(a) Of the idea we may say that whatever else it is, and apart from all
puzzles as to ideas of relations such as smallness, of negative
qualities such as injustice, or of human inventions such as beds, it is
opposed to that of which it is the idea as its intelligible formula or
law, the truth or validity--Herbart's word--of the phenomenon from the
point of view of nexus or system. The thing of sense in its relative
isolation is unstable. It is and is not. What gives stability is the
insensible principle or principles which it holds, as it were, in
solution. These are the ideas, and their mode of being is naturally
quite other than that of the sensible phenomena which they order. The
formula for an indefinite number of particular things in particular
places at particular times, and all of them presentable in sensuous
imagery of a given time and place, is not itself presentable in sensuous
imagery side by side with the individual members of the group it orders.
The law, e.g., of the equality of the radii of a circle cannot be
exhibited to sense, even if equal radii may be so exhibited. It is the
wealth of illustration with which Plato expresses his meaning, and the
range of application which he gives the idea--to the class-concepts of
natural groups objectively regarded, to categories, to aesthetic and
ethical ideals, to the concrete aims of the craftsman as well as to
scientific laws--that have obscured his doctrine, viz. that wherever
there is law, there is an idea.
The one in the many.
(b) The paradox of the one in the many is none, if the idea may be
regarded as supplying a principle of nexus or organization to an
indefinite multiplicity of particulars. But if Antisthenes is to be
answered, a further step must be taken. The principle of difference must
be carried into the field of the ideas. Not only sense is a principle of
difference. The ideas are many. The multiplicity in unity must be
established within thought itself. Otherwise the objection stands: man
is man and good is good, but to say that man is good is clearly to say
the thing that is not. Plato replies with the doctrine of the
interpenetration of ideas, obviously not of all with all, but of some
with some, the formula of identity in difference within thought itself.
Nor can the opponent fairly refuse to admit it, if he affirms the
participation of the identical with being, and denies the participation
of difference with being, or affirms it with not-being. The _Sophistes_
shows among other things that an identity-philosophy breaks down into a
dualism of thought and expression, when it applies the predicate of
unity to the real, just as the absolute pluralism on the other hand
collapses into unity if it affirms or admits any form of relation
whatsoever. Identity and difference are all-pervasive categories, and
the speech-form and the corresponding thought-form involve both. For
proposition and judgment involve subject and predicate and exhibit what
a modern writer calls "identity of reference with diversity of
characterization." Plato proceeds to explain by his principle of
difference both privative and negative predicates, and also the
possibility of false predication. It is obvious that without the
principle of difference error is inexplicable. Even Plato, however,
perhaps scarcely shows that with it, and nothing else but it, error is
explained.
Division.
(c) Plato's Division, or the articulation of a relatively indeterminate
and generic concept into species and sub-species with resultant
determinate judgments, presumes of course the doctrine of the
interpenetration of ideas laid down in the _Sophistes_ as the basis of
predication, but its use precedes the positive development of that
formula, though not, save very vaguely, the exhibition of it,
negatively, in the antinomies of the one and the many in the
_Parmenides_. It is its use, however, not the theory of it, that
precedes. The latter is expounded in the _Politicus_ (260 sqq.) and
_Philebus_ (16c sqq.). The ideal is progressively to determine a
universe of discourse till true _infimae species_ are reached, when no
further distinction in the determinate many is possible, though there is
still the numerical difference of the indefinite plurality of
particulars. The process is to take as far as possible the form of a
continuous disjunction of contraries. We must bisect as far as may be,
but the division is after all to be into limbs, not parts. The later
examples of the _Politicus_ show that the permission of three or more
co-ordinate species is not nugatory, and that the precept of dichotomy
is merely in order to secure as little of a _saltus_ as possible; to
avoid e.g. the division of the animal world into men and brutes. It is
the middle range of the [Greek: mesa] of _Philebus_ 17a that appeals to
Bacon, not only this but their mediating quality that appeals to
Aristotle. The _media axiomata_ of the one and the _middle term_ of the
other lie in the phrase. Plato's division is nevertheless neither
syllogism nor _exclusiva_. It is not syllogism because it is based on
the disjunctive, not on the hypothetical relation, and so extends
horizontally where syllogism strikes vertically downward. Again it is
not syllogism because it is necessarily and finally dialectical. It
brings in the choice of an interlocutor at each stage, and so depends on
a concession for what it should prove.[12] Nor is it Bacon's method of
exclusions, which escapes the imputation of being dialectical, if not
that of being unduly cumbrous, in virtue of the cogency of the negative
instance. The Platonic division was, however, offered as the scientific
method of the school. A fragment of the comic poet Epicrates gives a
picture of it at work.[13] And the movement of disjunction as truly has
a place in the scientific specification of a concept in all its
differences as the linking of lower to higher in syllogism. The two are
complementary, and the reinstatement of the disjunctive judgment to the
more honourable rôle in inference has been made by so notable a modern
logician as Lotze.
Combination.
(d) The correlative process of Combination is less elaborately sketched,
but in a luminous passage in the _Politicus_ (§ 278), in explaining by
means of an example the nature and use of examples, Plato represents it
as the bringing of one and the same element seen in diverse settings to
conscious realization, with the result that it is viewed as a single
truth of which the terms compared are now accepted as the differences.
The learner is to be led forward to the unknown by being made to hark
back to more familiar groupings of the alphabet of nature which he is
coming to recognize with some certainty. To lead on, [Greek: epagein],
is to refer back, [Greek: anagein],[14] to what has been correctly
divined of the same elements in clearer cases. Introduction to
unfamiliar collocations follows upon this, and, only so, is it possible
finally to gather scattered examples into a conspectus as instances of
one idea or law. This is not only of importance in the history of the
terminology of logic, but supplies a philosophy of induction.
Mental synthesis.
