Aristotelian Definition And The Discovery Of Archai

41
What is a definition? Often, especially when
speaking of Aristotelian logic, one encoun-
ters the answer: definitio fit per genus proxi-
mum et differentiam specificam (definition
proceeds from the closest genus and the
specific difference). Commonly, definition is
understood as a kind of taxonomical descrip-
tion by which a being is assigned a certain
universal genus that is then subsequently
further differentiated by its unique, specific
characteristics: the leopard is a feline ani-
mal belonging to the panther family, etc. As
such, a definition serves the linguistic func-
tion of preserving a categorical awareness
of a being, enabling humans to formulate a
concept to be applied to the beings that they
encounter in order to make them universally
recognizable and graspable. By applying the
conceptual categories of genus and species,
human beings are intellectually able to divide
a being into parts and to bring each of them
into an outline in virtue of their mutual simi-
larity and dissimilarity. In this way, beings
encountered in the world are placed within
an already existing organizational paradigm:
leopards belong to the genus “panther” with
the specific difference of possessing a light fur
coat covered in spots.1
One might argue that
such a method provides human beings with a
rational structure by which they are able to
harness and master natural beings by render-
ing them knowable and reducing their com-
plexity to orderable, catalogable (and hence
meaningful) configurations. Definitions, in
this view, originate a “demonstrative science”
through which nature may be possessed and
mastered.2
However, while the texts of Aristotle
(which the above interpretation might claim
as a source) may in fact betray a certain
inclination to employ definition for the sake
of coming to a dependable familiarity and
knowledge of a being, they point toward this
conception of definition as merely derivative
and secondary. Rather than an investigation
that cleaves beings from nature by abstrac-
tion into linguistic universals (genus and
species),3
I undertake to retrieve in Aristotle a
more primordial understanding of the activ-
ity of defining, which betrays a more imme-
diate relation to nature and reveals a curious
natural capacity that human beings harbor.
Human beings, among natural beings,
are perhaps uniquely capable of coming to
an awareness of an other being not merely
mediated through the structures provided
2
ARISTOTELIAN DEFINITION: ON THE
DISCOVERY OF ARCHAI
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ARISTOTELIAN DEFINITION
42
by human nature, but in accordance with
an unmediated encounter with the nature
of an other being. With this suggestion, I
allude to Aristotle’s ever present two-fold
description of the way we know the world
(according to us, according to itself)4
: that
is to say, human nature betrays a comport-
ment in which one can be aware of an other
being not merely through human nature (i.e.
through the application of the cultural, lin-
guistic, and habitual quotidian structures
that form any given human’s identity), but
by the unmediated encounter with the other
nature of that being, by the noetic reception
of the archê of an other entity. In this light,
definition would be the activity by which an
inquirer seeks to unhinge herself from pre-
cisely those universal structures that govern
a “definition” in the traditional understand-
ing of that term (the genus and species that
circulate in human cultural and linguistic
economies) in order to open herself intellec-
tually to the perception of the other being,
as other. Thus, in this essay I will argue that
Aristotle primarily understands definition as a
kind of phenomenological reduction in
which the inquirer turns toward a being in
such a way that she loosens herself from the
hermeneutic familiarity with a being in order
then to be disposed to it in such a way that
its nature, its archê, its ti esti becomes mani-
fest (dêlon). With these governing reflections
on Aristotle’s texts, I will describe a mode of
being in which humans may discover nature
(and its singular beings) based neither upon
mere sensuous perception nor strictly con-
ceptual mediation. I will show that, though
dialectical/conceptual deliberation does not
reveal archai, it does place us in the com-
portment (the hexis, the mode of being) in
which we are noetically receptive to archai
(Aristotle lists nous as an intellectual hexis/
comportment, after all5
). In addition, the
reader may already perceive that this account
of definition differs from the majority of the
literature referenced above, insofar as it con-
ceives of the activity of defining as primarily
philosophical/ontological and only secondar-
ily logical/scientific.
In the first part, in order to articulate this
primary conception of definition in Aristotle,
I will offer an interpretation of that struc-
ture by which Aristotle argues human beings
know anything at all: the prouparchousa
gnôsis.6
While prouparchousa gnôsis is often
translated as “pre-existent knowledge,”7
the present reading will suggest that it must
be understood not as an individual per-
son’s inner repository of previous empirical
experience, but rather as a kind of political,
hermeneutical horizon deeply informed by
Aristotle’s understanding of logos. Far from
data filed away in a cabinet lying between
the eyes and the ears, the prouparchousa
gnôsis seems rather to resemble a kind of
cultural horizon into which human beings
are born—a public, dialogically constituted
surrounding world that appropriates the
individual and bequeaths an identity and a
kind of citizenship. Most importantly, one’s
engagement with the world becomes shaped
and organized by the prouparchousa gnôsis.
Thus, as we will see through brief considera-
tions of Aristotle’s method in Physics I and
his solution to the epistemological problem
of the Meno in Posterior Analytics, one must
employ a dialectical critique of the proupar-
chousa gnôsis in order to begin to perform
the work of the definition of archai—which is
the same as to say, in order to begin to move
from an awareness of a being in accordance
with our nature, toward an awareness of
a being in accordance with its nature. Of
course, with this claim, I enter into the trou-
bled waters of Aristotelian dialectic.8
I will
indeed attempt to show that, for Aristotle,
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43
one gains access to the archai, or first princi-
ples, through the above-described dialectical
process.
In the second part, subsequent to provid-
ing an account of the prouparchousa gnôsis,
I will offer a reading of definition as it is pre-
sented in the Posterior Analytics. It is in this
text that we learn that definition is the mode
in which human beings undergo the experi-
ence of the archê of a being under inquiry.
Definition, Aristotle tells us, is the logos of
the archê. Yet, this definition is not achieved
through apodeixis, demonstration. Rather,
Aristotle argues that definitions serve as the
archai of demonstrations, so that demonstra-
tions depend upon what is said in a defini-
tion; for, those performing demonstrations
do not question their primary definitions, but
rather hold them as convictions. How then
do definitions come to be if not by demon-
stration? We will see that, through the work
of critically engaging the prouparchousa
gnôsis, the archê is subsequently made vis-
ible; the nature of the being is made manifest
(dêlon). The utterance of this vision of archê
Aristotle names a definition.
