i. _Before Aristotle_
The physical philosophers.
Logic needs as its presuppositions that thought should distinguish
itself from things and from sense, that the problem of validity should
be seen to be raised in the field of thought itself, and that analysis
of the structure of thought should be recognized as the one way of
solution. Thought is somewhat late in coming to self-consciousness.
Implied in every contrast of principle and fact, of rule and
application, involved as we see after the event, most decisively when we
react correctly upon a world incorrectly perceived, thought is yet not
reflected on in the common experience. Its so-called natural logic is
only the potentiality of logic. The same thing is true of the first
stage of Greek philosophy. In seeking for a single material principle
underlying the multiplicity of phenomena, the first nature-philosophers,
Thales and the rest, did indeed raise the problem of the one and the
many, the endeavour to answer which must at last lead to logic. But it
is only from a point of view won by later speculation that it can be
said that they sought to determine the predicates of the single
subject-reality, or to establish the permanent subject of varied and
varying predicates.[1] The direction of their inquiry is persistently
outward. They hope to explain the opposed appearance and reality wholly
within the world of things, and irrespective of the thought that thinks
things. Their universal is still a material one. The level of thought on
which they move is still clearly pre-logical. It is an advance on this
when Heraclitus[2] opposes to the eyes and ears which are bad witnesses
"for such as understand not their language" a common something which we
would do well to follow; or again when in the incommensurability of the
diagonal and side of a square the Pythagoreans stumbled upon what was
clearly neither thing nor image of sense, but yet was endowed with
meaning, and henceforth were increasingly at home with symbol and
formula. So far, however, it might well be that thought,
contradistinguished from sense with its illusions, was itself
infallible. A further step, then, was necessary, and it was taken at any
rate by the Eleatics, when they opposed their thought to the thought of
others, as the way of truth in contrast to the way of opinion. If
Eleatic thought stands over against Pythagorean thought as what is valid
or grounded against what is ungrounded or invalid, we are embarked upon
dialectic, or the debate in which thought is countered by thought.
Claims to a favourable verdict must now be substantiated in this field
and in this field alone. It was Zeno, the controversialist of the
Eleatic school, who was regarded in after times as the "discoverer" of
dialectic.[3]
Zeno's amazing skill in argumentation and his paradoxical conclusions,
particular and general, inaugurate a new era. "The philosophical
mind," says waiter Pater,[4] "will perhaps never be quite in health,
quite sane or natural again." The give and take of thought had by a
swift transformation of values come by something more than its own.
Zeno's paradoxes, notably, for example, the puzzle of Achilles and the
Tortoise, are still capable of amusing the modern world. In his own
age they found him imitators. And there follows the sophistic
movement.
The Sophists.
The sophists have other claims to consideration than their service to
the development of logic. In the history of the origins of logic the
sophistic age is simply the age of the free play of thought in which
men were aware that in a sense anything can be debated and not yet
aware of the sense in which all things cannot be so. It is the age of
discussion used as a universal solvent, before it has been brought to
book by a deliberate unfolding of the principles of the structure of
thought determining and limiting the movement of thought itself. The
sophists furthered the transition from dialectic to logic in two ways.
In the first place they made it possible. Incessant questioning leads
to answers. Hair-splitting, even when mischievous in intent, leads to
distinctions of value. Paradoxical insistence on the accidents of
speech-forms and thought-forms leads in the end to perception of the
essentials. Secondly they made it necessary. The spirit of debate run
riot evokes a counter-spirit to order and control it. The result is a
self-limiting dialectic. This higher dialectic is a logic. It is no
accident that the first of the philosophical sophists, Gorgias, on the
one hand, is Eleatic in his affinities, and on the other raises in the
characteristic formula of his intellectual nihilism[5] issues which
are as much logical and epistemological as ontological. The meaning of
the copula and the relation of thoughts to the objects of which they
are the thoughts are as much involved as the nature of being. It is
equally no accident that the name of Protagoras is to be connected, in
Plato's view at least, with the rival school of Heracliteans. The
problems raised by the relativism of Protagoras are no less
fundamentally problems of the nature of knowledge and of the structure
of thought. The _Theaetetus_ indeed, in which Plato essays to deal
with them, is in the broad sense of the word logical, the first
distinctively logical treatise that has come down to us. Other
sophists, of course, with more practical interests, or of humbler
attainments, were content to move on a lower plane of philosophical
speculation. As presented to us, for example, in Plato's surely not
altogether hostile caricature in the _Euthydemus_, they mark the
intellectual preparation for, and the moral need for, the advance of
the next generation.
Socrates.
Among the pioneers of the sophistic age Socrates stands apart. He has
no other instrument than the dialectic of his compeers, and he is as
far off as the rest from a criticism of the instrument, but he uses it
differently and with a difference of aim. He construes the give and
take of the debate-game with extreme rigour. The rhetorical element
must be exorcised. The set harangue of teacher to pupil, in which
steps in argument are slurred and the semblance of co-inquiry is
rendered nugatory, must be eliminated. The interlocutors must in truth
render an account under the stimulus of organized heckling from their
equals or superiors in debating ability. And the aim is heuristic,
though often enough the search ends in no overt positive conclusion.