(e) Back of Plato's illustration and explanation of predication and
dialectical inference there lies not only the question of their
metaphysical grounding in the interconnexion of ideas, but that of their
epistemological presuppositions. This is dealt with in the Theaetetus
(184b sqq.). The manifold affections of sense are not simply aggregated
in the individual, like the heroes in the Trojan horse. There must be
convergence in a unitary principle, soul or consciousness, which is that
which really functions in perception, the senses and their organs being
merely its instruments. It is this unity of apperception which enables
us to combine the data of more than one sense, to affirm reality,
unreality, identity, difference, unity, plurality and so forth, as also
the good, the beautiful and their contraries. Plato calls these
pervasive factors in knowledge [Greek: koina], and describes them as
developed by the soul in virtue of its own activity. They are objects of
its reflection and made explicit in the few with pains and
gradually.[15] That they are not, however, psychological or acquired
categories, due to "the workmanship of the mind" as conceived by Locke,
is obvious from their attribution to the structure of mind[16] and from
their correlation with immanent principles of the objective order.
Considered from the epistemological point of view, they are the implicit
presuppositions of the construction or [Greek: syllogismos][17] in which
knowledge consists. But as ideas,[18] though of a type quite apart,[19]
they have also a constitutive application to reality. Accordingly, of
the selected "kinds" by means of which the interpenetration of ideas is
expounded in the _Sophistes_, only motion and rest, the ultimate "kinds"
in the physical world, have no counterparts in the "categories" of the
_Theaetetus_. In his doctrine as to [Greek: en to poioun] or [Greek:
krinon], as generally in that of the activity of the [Greek: nous
apathês], Aristotle in the _de Anima_[20] is in the main but echoing the
teaching of Plato.[21]
ii. _Aristotle._
Plato's episodic use of logical distinctions[22] is frequent. His
recourse to such logical analysis as would meet the requirements of the
problem in hand[23] is not rare. In the "dialectical" dialogues the
question of method and of the justification of its postulates attains at
least a like prominence with the ostensible subject matter. There is
even formal recognition of the fact that to advance in dialectic is a
greater thing than to bring any special inquiry to a successful
issue.[24] But to the end there is a lack of interest in, and therefore
a relative immaturity of, technique as such. In the forcing atmosphere,
however, of that age of controversy, seed such as that sown in the
master's treatment of the uttered [Greek: logos][25] quickly germinated.
Plato's successors in the Academy must have developed a system of
grammatico-logical categories which Aristotle could make his own. Else
much of his criticism of Platonic doctrine[26] does, indeed, miss fire.
The gulf too, which the _Philebus_[27] apparently left unbridged between
the sensuous apprehension of particulars and the knowledge of universals
of even minimum generality led with Speusippus to a formula of knowledge
in perception ([Greek: epistêmonikê aisthêsis]). These and like
developments, which are to be divined from references in the
Aristotelian writings, jejune, and, for the most part, of probable
interpretation only, complete the material which Aristotle could utilize
when he seceded from the Platonic school and embarked upon his own
course of logical inquiry.
Syllogism.
This is embodied in the group of treatises later known as the
_Organon_[28] and culminates in the theory of syllogism and of
demonstrative knowledge in the _Analytics_. All else is finally
subsidiary. In the well-known sentences with which the _Organon_
closes[29] Aristotle has been supposed to lay claim to the discovery of
the principle of syllogism. He at least claims to have been the first to
dissect the procedure of the debate-game, and the larger claim may be
thought to follow. In the course of inquiry into the formal
consequences from probable premises, the principle of mediation or
linking was so laid bare that the advance to the analytic determination
of the species and varieties of syllogism was natural. Once embarked
upon such an analysis, where valid process from assured principles gave
truth, Aristotle could find little difficulty in determining the formula
of demonstrative knowledge or science. It must be grounded in principles
of assured certainty and must demonstrate its conclusions with the use
of such middle or linking terms only as it is possible to equate with
the real ground or cause in the object of knowledge. Hence the account
of axioms and of definitions, both of substances and of derivative
attributes. Hence the importance of determining how first principles are
established. It is, then, a fair working hypothesis as to the structure
of the _Organon_ to place the _Topics_, which deal with dialectical
reasoning, before the _Analytics_.[30] Of the remaining treatises
nothing of fundamental import depends on their order. One, however, the
_Categories_, may be regarded with an ancient commentator,[31] as
preliminary to the dialectical inquiry in the _Topics_. The other, on
thought as expressed in language ([Greek: Peri ermêneias]) is possibly
spurious, though in any case a compilation of the Aristotelian school.
If genuine, its naïve theory that thought copies things and other
features of its contents would tend to place it among the earliest works
of the philosopher.
The logical treatises.
Production in the form of a series of relatively self-contained
treatises accounts for the absence of a name and general definition of
their common field of inquiry. A more important lack which results is
that of any clear intimation as to the relation in which Aristotle
supposed it to stand to other disciplines. In his definite
classification of the sciences,[32] into First Philosophy, Mathematics
and Physics, it has no place. Its axioms, such as the law of
contradiction, belong to first philosophy, but the doctrine as a whole
falls neither under this head nor yet, though the thought has been
entertained, under that of mathematics, since logic orders mathematical
reasoning as well as all other. The speculative sciences, indeed, are
classified according to their relation to form, pure, abstract or
concrete, i.e. according to their objects. The logical inquiry seems to
be conceived as dealing with the thought of which the objects are
objects. It is to be regarded as a propaedeutic,[33] which, although it
is in contact with reality in and through the metaphysical import of the
axioms, or again in the fact that the categories, though primarily taken
as forms of predication, must also be regarded as kinds of being, is not
directly concerned with object-reality, but with the determination for
the thinking subject of what constitutes the knowledge correlative to
being. Logic, therefore, is not classed as one, still less as a branch
of one, among the 'ologies, ontology not excepted.
The way in which logical doctrine is developed in the Aristotelian
treatises fits in with this view. Doubtless what we have is in the main
a reflex of the heuristic character of Aristotle's own work as pioneer.
