Aristotle
Aristotle states very clearly:--"We believe everything either through
Syllogism, or from Induction."[63] Here, as well as in several other
passages, he notes the two processes as essentially distinct. The
Syllogism requires in its premisses at least one general proposition;
nor does Aristotle conceive the "generalities as the original
data:"[64] he derives them from antecedent Induction. The two
processes are (as he says) opposite in a certain way; that is, they
are complementary halves of the same whole; Induction being the
establishment of those universals which are essential for the
deductive march of the Syllogism; while the two together make up the
entire process of scientific reasoning. But he forgets or
relinquishes this antithesis, when he presents to us the Inductive
process as a given variety of Syllogism. And the objection to such a
doctrine becomes the more manifest, since in constructing his
Inductive Syllogism, he is compelled to admit either that there is no
middle term, or that the middle term is subject of the conclusion, in
violation of the syllogistic canons.[65]
[Footnote 63: Ibid. II. xxiii. p. 68, b. 13: [Greek: a(/panta ga\r
pisteu/omen ê)\ dia\ sullogismou= ê)\ e)x e)pagôgê=s]. Here Induction
includes Example, though in the next stage he puts the two apart.
Compare Anal. Poster. I. i. p. 71, a. 9.]
[Footnote 64: See Mr. John Stuart Mill's System of Logic, Bk. II. ch.
iii. a. 4, p. 219, 5th ed.]
[Footnote 65: Aldrich (Artis Log. Rudim. ch. iii. 9, 2, p. 175) and
Archbishop Whately (Elem. of Logic, ch. i. p. 209) agree in treating
the argument of Induction as a defective or informal Syllogism: see
also to the same purpose Sir.** W. Hamilton, Lectures on Logic, vol.
i. p. 322. Aldrich treats it as a Syllogism in _Barbara_, with the
minor suppressed; but Whately rejects this, because the minor
necessary to be supplied is false. He maintains that the premiss
suppressed is the major, not the minor. I dissent from both. It
appears to me that the opinion which Whately pronounces to be a
fallacy is the real truth: "Induction is a distinct kind of argument
from the Syllogism" (p. 208). It is the essential property of the
Syllogism, as defined by Aristotle and by every one after him, that
the truth of the conclusion follows _necessarily_ from the truth of
its premisses: that you cannot admit the premisses and reject the
conclusion without contradicting yourself. Now this is what the best
Induction never attains; and I contend that the presence or absence
of this important characteristic is quite enough to constitute "two
_distinct kinds_ of argument." Whately objects to Aldrich (whom
Hamilton defends) for supplying a suppressed _minor_, because it is
"manifestly false" (p. 209). I object to Whately's supplied _major_,
because it is uncertified, and therefore cannot be used to prove any
conclusion. By clothing arguments from Induction in syllogistic form,
we invest them with a character of necessity which does not really
belong to them. The establishment of general propositions, and the
interpretation of them when established (to use the phraseology of
Mr. Mill), must always be distinct mental processes; and the forms
appropriate to the latter, involving necessary sequence, ought not to
be employed to disguise the want of necessity--the varying and
graduated probability, inherent in the former. Mr. Mill says (Syst.
Log. Bk. III. ch. iii. s. 1, p. 343, 5th ed.:)--"As Whately remarks,
every induction is a syllogism with the major premiss suppressed; or
(as I prefer expressing it) every induction may be thrown into the
form of a syllogism, by supplying a major premiss." Even in this
modified phraseology, I cannot admit the propriety of throwing
Induction into syllogistic forms of argument. By doing this we efface
the special character of Induction, as the jump from particular
cases, more or fewer, to an universal proposition comprising them and
an indefinite number of others besides. To state this in forms which
imply that it is a necessary step, involving nothing more than the
interpretation of a higher universal proposition, appears to me
unphilosophical. Mr. Mill says with truth (in his admirable chapter
explaining the real function of the major premiss in a Syllogism, p.
211), that the individual cases are all the evidence which we
possess; the step from them to universal propositions ought not to be
expressed in forms which suppose universal propositions to be already
attained.
I will here add that, though Aldrich himself (as I stated at the
beginning of this note) treats the argument from Induction as a
defective or informal Syllogism, his anonymous Oxonian editor and
commentator takes a sounder view. He says (pp. 176, 177, 184, ed.
1823. Oxon.):--
"The principles acquired by human powers may be considered as
twofold. Some are _intuitive_, and are commonly called Axioms; the
other class of general principles are those acquired by Induction.
But it may be doubted whether this distinction is correct. It is
highly probable, if not certain, that those primary Axioms generally
esteemed _intuitive_, are in fact acquired by an inductive process;
although that process is less discernible, because it takes place
long before we think of tracing the actings of our own minds. It is
often found necessary to facilitate the understanding of those
Axioms, when they are first proposed to the judgment, by
illustrations drawn from individual cases. But whether it is, as is
generally supposed, the mere _enunciation_ of the principle, or the
_principle itself_, which requires the illustration, may admit of a
doubt. It seems probable, however that, such illustrations are
nothing more than a recurrence to the original method by which the
knowledge of those principles was acquired. Thus, the repeated trial
or observation of the necessary connection between mathematical
coincidence and equality, first authorizes the general position or
Axiom relative to that subject. If this conjecture is founded in
fact, it follows that both _primary_ and _ultimate_ principles have
the same nature and are alike acquired by the exercise of the
inductive faculty." "Those who acquiesce in the preceding
observations will feel a regret to find _Induction_ classed among
defective or informal Syllogisms. It is in fact prior in its order to
Syllogism; nor can syllogistic reasoning he carried on to any extent
without previous Induction" (p. 184).]
