When Aristotle called syllogism X6yos, he meant that it is a combination of premises involving a conclusion of necessity.
Nevertheless, deduction or syllogism is not independent of the other processes of inference.
The Posterior Analytics, on demonstrative syllogism, or science; 5.
Secondly, he made no division of logic. In the Categories he distinguished names and propositions for the sake of the classification of names; in the De Interpretatione he distinguished nouns and verbs from sentences with a view to the enunciative sentence: in the Analytics he analysed the syllogism into premisses and premisses into terms and copula, for the purpose of syllogism.
In this way the Presocratics and Sophists, and still more Socrates and Plato, threw out hints on sense and reason, on inferential processes and scientific methods which may be called anticipations of logic. But Aristotle was the first to conceive of reasoning itself as a definite subject of a special science, which he called analytics or analytic science, specially designed to analyse syllogism and especially demonstrative syllogism, or science, and to be in fact a science of sciences.
The Prior Analytics, on syllogism; 4.
The Topics, on dialectical syllogism; or argument; 6.
The Sophistical Elenchi, on sophistical or contentious syllogism, or sophistical fallacies.
The main problem which Aristotle set before him was the analysis of syllogism, which he defined as " reasoning in which certain things having been posited something different from them of necessity follows by their being those things " (Prior Analytics, i.
24) we owe the triple distinction into inference from particular to particular (irapf16ecy i ug, example, or what we call " analogy "), inference from particular to universal (i raywy17, induction), and inference from universal to particular (ouXXoyco-Os, syllogism, or deduction).
But he thought that inferences other than syllogism are imperfect; that analogical inference is rhetorical induction; and that induction, through the necessary preliminary of syllogism and the sole process of ascent from sense, memory and experience to the principles of science, is itself neither reasoning nor science.
To be perfect he thought that all inference must be reduced to syllogism of the first figure, which he regarded as the specially scientific inference.
Accordingly, the syllogism appeared to him to be the rational process (wet X6yov), and the demonstrative syllogism fran inductively discovered principles to be science (Eirurrr7un).
Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.
As then the reasoning of the syllogism was the main problem of Aristotle's logic, what was his analysis of it?
In distinguishing inner and outer reason, or reasoning and discourse, he added that it is not to outer reason but to inner reason in the soul that demonstration and syllogism are directed (Post.
In the Analytics he took the final step of originating the logical analysis of the proposition as premise into subject and predicate as terms mediated by the copula, and analysed the syllogism into these elements.
But he laid too much stress on reasoning as syllogism or deduction, and on deductive science; and he laid too much stress on the linguistic analysis of rational discourse into proposition and terms. These two defects remain ingrained in technical logic to this day.
Bacon, like Aristotle, was anticipated in this or that point; but, as Aristotle was the first to construct a system of deduction in the syllogism and its three figures, so Bacon was the first to construct a system of induction in three ministrations, in which the requisites of induction, hitherto recognized only in sporadic hints, were combined for the first time in one logic of induction.
Aristotle's logic has often been called formal logic; it was really a technical logic of syllogism analysed into linguistic elements, and of science rested on an empirical basis.
But the same passage relegates conceptions and their combinations to the De Anima, and confines the De Inter pretatione to names and propositions in conformity with the linguistic analysis which pervades the logical treatises of Aristotle, who neither brought his psychological distinction between conceptions and their combinations into his logic, nor advanced the combinations of conceptions as a definition of judgment (Kcp16cs), nor employed the mental distinction between conceptions and judgments as an analysis of inference, or reasoning, or syllogism: he was no conceptual logician.
The science of inference again rightly emphasizes the formal thinking of the syllogism in which the combination of premises involves the conclusion.
Moreover, the study of analogical and inductive inference is necessary to that of the syllogism itself, because they discover the premises of syllogism.
The formal thinking of syllogism alone is merely necessary consequence; but when its premises are necessary principles, its conclusions are not only necessary consequents but also necessary truths.
Hence the manner in which induction aided by identification discovers necessary principles must be studied by the logician in order to decide when the syllogism can really arrive at necessary conclusions.
Aristotle's was a logic which steered, as Trendelenburg has shown, between Kantian formalism and Hegelian metaphysics; it was a logic which in the Analytics investigated the syllogism as a means to understanding knowledge and science: it was a logic which, starting from the psychological foundations of sense, memory and experience, built up the logical structure of induction and deduction on the profoundly Aristotelian principle that " there is no process from universals without induction, and none by induction without sense."
False Views of Syllogism arising from False Views of Judg- ment.
But as yet he had only glimpses of a logical method which should invigorate the syllogism by the co-operation of ancient geometry and modern algebra.
Whately defined it as "a conditional syllogism with two or more antecedents in the major and a disjunctive minor."
Logic falls, according to Ramus, into two parts - invention (treating of the notion and definition) and judgment (comprising the judgment proper, syllogism and method).
'AvaX uru oa bo rEpa: Analytica Posteriora: On demonstration, or demonstrative or scientific syllogism (hirobec u, rO Elktlkos 71-c0-T771.1.0PLKOS (7vXXoyLap)S).
T07ru: To pica : On dialectical syllogism (ScaXEKTLKOS auXAoyLapbs), so called from consisting mainly of commonplaces (rolrol, loci), or general sources of argument.