DEFINITION AND THE
PROUPARCHOUSA GNÔSIS
As mentioned before, at the beginning of
the Posterior Analytics, Aristotle states that
all teaching and learning proceed from
an already-present and already-governing
knowledge(ἐκπρoϋπαρχoύσης...γνώσεως)
(71a2). Since human beings are the beings
whose function and nature is formed and
determined by logos,9
everything that human
beings do, qua human beings, is shaped by
a logos-structure that precedes them, that
already governs the meaning-horizon into
which they are situated. Every form that
a logos can take finds its origin in this pre-
existent knowledge; it is a logos-structure
that bestows upon humans a language and
a configuration of already-governing sci-
ences and arts: “the learned sciences and
each of the other technai . . . Similarly also
in the case of the logoi—both those through
syllogism and those through induction” (my
translation, 71a3–6). All uniquely human
disclosure and meaningful awareness pro-
ceed from the prouparchousa gnôsis. Further,
Aristotle argues that even rhetoric emerges
out of the prouparchousa gnôsis: “and that
with which rhetorical arguments persuade is
the same” (my translation, 71a9–10). Thus,
it would seem that, for Aristotle, every activ-
ity that human beings perform that has to
do with logos (that is to say, every activity
that human beings perform that pertains
to their unique nature) comes to be from out
of the already-present,hegemonic structure of
gnôsis. From a general Aristotelian point of
view, this claim should not be surprising; for,
as is said in the Physics, things always come
to be from something else (189b32). As will
become clear later, this ontological observa-
tion holds not only for the beings of nature
but also for discourse.
The argument that Aristotle proceeds
to articulate—the three ways in which
already-present gnôsis is “necessary”—helps
to secure this claim. Aristotle writes that on
the one hand “sometimes it is necessary to
pre-suppose that something is” (my transla-
tion, Posterior Analytics 71a12). He gives
the example: it is always the case that either
an affirmation or a denial is true. In mak-
ing affirmations or denials, one must pre-
suppose that they both cannot be true. Such
a principle is not demonstrated in making
affirmations or denials, but is assumed to
be a fact in advance of whatever is achieved
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44
in the articulation. This principle is a kind
of postulate of speech that simultaneously
governs speech. All knowledge must presup-
pose such principles of speech in advance.
Second, Aristotle posits the form of necessity
that is most important for the present read-
ing of definition: “sometimes what the thing
being spoken is must be [already] understood
[or agreed upon]” (my translation, 71a13).
Aristotle’s example is a “triangle.” I interpret
this to mean that there must be a preexistent
conceptual frame through which the thing
being discussed would have meaning at all:
the concept of “triangle” must already cir-
culate in a prevailing conceptual economy if
it is to be meaningful in knowledge. Third,
sometimes one must have both together. For
this combination,Aristotle offers the example
of a “unit.” A unit is a kind of principle that
we must already understand (qua concept) if
we are to utilize it in speech and we must
presume its existence as a postulate: a unit,
to quote Euclid, is that “by virtue of which
each of the things that exists is called one.”10
Here, a unit exhibits already-present gnôsis
in both ways: (1) A unit is not a number; it is
a postulate11
for the possibility of numbering,
a principle assumed in advance of the activity
of numbering. (2) Moreover, a unit is simul-
taneously a concept that must already be
present in the common language in advance
of numbering. Both of these “necessities” for
knowledge are secured by inherited speech,
by an already-present logos-structure.
Yet, what does the prouparchousa gnôsis
have to do with the activity of definition? A
consideration of Aristotle’s initial mode of
inquiry into archai will point us to an answer.
As has been observed with much debate,12
Aristotle often begins inquiry having to do
with the archai with an elucidation of the
endoxa that subtend the prevailing thoughts
on the subject under inquiry. In the Physics,
for instance, Aristotle prefaces his investiga-
tion into the archê of nature with a survey of
the arguments about the subject that are cir-
culating in his surrounding world. Aristotle
engages in a confrontation13
with Parmenides
and the Eleatics (as well as with the phusikoi)
in order to make nature more explicit and
perceivable and, thereby, to be able to show
that nature and the motions over which it
rules admit of being (a claim at risk in the
arguments of the Eleatics). In the present
reading, Aristotle’s activity in these instances
amounts to dialectically/critically engaging
his own conceptual/cultural resources (the
prouparchousa gnôsis) in order to more
clearly elucidate the universal concept, qua
common concept, of nature, so that he may
then intellectually perceive the archê of nature
in a definition. That is, in order to reach an
acquaintance with something in accordance
with its essence (in a definition), for Aristotle,
we must first critically engage the arguments
that already inform and shape what we think
in accordance with our essence (logos, or the
prouparchousa gnôsis).
The necessity of this dialectical procedure
for the intuition of the archê of nature in the
Physics is made evident in Aristotle’s solution
to the epistemological problem presented
by Plato’s Meno, namely, how do we come
to knowledge if we cannot learn what we
already know and we cannot come to know
something that we do not yet know at all? Of
course, Aristotle’s solution to this problem
hinges upon the observation that it is possible
to be familiar with something in more than
one way: one can know something in a gen-
eral way and one can know something sim-
ply. The much discussed passage at the end
of the Posterior Analytics14
details a descrip-
tive sequence that moves from aisthêsis, to
memory, to experience, and then to the uni-
versal, which might otherwise be interpreted
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45
as the formation of an individual person’s
subjective repository of previous empirical
experience. Yet, it should be remembered
that in this passage Aristotle, again, invokes
the dilemma of the Meno by claiming that
we cannot already be born with a potency
to be disposed toward beings in the man-
ner of epistêmê, yet, we also cannot simply
take (lambanô) them from being without
somehow having already had them before
(again, “ἐκ . . . πρoϋπαρχoύσης γνώσεως”)
(99b25–30). Thus, the empirical interpreta-
tion of the text would have to ignore this ini-
tial sentence that, again, insists that we are
already disposed (in an imprecise way) with
the universal. Humans, for Aristotle, are born
with the capacity to acquire logos and logoi,
not with the capacity to originally employ
logical procedures to subjectively construct
universals—either vague universals or pre-
cise ones. Children become enveloped by the
logos-world, the prouparchousa gnôsis, and
only subsequent to becoming adult humans,
to acquiring logos in an active and wakeful
way, can they cultivate a critical disposi-
tion to this prouparchousa gnôsis in order
to begin the process of becoming familiar
with the nature of a being by its own nature;
that is to say, only subsequent to becoming
humans can a being be disclosed to them in
the way of epistêmê.
