seem to indicate that he accepted the
possibility of self-contradiction. Some do not.
EFL, 4/11/96
THE LIAR PARADOX
This is a riddle that we learned when we were children, still in
short pants: "Adam said all men were liars; therefore Adam was a
liar; therefore what Adam said was not true; therefore Adam was not
a liar; therefore what Adam said was true . . . " I think you "get
it."
1. The notorious liar paradox is most often ascribed to Epimenides,
a shadowy sixth century (not even that is certain) figure about
whom little is known for sure. One may consult the Oxford Classical
Dictionary or Kathleen Freeman, The Presocratic Philosophers, under
his name for excellent accounts of what we know about this ancient
sage. One suspects that the reason for the ascription to Epimenides
is the allusion to the paradox in St. Paul's letter to Titus,
chapter 1, verse 12: "One of themselves, even a prophet of their
own, said, The Cretans are always liars . . . " Paul did not name
his source, it will be noted, but Clement of Alexandria, about 200
A.D., undertook to do so in his Stromata, I, 59 (II 37, 21 St):
"The seventh [of the Seven Wise Men of the ancient world] some
said was Periander the Athenian, others Anarcharsis the Scythian,
and others Epimenides the Cretan, whom the apostle Paul recalls in
his letter to Titus . . . " with the quotation as above. Elsewhere
(Protrepticus, p. 32, as in Loeb ed. p. 78) Clement also reveals
that he was aware that the Alexandrian poet, Callimachus (ca. 250
B.C.) used this line, Cretans always lie, but of course Callimachus
was not a Cretan. Anyhow, it seems obvious that it was the wide
cast of the Christian biblical and patristic traditions that
resulted in the impression that Epimenides was the author of this
line, and that the paradox came to be known as the "Epimenides
paradox." That won't do. We have no idea where Clement got his
information. We know too little about Epimenides, except that he
was just the sort of semi-mythical figure who would have attracted
such a story. See Hermann Diels, Die Fragmente der Vorsokratiker,
"Epimenides," sect. B. no. 1.
2. Whence then the liar paradox? Even if Epimenides did say that
Cretans are always liars, there is nothing to indicate that he said
it self-consciouly as a Cretan, with the paradox in mind. Yet that
is what we are interested in. We really don't care whether Cretans
are liars or not, but only rather in the peculiar situation of
anyone, Cretan or not, who says that he himself is always a liar.
The earliest person who seems to have brought this aspect of the
matter up is said (by Diogenes Laertius, II, 108 in the early third
century A.D.) to have been one Eubulides of Miletus, a Megarian
philosopher of the fourth century B.C., several centuries before
Paul, not to mention Clement: "To the school of Euclides belongs
Eubulides of Miletus, the author of many dialectical arguments in
an interrogatory form, namely The Liar . . . " Of course this is
only an attribution, independent perhaps of Paul and Clement, but
unfortunately somewhat later than theirs. On the other hand, the
first actual textual reference that I can find is Aristotle's in On
Sophistical Refutations, 180b2: "Similar is the argument about
whether the same man can both lie and tell the truth at the same
time." Considered in conjunction with his remarks in Metaphysics,
1012b15-18 and 1063b30-35, and in Nichomachean Ethics, 1146a21,
they would seem to indicate that Aristotle was well aware of this
problem. He also makes use of it in Gamma, Metaphysics, v and vi,
to rebut those who would deny his Law of Contradiction. Eubulides,
it might be mentioned, was his contemporary. We know that Plato was
interested in self-contradicting statements, and that within a
couple of generations the problem was receiving more attention,
especially from the Stoic philosopher, Chrysippus (for which
consult von Arnim, Stoicorum veterum fragmenta, II, page 92). It
seems that the liar paradox may have been a commonplace of the
philosophers of Greece in the classical age.