But it at least satisfies the requirement that the inquiry shall carry
the plain man along with it. Actual modes of expression are shown to
embody distinctions which average intelligence can easily recognize and
will readily acknowledge, though they may tend by progressive
rectification fundamentally to modify the assumption natural to the
level of thought from which he begins. Thus we start[34] from the point
of view of a world of separate persons and things, in which thought
mirrors these concrete realities, taken as ultimate subjects of
predicates. It is a world of communication of thought, where persons as
thinkers need to utter in language truths objectively valid for the
_mundus communis_. In these truths predicates are accepted or rejected
by subjects, and therefore depend on the reflection of fact in [Greek:
logoi] (propositions). These are combinatory of parts, attaching or
detaching predicates, and so involving subject, predicate and
copula.[35] At this stage we are as much concerned with speech-forms as
the thought-forms of which they are conventional symbols, with Plato's
analysis, for instance, into a noun and a verb, whose connotation of
time is as yet a difficulty. The universal of this stage is the
universal of fact, what is recognized as predicable of a plurality of
subjects. The dialectical doctrine of judgment as the declaration of one
member of a disjunction by contradiction, which is later so important,
is struggling with one of its initial difficulties,[36] viz. the
contingency of particular events future, the solution of which remains
imperfect.[37]
The Categories.
The doctrine of the _Categories_ is still on the same level of
thought,[38] though its grammatico-logical analysis is the more advanced
one which had probably been developed by the Academy before Aristotle
came to think of his friends there as "them" rather than "us." It is
what in one direction gave the now familiar classification of parts of
speech, in the other that of thought-categories underlying them. If we
abstract from any actual combination of subject and predicate and
proceed to determine the types of predicate asserted in simple
propositions of fact, we have on the one hand a subject which is never
object, a "first substance" or concrete thing, of which may be
predicated in the first place "second substance" expressing that it is a
member of a concrete class, and in the second place quantity, quality,
correlation, action and the like. The list follows the forms of the
Greek language so closely that a category emerges appropriated to the
use of the perfect tense of the middle voice to express the relation of
the subject to a garb that it dons. In all this the individual is the
sole self-subsistent reality. Truth and error are about the individual
and attach or detach predicates correctly and incorrectly. There is no
committal to the metaphysics in the light of which the logical inquiry
is at last to find its complete justification. The point of view is to
be modified profoundly by what follows--by the doctrine of the
class-concept behind the class, of the form or idea as the constitutive
formula of a substance, or, again, by the requirement that an essential
attribute must be grounded in the nature or essence of the substance of
which it is predicated, and that such attributes alone are admissible
predicates from the point of view of the strict ideal of science. But we
are still on the ground of common opinion, and these doctrines are not
yet laid down as fundamental to the development.
The Topics.
Dialectic then, though it may prove to be the ultimate method of
establishing principles in philosophy,[39] starts from probable and
conceded premises,[40] and deals with them only in the light of common
principles such as may be reasonably appealed to or easily established
against challenge. To the expert, in any study which involves contingent
matter, i.e. an irreducible element of indetermination, e.g. to the
physician, there is a specific form of this, but the reflection that
this is so is something of an afterthought. We start with what is prima
facie given, to return upon it from the ground of principles clarified
by the sifting process of dialectic[41] and certified by [Greek: nous].
The _Topics_ deal with dialectic and constitute an anatomy of
argumentation, or, according to what seems to be Aristotle's own
metaphor, a survey of the tactical vantage-points ([Greek: topoi]) for
the conflict of wits in which the prize is primarily victory, though it
is a barren victory unless it is also knowledge. It is in this treatise
that what have been called "the conceptual categories"[42] emerge, viz.
the _predicables_, or heads of predication as it is analysed in relation
to the provisional theory of definition that dialectic allows and
requires. A predicate either is expressive of the essence or part of the
essence of the subject, viz. that original group of mutually underivable
attributes of which the absence of any one destroys its right to the
class-name, or it is not. Either it is convertible with the subject or
it is not. Here then judgment, though still viewed as combinatory, has
the types which belong to coherent systems of implication discriminated
from those that predicate coincidence or accident, i.e. any happening
not even derivatively essential from the point of view of the grouping
in which the subject has found a place. In the theory of dialectic any
predicate may be suggested for a subject, and if not affirmed of it,
must be denied of it, if not denied must be affirmed. The development of
a theory of the ground on which subjects claim their predicates and
disown alien predicates could not be long postponed. In practical
dialectic the unlimited possibility was reduced to manageable
proportions in virtue of the groundwork of received opinion upon which
the operation proceeded. It is in the _Topics_, further, that we clearly
have a first treatment of syllogism as formal implication, with the
suggestion that advance must be made to a view of its use for material
implication from true and necessary principles. It is in the
_Topics_,[43] again, that we have hints at the devices of an inductive
process, which, as dialectical, throw the burden of producing
contradictory instances upon the other party to the discussion. In
virtue of the common-stock of opinion among the interlocutors and their
potentially controlling audience, this process was more valuable than
appears on the face of things. Obviously tentative, and with limits and
ultimate interpretation to be determined elsewhere, it failed to bear
fruit till the Renaissance, and then by the irony of fate to the
discrediting of Aristotle. In any case, however, definition, syllogism,
induction all invited further determination, especially if they were to
take their place in a doctrine of truth or knowledge. The problem of
analytic, i.e. of the resolution of the various forms of inference into
their equivalents in that grouping of terms or premises which was most
obviously cogent, was a legacy of the _Topics_. The debate-game had
sought for diversion and found truth, and truth raised the logical
problem on a different plane.
Class concept.
The Prior Analytics.
At first the problem of formal analysis only. We proceed with the talk
of instances and concern ourselves first with relations of inclusion and
exclusion. The question is as to membership of a class, and the dominant
formula is the _dictum de omni et nullo_. Until the view of the
individual units with which we are so far familiar has undergone radical
revision, the primary inquiry must be into the forms of a
class-calculus. Individuals fall into groups in virtue of the possession
of certain predicates. Does one group include, or exclude, or intersect
another with which it is compared? We are clearly in the field of the
diagrams of the text-books, and much of the phraseology is based upon an
original graphic representation in extension. The middle term, though
conceived as an intermediary or linking term, gets its name as
intermediate in a homogeneous scheme of quantity, where it cannot be of
narrower extension than the subject nor wider than the predicate of the
conclusion.[44] It is also, as Aristotle adds,[45] middle in position in
the syllogism that concludes to a universal affirmative.[45] Again, so
long as we keep to the syllogism as complete in itself and without
reference to its place in the great structure of knowledge, the nerve of
proof cannot be conceived in other than a formal manner. In analytic we
work with an ethos different from that of dialectic. We presume truth
and not probability or concession, but a true conclusion can follow from
false premises, and it is only in the attempt to derive the premises in
turn from their grounds that we unmask the deception. The passage to the
conception of system is still required. The _Prior Analytics_ then are
concerned with a formal logic to be knit into a system of knowledge of
the real only in virtue of a formula which is at this stage still to
seek. The forms of syllogism, however, are tracked successfully through
their figures, i.e. through the positions of the middle term that
Aristotle recognizes as of actual employment, and all their moods, i.e.