In the ensuing argument of the second
part, the essay will highlight the following
points about definition: (1) a definition is a
way for a human to break out of the com-
mon conceptual economy (logos as endoxa)
that governs her awareness of another being
(awareness according to us)—by, neverthe-
less, employing the very same logos/endoxa
critically/dialectically—in order to become
aware of an other being by its nature (aware-
ness according to the being itself); (2) yet,
this logical activity is not one that abstracts
from nature in the way of mathematics or
the diareisis of Platonism, or even as what
we commonly call “science” but rather, (3)
it is achieved in the comportment (hexis) in
which one is attuned with the archê of what
something is (ti esti). The consequences of
this account will be a conception of defini-
tion that forces a distinction between its
use in philosophical/ontological activity
and its use in scientific activity. Further, it
will occasion a certain alignment of logi-
cal activity with nature, thereby securing
Proclus’ intuitions15
that, for Aristotle, logic
and the rational disclosure of nature are not
things to be distinguished from nature and
are clearly not necessarily abstractions of
nature; indeed, remarkably, Aristotle thinks
in the Metaphysics that the very same ousia
that governs the generations of biological
forms also rules over what can be meaning-
fully said about them in syllogism: “ousia is
the archê of everything, for syllogisms come
from ti esti, while [among biological forms]
generations do” (my translation, 1034a32). I
will show that this form of disclosure, defini-
tion, is an articulation of what provides the
continuity (sunecheia, the oneness that every
form, eidos, must exhibit if it is to admit of
being) to a natural being, a definition that is
the articulation of that ousia that both com-
pels the activities and motions that constitute
the nature of a being and inscribes itself upon
the intellectual perception and, subsequently,
meaningful discourse about that being.16
DEFINITION AND THE VISION OF
ARCHÊ
As is well known, Aristotle offers one of his
more thorough accounts of definition in the
Posterior Analytics. Here, in a text dealing
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46
principally with demonstration (apodeixis),
Aristotle famously differentiates a demon-
stration from a definition (horismos) in order
to refute any claim that definition can show
itself as a proof or that apodeixis proves a
definition.
Toward the end of his discussion of
definition’s relationship to demonstration,
Aristotle claims that there are three different
ways that definition is said17
: (1) on the one
hand, definition is spoken of as a logos of
what something is (ti esti) (APo 93b30). Of
this first definition of definition, we can say
that it most likely refers to an account of
something insofar as it belongs incidentally
to or “comes along with” (sumbebêkos) a
substance (ousia), since otherwise it would
essentially carry the same meaning as the
third and more primary articulation of horis-
mos. Aristotle confirms my suspicion here
by offering “triangular” as an example of
this first way that definition can be said and
“triangular” is a characteristic that can only
belong to a being incidentally (kata sum-
bebêkos), not primarily.18
(2) On the other
hand, definition bespeaks a mode of speech
that in quite limited cases can make mani-
fest “why something is”—a privilege usu-
ally reserved for epistêmê. As such, Aristotle
argues, this second way that definition is said
would be “like” a demonstration of what
something is (93b39); that is, definition can
resemble a demonstration. In other words,
the definition in the form of a syllogism may
bespeak “why something is” in unique cases.
For instance, in a certain way, the definition
of thunder (as “the extinguishing of fire in
the clouds”) already includes an account
of why thunder is, but not in the form of a
proof.19
(3) Finally, Aristotle offers the third
and more primary way the word “definition”
becomes used: “definition is the laying down
of the indemonstrable immediate [principles
(archai)] of what something is (ti esti) 20
” (my
translation, 94a8).21
It is this final and more
primary conception of definition that inter-
ests us here. For, the third form most differ-
entiates definition from apodeixis while also
articulating the technical part that defini-
tion plays in any demonstration. Earlier in
Posterior Analytics II Aristotle had already
offered a reading of what is later called the
third form of definition and this reading will
help us to unpack the difficult definition of
horismos above while also enabling us to
understand the nature of horismos, insofar as
it discloses natural beings in a unique way.
In his explication of the way a defini-
tion differs from a demonstration, Aristotle
lays out three different characteristics that
belong to a horismos that do not belong to
apodeixis. (1) On the one hand, definition
is an archê for a demonstration. (2) On the
other hand, definition is of “what something
is and of substance.” (3) Thirdly, definition
makes what something is visible—it makes
evident what something is, it does not prove
ti esti (my translation, 90b30ff.). As to the
first of our characteristics, Aristotle comes
to articulate one attribute of definition by
assigning to it the role of archê. Aristotle
writes that definitions are the archai upon
which demonstrations rely, the archai that
apodeixis must assume are without being
able to demonstrate them. We must consider
precisely what this means, for Aristotle also
states that this “has been shown earlier,”
recalling a claim that “either the archai will
be demonstrable and thus be archai of archai
and this would be carried to infinity, or the
first definition will be indemonstrable” (my
translation, 90b23ff.). By the phrase “has
been shown earlier,” Aristotle refers to a
passage in Posterior Analytics I in which he
argues that, even though the first principles
are not demonstrable or provable, in order
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47
to be disposed toward a being in scientific
knowledge (epistêmê ), we must be famil-
iar with and believe (pisteuein)22
in the first
principles even more than we do in conclu-
sions of our demonstrations (72a37–38).