The paradox, or riddle, is probably known to nearly every small
child, in the form like that given above at the beginning of this
exposition. So at least it was sprung on me at the tender age of
five, by my smart older brother, eight. I was unable to withstand
this bit of brilliant expertise, which I wager is tried out on most
gullible younger brothers by older brothers, etc.
3. What is the problem? It is commonly referred to as a self-
referential statement, and many examples are adduced. It is fun to
think up all those examples, but this example will do, and all the
rest are marginal improvements upon the original, the case of the
liar. But it won't do to call it a self-referential statement. That
is not sufficiently specific. If you, John Jones, say, "My name is
John Jones," that is a self-referential statement. What we are
dealing with here and now is a self-contradictory statement, one
that invalidates itself. You may or may not banish it (with a
number of devices), AS YOU WISH.
4. What is so strange about self-contradiction? We have inherited
a particular tradition of logic from the ancient Greeks, based upon
Aristotle's law of (perhaps better said here) non-contradiction.
Your or my statement that "All men are liars" is an impossibility
only in the light of certain assumptions, assumptions that are
inherited by way of that particular and limited tradition. But it
was not the only logical tradition that they knew. There was
another which can be traced back to Plato in his Parmenides, to the
anonymous Dissoi Logoi, and the presocratic philosphers,
Parmenides' "two Ways" and some of Heraclitus' "dark" sayings, a
tradition that supports all sorts of paradoxicalities and
contradictions. Further, note that there are large and important
realms of life wherein paradox is axiomatic. It is also an irony
that Aristotle himself uses self-contradiction to rebut those who
would gainsay his law.
5. I conclude with a brief bibliography of some references:
Ancient authors:
St. Paul, Titus, i, 12
Clement of Alexandria, Stromateis, I, 59 (II, 37, 21 St.)
Protrepticus, ii, 32 (Loeb, p. 78)
Plato, Theaetetus, 171A-C
Aristotle, Soph. El., 25, 180b2
Metaph. 1012b15-18 and 1063b30-35;
Book IV (Gamma), chaps. v and vi
Eth. Nich., 1146a21
Chrysippys, in von Arnim, Stoicorum veterum fragmenta, II,
p. 92
Callimachus, Hymn I, hymn to Zeus, lines 8-9
Plutarch, Aemilius Paulus, xxiii, 6, in Lives
de comm. not., 1059D (Loeb, Moralia, XIII/2, p.
666)
Cicero, Acad., II, xxx 96 (Loeb, p. 588)
de div., II, iv, 11 (Loeb, p. 380)
Sextus Empiricus, adv. math., VII, 13 and 388-89 (Loeb,
II, 8 & 206)
Outlines of Pyrrhonism, I, i, 14 (Loeb,
I, 10)
Diogenes Laertius, II, 108; VII, 196 (attribution to
Eubulides)
Alexander of Aphrodisias, Comment. in Aristot. Gr, ed.
Hayduck, vol. 1 p. 340; vol. 3, p. 170
Modern authors:
Pauly-Wissowa, Realencyclopaedie der class. Alt. VI, 1,
870
Der kleine Pauly, II, 399 - 400
Pauly-Wissowa, Suppl., V, 707
Guthrie, Hist. of Greek Phil., III, 488 - 506
W. & M. Kneale, Dev. of Logic, 114, and index, s. v. "liar"
Bonitz, Index Arist., 292, under "Eubulides"
Grote, Plato, III, 482 f. and notes
Zeller, Philos. der Gr., II a4, 264f.
Gomperz, Griech. Denker, II, 154ff
Windelband, Hist. Phil., I, ii, sect. 8 (p. 89)
Prantl, Gesch. der Logik, I, 33 ff., 40ff.
Ritter, Rh. Mus. (1828), p. 331 f.