We must presume Syllogisms without a middle term, when we read:--"The
Syllogism through a middle term is _by nature_ prior, and of greater
cognitive efficacy; but _to us_ the Syllogism through Induction is
plainer and clearer."[66] Nor, indeed, is the saying, when literally
taken, at all well-founded; for the pretended Syllogisms from
Induction and Example, far from being clear and plain, are more
involved and difficult to follow than _Barbara_ and _Celarent_. Yet
the substance of Aristotle's thought is true and important, when
considered as declaring the antithesis (not between varieties of
Syllogisms, but) between Induction and Example on the one part, and
Syllogism (Deduction) on the other. It is thus that he sets out the
same antithesis elsewhere, both in the Analytica Posteriora and the
Topica.[67] Prior and more cognizable _by nature_ or _absolutely_,
prior and more cognizable _to us_ or _in relation to us_--these two
are not merely distinct, but the one is the correlate and antithesis
of the other.
[Footnote 66: Analyt. Prior. II. xxiii. p. 68, b. 35: [Greek: phu/sei
me\n ou)=n pro/teros kai\ gnôrimô/teros o( dia\ tou= me/sou
sullogismo/s, ê(mi=n d' e)narge/steros o( dia\ tê=s e)pagôgê=s.]]
[Footnote 67: Analyt. Post. I. ii. p. 72, a. 2, b. 29; Ethic. Nik.
VI. iii**. p. 1139, b. 28: [Greek: ê( me\n dê\ e)pagôgê\ a)rchê/
e)sti kai\ tou= katho/lou=, o( de\ sullogismo\s e)k tô=n katho/lou.
ei)si\n a)/ra a)rchai\ e)x ô(=n o( sullogismo/s, ô(=n ou)k e)/sti
sullogismo/s; e)pagôgê\ a)/ra.] Compare Topica, I. xii. p. 105, a.
11; VI. iv. pp. 141, 142**; Physica, I. i. p. 184, a. 16; Metaphysic.
E. iv. p. 1029, b**. 4-12. Compare also Trendelenburg's explanation
of this doctrine, Erläuterungen zu den Elementen der Aristotelischen
Logik, sects. 18, 19, 20, p. 33, seq.]
_To us_ the particulars of sense stand first, and are the earliest
objects of knowledge. _To us_, means to the large variety of
individual minds, which grow up imperceptibly from the simple
capacities of infancy to the mature accomplishments of adult years;
each acquiring its own stock of sensible impressions, remembered,
compared, associated; and each learning a language, which both
embodies in general terms and propositions the received
classification of objects, and communicates the current emotional
beliefs. We all begin by being learners; and we ascend by different
paths to those universal notions and beliefs which constitute the
common fund of the advanced intellect; developed in some minds into
_principia_ of philosophy with their consequences. _By nature_, or
_absolutely_, these _principia_ are considered as prior, and as
forming the point of departure: the advanced position is regarded as
gained, and the march taken is not that of the novice, but that of
the trained adult, who having already learnt much, is doubly equipped
either for learning more or for teaching others; who thus stands on a
summit from whence he surveys nature as a classified and coherent
whole, manifesting herself in details which he can interpret and
sometimes predict. The path of knowledge, seen _relatively to us_, is
one through particulars, by way of example to fresh particulars, or
by way of induction to universals. The path of knowledge, _by nature_
or _absolutely_, is from universals by way of deduction either to new
universals or to new particulars. By the cognitive _nature_ of man,
Aristotle means the full equipment, of and for cognition, which our
mature age exhibits; _notiora naturâ_ are the acquisitions, points of
view, and processes, familiar in greater or less perfection to such
mature individuals and societies. _Notiora nobis_ are the facts and
processes with which all of us begin, and which belong to the
intellect in its highest as well as its lowest stage; though, in the
higher stages, they are employed, directed, and modified, by an
acquired intellectual capital, and by the permanent machinery of
universal significant terms in which that capital is invested.
Such is the antithesis between _notiora naturâ_ (or _simpliciter_)
and _notiora nobis_ (or _quoad nos_), which Aristotle recognizes as a
capital point in his philosophy, and insists upon in many of his
writings. The antithesis is represented by Example and Induction, in
the point of view--_quoad nos_--last mentioned; by Syllogism or
Deduction, in the other point of view--_naturâ_. Induction (he
says),[68] or the rising from particulars to universals, is plainer,
more persuasive, more within the cognizance of sensible perception,
more within the apprehension of mankind generally, than Syllogism;
but Syllogism is more cogent and of greater efficacy against
controversial opponents. What he affirms here about Induction is
equally true about the inference from Example, that is, the inference
from one or some particulars, to other analogous particulars; the
rudimentary intellectual process, common to all human and to many
animal minds, of which Induction is an improvement and an exaltation.
While Induction will be more impressive, and will carry assent more
easily with an ordinary uncultivated mind, an acute disputant may
always deny the ultimate inference, for the denial involves no
contradiction. But the rightly constructed Syllogism constrains
assent;[69] the disputant cannot grant the premisses and deny the