all differences of affirmative and negative, universal and particular
within the figures, the cogent or legitimate forms are alone left
standing, and the formal doctrine of syllogism is complete. Syllogism
already defined[46] becomes through exhibition in its valid forms clear
in its principle. It is a speech-and-thought-form ([Greek: logos]) in
which certain matters being posited something other than the matters
posited necessarily results because of them, and, though it still needs
to receive a deeper meaning when presumed truth gives way to necessary
truth of premises, the notion of the class to that of the class-concept,
collective fact to universal law, its formal claim is manifest. "Certain
matters being posited." Subject and predicate not already seen to be
conjoined must be severally known to be in relation with that which
joins them, so that more than one direct conjunction must be given. "Of
necessity." If what are to be conjoined are severally in relation to a
common third it does perforce relate or conjoin them. "Something other."
The conjunction was by hypothesis not given, and is a new result by no
means to be reached, apart from direct perception save by use of at
least two given conjunctions. "Because of them," therefore. Yet so long
as the class-view is prominent, there is a suggestion of a begging of
the question. The class is either constituted by enumeration of its
members, and, passing by the difficulty involved in the thought of "its"
members, is an empirical universal of fact merely, or it is grounded in
the class-concept. In the first case it is a formal scheme which helps
knowledge and the theory of knowledge not at all. We need then to
develop the alternative, and to pass from the external aspect of
all-ness to the intrinsic ground of it in the universal [Greek: kath'
auto kai ê auto], which, whatsoever the assistance it receives from
induction in some sense of the word, in the course of its development
for the individual mind, is secured against dependence on instances by
the decisive fiat or guarantee of [Greek: nous], insight into the
systematic nexus of things. The conception of linkage needs to be
deepened by the realization of the middle term as the ground of nexus in
a real order which is also rational.
Problem of inference.
Nous.
Aristotle's solution of the paradox of inference, viz. of the fact that
in one sense to go beyond what is in the premises is fallacy, while in
another sense not to go beyond them is futility, lies in his formula of
implicit and explicit, potential and actual.[47] The real nexus
underlying the thought-process is to be articulated in the light of the
voucher by intelligence as to the truth of the principles of the various
departments of knowledge which we call sciences, and at the ideal limit
it is possible to transform syllogism into systematic presentation, so
that, differently written down, it is definition. But for human thought
sense, with its accidental setting in matter itself incognizable is
always with us. The activity of [Greek: nous] is never so perfectly
realized as to merge implication in intuition. Syllogism must indeed be
objective, i.e. valid for any thinker, but it is also a process in the
medium of individual thinking, whereby new truth is reached. A man may
know that mules are sterile and that the beast before him is a mule, and
yet believe her to be in foal "not viewing the several truths in
connexion."[48] The doctrine, then, that the universal premise contains
the conclusion not otherwise than potentially is with Aristotle
cardinal. The datum of sense is only retained through the universal.[49]
It is possible to take a universal view with some at least of the
particular instances left uninvestigated.[50] Recognition that the
class-concept is applicable may be independent of knowledge of much that
it involves. Knowledge of the implications of it does not depend on
observation of all members of the class. Syllogism as formula for the
exhibition of truth attained, and construction or what not as the
instrumental process by which we reach the truth, have with writers
since Hegel and Herbart tended to fall apart. Aristotle's view is other.
Both are syllogisms, though in different points of view. For this
reason, if for no other, the conception of movement from the potential
possession of knowledge to its actualization remains indispensable.
Whether this is explanation or description, a problem or its solution,
is of course another matter.
Posterior Analytics.
In the _Posterior Analytics_ the syllogism is brought into decisive
connexion with the real by being set within a system in which its
function is that of material implication from principles which are
primary, immediate and necessary truths. Hitherto the assumption of the
probable as true rather than as what will be conceded in debate[51] has
been the main distinction of the standpoint of analytic from that of
dialectic. But the true is true only in reference to a coherent system
in which it is an immediate ascertainment of [Greek: nous], or to be
deduced from a ground which is such. The ideal of science or
demonstrative knowledge is to exhibit as flowing from the definitions
and postulates of a science, from its special principles, by the help
only of axioms or principles common to all knowledge, and these not as
premises but as guiding rules, all the properties of the subject-matter,
i.e. all the predicates that belong to it in its own nature. In the case
of any subject-kind, its definition and its existence being avouched by
[Greek: nous], "heavenly body" for example, the problem is, given the
fact of a non-self-subsistent characteristic of it, such as the eclipse
of the said body, to find a ground, a [Greek: meson] which expressed the
[Greek: aition], in virtue of which the adjectival concept can be
exhibited as belonging to the subject-concept [Greek: kath auto] in the
strictly adequate sense of the phrase in which it means also [Greek: hê
auto].[52] We are under the necessity then of revising the point of view
of the syllogism of all-ness. We discard the conception of the universal
as a predicate applicable to a plurality, or even to all, of the members
of a group. To know merely [Greek: kata pantos] is not to know, save
accidentally. The exhaustive judgment, if attainable, could not be known
to be exhaustive. The universal is the ground of the empirical "all" and
not conversely. A formula such as the equality of the interior angles of
a triangle to two right angles is only scientifically known when it is
not of isosceles or scalene triangle that it is known, nor even of all
the several types of triangle collectively, but as a predicate of
triangle recognized as the widest class-concept of which it is true, the
first stage in the progressive differentiation of figure at which it can
be asserted.[53]
Three points obviously need development, the nature of definition, its
connexion with the syllogism in which the middle term is cause or
ground, and the way in which we have assurance of our principles.
Definition.
The middle term.