Deycks, De Megaricorum doctrina (1827)
Peake's Commentary on the Bible, sect. 795e, p. 915
Paul V. Spade, The Mediaeval Liar: A Catalogue of the
"Insolubilia" Literature, Toronto, Institute of
Mediaeval Studies, 1975
Paul V. Spade, Peter of Ailly: Concepts and Insolubles,
1980
Robert L. Martin, Recent Essays on Truth and the Liar
Paradox, Oxford, 1984
There are in addition a number of references to The Liar Paradox,
Berry Paradox, Richard's paradox and other alternative versions of
the same, which you can find in most any good history of modern
mathematics (since Georg Cantor, who seems to have started it up
again with his set of all sets that are not members of themselves).
Some good ones are Mathematics, The Loss of Certainty, by Morris
Kline (Oxford, 1980), Pi in the Sky, by John D. Barrow (Boston,
Little, Brown, 1992), Infinity and the Mind, by Rudy Rucker
(Princeton, 1995), Goedel's Proof, by Nagel and Newman (London,
Routledge, 1958). Goedel's famous proof or theorem (1931), which
created quite a stir among mathematicians and logicians of our
time, is based upon a self-contradictory statement. It is an heir
of the Liar Paradox.
This bibliography is not exhaustive. Additions welcome.
EFL, 4/1/96
THE LIAR (again)
The Liar paradox has succeeded in churning up alot of discussion.
At least it has brought some of you out of the woodwork in
increasing numbers here. Fine. It always seems to do so. The amount
of discussion devoted to it throughout the present century is
contemporary witness to that. The bibliography cited in last
Thursday's msg is witness over many centuries. There just seems to
be something about it that gets under our skins.
By the way, Abe Shulsky, thanks for reminding us of the barber.
John Barrow, in Pi in the Sky (p. 110) tells us that this example
was proferred by Bertrand Russell: "A man of Seville is shaved by
the Barber of Seville if and only if the man does not shave
himself. Does the Barber shave himself?" Figaro, Figaro . . .
No doubt the forms of this paradox that could be thought up are
endless in number, and Georg Cantor has the last laugh: there are
an infinite number of liars.
But seriously: in addressing a problem of this sort, whether raised
by Aristotle, Russell, or any of the others, including us here,
please try to go beyond the ARGUMENT. You can argue about this
until the cows come home, in all sorts of ways, depending on where
you are coming from, i.e. the assumptions you wish to make. It is
the assumptions that count. What are they (in any particular
argument)? What were Aristotle's? What might they be? What can they
be? THIS is what is worth exploring.
GAMMA (IV) METAPHYSICS, chapter vii
The Law of the Excluded Middle
1. there is no middle term to a contradiction, oude metaxu
antiphaseOs endechetai einai outhen, all' anagkE E phanai
E apophanai hen kath' henos hotioun, 1011b23-b24
2. truth and falsity are defined in terms of what is and what is
not. "To be OR not to be" cannot be said, oute to on legetai mE
einai E einai oute to mE on, b25-b29 [a thing either is or it
isn't. The language is ambiguous here, but the intent is clear]
3. there are two kinds of possible intermediates: (1) mixture of
opposites, and (2) neither of opposites. (2) is no intermediate;
(1) it is not clear that this is really an intermediate [but a
combination of opposites], b29-1012a1 [begs the question]
4. thought affirms or denies, correctly or incorrectly, by
definition, touto d' ex horismou dElon, a2-a5
5. [rebuttals of a middle term]
a. there would have to be a middle term in all contradictions,
a5-a9 [metaxu is implied in text]
b. impossibility of a middle term between some things, like odd
and even numbers, by definition, ek tou horismou dElon, a9-
a12
c. infinite regress, a12-a15 [Is he thinking of Zeno as he uses
the word hEmiolia, "half as much again?"]
