If their view is correct, the theory appears to be a remarkable example of deductive reasoning.
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.
But an inductive and deductive treatment, both comprehensive and in due proportion, does not as yet (19to) exist, and awaits fuller external evidence.'
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.
It may be held to recognize the validity of divine laws, for example; or it may be confined to the deductive process of applying those laws to particular cases, known as "cases of conscience" (see Casuistry).
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.
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.
Hence, without his saying it in so many words, Aristotle's logic perforce became a logic of deductive reasoning, or syllogism.
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.
Among the dialecticians, Socrates had used inductive arguments to obtain definitions as data of deductive arguments against his opponents, and Plato had insisted on the processes of ascending to and descending from an unconditional principle by the power of giving and receiving argument.
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.
R9) with a detailed system of empiricism, according to which sense is the primary knowledge of particulars, memory is the retention of a sensation, experience is the sum of many memories, induction infers universals, and intelligence is the true apprehension of the universal principles of science, which is rational, deductive, demonstrative, from empirical principles.
Beneath deductive logic, in the logic of Aristotle and the canonic of the Epicureans, there already lay the basis of empirical logic: sensory experience is the origin of all inference and science.
The founder of logic anticipated the latest logic of science, when he recognized, not only the deduction of mathematics, but also the experience of facts followed by deductive explanations of their causes in physics.
The consilience of empirical and deductive processes was an Aristotelian discovery, elaborated by Mill against Bacon.
On the whole, however, Aristotle, Bacon and Mill, purged from their errors, form one empirical school, gradually growing by adapting itself to the advance of science; a school in which Aristotle was most influenced by Greek deductive Mathematics, Bacon by the rise of empirical physics at the Renaissance, and Mill by the Newtonian combination of empirical facts and mathematical principles in the Principia.
Lastly, the science of inference is not indeed the science of sensation, memory and experience, but at the same time it is the science of using those mental operations as data of inference; and, if logic does not show how analogical and inductive inferences directly, and deductive inferences indirectly, arise from experience, it becomes a science of mere thinking without knowledge.
Sense is the evidence of inference; directly of analogical and inductive, directly or indirectly of deductive, inference; and therefore, if logic refuses to include sensory beliefs among judgments, it will omit the fundamental constituents of inference, inference will no longer consist of judgments but of sensory beliefs plus judgments, and the second part of logic, the logic of judgment, the purpose of which is to investigate the constituents of inference, will be like Hamlet without the prince of Denmark.
But in the sense in which deductive analysis is opposed to deductive synthesis, analysis is deduction from real consequence as logical ground principiatum as principium) cognoscendi) to real ground (principium essendi), e.g.
As the second premise is supposed to be convertible, he reduced the inductive to a deductive syllogism as follows: Every S is P. Every S is P.
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.
All we aspire to add is that, in order to attain to real truth, we must proceed gradually from sense, memory and experience through analogical particular inference, to inductive and deductive universal inference or reasoning.
If, and only if, the study of deductive logic begins with Aristotle, and the study of inductive logic with Aristotle and Bacon, it will be profitable to add the works of the following recent German and English authors: Authorities.
Stanley Jevons, The Principles of Science (3rd ed., London, 1879); Studies in Deductive Logic (London, 1880); H.
Meyer, Ueberweg's System der Logik, fiinfte vermehrte Auflage (Bonn, 1882); Max Miller, Science of Thought (London, 1887); Carveth Read, On the Theory of Logic (London, 1878); Logic, Deductive and Inductive (2nd ed., London, 1901); E.
Rather a scientific process, which as experiential may be called inductive, but which is in other regards deductive as syllogism, is set up in constrast to syllogism YvI.
The reformed Aristotelian logic of the first-named with its inductio demonstrativa, the mathematicophysical analysis followed by synthesis of the second, the exclusiva, or method of exclusions of the last, agree at least in this, that the method of science is one and indivisible, while containing both an inductive and a deductive moment.
Equally, too, the deductive character, apparently in intention as well as in actual fact, of Mill's experimental methods fails to recall the point of theory that the process is essentially one from particular to particular.
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.
But he was certainly not ignorant of what may be called a deductive method, and of a kind of hypothesis.
His Studies in Deductive Logic, consisting mainly of exercises and problems for the use of students, was published in 1880.
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.