Definition is either of the subject-kind or of the property that is
grounded in it. Of the self-subsistent definition is [Greek: ousias tis
gnôrismos][54] by exposition of genus and differentia.[55] It is
indemonstrable. It presumes the reality of its subject in a postulate of
existence. It belongs to the principles of demonstration. _Summa genera_
and groups below _infimae species_ are indefinable. The former are
susceptible of elucidation by indication of what falls under them. The
latter are only describable by their accidents. There can here be no
true differentia. The artificiality of the limit to the articulation of
species was one of the points to which the downfall of Aristotle's
influence was largely due. Of a non-self-subsistent or attributive
conception definition in its highest attainable form is a recasting of
the syllogism, in which it was shown that the attribute was grounded in
the substance or self-subsistent subject of which it is. Eclipse of the
moon, e.g. is privation of light from the moon by the interposition of
the earth between it and the sun. In the scientific syllogism the
interposition of the earth is the middle term, the cause or "because"
([Greek: dioti]), the residue of the definition is conclusion. The
difference then is in verbal expression, way of putting, inflexion.[56]
If we pluck the fruit of the conclusion, severing its nexus with the
stock from which it springs, we have an imperfect form of definition,
while, if further we abandon all idea of making it adequate by
exhibition of its ground, we have, with still the same form of words, a
definition merely nominal or lexicographical. In the aporematic
treatment of the relation of definition and syllogism identical as to
one form and in one view, distinct as to another form and in another
view, much of Aristotle's discussion consists. The rest is a
consideration of scientific inquiry as converging in [Greek: mesou
zêtêsis], the investigation of the link or "because" as ground in the
nature of things. [Greek: To men gar aition to meson][57] real ground
and thought link fall together. The advance from syllogism as formal
implication is a notable one. It is not enough to have for middle term a
_causa cognoscendi_ merely. We must have a _causa essendi_. The planets
are near, and we know it by their not twinkling,[58] but science must
conceive their nearness as the cause of their not twinkling and make the
_prius_ in the real order the middle term of its syllogism. In this
irreversible catena proceeding from ground to consequent, we have left
far behind such things as the formal parity of genus and differentia
considered as falling under the same predicable,[59] and hence justified
in part Porphyry's divergence from the scheme of predicables. We need
devices, indeed, to determine priority or superior claim to be "better
known absolutely or in the order of nature," but on the whole the
problem is fairly faced.[60]
Of science Aristotle takes for his examples sometimes celestial physics,
more often geometry or arithmetic, sometimes a concrete science, e.g.
botany.[61] In the field of pure form, free from the disconcerting
surprises of sensible matter and so of absolute necessity, no difficulty
arises as to the deducibility of the whole body of a science from its
first principles. In the sphere of abstract form, mathematics, the like
may be allowed, abstraction being treated as an elimination of matter
from the [Greek: synolon] by one act. When we take into account relative
matter, however, and traces of a conception of abstraction as admitting
of degree,[62] the question is not free from difficulty. In the sphere
of the concrete sciences where law obtains only [Greek: hôs epi to polu]
this ideal of science can clearly find only a relative satisfaction with
large reserves. In any case, however, the problem as to first principles
remains fundamental.
Formal and scientific principles.
Induction and dialectic.
Knowledge and reality.
Conclusions as to induction.
If we reject the infinite regress and the circle in proof (_circulus in
probando_) which resolves itself ultimately into proving A by B and B by
A,[63] we are confronted by the need for principles of two kinds, those
which condition all search for truth, and those which are the peculiar
or proper principles of special sciences, their "positions," viz. the
definitions of their subjects and the postulates of the existence of
these. All are indemonstrable and cannot be less sure than the body of
doctrine that flows from them. They must indeed be recognized as true,
primary, causative and the like. But[64] they are not congenitally
present in the individual in a determinate shape. The doctrine of
latency is mystical and savours of Plato's reminiscence (_anamnesis_).
Yet they must have something to develop from, and thereupon Aristotle
gives an account of a process in the psychological mechanism which he
illustrates by comparative psychology, wherein a [Greek: logos] or
meaning emerges, a "first" universal recognized by induction. Yet
[Greek: nous], intelligence, is the principle of first principles. It is
infallible, while, whatever the case with perception of the special
sensibles,[65] the process which combines particulars is not. On the
side of induction we find that experience is said to give the specific
principles,[66] "the phenomena being apprehended in sufficiency." On the
side of intuition, self-evidence of scientific principles is spoken
of.[67] Yet dialectic is auxiliary and of methodological importance in
their establishment.[68] Mutually limiting statements occur almost or
quite side by side. We cannot take first principles "as the bare
precipitate of a progressively refined analysis"[69] nor on the other as
constitutive a priori forms. The solution seems to lie in the conception
of a process that has a double aspect. On the one hand we have
confrontation with fact, in which, in virtue of the rational principle
which is the final cause of the phenomenal order, intelligence will find
satisfaction. On the other we have a stage at which the rational but as
yet not reasoned concepts developed in the medium of the psychological
mechanism are subjected to processes of reflective comparison and
analysis, and, with some modification, maintained against challenge,
till at length the ultimate universals emerge, which rational insight
can posit as certain, and the whole hierarchy of concepts from the
"first" universals to [Greek: ta amerê] are intuited in a coherent
system. Aristotle's terminology is highly technical, but, as has often
been observed, not therefore clear. Here two words at least are
ambiguous, "principle" and "induction." By the first he means any
starting-point, "that from which the matter in question is primarily to
be known,"[70] particular facts therefore, premises, and what not. What
then is meant by principles when we ask in the closing chapter of his
logic how they become known? The data of sense are clearly not the
principles in question here. The premises of scientific syllogisms may
equally be dismissed. Where they are not derivative they clearly are
definitions or immediate transcripts from definitions. There remain,
then, primary definitions and the postulates of their realization, and
the axioms or common principles, "which he must needs have who is to
reach any knowledge."[71] In the case of the former, special each to its
own science, Aristotle may be thought to hold that they are the product
of the psychological mechanism, but are ascertained only when they have
faced the fire of a critical dialectic and have been accepted from the
point of view of the integral rationality of the system of concepts.