6. assertion = being; denial = not-being, a15-a17
7. origins of the erroneous opinions, a17-a21
8. [to rebut] one must begin with definition, a21-a24
9. Heraclitus' and Anaxagoras' errors, a24-a28
The Law of the Excluded Middle is given high billing in ensuing
logical tradition. It seems here like a corollary of the Law of
Contradiction. It has been the subject of argument. There are many
who gainsay it. Perhaps the answer is suggested by the noticeable
frequency with which Aristotle mentions "definition" above. The
word is used six times in this short chapter. Could it be that the
whole matter depends upon definition, that the Law itself is a
definition, and beyond the reach of argument?
However, it is the Law of Contradiction itself that is the
centerpiece of chaps. iii through viii of this Book Gamma (IV), and
must remain the main object of our attention.
EFL, 4/18/96
(Next week's comment will be posted late, possibly by the weekend)
METAPHYSICS, GAMMA (IV), chapter viii
Final Remarks on the Law of Contradiction
1. one cannot allow unqualified, "categorical" statements that
nothing or everything is true, a29-a33
2. Heraclitus cited as an example, a33-b4
3. it is a question of [definite] meaning (as stated at 1006a21),
b5-b13
4. the common talk refutes itself, b13-b22
5. parting reference to presocratic physical theories [viz.
Parmenides' and Heraclitus', b22-b28
6. comment on the nature of motion, b28-b31
Look back now over the last five chapters, chapters iv - viii,
Aristotle's defense of his Law of Contradiction. It is at best a
rambling, sometimes repetitive discussion. Whether due to
Aristotle, to students, or to editors and copyists, who knows? But
it is what we have. Let us try to sum it up:
Chapter iv appears to take stand against the throulomenon, the
common talk (the apt word used by Aristotle later at 1012b14),
using self-styled elenchic proofs. Names must mean something.
There must be affirmation and denial, truth and falsity, if
there is to be any meaningful speech at all.
Chapter v takes a more professional stand against the
sensationalist philosophers, a number of whom are named:
there is more to the world than mere appearance. There is
always a substrate.
Chapter vi continues against sensationalism, and raises the
important argument of self-contradiction.
Chapter vii introduces the corollary Law of the Excluded
Middle, and dialectical arguments to support it.
Chapter viii, the finale, for the most part repeats briefly
points that have been made before.
Of all the arguments two can be pointed out as having more force
than the remainder: (1) that there must be affirmation and denial,
truth and falsity, in short definition, if speech is to mean
anything, and (2) denial of the Law is self-defeating; it is self-
contradictory. As Judy pointed out, these are excellent dialectical
arguments.
There are two limitations that must be put to the Law of
Contradiction, one of which Aristotle would have to answer for; the
other, not (since it exceeds his purpose here):
(1) The Law applies to things and their attributes and properties,
to what can be predicated of things. It applies to onta, beings (to
revert to the scheme of this very Book Gamma). But being means many
things, pollachOs legetai to on, of which the onta are just one
part. The Law does not apply to being qua being, on hE on, inasmuch
as being qua being has no attributes, no properties, no predicates.
It is pure and absolute being, being by itself.
(2) The Law applies to things, not to people. For one thing, people
are never kath' hauta, never "in one respect." Human nature taken
individually or collectively is always a paradox. It is "sexual" in
more ways than one. That it is divided into two sexes is obvious to
us. That it is divided into mind and body is equally crucial,
although there are those who deny or dismiss this. These are two
primary divisions of human nature, and there are others, many
others, less primary but no less telling. It is on their account
that there can never be a "same respect" in any statement about us
humans. For ages our literature has recognized this, if you care to
search it out or recall it. But if you don't care for the advice of
others, experiment for yourself: for every statement you make, the
opposite statement can equally well be made. Man is free and not
free. He is saintly and beastly . . . The social sciences will
require quite another logic than Aristotle's or Bacon's.