Since the first principles (archai) are ruling
origins of beings and shape and determine
not only their physical being, but even what
becomes said about them (even as endoxa)
and, indeed, the knowing of them (72a30),23
then it is of utmost importance to dis-
play the first archai and to hold conviction
as to their disclosure if what becomes proved
about them in a demonstration is to hold any
reliable currency. One needs to be secure
in one’s conviction that the being about
which a demonstration will be made is held
in accordance with its archê; for, the archê
enters into the demonstration assumed and,
for Aristotle, is not knowable (in the form of
an epistêmê, qua demonstration), since “the
archê of apodeixis is not apodeixis and the
archê of epistêmê is not epistêmê” (100b12).
For Aristotle, apodeixis takes the archê for
granted. In the comportment of scientific
investigation (for Aristotle, apodeixis and
its epistêmê), therefore, we presume the first
principle of the being that we investigate.
If, indeed, (1) a definition is of the archê,
a first principle of a being that is not only a
logical first principle but also one that rules
over the very nature of that being, and (2)
this first principle is presumed by logical/
scientific investigation, then does this not
necessitate the interpretation that the pri-
mary function of definition is philosophical/
ontological and only in a secondary sense
logical/scientific? Perhaps such an observa-
tion, while certainly ancient,24
is not foreign
to the contemporary world. If we direct our
gaze not only toward syllogism but even
toward experimental, empirical science, we
may have the same question. For it seems
to me questionable whether experimen-
tal physicists who conduct the acceleration
and collision of particles in the Hadron col-
lider are asking questions about the archê of
nature—the archê of physics. Moreover, we
might wonder whether the electrical stimu-
lation of a severed muscle submerged in a
cylinder filled with saline by biologists seeks
an answer to the question “what is life?”—
the very object of biology. Are these experi-
ments not conducted with presumed answers
to the questions “What is nature?” “What is
life?”—answers that they inherit from the
hermeneutical situation in which they find
themselves? Or do they genuinely seek the
archai that rule over their work and argu-
ments? Whatever our answer, for Aristotle,
scientific knowledge does not aim at archai;
one will have grasped the archê of what
something is in some other way.
In order to consider how an archê is
grasped in a definition in such a way that
it makes the being of something visible, for
Aristotle, first we need to repeat what archê
means in its primary sense and state in what
way a definition is philosophical/ontologi-
cal and not merely logical/scientific. In the
Physics, Aristotle argues that nature is an
archê for motion (192b21)—in this context,
we mean not just any haphazard motion,
but rather nature is an archê for the pri-
mary activity of any being by nature. Thus,
the archê rules over the primary activity that
preserves and secures the being of a being.The
archê provides the ruling activity that holds
the being together in a unity as the being that
it is; it provides the continuity (sunecheia)
that is necessary not only for the being to
exist, but even for its graspability in thought
or perception (Metaphysics 1036a 7), insofar
as the being is to be grasped “as” any one25
thing and not a “heap” (1040b5–15). Thus,
a definition is not some simple premise from
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48
which demonstrations begin; it is a unique
articulation of an archê, an archê that rules
over a demonstration, yet remains indemon-
strable by apodeixis. Moreover, a definition
is an articulation of the archê of the primary
activity of the being26
(its τὸ τί ἦν εἶναι); a
definition bespeaks the nature of something
in the primary sense.
But what does the activity of primary
definition look like, qua articulation of the
archê? In the literature, there remains much
disagreement about how archai are made
manifest to us. Earlier we noted the debate
between those who locate within dialec-
tic (and its engagement with the endoxa) a
path toward the archai (for instance, Owen,
1986) and those who, in opposition to dia-
lectical method, posit sensuous perception
and empirical analysis as the way to archai
(e.g. Bolton, in Lindsay (ed.), 1991). While
it is clear from the first part of the present
essay that my thinking on the matter is
more inclined toward the dialectical than
the empirical mode of inquiry into archai
(insofar as moving from an awareness of a
being according to us to an awareness of a
being according to itself is articulated above
as fundamentally dialectical), nevertheless,
strict adherence to the endoxa without quali-
fication seems problematic for a number of
reasons. For instance, the endoxa represent
an awareness of a being according to us,
according to the prouparchousa gnôsis. If
we remain there, if we remain in preexist-
ent familiarity, how do we grasp the being
according to itself? Further, endoxa are logoi
and, if we were to assert a conceptual/a pri-
ori relation to the archai (see n 12), then
we would have to ignore many passages
in which Aristotle appeals to aisthêsis and
nous; for, aisthêsis stars prominently in the
description of coming to archai at the end of
Posterior Analytics II.19 and nous—which is
often described as being “of archai” across
the corpus—is without logos (Nicomachean
Ethics 1142a27), thus without endoxa.27
At
the opposite extreme, if archai“come directly
from sensation and experience” (Halper, in
Sim (ed.), 1999, p. 216),28
then how do we
incorporate the prouparchousa gnôsis, from
which all knowing proceeds, whether syl-
logistic, epagogic, or rhetorical? Even if we
wanted to argue that preexistent knowledge
is wholly explainable by subjective, personal,
individual experience in Aristotle—and it
seems to me that there are strong reasons to
argue against this29
(not only in the case of
socially structured concepts such as justice,
truth, nature, etc. but also in more concrete
concepts like species and organism)—the
example of “a unit” that Aristotle offers as
an explanation of the way that the proupar-
chousa gnôsis is necessary seems to prevent
strictly empirical explanation. Allow me to
repeat it here. A unit is a form of principle
that we must already understand if we are to
utilize it in speech and we must presume its
existence as a postulate. As we saw, accord-
ing to Euclid a unit is that“by virtue of which
each of the things that exists is called one.”30
Here, to recall what was observed above, a
unit exhibits already-present, presupposed
gnôsis in two ways: (1) as a postulate and (2)
as a concept. Both of these “necessities” for
knowledge are secured by inherited speech,
the already-present logos-structure; they are
not appropriated by the senses of an individ-
ual perceiver. Even if the concept of unit were
wholly available to sensuous impression (and
there are reasons to doubt this), its existence
as a postulate for the possibility for num-
bering is not constituted by individualized,
subjective experience, since as a postulate it
makes possible the experience of number-
ing. However, one must be careful here not
to attribute to Aristotle a Kantian a priori.