Axioms, on the other hand, in which the sciences interconnect[72]
through the employment of them in a parity of relation, seem to be
implicit indeed in the psychological mechanism, but to come to a kind of
explicitness in the first reflective reaction upon it, and without
reference to any particular content of it. They are not to be used as
premises but as immanent laws of thought, save only when an inference
from true or admitted premises and correct in form is challenged. The
challenge must be countered in a _reductio ad impossibile_ in which the
dilemma is put. Either this conclusion or the denial of rationality.
Even these principles, however, may get a greater explicitness by
dialectical treatment.[73] The relation, then, of the two orders of
principle to the psychological mechanism is different. The kind of
warrant that intelligence can give to specific principles falls short of
infallibility. Celestial physics, with its pure forms and void of all
matter save extension, is not such an exemplary science after all.
Rationality is continuous throughout. A [Greek: logos] emerges with some
beings in direct sequence upon the persistence of impressions.[74] Sense
is of the "first" universal, the form, though not of the ultimate
universal. The rally from the rout in Aristotle's famous metaphor is of
units that already belong together, that are of the same regiment or
order. On the other hand, rationality has two stages. In the one it is
relatively immersed in sense, in the other relatively free. The same
break is to be found in the conception of the relation of receptive to
active mind in the treatise _Of the Soul_.[75] The one is impressed by
things and receives their form without their matter. The other is free
from impression. It thinks its system of concepts freely on the occasion
of the affections of the receptivity. Aristotle is fond of declaring
that knowledge is of the universal, while existence or reality is
individual. It seems to follow that the cleavage between knowledge and
reality is not bridged by the function of [Greek: nous] in relation to
"induction." What is known is not real, and what is real is not known.
The _nodus_[76] has its cause in the double sense of the word
"universal" and a possible solution in the doctrine of [Greek: eidos].
The "form" of a thing constitutes it what it is, and at the same time,
therefore, is constitutive of the group to which it belongs. It has both
individual and universal reference. The individual is known in the
[Greek: eidos], which is also the first universal in which by analysis
higher universals are discoverable. These are predicates of the object
known, ways of knowing it, rather than the object itself. The suggested
solution removes certain difficulties, but scarcely all. On seeing
Callias my perception is of man, not Callias, or even man-Callias. The
recognition of the individual is a matter of his accidents, to which
even sex belongs, and the gap from lowest universal to individual may
still be conceived as unbridged. It is in induction, which claims to
start from particulars and end in universals,[77] that we must, if
anywhere within the confines of logical inquiry, expect to find the
required bridge. The Aristotelian conception of induction, however, is
somewhat ambiguous. He had abandoned for the most part the Platonic
sense of the corresponding verb, viz. to lead forward to the as yet
unknown, and his substitute is not quite clear. It is scarcely the
military metaphor. The adducing of a witness for which he uses the
verb[78] is not an idea that covers all the uses.[79] Perhaps
confrontation with facts is the general meaning. But how does he
conceive of its operation? There is in the first place the action of the
psychological mechanism in the process from discriminative sense upwards
wherein we realize "first" universals.[80] This is clearly an
unreflective, pre-logical process, not altogether lighted up by our
retrojection upon it of our view of dialectical induction based thereon.
The immanent rationality of this first form, in virtue of which at the
stage when intelligence acts freely on the occasion of the datum
supplied it recognizes continuity with its own self-conscious process,
is what gives the dialectical type its meaning. Secondly we have this
dialectical "induction as to particulars by grouping of similars"[81]
whose liability to rebuttal by an exception has been already noted in
connexion with the limits of dialectic. This is the incomplete induction
by simple enumeration which has so often been laughed to scorn. It is a
heuristic process liable to failure, and its application by a nation of
talkers even to physics where non-expert opinion is worthless somewhat
discredited it. Yet it was the fundamental form of induction as it was
conceived throughout the scholastic period. Thirdly we have the limiting
cases of this in the inductive syllogism [Greek: dia pantôn],[82] a
syllogism in the third figure concluding universally, and yet valid
because the copula expresses equivalence, and in analogy[83] in which,
it has been well said, instances are weighed and not counted. In the
former it has been noted[84] that Aristotle's illustration does not
combine particular facts into a lowest concept, but specific concepts
into a generic concept, and[85] that in the construction of definite
inductions the ruling thought with Aristotle is already, though vaguely,
that of causal relation. It appears safer, notwithstanding, to take the
less subtle interpretation[86] that dialectical induction struggling
with instances is formally justified only at the limit, and that this,
where we have exhausted and know that we have exhausted the cases, is in
regard to individual subjects rarely and accidentally reached, so that
we perforce illustrate rather from the definite class-concepts falling
under a higher notion. After all, Aristotle must have had means by
which he reached the conclusions that horses are long-lived and lack
gall. It is only then in the rather mystical relation of [Greek: nous]
to the first type of induction as the process of the psychological
mechanism that an indication of the direction in which the bridge from
individual being to universal knowledge is to be found can be held to
lie.
Summary.
Enough has been said to justify the great place assigned to Aristotle in
the history of logic. Without pressing metaphysical formulae in logic
proper, he analysed formal implication grounded implication as a mode of
knowledge in the rationality of the real, and developed a justificatory
metaphysic. He laid down the programme which the after history of logic
was to carry out. We have of course abandoned particular logical
positions. This is especially to be noted in the theory of the
proposition. The individualism with which he starts, howsoever
afterwards mitigated by his doctrine of [Greek: to ti ên einai] or
[Greek: eidos] constituting the individual in a system of intelligible
relations, confined him in an inadmissible way to the subject-attribute
formula. He could not recognize such vocables as the impersonals for
what they were, and had perforce to ignore the logical significance of
purely reciprocal judgments, such as those of equality. There was
necessarily a "sense" or direction in every proposition, with more than
the purely psychological import that the advance was from the already
mastered and familiar taken as relatively stable, to the new and
strange. Many attributes, too, were predicable, even to the end, in an
external and accidental way, not being derivable from the essence of the
subject. The thought of contingency was too easily applied to these
attributes, and an unsatisfactory treatment of modality followed. It is
indeed the doctrine of the intractability of matter to form that lies at
the base of the paradox as to the disparateness of knowledge and the
real already noted. On the one hand Aristotle by his doctrine of matter
admitted a surd into his system. On the other, he assigned to [Greek:
nous] with its insight into rationality too high a function with regard
to the concrete in which the surd was present, a power to certify the
truth of scientific principles. The example of Aristotle's view of
celestial physics as a science of pure forms exhibits both points. On
the Copernican change the heavenly bodies were recognized as concrete
and yet subject to calculable law. Intelligence had warranted false
principles. The moral is that of the story of the heel of Achilles.