I challenge you younger people who are taking part in this
Metaphysics list, especially you lurkers: you are going to have to
chance some bold new approach not just to this matter but to all
ancient philosophy, if you are going to rescue it from the doldrums
it is now in, from the increasing sterility of this century which
has brought many people to turn their backs on it, leaving it to
the professionals. I suggest to you that you kick over the traces
of tradition, starting right here with this Law of (Non-)
Contradiction. Its reach is restricted by definition to predication
and to the attributes of mindless entities and the non-living
aspects of mankind.
Once more I will append an addendum in the form of a little essay
on this topic written some years ago.
EFL, 4/27/96
ON THE LAW OF CONTRADICTION IN ARISTOTLE'S METAPHYSICS
It is well known that the law of contradiction, so-called, is a
fundamental axiom of Aristotle's philosophy. The law is discussed
at some length by Aristotle in Book Gamma (IV), chapters iii -
viii, of the Metaphysics. It is stated in chapter iii in three
different ways:
(1) to gar auto hama huparchein te kai mE huparchein adunaton
tOi autOi kai kata to auto, the same [attribute] cannot belong
and not belong to the same [subject] at the same time and in
the same respect;
(2) adunaton gar tauton einai kai mE einai, the same [thing]
cannot be and not be;
(3) mE endechetai hama huparchein tOi autOi tanantia,
opposites cannot be attributed to the same at the same time.
The discussion of the law follows in chapters iv - viii. Since the
law is an axiom, and cannot be proven, in the apodictic sense of
the word, "proof," than a substitute dialectical proof takes the
form of a refutation of the law's denial. This is very simple: if
you deny the law, then your own denial is invalid, if not
meaningless. Your denial depends upon it. The merest word must be
saved from the possibility of contradicting itself. No difficulty
need attend that observation, at least for most of us. Yet it is
interesting to note that the discussion is continued by Aristotle
for several pages. Why? The ensuing discussion reveals the context
of the present business: the views of several of the presocratic
philosophers and sophists (and their followers). Several competing
doctrines, such as Protagoras' "man is the measure of all things"
and Heraclitus' "everything changes; nothing remains," seemed to
deny the law of contradiction. It was to combat these doctrines
that Aristotle went to such lengths to fortify his law.
The irony of it is that the law is useless for Aristotle's
metaphysics. Indeed it is worse than useless; it is contradictory.
It is surprising that more has not been made of this irony before.
For the law applies to the world of subjects and attributes, the
world of things, of physics, but Aristotle's inquiry transcends
that world. Pure being, on hE on, is without attributes. The sort
of contradictions that one lands in, when one discusses it, had
already been indicated by Plato in his dialogue, the Parmenides.
"It seems that, whether there is or is not a One, both that One and
the Others alike are and are not, and appear and to not appear to
be all manner of things in all manner of ways, with respect to
themselves and to one another" (166C).
Do not be deceived that Plato was only talking about the One, to
hen. In the dialogue the One is continually measured against Being,
to on. The same conlusion was applicable to it. (After all, are
they not the same? Legetai isachOs to on kai to hen. Bonitz, Index,
pages 220 & 223.) Plato restrained his explicit discussion there to
the One, partly no doubt because that was what his title personage,
Parmenides, was most famous for. He, Parmenides, was reputed to
have said, some two generations before, that everything was one.
That was not exactly what he said, but it was what he was
remembered to have said. Actually what he said was oude pot' En
oud' estai, epei nun estin homou pan, hen, suneches, "(it) was not
nor will be ever, since all is now, all together, one, continuous."
What he was talking about was not the universe and everything in
it, as if that were all one timeless, homogenous, indivisible mass.
Rather what he was talking about was estin, being, or to on, as it
is later called, using a participle rather than the present tense,
third person, singular for this mysterious new conception.
Parmenides was trying to conceive for the first time (what we would
call) an abstraction, for that is what it was and is. Such a thing
was unheard of at that time. No wonder he was misunderstood, or
that his seeming absurdity became notorious. So it was good drama
on Plato's part - and Plato was ever the dramatist in his dialogues
- when he had his Parmenides discourse on the One. But it was also
Being that he was talking about, and the contradictions of the
absolute One are equally applicable to Being.