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49
For, what counts as preexistent knowledge
(inherited speech) is not compatible with the
“categories of the understanding.”31
Rather,
as was stated before, the prouparchousa
gnôsis is social and political and, as such, it
is changeable, subject to criticism and mal-
leability, and it varies according to cultures
and practices.
I will conclude with what I hope is an
example that elucidates how we arrive at pri-
mary definitions and their archai in a way that
reflects the movement from being aware of a
being according to us toward being aware of
a being according to itself. Despite the risk of
confusing the matter by employing an exam-
ple related to geometry and its demonstrative
knowledge, I would like to reference a geo-
metrical proposition from Euclid’s Elements
in relation to the contemporary endoxa sur-
rounding that proposition. One of the prob-
lems with employing such an example is that
Euclid’s method is apodeixis and the way to
definitions is not. Another problem lies in the
fact that the object of geometry is not prop-
erly ousia inAristotle’s view32
and a definition
in the primary sense is of ousia. Nevertheless,
I think this example will help to illuminate
how we find our way to archai in a similar
manner to the one that Aristotle himself uses
often to describe phenomena difficult to
put into speech: analogy; for, in the Physics,
almost every example that Aristotle offers
of natural beings is drawn from technê—
a house, or a statue, etc.—even though he
specifically argues that technological arti-
facts do not actually have a nature proper
to themselves.33
It is in the spirit of analogy
that I offer the following example. If we con-
sider the algebraic formulation A2
+ B2
= C2
,
presumably everyone reading this essay will
recognize it immediately. Moreover, the for-
mulation might quickly invoke within the
mind a narrative involving how and when we
learned the formula; perhaps we will remem-
ber how we have employed it in geometry
class to mechanically solve problems; images
of triangles might surface in our mind’s eye.
We know a great deal about this concept
and we would not know the concept at all
if we were not educated in a culture and sur-
rounding world that considered it important
to discuss. The algebraic concept circulates
in our conceptual economy, in the economy
that has appropriated us; and in a certain
way, we have access to the mathematics of a
triangle because of the common concept that
this formula conveys. That is to say, we have
a certain awareness of the being of triangles,
and hence of right triangles, because of this
formula that has been written upon us by the
surrounding linguistic world. Thus, without
too much distortion, we can say that the
algebraic formula resides in the structure of
preexistentknowledgethatIdescribeabove—
the prouparchousa gnôsis. Moreover, it
clearly exhibits itself as a form of endoxa—of
the wise opinions of mathematicians without
whom we almost certainly would not have
access to triangles in the same way. However,
in my experience, despite their ability to
utilize the formula, to solve mathematical
problems with it, to discuss characteristics
of triangles as a consequence of being famil-
iar with the Pythagorean theorem, students
reading Euclid for the first time often have
not had an immediate encounter with the
actual structure of equalities; in all of their
procedural experience with the formula, they
have not actually encountered the phenom-
enon that is abstractly represented by the
algebraic formulation (with which they are
familiar in almost precisely the same way as
a dictionary “definition”). Indeed, often they
have never even considered that there are
actual squares involved. Perhaps it was dif-
ferent for the mathematicians of Euclid’s day;
4/3/2013 9:20:04 PM

50
but, with widespread practical knowledge of
the formula in the contemporary world, if
one is to grasp the principle that underlies
the algebraic statement, perhaps one must
interrogate this common knowledge, this
prouparchousa gnôsis34
that first makes pos-
sible my awareness of the structure of equali-
ties suggested in the formula. One way to
do that would be an historical investigation
into the endoxa surrounding the content of
the algebra. Euclid provides such an occasion
for interrogation. Proposition I.47 in Euclid’s
Elements actually exhibits the fundamental
intuition that is assumed in the algebraic
formulation—it makes the equalities in the
properties of the squares explicit and visi-
ble.35
Moreover, in following Euclid, we are
able to dialogically engage the triangle, to
critically analyze what we already know
about it, to add and subtract figures from its
sides and compare their equalities. In doing
this, we prepare ourselves for a fundamental
insight, a noetic vision, an intuition in which
we see the very meaning of the Pythagorean
theorem we have already been employing
without truly understanding it. It was pre-
cisely the critical engagement and the lin-
guistic assessment of the triangle that placed
us in the position for the “ah ha!” moment
of seeing what the Pythagorean theorem
means. However, it seems that the seeing of
this fundamental meaning cannot be reduced
to the discursive engagement that placed us
in the position to be able to see. The seeing
is rather something in addition to the logical
moves in the proposition. I would argue that
while the seeing of the equality would not be
possible without the discursive assessment
of the triangle in the proposition, it can-
not be reduced to the discursive assessment.
Perhaps this is what Aristotle means when
he says in passages that I have quoted above
that (1) “it would be nous that is of archai”
(APo 100b13),36
“nous is of definitions” (NE
1142a25), and (2) intellectual intuition is
without logos (1142a27). Dialogical engage-
ment with the prouparchousa gnôsis places
us in a receptive comportment with respect
to the archai, places us in the hexis in which
we can intellectually perceive the being of a
being37
—but the reception of the archai can-
not be reduced to rational, dialogical engage-
ment, to the logos. A curious consequence
of the latter is that it might be possible to
argue that the discursive content of A2
+ B2
=
C2
with which we started is nevertheless
identical to what would be articulated as a
consequence of the dialectical work that led
us to the intellectual vision of the meaning of
proposition I.47.38
In merely articulating the
content of two conceptual representations of
the triangle, one cannot perceive a difference.
The immediate perception of the meaning
of the equalities requires the addition of the
noetic perception. Moreover, if the articula-
tion of the content of the two forms is iden-
tical, then this means that the vision of the
archê is experiential, not strictly conceptual.
And, one achieves the experience through
dialogically working through the proposi-
tion in order to work back toward its pri-
mary meaning, rather than simply presuming
the meaning in the algebraic formulation
and proceeding with the science of algebraic
manipulations. The latter is a demonstrative
science; the former is a philosophical, con-
templative reflection on nature.
