For De Maillet not only has a definite conception of the plasticity of living things, and of the production of existing species by the modification of their predecessors, but he clearly apprehends the cardinal maxim of modern geological science, that the explanation of the structure of the globe is to be sought in the deductive application to geological phenomena of the principles established inductively by the study of the present course of nature.
Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.
If their view is correct, the theory appears to be a remarkable example of deductive reasoning.
By his method of observation and induction as thus explained, his philosophy will be found to be marked off very clearly, on the one hand from the deductive construction of notions of an absolute system, as represented either by Schelling or Hegel, which Cousin regards as based simply on hypothesis and abstraction, illegitimately obtained; and on the other, from that of Kant, and in a sense, of Sir W.
He lectured on logic, deductive and inductive, systematic psychology and ethical theory.
But an inductive and deductive treatment, both comprehensive and in due proportion, does not as yet (19to) exist, and awaits fuller external evidence.'
Stanley Jevons, The Principles of Science (3rd ed., London, 1879); Studies in Deductive Logic (London, 1880); H.
But he was certainly not ignorant of what may be called a deductive method, and of a kind of hypothesis.
Celestial Mechanics is, strictly speaking, that branch of applied mathematics which, by deductive processes, derives the laws of motion of the heavenly bodies from their gravitation towards each other, or from the mutual action of the parts which form them.
But while we have yet to wait for that expansion of principal triangulation which will bring Asia into connexion with Europe by the direct process of earth measurement, a topobetween graphical connexion has been effected between Russian Russ/an and Indian surveys which sufficiently proves that the and deductive methods employed by both countries for the Indian determination of the co-ordinate values of fixed points so surveys.
Thus, while arithmetic may be defined as that branch of deductive reasoning concerning classes and relations which is concerned with the establishment of propositions concerning cardinal numbers, it must be added that the introduction of cardinal numbers makes no great break in this general science.
Whatever be the historical worth of this story, it may safely be said that it cannot be disproved by deductive reasoning from the premisses of abstract logic. The most we can do is to assert that a universe in which such things are liable to happen on a large scale is unfitted for the practical application of the theory of cardinal numbers.
Mechanics (including dynamical astronomy) is that subject among those traditionally classed as "applied" which has been most completely transfused by mathematics - that is to say, which is studied with the deductive spirit of the pure mathematician, and not with the covert inductive intention overlaid with the superficial forms of deduction, characteristic of the applied mathematician.
Ratiocinari, to use the reasoning faculty) is classified from Aristotle downwards as deductive (from generals to particulars) and inductive (from particulars to generals); see Logic, Induction, Syllogism.
These attempts at the unification of algebra, and its separation from other branches of mathematics, have usually been accompanied by an attempt to base it, as a deductive science, on certain fundamental laws or general rules; and this has tended to increase its difficulty.
More particularly by the confusion in which he left the relation between the two logical principles of identity and of sufficient reason underlying respectively analytic and synthetic, deductive and inductive thought, he may be said to have undermined in another way the idealism he strove to establish.
Relative to the uncertain connexion of length, capacity and weight in the ancient metrological systems of the East, Sir Charles Warren, R.E., has obtained by deductive analysis a new equivalent of the original cubit (Palestine Exploration Fund Quarterly, April, July, October 1899).
He asserts that in Scotland the inductive method was unknown, and that although Smith spent some of the most important years of his youth in England, where the inductive method was supreme, he yet adopted the deductive method because it was habitually followed in Scotland.
What may justly be said of Smith is that the deductive bent was not the predominant character of his mind, nor did his great excellence lie in the "dialectic skill" which Buckle ascribes to him.
That Smith does, however, largely employ the deductive method is certain; and that method is legitimate when the premises from which the deduction sets out are known universal facts of human nature and properties of external objects.
Number in arithmetic, magnitude in geometry, stars in astronomy, a man's good in ethics; concentrates itself on the causes and appropriate principles of its subject, especially the definition of the subject and its species by their essences or formal causes; and after an inductive intelligence of those principles proceeds by a deductive demonstration from definitions to consequences: philosophy is simply a desire of this definite knowledge of causes and effects.
It was counteracted to some extent by the study at the universities of the deductive logic of Aristotle and the inductive logic of Bacon, by parts of Mill's own logic, and by the natural realism of Reid, Stewart, and Hamilton, which met Hume's scepticism by asserting a direct perception of the external world.
The work as a whole is a striking example of the weakness of treating economic problems from a purely a priori standpoint by the deductive method.
Deductive or Syllogistic Inference, from universal to particular, e.g.
On the whole, then, analogical, inductive and deductive inferences are not the same but three similar and closely connected processes.
Now, as an inductive combination of premises does not necessarily involve the inductive conclusion, induction normally leads, not to a necessary, but to a probable conclusion; and whenever its probable conclusions become deductive premises, the deduction only involves a probable conclusion.
Necessary principles, discovered by this process of induction and identification, become premises of deductive demonstration to conclusions which are not only necessary consequents on the premises, but also equally necessary in reality.
In fact, analogical, inductive and deductive inferences, though different processes of combining premises to cause different conclusions, are so similar and related, so united in principle and interdependent, so consolidated into a system of inference, that they cannot be completely investigated apart, but together constitute a single subject of science.
Rather it began as a science of reasoning (Xbyos), of syllogism (vvXXoycvA6s), of deductive inference.
As it happened this deductive tendency helped the development of logic. The obscurer premises of analogy and induction, together with the paucity of experience and the backward state of physical science in Aristotle's time would have baffled even his analytical genius.
Aristotle's analysis of the syllogism showed man how to advance by combining his thoughts in trains of deductive reasoning.
The Deductive Syllogism.
The Inductive Syllogism, like the deductive, is first systematized by Aristotle, who described it as o E brawl/Cis ovXXoycaµos.
It connects the moral world by a deductive process with the fundamental idea of knowledge and being; it offers a view of the entire world of human action which at all events aims at being exhaustive; it presents an arrangement of the matter of the science which tabulates its constituents after the model of the physical sciences; and it supplies a sharply defined treatment of specific moral phenomena in their relation to the fundamental idea of human life as a whole.
Modern theoretical astronomy, taken in the most limited sense, is based upon Celestial Mechanics, the science by which, using purely deductive mechanical methods, the laws of motion of the heavenly bodies are derived by deductive methods from their mutual gravitation towards each other.
P p p Although the Socratic induction forms a striking feature of Plato's dialogues, his ideal method of ethics is purely deductive; he admits common sense only as supplying provisional steps and starting-points from which the mind is to ascend to knowledge of absolute good, through which knowledge alone, as he conceives, the lower notions of particular goods are to be truly conceived.
Indeed, he seems himself quite undecided on this question; since, though he generally represents ethical method as deductive, he also speaks of the " original judgment that this action is right and that wrong."
This excess of the deductive spirit explains at once both the merits and the defects of his two great works, which will probably remain political classics, though they are less and less likely to be used as practical guides.
His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880.
The true scientific procedure is by hypothesis followed up and tested by verification; the most powerful instrument is the deductive method, which Bacon can hardly be said to have recognized.
The question therefore arises, how we are to discover "All M is P," and this question Wundt answers by adding an inductive method, which involves inverting the inductive syllogism in the style of Aristotle into a deductive syllogism from a hypothesis in the style of Jevons, thus: - (I) (2) S is P. Every M is P.
The result is that both Sigwart and Wundt transform the inductive process of adducing particular examples to induce a universal law into a deductive process of presupposing a universal law as a ground to deduce particular consequences.