Something can be found and something is found. Common names are fitted
for use by the would-be users being first delivered from abortive
conceptions, and thereupon enabled to bring to the birth living and
organic notions.
Aristotle would assign to Socrates the elaboration of two logical
functions:--general definition and inductive method.[6] Rightly, if we
add that he gives no theory of either, and that his practical use of
the latter depends for its value on selection.[7] It is rather in
virtue of his general faith in the possibility of construction, which
he still does not undertake, and because of his consequent insistence
on the elucidation of general concepts, which in common with some of
his contemporaries, he may have thought of as endued with a certain
objectivity, that he induces the controversies of what are called the
Socratic schools as to the nature of predication. These result in the
formulation of a new dialectic or logic by Plato. Manifestly Socrates'
use of certain forms of argumentation, like their abuse by the
sophists, tended to evoke their logical analysis. The use and abuse,
confronted one with the other, could not but evoke it.
Antisthenes.
The one in the many, the formula which lies at the base of the
possibility of predication, is involved in the Socratic doctrine of
general concepts or ideas. The nihilism of Gorgias from the Eleatic
point of view of bare identity, and the speechlessness of Cratylus
from the Heraclitean ground of absolute difference, are alike
disowned. But the one in the many, the identity in difference, is so
far only postulated, not established. When the personality of Socrates
is removed, the difficulty as to the nature of the Socratic universal,
developed in the medium of the individual processes of individual
minds, carries disciples of diverse general sympathies, united only
through the practical inspiration of the master's life, towards the
identity-formula or the difference-formula of other teachers. The
paradox of predication, that it seems to deny identity, or to deny
difference, becomes a _pons asinorum_. Knowledge involves synthesis or
nexus. Yet from the points of view alike of an absolute pluralism, of
a flux, and of a formula of bare identity--and _a fortiori_ with any
blending of these principles sufficiently within the bounds of
plausibility to find an exponent--all knowledge, because all
predication of unity, in difference, must be held to be impossible.
Plato's problem was to find a way of escape from this impasse, and
among his Socratic contemporaries he seems to have singled out
Antisthenes[8] as most in need of refutation. Antisthenes, starting
with the doctrine of identity without difference, recognizes as the
only expression proper to anything its own peculiar sign, its name.
This extreme of nominalism for which predication is impossible is,
however, compromised by two concessions. A thing can be described as
like something else. And a compound can have a [Greek: logos] or
account given of it by the (literally) adequate enumeration of the
names of its simple elements or [Greek: prôta].[9] This analytical
[Greek: logos] he offers as his substitute for knowledge.[10] The
simple elements still remain, sensed and named but not known. The
expressions of them are simply the speech-signs for them. The account
of the compound simply sets itself taken piecemeal as equivalent to
itself taken as aggregate. The subject-predicate relation fails really
to arise. Euclides[11] found no difficulty in fixing Antisthenes' mode
of illustrating his simple elements by comparison, and therewith
perhaps the "induction" of Socrates, with the dilemma; so far as the
example is dissimilar, the comparison is invalid; so far as it is
similar, it is useless. It is better to say what the thing is. Between
Euclides and Antisthenes the Socratic induction and universal
definition were alike discredited from the point of view of the
Eleatic logic. It is with the other point of doctrine that Plato comes
to grips, that which allows of a certainty or knowledge consisting in
an analysis of a compound into simple elements themselves not known.
The syllable or combination is, he shows, not known by resolution of
it into letters or elements themselves not known. An aggregate
analysed into its mechanical parts is as much and as little known as
they. A whole which is more than its parts is from Antisthenes' point
of view inconceivable. Propositions analytical of a combination in the
sense alleged do not give knowledge. Yet knowledge is possible. The
development of a positive theory of predication has become quite
crucial.
Plato.
Plato's logic supplies a theory of universals in the doctrine of ideas.
Upon this it bases a theory of predication, which, however, is
compatible with more than one reading of the metaphysical import of the
ideas. And it sets forth a dialectic with a twofold movement, towards
differentiation and integration severally, which amounts to a
formulation of inference. The more fully analysed movement, that which
proceeds downward from less determinate to more determinate universals,
is named Division. Its associations, accordingly, are to the modern ear
almost inevitably those of a doctrine of classification only. Aristotle,
however, treats it as a dialectical rival to syllogism, and it
influenced Galilei and Bacon in their views of inference after the
Renaissance. If we add to this logic of "idea," judgment and inference,
a doctrine of categories in the modern sense of the word which makes the
_Theaetetus_, in which it first occurs, a forerunner of Kant's _Critique
of Pure Reason_, we have clearly a very significant contribution to
logic even in technical regard. Its general philosophical setting may be
said to enhance its value even as logic.