To return to logic proper. The Aristotelian theory of the universal of
science as secure from dependence on its instances and the theory of
linking in syllogism remain a heritage for all later logic, whether
accepted in precisely Aristotle's formula or no. It is because the
intervening centuries had the Aristotelian basis to work on, sometimes
in reduced quantity and corrupt form, but always in some quantity and
some form, that the rest of our logical tradition is what it is. We
stand upon his shoulders.
iii. _Later Greek Logic._
After Aristotle we have, as regards logic, what the verdict of after
times has rightly characterized as an age of _Epigoni_. So far as the
Aristotelian framework is accepted we meet only minor corrections and
extensions of a formal kind. If there is conscious and purposed
divergence from Aristotle, inquiry moves, on the whole, within the
circle of ideas where Aristotelianism had fought its fight and won its
victory. Where new conceptions emerge, the imperfection of the
instruments, mechanical and methodological, of the sciences renders
them unfruitful, until their rediscovery in a later age. We have
activity without advance, diversity without development. Attempts at
comprehensiveness end in the compromises of eclecticism.
The Peripatetics.
Illustrations are not far to seek. Theophrastus and in general the
elder Peripatetics, before the rise of new schools with new lines of
cleavage and new interests had led to new antagonisms and new
alliances, do not break away from the Aristotelian metaphysic. Their
interests, however, lie in the sublunary sciences in which the
substantive achievement of the school was to be found. With
Theophrastus, accordingly, in his botanical inquiries, for example,
the alternatives of classification, the normal sequence of such and
such a character upon such another, the conclusion of rational
probability, are what counts. It is perhaps not wholly fanciful to
connect with this attitude the fact that Aristotle's pupils dealt with
a surer hand than the master with the conclusions from premises of
unlike modality, and that a formal advance of some significance
attributable to Theophrastus and Eudemus is the doctrine of the
hypothetical and disjunctive syllogisms.
The Stoics.
The Stoics are of more importance. Despite the fact that their
philosophic interests lay rather in ethics and physics, their activity
in what they classified as the third department of speculation was
enormous and has at least left ineffaceable traces on the terminology
of philosophy. Logic is their word, and consciousness, impression and
other technical words come to us, at least as technical words, from
Roman Stoicism. Even inference, though apparently not a classical
word, throws back to the Stoic name for a conclusion.[87] In the
second place, it is in the form in which it was raised in connexion
with the individualistic theory of perception with which the Stoics
started, that one question of fundamental importance, viz. that of the
criterion of truth, exercised its influence on the individualists of
the Renaissance. Perception, in the view of the Stoics, at its highest
both revealed and guaranteed the being of its object. Its hold upon
the object involved the discernment that it could but be that which it
purported to be. Such "psychological certainty" was denied by their
agnostic opponents, and in the history of Stoicism we have apparently
a modification of the doctrine of [Greek: phantasia katalêptikê] with
a view to meet the critics, an approximation to a recognition that the
primary conviction might meet with a counter-conviction, and must then
persist undissipated in face of the challenge and in the last resort
find verification in the haphazard instance, under varying conditions,
in actual working. The controversy as to the self-evidence of
perception in which the New Academy effected some sort of conversion
of the younger Stoics, and in which the Sceptics opposed both, is one
of the really vital issues of the decadence.
Another doctrine of the Stoics which has interest in the light of
certain modern developments is their insistence on the place of the
[Greek: lekton] in knowledge. Distinct alike from thing and mental
happening, it seems to correspond to "meaning" as it is used as a
technical phrase now-a-days. This anticipation was apparently sterile.
Along the same lines is their use of the hypothetical form for the
universal judgment, and their treatment of the hypothetical form as
the typical form of inference.
The Stoical categories, too, have an historical significance. They are
apparently offered in place of those of Aristotle, an acquaintance
with whose distinctions they clearly presume. Recognizing a linguistic
side to "logical" theory with a natural development in rhetoric, the
Stoics endeavour to exorcise considerations of language from the
contrasted side. They offer pure categories arising in series, each
successive one presupposing those that have gone before. Yet the
substance, quality, condition absolute ([Greek: pôs echon]) and
condition relative of Stoicism have no enduring influence outside the
school, though they recur with eclectics like Galen. The Stoics were
too "scholastic" in their speculations.
Epicureans.
In Epicureanism logic is still less in honour. The practical end,
freedom from the bondage of things with the peace it brings, is all in
all, and even scientific inquiry is only in place as a means to this
end. Of the apparatus of method the less the better. We are in the
presence of a necessary evil. Yet, in falling back, with a difference,
upon the atomism of Democritus, Epicurus had to face some questions of
logic. In the inference from phenomena to further phenomena positive
verification must be insisted on. In the inference from phenomena to
their non-phenomenal causes, the atoms with their inaccessibility to
sense, a different canon of validity obtains, that of
non-contradiction.[88] He distinguishes too between the inference to
combination of atoms as universal cause, and inference to special
causes beyond the range of sense. In the latter case alternatives may
be acquiesced in.[89] The practical aim of science is as well achieved
if we set forth possible causes as in showing the actual cause. This
pococurantism might easily be interpreted as an insight into the
limitations of inverse method as such or as a belief in the plurality
of causes in Mill's sense of the phrase. More probably it reflects the
fact that Epicurus was, according to tradition through Nausiphanes, on
the whole dominated by the influences that produced Pyrrhonism.
Democritean physics without a calculus had necessarily proved sterile
of determinate concrete results, and this was more than enough to
ripen the naturalism of the utilitarian school into scepticism. Some
reading between the lines of Lucretius has led the "logic" of Epicurus
to have an effect on the modern world, but scarcely because of its
deserts.
The Sceptics.
