When Aristotle called syllogism X6yos, he meant that it is a combination of premises involving a conclusion of necessity.
Moreover, the study of analogical and inductive inference is necessary to that of the syllogism itself, because they discover the premises of syllogism.
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.
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.
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.
Inference from universal to particular by Syllogism, descendendo.
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 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.
False Views of Syllogism arising from False Views of Judg- ment.
Logic falls, according to Ramus, into two parts - invention (treating of the notion and definition) and judgment (comprising the judgment proper, syllogism and method).
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.
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.
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.
In order to acquire the knowledge of the true and primary principles of scientific knowledge, and especially the intelligence of the universal essence of the subject, which is always true, the process of knowledge consists of (I) sense (a'lcO o s), which receives the essence as individual, (2) memory (uvi j), which is a retention of sensible impression, (3) experience (cµirecpia),which consists of a number of similar memories, (4) induction (brayw-y), which infers the universal as a fact (TO iTC), (5) intellect (vas), which apprehends the principle (apxit); because it is a true apprehension that the universal induced is the very essence and formal cause of the subject: thereupon, scientific syllogism (i rcnf µovucos vvXXoycvµos), making the definition (opeg ios) of this essence the middle term (TO, c Vov), becomes a demonstration (6.7rOSee es) of the consequences which follow from the essence in the conclusion.
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.
Nevertheless, deduction or syllogism is not independent of the other processes of inference.
Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.
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 Posterior Analytics, on demonstrative syllogism, or science; 5.
The Topics, on dialectical syllogism; or argument; 6.
The Sophistical Elenchi, on sophistical or contentious syllogism, or sophistical fallacies.