In offering an account of primary defi-
nition in Aristotle, we have shown (1) that
definition betrays a fundamental interpene-
tration of the ontological and logical, insofar
as it is the very same archê that rules over
the motions of the natural being that also—
through a definition—rules over any syl-
logisms about it. And we have seen (2) that
definition exhibits a mode of being in which
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51
humans may discover nature (and its singular
beings) based neither upon mere sensuous
perception nor strictly conceptual media-
tion. Though dialectical/conceptual delibera-
tion does not reveal archai, it does place us
in the comportment (the hexis, the mode of
being) in which we are noetically receptive to
archai. With these two observations, we have
made clear how, for Aristotle, the activity of
defining is primarily philosophical/ontologi-
cal and only secondarily logical/scientific.
Russell Winslow
NOTES
1
As Jack Lynch notes in his “Johnson’s
Encyclopedia,” this description of deinition
derives from Porphyry’s interpretation of
Aristotle’s Posterior Analytics (in the Isagoge)
and Boethius’ own commentary on it. “From
this Scholastic tradition emerged the ‘genus—
differentiae’ mode of deinition, summarized as
‘Deinitio it per genus proximum et differen-
tiam speciicam’: a deinition identiies the kind
and offers a means of distinguishing it from
other examples of that kind. The genus and
a minimally adequate number of differentiae
provide a deinition. Much lexicographical
practice even today employs some version of
this genus-differentiae deinition” (Linch and
McDermott, 2005, p. 131).
2
The accounts of Aristotelian deinition in the
literature share a commitment to the concep-
tion of the purpose of deinition as, irst and
foremost, a “foundation for demonstrative
science” (Deslauriers, 2007, p. 2), insofar
as deinition articulates the irst principles
employed in those sciences. Indeed, for some,
the “discovery of irst principles” and the con-
sequent articulation of those irst principles,
qua deinition, is “the scientist’s . . . province”
(Sim, 1999, p. xiii). My paper will argue for a
conception of deinition that is prior to a foun-
dation for demonstrative science and formal
logic.
3
While I ind Deslauriers’ account of deinition
compelling—especially insofar as
(1) she suggests that through deinition “we
discover a link between logic and metaphysics”
(Deslauriers, 2007, pp. 1, 59, and chapter 3),
and (2) she distinguishes between the prior
deinitions that “reveal substance to us” and
the derivative forms of deinition (Deslauriers,
2007, p. 10), and (3) she argues that immediate
deinitions are the most philosophically impor-
tant to Aristotle (Deslauriers, 2007,
p. 44), I disagree with her claim that “immedi-
ate” deinition, the more primordial conception
of deinition, is understood by Aristotle as a
“genus and a set of differentiae” (Deslauriers,
2007, p. 211). I will argue that these concep-
tual categories are already a move into abstrac-
tion from the archê, which is the irst object of
a deinition.
4
See, for example, Physics I.1, 184a17–18 and
Posterior Analytics I.2, 71b35.
5
In the Nicomachean Ethics, Aristotle deines
virtue as a hexis, which is to say, a habit/com-
portment of the soul in which “we hold/bear”
(echomen) ourselves “well” or “badly” toward
the passions (1105b25–26). Later, in book VI,
Aristotle employs this term (hexis) again to
describe the intellectual virtues insofar as they
are comportments in which truth is disclosed.
Nous is included among these (1139b12–13).
Also, in Posterior Analytics, Aristotle employs
the term hexis to describe nous when he begins
the investigation into which form of “knowing
hexis” knows the archai (99b19). Here and
for the rest of the essay the quotations from
Aristotle’s texts are based on the editions/
translations listed in the References, although I
often offer alternative renditions of the Greek.
6
APo 71a2.
7
See, for example, Tredennick (1960).
8
The positions in the debate may be perused in
Sim (1999). See also Irwin, 1988, pp. 1–70.
9
“The work of the human is a certain life, and
this is the activity and action of the soul with
logos” (NE 1098a14).
10
Heath, 1956, p. 277.
11
In this context I italicize “postulate” in order
to draw attention to the character of a sub-
structure that this particular already-present
gnôsis exhibits. It serves as what we might
call a “holding place” for the content/
meaningfulness of numbering—one must
already have an awareness of “unit” if one
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52
is to perform the activity of gathering like
“units” into number.
12
The function of endoxa in Aristotle’s method
of discovery has engendered a great deal of
debate between those who, on the one hand,
wish to see a conceptual/a priori methodology
at work and those who, on the other, wish to
see an empirical method at work. With regard
to Aristotle’s Physics, for example, compare
Owen, G. E. L.’s “Tithenai ta Phainomena”
(Owen, 1986, pp. 239–51) with Robert
Bolton’s challenge to Owen in “Aristotle’s
Method in Natural Science: Physics I” (Judson,
1991, pp. 1–30).
13
I use the term confrontation in order to convey
critical engagement, but not necessarily total
negation. I would argue that Aristotle appro-
priates as much as he refutes his predecessors.
14
99b15–100b4.
15
In his Commentary on Euclid’s Elements
(Morrow, 1970, p. 11), Proclus appears struck
by a curious tendency he sees in Aristotle’s
understanding, on the one hand, of the relation
of mathematics to nature and, on the other, of
the relation of logic to nature. More specii-
cally, Proclus draws our attention to the fact
that Aristotle criticizes mathematical explana-
tions of nature, arguing that they abstract from
physis. Of course, in Proclus’ reading, Aristotle
fails to think clearly about the relation of the
sensible and mathematical. Proclus wants
to argue that attending to sensuous beings
unhinges one’s logic and knowledge from true
nature, while mathematical beings secure an
accurate account of it. Yet, Aristotle argues for
the reverse; the accuracy of logical disclosure
of nature, for him, is better secured by attend-
ing to physical beings. Physical and particular
beings give themselves as logical principles
(archai) somehow already, while mathematical
beings are abstractions of this sensuous experi-
ence. For instance, in Physics II.2 Aristotle
explicitly denies that mathematics offers an
account of nature as such. “The mathematician
does busy himself about the things men-
tioned,” Aristotle writes, speaking of natural
bodies, “but not insofar as each is a limit of a
natural body” (193b32). Rather, the math-
ematician assesses the surfaces, lengths, and
volumes of natural bodies by abstraction—by
separating these “formal” characteristics from
the motion and matter of a being in becom-
ing. Yet, strangely and remarkably, as Proclus
notes, Aristotle does not come to the same
conclusion about logic and its relationship to
nature. Logic—and the broader structure into
which it is situated: reason (logos)—we can
therefore conclude, is not an abstraction or a
separation from the sensuous and particular
beings of nature, for Aristotle, but rather logos
must somehow be thought of as an expression
of these beings of nature; or, perhaps better,
logical structures, in contrast to mathematical
structures, must be included when thinking of
natural beings in the world.