The school of Pyrrho has exercised a more legitimate influence. Many
of the arguments by which the Sceptics enforced their advocacy of a
suspense of judgment are antiquated in type, but many also are, within
the limits of the individualistic theory of knowledge, quite
unanswerable. Hume had constant recourse to this armoury. The major
premise of syllogism, says the Pyrrhonist, is established inductively
from the particular instances. If there be but one of these uncovered
by the generalization, this cannot be sound. If the crocodile moves
its upper, not its lower, jaw, we may not say that all animals move
the lower jaw. The conclusion then is really used to establish the
major premise, and if we still will infer it therefrom we fall into
the circular proof.[90] Could Mill say more? But again. The inductive
enumeration is either of all cases or of some only. The former is in
an indeterminate or infinite subject-matter impossible. The latter is
invalid.[91] Less familiar to modern ears is the contention that proof
needs a standard or criterion, while this standard or criterion in
turn needs proof. Or still more the dialectical device by which the
sceptic claims to escape the riposte that his very argument presumes
the validity of this or that principle, viz. the doctrine of the
equipollence of counter-arguments. Of course the counter-contention is
no less valid! So too when the reflection is made that scepticism is
after all a medicine that purges out itself with the disease, the
disciple of Pyrrho and Aenesidemus bows and says, Precisely! The
sceptical suspension of judgment has its limits, however. The
Pyrrhonist will act upon a basis of probabilities. Nay, he even treats
the idea of cause[92] as probable enough so long as nothing more than
action upon expectation is in question. He adds, however, that any
attempt to establish it is involved in some sort of dilemma. That, for
instance, cause as the correlate of effect only exists with it, and
accordingly, cause which is come while effect is still to come is
inconceivable.[93] From the subjectivist point of view, which is
manifestly fundamental through most of this, such arguments suasory of
the Pyrrhonist suspense of judgment ([Greek: epochê]) are indeed hard
to answer. It is natural, then, that the central contribution of the
Sceptics to the knowledge controversy lies in the modes ([Greek:
tropoi]) in which the relativity of phenomena is made good, that these
are elaborated with extreme care, and that they have a modern ring and
are full of instruction even to-day. Scepticism, it must be confessed,
was at the least well equipped to expose the bankruptcy of the
post-Aristotelian dogmatism.
It was only gradually that the Sceptic's art of fence was developed.
From the time of Pyrrho overlapping Aristotle himself, who seems to
have been well content to use the feints of more than one school among
his predecessors, while showing that none of them could claim to get
past his guard, down through a period in which the decadent academy
under Carneades, otherwise dogmatic in its negations, supplied new
thrusts and parries, to Aenesidemus in the late Ciceronian age, and
again to Sextus Empiricus, there seems to have been something of
plasticity and continuous progress. In this matter the dogmatic
schools offer a marked contrast. In especial it is an outstanding
characteristic of the younger rivals to Aristotelianism that as they
sprang up suddenly into being to contest the claims of the
Aristotelian system in the moment of its triumph, so they reached
maturity very suddenly, and thereafter persisted for the most part in
a stereotyped tradition, modified only when convicted of indefensible
weakness. The 3rd century B.C. saw in its first half the close of
Epicurus' activity, and the life-work of Chrysippus, the refounder of
Stoicism, is complete before its close. And subsequent variations seem
to have been of a negligible where not of an eclectic character. In
the case of Epicureanism we can happily judge of the tyranny of the
literal tradition by a comparison of Lucretius with the recorded
doctrine of the master. But the rule apparently obtains throughout
that stereotype and compromise offer themselves as the exhaustive
alternative. This is perhaps fortunate for the history of doctrine,
for it produces the commentator, your Aspasius or Alexander of
Aphrodisias, and the substitute for the critic, your Cicero, or your
Galen with his attempt at comprehension of the Stoic categories and
the like while starting from Aristotelianism. Cicero in particular is
important as showing the effect or philosophical eclecticism upon
Roman cultivation, and as the often author and always popularizer of
the Latin terminology of philosophy.
The cause of the stereotyping of the systems, apart from political
conditions, seems to have been the barrenness of science. Logic and
theory of knowledge go together, and without living science, theory of
knowledge loses touch with life, and logic becomes a perfunctory
thing. Under such circumstances speculative interest fritters itself
and sooner or later the sceptic has his way. Plato is full of the
faith of mathematical physics. Aristotle is optimistic of achievement
over the whole range of the sciences. But the divorce of science of
nature from mathematics, the failure of biological inquiry to reach so
elementary a conception as that of the nerves, the absence of
chemistry from the circle of the sciences, disappointed the promise of
the dawn and the relative achievement of the noon-day. There is no
development. Physical science remains dialectical, and a physical
experiment is as rare in the age of Lucretius as in that of
Empedocles. The cause of eclecticism is the unsatisfying character of
the creeds of such science, in conjunction with the familiar law that,
in triangular or plusquam-triangular controversies a common hatred
will produce an alliance based on compromise. A bastard Platonism
through hostility to Stoicism may become agnostic. Stoicism through
hostility to its sceptical critics may prefer to accept some of the
positions of the dogmatic nihilist.
Neoplatonism.
Of the later schools the last to arise was Neoplatonism. The
mathematical sciences, at least, had not proved disappointing. For
those of the school of Plato who refused the apostasy of the new
academy, there was hope either in the mathematical side of the
Pythagoreo-Platonic tradition, or in its ritual and theological side.
Neoplatonism is philosophy become theosophy, or it is the sermon on
the text that God geometrizes. It is of significance in the general
history of thought as the one great school that developed after the
decadence had set in. In its metaphysic it showed no failure in
dialectical constructiveness. In the history of logic it is of
importance because of its production of a whole series of commentators
on the Aristotelian logic. Not only the _Introduction_ of Porphyry,
which had lasting effects on the Scholastic tradition, but the
commentaries of Themistius, and Simplicius. It was the acceptance of
the Aristotelian logic by Neoplatonism that determined the
Aristotelian complexion of the logic of the next age. If Alexander is
responsible for such doctrines as that of the _intellectus
acquisitus_, it is to Porphyry, with his characteristically Platonist
preference for the doctrine of universals, and for classification,
that we owe the scholastic preoccupation with the realist controversy,
and with the _quinque voces_, i.e. the Aristotelian predicables as
restated by Porphyry.