Aristotle
come to the Topica: here I put it forward briefly, in order that the
reader may better understand, by contrast, its extreme antithesis,
viz., Demonstrative Science and Necessary Truth as conceived by
Aristotle. First, instead of two debaters, one of whom sets up a
thesis which he professes to understand and undertakes to maintain,
while the other puts questions upon it,--Demonstrative Science
assumes a teacher who knows, and a learner conscious of ignorance but
wishing to know. The teacher lays down premisses which the learner is
bound to receive; or if they are put in the form of questions, the
learner must answer them as the teacher expects, not according to his
own knowledge. Secondly, instead of the unbounded miscellany of
subjects treated in Dialectic, Demonstrative Science is confined to a
few special subjects, in which alone appropriate premisses can be
obtained, and definitions framed. Thirdly, instead of the several
heterogeneous authorities recognized in Dialectic, Demonstrative
Science has _principia_ of its own, serving as points of departure;
some _principia_ common to all its varieties, others special or
confined to one alone. Fourthly, there is no conflict of authorities
in Demonstrative Science; its propositions are essential, universal,
and true _per se_, from the commencement to the conclusion; while
Dialectic takes in accidental premisses as well as essential.
Fifthly, the _principia_ of Demonstrative Science are obtained from
Induction only; originating in particulars which are all that the
ordinary growing mind can at first apprehend (_notiora nobis_), but
culminating in universals which correspond to the perfection of our
cognitive comprehension (_notiora naturâ_.)[6]
[Footnote 6: Aristot. Topica, VI. iv. p. 141, b. 3-14. [Greek: oi(
polloi\ ga\r ta\ toiau=ta prognôri/zousin; ta\ me\n ga\r tê=s
tuchou/sês, ta\ d' a)kribou=s kai\ perittê=s dianoi/as katamathei=n
e)sti/n.] Compare in Analyt. Post. I. xii. pp. 77-78, the contrast
between [Greek: ta\ mathê/mata] and [Greek: oi( dia/logoi].]
Amidst all these diversities, Dialectic and Demonstrative Science
have in common the process of Syllogism, including such assumptions
as the rules of syllogizing postulate. In both, the conclusions are
hypothetically true (_i.e._ granting the premisses to be so). But, in
demonstrative syllogism, the conclusions are true universally,
absolutely, and necessarily; deriving this character from their
premisses, which Aristotle holds up as the cause, reason, or
condition of the conclusion. What he means by Demonstrative Science,
we may best conceive, by taking it as a small [Greek: te/menos] or
specially cultivated enclosure, subdivided into still smaller
separate compartments--the extreme antithesis to the vast common land
of Dialectic. Between the two lies a large region, neither
essentially determinate like the one, nor essentially indeterminate
like the other; an intermediate region in which are comprehended the
subjects of the treatises forming the very miscellaneous Encyclopædia
of Aristotle. These subjects do not admit of being handled with equal
exactness; accordingly, he admonishes us that it is important to know
how much exactness is attainable in each, and not to aspire to
more.[7]
[Footnote 7: Aristot. Ethic. Nikom. I. p. 1094, b. 12-25; p. 1098, a.
26-b. 8; Metaphys. A. p. 995, a. 15; Ethic. Eudem. I. p. 1216, b.
30-p. 1217, a. 17; Politic. VII. p. 1328, a. 19; Meteorolog. I. p. 338,
a. 35. Compare Analyt. Post. I. xiii. p. 78, b. 32 (with Waitz's
note, II. p. 335); and I. xxvii. p. 87, a. 31.
The passages above named in the Nikomachean Ethica are remarkable:
[Greek: le/goito d' a)\n i(kanô=s, ei) kata\ tê\n u(pokeime/nên
u(/lên diasaphêthei/ê; to\ ga\r a)kribe\s ou)ch o(moi/ôs e)n a(/pasi
toi=s lo/gois e)pizêtête/on, ô(/sper ou)d' e)n toi=s
dêmiourgoume/nois. tê\n a)kri/beian mê\ o(moi/ôs e)n a(/pasin
e)pizêtei=n (chrê/), a)ll' e)n e(ka/stois kata\ tê\n u(pokeime/nên
u(/lên, kai\ e)pi\ tosou=ton e)ph' o(/son oi)kei=on tê=| methodô=|.]
Compare Metaphys. E. p. 1025, b. 13: [Greek: a)podeiknu/ousin ê)\
a)nagkai/oteron ê)\ malakô/teron.]
The different degrees of exactness attainable in different
departments of science, and the reasons upon which such difference
depends are well explained in the sixth book of Mr. John Stuart
Mill's System of Logic, vol. II. chap. iii. pp. 422-425, 5th ed.
Aristotle says that there can be no scientific theory or cognition
about [Greek: to\ sumbebêko/s] which he defines to be that which
belongs to a subject neither necessarily, nor constantly, nor
usually, but only on occasion (Metaphys. E. p. 1026, b. 3, 26, 33; K.
p. 1065, a. 1, meaning [Greek: to\ sumbebêko\s mê\ kath'
au(to/],--Analyt. Post. I. 6, 75, a. 18; for he uses the term in two
different senses--Metaph. [Greek: D]. p. 1025, a. 31). In his view,
there can be no science except about constant conjunctions; and we
find the same doctrine in the following passage of Mr. Mill:--"Any
facts are fitted, in themselves, to be a subject of science, which
follow one another according to constant laws; although those laws
may not have been discovered, nor even be discoverable by our
existing resources. Take, for instance, the most familiar class of
meteorological phenomena, those of rain and sunshine. Scientific
inquiry has not yet succeeded in ascertaining the order of antecedence
and consequence among these phenomena, so as to be able, at least in
our regions of the earth, to predict them with certainty, or even with
any high degree of probability. Yet no one doubts that the phenomena
depend on laws. . . . . Meteorology not only has in itself every
requisite for being, but actually is, a science; though from the
difficulty of observing the facts upon which the phenomena depend (a
difficulty inherent in the peculiar nature of those phenomena), the
science is extremely imperfect; and were it perfect, might probably be
of little avail in practice, since the data requisite for applying its
principles to particular instances would rarely be procurable.