16
Here one might consider the initude of the
human intellectual encounter with the form
of natural beings in Aristotle. Indeed, the very
fact that we can engage critically the existing
arguments and concepts shows that these argu-
ments do not exhaust the ousia of the other.
It is the irreducibility of the other that keeps
arguments unstable, revisable, always in the
process of dissolving and being reconstituted
anew. Even if the reception of the form of the
other being is noetic, that reception might be
subject to malleability and change (perhaps
even “corruption”) at the very moment it is
raised into discourse (which is to say, at the
very moment it is incorporated into speech).
Perhaps this initude bespeaks the urgency
behind the activity of deinition: we could even
say that it is the force of deinition that keeps
discursivity on its tiptoes.
17
There is much disagreement in the literature
with respect to these three forms of deinition.
For reasons that are clear from the argu-
ments below, I differ from the reading that
the irst and the third articulations of deini-
tion are identical (e.g. in Ross’ commentary
on Aristotle’s Prior and Posterior Analytics
(Ross, 1949, pp. 634–9). Further, I remain
unconvinced that these passages indicate
a developmental conception of deinition.
In his “Deinition and Scientiic Method in
Aristotle’s Posterior Analytics and Generation
of Animals,” Robert Bolton offers a reading of
these three types of deinition as if they would
represent three consecutive points of achiev-
ing a deinition. For Bolton, irst we are aware
of something in accordance with its general
sensuously perceived characteristics (this is
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53
conceived as a irst deinition), then we are
aware of something that exhibits why some-
thing has the characteristics in the irst deini-
tion (this is second), and then we continue our
inquiry to clarify the features most basic to our
irst sensuously perceived characteristics (this
is the third and most primary “indemonstrable
deinition”). I do not think Aristotle suggests
that there are consecutive degrees of deinition
through which a deinition passes. Rather,
I think Aristotle is speaking of two incidental
(sumbebêkos) ways we speak of deinition
and then also the primary way we speak of
deinition, the third being the primary sense of
deinition. Bolton’s summary of this process is
to be found Gotthelf and Lennox, 1987,
pp. 145–6.
18
Aristotle conirms this assertion in his recapitu-
lation of the three forms of deinition (94a11),
in which this irst kind is said to be “the con-
clusion of a demonstration” (94a14). Clearly,
Aristotle has already said numerous times that
it is not demonstration, but deinition that
accounts for what something is (ti esti) and,
moreover, that deinition and what something
is (ti esti) cannot be proved. Yet, there is a way
in which a deinition can resemble a demon-
stration in form, but not in such a way that it
proves anything about the primary substance,
but rather, in such a way that it makes mani-
fest something incidental (sumbebêkos) to or
something that “comes along with” substance.
19
“For it is different to tell why thunder is and
to tell what thunder is. For it will be said:
‘because ire is extinguished in the clouds.’ But
[the question] ‘what is ire?’ [is answered by]
‘noise from extinguishing ire in the clouds’”
(94a3). Aristotle explains that the former is a
continuous demonstration (moving forward in
the way that syllogisms do) while the latter is a
deinition.
20
In Posterior Analytics, Aristotle writes that
deinition is of the ti esti and ousia (91a1).
Yet, in Metaphysics, he writes that deinition
is a logos of the τὸ τί ἦν εἶναι (1030a7).
With Aristotle, my essay presumes a certain
synonymy between the three phrases.
21
Aristotle has earlier stated that “it is clear that
the essences (ti esti) of things [whose cause is
not other than themselves] will be also imme-
diate and [will be] irst principles (archai)”:
which is to say that their “ti esti must be
assumed” (as in the case of a demonstration)
or they must be “made manifest in some other
way” (93b22–24). We will presently pursue
this “other way.”
22
For the importance of conviction and belief in
Aristotle’s logical thinking, see Baracchi, 2008,
pp. 27–8.
23
On this point consider, once more, the claim
in Metaphysics VII.9 that “just as in demon-
stration, ousia is the archê of everything, for
syllogisms come from ti esti, while [among
biological forms] generations do” (1034a32).
Thus, the ousia of something rules over,
provides continuity and completeness, qua
archê, both to thinking and rational disclosure
and to the generation of natural beings. As
shown in the irst part of the present essay, the
continuity in Aristotle between the motions
of generation and those of logic (and the fact
that the latter depend upon the former) signal
a deep connection between the ontological and
the logical.
24
While it does not employ the language of
deinition, there is a version of such a structure
articulated already in the discussion of the
divided line in Plato’s Republic, stating that
science is not concerned with the archai as
such, but rather begins with hypotheses about
the forms and proceeds from these hypoth-
eses with its scientiic work—it operates with
presumed conceptions of archai. Philosophy,
too, begins with the hypotheses but turns back
from the hypotheses (rather than simply pro-
ceeding from them) to the beginning (510b).
25
Oneness is precisely the origin of one of the
problems with thinking deinition in the
Metaphysics (1037b11); for, insofar as a
deinition is composed of several concepts, it
must nevertheless exhibit oneness insofar as
it is to articulate something that is one and
continuous.