ZocearLKoL g XEyXoL: Sophistici Elenchi: On sophistic (roccaTLKOS) or eristic syllogism (EpLaTLKOS avXAoytapos), so called from the fallacies used by sophists in refutation (€AEy X os) of their opponents.
So also he might add the appendix to the Sophistical Elenchi, long after he had written that book, and perhaps, to judge from its being a general claim to have discovered the syllogism, when the founder of logic had more or less realized that he had written a number of connected treatises on reasoning.
In analysing the syllogism, he first says that a premiss is an affirmative or negative sentence, and then that a term is that into which a premiss is dissolved, i.e.
Because the crossing of terms in a syllogism requires it.
In the syllogism " Every man is mortal and Socrates is a man," if in the minor premiss the copula " is " were not disengaged from the predicate " man," there would not be one middle term " man " in the two premisses.
It is not necessary in every proposition, but it is necessary in the arrangement of a syllogism, to extricate the terms of its propositions from the copula; e.g.
Example (7rapabayma) is not called rhetorical induction, and consideration (EVBuµnya) is not called rhetorical syllogism, as they are in the Rhetoric, and in the Analytics.
Induction (E7rayo.y17) and syllogism (ovXXcytcr oc), the general forms of inference, do not occur in the Rhetoric to Alexander.
We cannot write a history of the varied origin of logic, beyond putting the rudimentary logic of the proposition in the De Interpretatione before the less rudimentary theory of categories as significant names capable of becoming predicates in the Categories, and before the maturer analysis of the syllogism in the Analytics.
As he says at the end of the Sophistical Elenchi on the syllogism, he had no predecessor, but took pains and laboured a long time in investigating it.
He got so far as gradually to write short discourses and long treatises, which we, not he, now arrange in the order of the Categories or names; the De Interpretatione on propositions; the Analytics, Prior on syllogism, Posterior on scientific syllogism; the Topics on dialectical syllogism; the Sophistici Elenchi on eristical or sophistical syllogism; and, except that he had hardly a logic of induction, he covered the ground.
Then Aristotle himself regarded rhetoric as partly science and partly dialectic, perhaps he would have said that his works on reasoning are some science and others not, and that, while the investigation of syllogism with a view to scientific syllogism in the Analytics is analytic science, the investigation of dialectical syllogism, in the Topics, with its abuse, eristical syllogism, in the Sophistici Elenchi, is dialectic. At any rate, these miscellaneous works on reasoning have no right to stand first in Aristotle's writings under any one name, logic or Organon.
Logically regarded, the origin of all teaching and learning of an intellectual kind is a process of induction (Enraywyi) from particulars to universal, and of syllogism (ovXXoyco-p5s) from universal to further particulars; induction, whenever it starts from sense, becomes the origin of scientific knowledge (bruiriran); while there is also a third process of example (1rapaSeiyµa) from particular to particular, which produces only persuasion.
In acquiring scientific knowledge, syllogism cannot start from universals without induction, nor induction acquire universals without sense.
At the same time, there are three species of syllogism, scientific, dialectical and eristical or sophistical; and in consequence there are different ways of acquiring premisses.
Nor does the process of acquiring the premisses of eristical syllogism, which is fallacious either in its premisses or in its process, differ, except that, when the premisses are fallacious, the dialectical interrogations must be such as to cause this fallacy.
Hence, as science and dialectic are different, so scientific induction and syllogism must be distinguished from dialectical induction and syllogism.
But it is by a different process of sense, memory, experience, induction, intelligence, syllogism, that science becomes knowledge of real causes, of real effects, and especially of real essences from which follow real consequences, not beyond, but belonging to real substances.
Otherwise, logical ground remains logical ground, as in any noncausal syllogism, such as the familiar one from " All men are mortal," which causes me to know that I shall die, without telling me the cause of death.
Under the head of notion are considered, firstly, the subjective forms of conception, judgment and syllogism; secondly, their realization in objects as mechanically, chemically or teleologically constituted; and thirdly, the idea first of life, and next of science, as the complete interpenetration of thought and objectivity.
Judgment is completed in the syllogism; the syllogistic form as the perfection of subjective thought passes into objectivity, where it first appears embodied in a mechanical system; and the teleological object, in which the members are as means and end, leads up to the idea of life, where the end is means and means end indissolubly till death.
Thus in the example of syllogism given above, " border-war between Thebes and Athens " is the minor term, " evil " the major term, and " border-war " the middle term.
Deduction or syllogism is superior to analogy and induction in combining premises so as to involve or contain the conclusion.
The truth is that, though the premises contain the conclusion, neither premise alone contains it, and a man who knows both but does not combine them does not draw the conclusion; it is the synthesis of the two premises which at once contains the conclusion and advances our knowledge; and as syllogism consists, not indeed in the discovery, but essentially in the synthesis of two premises, it is an inference and an advance on each premise and on both taken separately.
As again the synthesis contains or involves the conclusion, syllogism has the advantage of compelling assent to the consequences of the premises.
Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.
'AvaXurcxa 7rpbmmpa: Analytica Priora: On syllogism, with a view to demonstration.
Inference from universal to particular by Syllogism, descendendo.