Aristotle was aware of this too. His investigation of ousia, in
Book Z (VII), reveals its transcendence. Its attributes and
properties are successively stripped away in chapters iv and v.
What remains is hardly amenable to the law of contradiction as he
initially stated it. Nor do any other statements of the law apply.
As he analyzes ousia it becomes clear that it both is and is not,
and it is two opposites, because it is both (1) an abstraction, and
(2) in everything, everywhere, always. It is in mind and body. This
condition lies at the root of the contradiction that is imbedded in
the concept of pure Being.
Being can always be approached, then, from either of two ways.
Those two ways cannot be reduced to one, or reconciled. Every time
Aristotle tried to do this in the Metaphysics, the terms that he
used to do it themselves split in two, repeating the division.
Substance is analyzed into matter and form. Of each of these there
are two kinds, and so forth. In the Metaphysics and in metaphysics
proper, every explanation must preserve the contradiction of bodily
and mental aspects.
What Aristotle and Plato and Parmenides were up against was what we
call today the mind-body problem. It has never been solved, in the
senses that (1) the one was reduced to the other, or (2) the
relation between them was explained. Those who think they have
solved it have (if you look closely) done no more than express an
arbitrary opinion, or the cultural presuppositions of their age.
Wherever the problem is present it will provide contradictions.
Aristotle's logic will not apply. Some new sort of logic, one that
recognizes contradictions, will be needed. It will be the last word
in metaphysics as well as in any discipline that touches minds and
bodies, any human science, any psychology, any political science,
economics, sociology and so forth. It will be another new
"organon."
This is worth testing. First of all it can be tested and is perhaps
best tested in your own experience. This is a testing ground within
every man's reach. The claims of freedom and authority in the
classroom or in the family or in the community are examples of
psychological, social and political questions that touch each one
of us very closely. In these we can feel personally and deeply how
one position, once take up, usually excludes another in our own
purview, but not in the whole. It is not merely egoism that
prevents our consideration of an opposite viewpoint. It is also the
failure of an inapproriate logic, the failure to see that in the
human realm in the case of every possible true statement the
opposite is also true. That is the axiom here. Try it out.
It is an axiom that has been recognized for a long time. Literature
abounds with testimonies to it. Suggestions may be found from
Alcmaeon's doctrine of opposites to C. G. Jung's enantiodromia; in
John Stuart Mill's essay On Liberty, chap. ii; in Abbot Lawrence
Lowell's little known study, Conflicts of Principle (1932); in
Hermann Hesse's Siddhartha (last chapter); in Pascal's Pensees
(#791); in De Tocqueville's Democracy in America (II, v and vi).
These widely dispersed samples appear quite independent. Peter
Abelard's Sic et non and Nicholas Cusanus' coincidentia oppositorum
might have provided hints, as might other ventures in the ancient
art of dialectic. The most thoroughgoing and purposeful exploration
of the duplicity of all statements in the field of psychology is to
be found in the two great novels of Fyodor Dostoyevsky, Crime and
Punishment and The Brothers Karamazov. It is the common theme of
these two novels, referred to explicitly twice near the end of the
former and three times near the end of the latter in nearly
identical statements, a repetition that surely indicates a high
degree of purpose on the part of the writer. Find them.
All of this is the unfolding of two surprises that are to be found
in Aristotle's Metaphysics: (1) the famous law of contradiction
itself contradicts the true logic of metaphysics. It is the
opposite of what actually pertains in the transcendent realm of
abstractions, because (2) the Metaphysics raises a problem, the
mind-body problem, which is insoluble by any single formula. With
the introduction of the mental we enter the realm of opposites and
contradictions. The Metaphysics provides a paradigm for psychology,
individual and social, and all its ramifications.
E. F. Little
Claremont, California
1985 (slightly revised, 1996)