26
This conception of a deinition as a philo-
sophical articulation of what makes a being
one, continuous, and intimately connected
to a being’s substance is even stronger
in Metaphysics VII than in the Posterior
Analytics. For example: “a deinition and a to
ti ên einai belong primarily and simply to
ousia . . . [and a deinition] belongs to some-
thing that is one, not by being continuous in
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54
the way that the Iliad is, nor by being bundled
together, but [by being continuous] in just the
ways one is meant” (1030b15). Compare also:
1036a1, 1037b25, and 1038a20.
27
In the words of T. H. Irwin, “Aristotle’s
description of dialectical method seems to offer
no grounds for believing that it systematically
reaches objective irst principles, it reaches a
more coherent version of the beliefs we began
with, solving the puzzles revealed by our exam-
ination of the initial beliefs. But coherence
within common beliefs does not seem to be a
ground for claiming to have found objective
principles” (1988, p. 8).
28
Halper also argues that the procedure at the
beginning of the Physics and other texts that
open with an engagement of the endoxa “can-
not quite count as science” (Sim, 1999, p. 216).
I agree with him here; for, as I argue above,
philosophical work involves the disclosure of
archai, not scientiic work. Thus, I would want
to argue that the irst books of those texts
originate a philosophical comportment, a
comportment concerned with moving from
awareness of nature (in the case of the
Physics) according to us . . . to an awareness
of the archê of nature.
29
See my “On the Nature of ‘Logos’ in Aristotle”
in Winslow, 2006, pp. 163–80.
30
Heath, 1956, p. 277.
31
Kant, 1855, p. 58.
32
Phys. 193b32.
33
NE 1140a15.
34
For a contrasting view, compare Robert
Bolton’s essay “Aristotle’s Posterior Analytics
and Generation of Animals” (in Gotthelf and
Lennox, 1987, p. 120) in which he argues
mostly against the view that Aristotle’s prin-
cipal method of discovery is dialectic. Bolton,
quoting the Topics (142a6–7, 141b15–19),
sees deinition as more intimately connected to
apodeixis, arguing that deinition according to
our nature is speciically criticized by Aristotle
as being for people who lack the intellectual
capacity for syllogism. Yet, I would argue that
Aristotle means something quite different in
these passages from the Topics. Namely, that
there is a way that one can form deinitions
in accordance with our nature, “according to
us” (see, for example, Phys. I.1, 184a17–18),
which is to say, in accordance with the
cultural/linguistic constitution in which we ind
ourselves. These derivative deinitions do not
enable us to break out of that cultural consti-
tution and such breaking out is a requirement
in the generation of deinitions “according
to nature.” These derivative deinitions are
formed by those who cannot or do not employ
rationality wakefully and originally, but rather
resemble the formation of deinitions and
games by those bounded souls in Plato’s cave
allegory (Bloom, 1969, pp. 516c–d), who hold
contests and word-guessing games based upon
the ruling cave prouparchousa gnôsis). In fact,
there are ways in which even syllogism does
not and cannot break out of its cultural con-
stitution such that it can generate a comport-
ment of knowing—as we recall from Aristotle’s
assertion in Nicomachean Ethics that there
are people (children and drunk people, for
instance) that are able to string together sci-
entiic demonstrations, but do not know what
they are saying (Bywater, 1894, p. 1147a20).
In the case of children, we can see very clearly
how they may rehearse the deinitions (similar
to my example of the Pythagorean theorem
below) they have been habituated to state in
support of a geometrical proof, but they do
not have the relected insight that comes from
the intellectual experience of deinition in its
primary, noetic sense. Nevertheless, contrary to
Bolton, I see these derivative forms of deini-
tion as important, perhaps even necessary,
insofar as they are a part of the structure of
preexistent knowledge out of which we come
to know anything at all.
35
“In right-angled triangles the square on the side
subtending the right angle is equal to the squares
on the sides containing the right angle. Let ABC
be a right-angled triangle having the angle BAC
right; I say that the square on BC is equal to the
squares on BA, AC. For let there be described
on BC the square BDEC, and on BA, AC the
squares GB, HC. . . . Therefore the whole square
BDEC is equal to the two squares GB, HC”
(Heath, 1956, pp. 349–50).
D L E
C
B M
F
G
A
K
H
4/3/2013 9:20:04 PM

55
36
The relation between nous and aisthêsis in the
reception of archai is not uncomplicated. They
are both immediate perceptive capacities that
when attuned in the right way toward their
objects are never wrong: “sense perception
when directed at its proper objects is always
truthful” (427b11); “The thinking of indivis-
ible things is one of those acts in which false-
hood is not possible” (430a27). Despite this
claim that nous and aisthêsis are never wrong,
there have been compelling readings that assert
a certain possibility of a initude or (even)
fallibility of nous: for example, Brague, 1990;
Bäck, “Aristotle’s Discovery of First Principles,”
in Sim, 1999, pp. 163–81; Baracchi, 2008.
37
Aristotle’s conception of noetic perception is
highly debated and controversial in the litera-
ture. A sustained meditation on nous would
require an essay on its own and is, conse-
quently, not possible here. One might attribute
the dificulty of the interpretation of nous to the
confused state of certain key manuscripts
that include Aristotle’s relections on nous,
as Martha Nussbaum writes in “The Text of
Aristotle’s de Anima” in Nussbaum and Rorty,
1992, p. 2. Or, one might also simply suggest,
as Martin Heidegger has, that nous continues
to elude Aristotle insofar as “it is the phe-
nomenon that causes him the most dificulty”
(Heidegger, 1997, p. 41). Further, one might
try to offer an interpretation of certain dificult
passages while still qualifying what one writes
by saying, as K. V. Wilkes does: “I cannot
understand this chapter [de Anima III.5],
and none of the secondary literature has
so far helped me to do so” (Nussbaum and
Rorty, 1992, p. 125). I argue for a receptive
(dektikon) conception of nous based upon the
comparison of aisthêsis and nous in De Anima
(Winslow, 2009).
38
We are reminded here again of that passage
quoted earlier in Aristotle’s Nicomachean
Ethics VII on the difference between a geom-
eter and a child performing demonstrations.
The demonstrations that they place on a black
board are identical. However, the difference
may lie in the intellectual perception of the
geometer—he has seen, while the child is
merely repeating the content of the demonstra-
tion (1147a20).
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