"A case may be conceived of an intermediate character between the
perfection of science, and this its extreme imperfection. It may
happen that the greater causes, those on which the principal part of
the phenomena depends, are within the reach of observation and
measurement; so that, if no other causes intervened, a complete
explanation could be given, not only of the phenomenon in general,
but of all the variations and modifications which it admits of. But
inasmuch as other, perhaps many other, causes, separately
insignificant in their effects, co-operate or conflict in many or in
all cases with those greater causes, the effect, accordingly,
presents more or less of aberration from what would be produced by
the greater causes alone. Now if these minor causes are not so
constantly accessible, or not accessible at all, to accurate
observation, the principal mass of the effect may still, as before,
be accounted for, and even predicted; but there will be variations
and modifications which we shall not be competent to explain
thoroughly, and our predictions will not be fulfilled accurately, but
only approximately.
"It is thus, for example, with the theory of the Tides. . . . . And
this is what is or ought to be meant by those who speak of sciences
which are not exact sciences. Astronomy was once a science, without
being an exact science. It could not become exact until not only the
general course of the planetary motions, but the perturbations also,
were accounted for and referred to their causes. It has become an
exact science because its phenomena have been brought under laws
comprehending the whole of the causes by which the phenomena are
influenced, whether in a great or only in a trifling degree, whether
in all or only in some cases, and assigning to each of those causes
the share of effect that really belongs to it. . . . . The science of
human nature falls far short of the standard of exactness now
realized in Astronomy; but there is no reason that it should not be
as much a science as Tidology is, or as Astronomy was when its
calculations had only mastered the main phenomena, but not the
perturbations."]
In setting out the process of Demonstration, Aristotle begins from
the idea of teaching and learning. In every variety thereof some
_præcognita_ must be assumed, which the learner must know before he
comes to be taught, and upon which the teacher must found his
instruction.[8] This is equally true, whether we proceed (as in
Syllogism) from the more general to the less general, or (as in
Induction) from the particular to the general. He who comes to learn
Geometry must know beforehand the figures called circle and triangle,
and must have a triangular figure drawn to contemplate; he must know
what is a unit or monad, and must have, besides, exposed before him
what is chosen as the unit for the reasoning on which he is about to
enter. These are the _præcognita_ required for Geometry and
Arithmetic. Some _præcognita_ are also required preparatory to any
and all reasoning: _e.g._, the maxim of Identity (fixed meaning of
terms and propositions), and the maxims of Contradiction and of
Excluded Middle (impossibility that a proposition and its
contradictory can either be both true or both false.)[9] The learner
must thus know beforehand certain Definitions and Axioms, as
conditions without which the teacher cannot instruct him in any
demonstrative science.
[Footnote 8: Analyt. Post. I. i. pp. 71-72; Metaphys. A. IX. p. 992,
b. 30.]
[Footnote 9: Aristot. Analyt. Post. I, i. p. 71, a. 11-17. [Greek:
a(/pan ê)\ phê=sai ê)\ a)pophê=sai a)lêthe/s].]
Aristotle, here at the beginning, seeks to clear up a difficulty
which had been raised in the time of Plato as between knowledge and
learning. How is it possible to _learn_ at all? is a question started
in the Menon.[10] You either know a thing already, and, on this
supposition, you do not want to learn it; or you do not know it, and
in this case you cannot learn it, because, even when you have learnt,
you cannot tell whether the matter learnt is what you were in search
of. To this difficulty, the reply made in the Menon is, that you
never _do_ learn any thing really new. What you are said to learn, is
nothing more than reminiscence of what had once been known in an
anterior life, and forgotten at birth into the present life; what is
supposed to be learnt is only the recall of that which you once knew,
but had forgotten. Such is the Platonic doctrine of Reminiscence.
Aristotle will not accept that doctrine as a solution; but he
acknowledges the difficulty, and intimates that others had already
tried to solve it without success. His own solution is that there are
two grades of cognition: (1) the full, complete, absolute; (2) the
partial, incomplete, qualified. What you already know by the first of
these grades, you cannot be said to learn; but you may learn that
which you know only by the second grade, and by such learning you
bring your incomplete cognition up to completeness.
[Footnote 10: Plato, Menon. p. 80.]
Thus, you have learnt, and you know, the universal truth, that every
triangle has its three angles equal to two right angles; but you do
not yet know that A B C, D E F, G H I, &c., have their two angles
equal to two right angles; for you have not yet seen any of these
figures, and you do not know that they _are_ triangles. The moment
that you see A B C, or hear what figure it is, you learn at one and
the same time two facts: first, that it is a triangle; next, by
virtue of your previous cognition, that it possesses the
above-mentioned property. You knew this _in a certain way_ or
incompletely before, by having followed the demonstration of the