THE year 1843 marked the publication of John Stuart Mill's A System of Logic, Ratiocinative and Inductive, Being a Connected View of the Principles of Evidence and the Methods of Scientific Investigation. The book was an instant success. Comte's influence upon John Stuart Mill is betrayed in much of A System of Logic; Mill, however, takes pains to state that his theory of inductive reasoning was the result of his own independent investigation. The fact that John Stuart Mill's great work in the development of opinion had the deepest effect on the thinking world is unquestionable.
[NAMES AND PROPOSITIONS - JOHN STUART MILL - FROM 'A SYSTEM OF LOGIC']
LOGIC is not the science of belief, but the science of proof, or evidence; and its province must be restricted to that portion of our knowledge which consists of inferences from truths previously known, whether those antecedent data be general propositions or particular observations and perceptions. It includes the subservient operations of naming, definition and classification.
A proposition may be defined as 'discourse in which something is affirmed or denied of something.' Every proposition consists of three parts--subject, predicate and copula. The predicate is the name denoting that which is affirmed or denied. The subject is the name denoting the person or thing of which something is affirmed or denied. The copula is the sign denoting that there is affirmation or denial.
Thus in the proposition 'the earth is round,' the predicate is the word 'round,' which denotes the quality affirmed or 'predicted'; the subject is the words 'the earth,' of which the quality is predicted; and the copula is the word 'is,' which is a mark of affirmation.
Every act of belief supposes two nameable things; every proposition consists of two names, and affirms or denies one of these names or the other.
Propositions may be affirmative, e.g. 'Caesar is dead,' or negative, e.g. 'Caesar is not dead.' They may be universal, e.g. 'All men are mortal,' or particular, e.g. 'Some men are mortal, or indefinite, e.g. 'Man is mortal,' or singular, e.g. 'Caesar is mortal.'
When we further examine the general nature of the assertions of propositions, we find that in every proposition is either existence, co-existence, sequence, causation, or resemblance. This five-fold division is an exhaustive classification of matters of fact; of all things that can be believed or tendered for belief, of all questions that can be propounded and all answers that can be returned to them.
A distinction must be drawn between what may be called real and verbal propositions, between such propositions as predicate of the subject more than its name connotes, and such propositions as merely express what is connoted by the significance of the subject name. Thus, 'Man is a rational being' is a verbal proposition; while 'Man is liable to malaria' is a real proposition.
A definition is a proposition declaratory of the meaning of a name, and the meaning of a name is its connotation. The meaning of the word may be expressed by replacing it by two or more words which together cover the same connotation, and a perfect definition declares all the facts which a name signifies. A proposition which defines a name by one of its accidents is 'a description,' not a definition.
THERE are two main types of reasoning: Induction--inference of a proposition from propositions less general; and Ratiocination, or Syllogism--inference of a proposition from propositions equally general or more general. All valid ratiocination may be arranged in certain forms or figures known as syllogisms. A syllogism consists of three propositions, namely, the proposition to be proved, the 'conclusion,' and two other propositions which prove it--the premises. There must be three, and only three terms--the subject and predicate of the conclusion, called respectively the minor and major terms, and another called the 'middle term,' which must not occur in both premises.
If we analyse the process involved in every syllogism we find that it is based on two principles. The first, which is the principle of affirmative syllogisms, is that things which co-exist with the same thing, co-exist with one another. The second, which is the principle of negative syllogisms, is that a thing that co-exists with another thing with which a third thing does not co-exist, is not co-existent with that third thing.
We have now to inquire whether the syllogistic process, that of reasoning from general to particulars, is or is not a process of inference. When we say:
All men are mortal; The king is a man; Therefore, the king is mortal, do the premises prove the conclusion, is there any real inference? It is evident that if the proposition 'all men are mortal' be true the king must be included in the assertion, and therefore the syllogistic process is superfluous. Regarded correctly, the inference is made in the major premise. We know nothing about all men; but from the observation of many men we infer that all men are mortal.
General propositions, therefore, are merely registers of inferences made and short formulae for making more; and the conclusion is not an inference drawn from the formula but an inference drawn according to the formula. The major premise expresses individual cases. The minor premise is the place of comparison.
A, B, C, my father and my forefathers, and an indefinite number of other persons were mortal. The king resembles all these persons in the attributes connoted by the word man. Therefore, he further resembles them in the attribute mortality.
We thus obtain a universal type of the reasoning process. Certain individuals have a given attribute; an individual or individuals resemble the former in certain other attributes; therefore they resemble them also in the given attribute.
Where the resemblances necessary for inference are obvious to the senses, as in the king's resemblance to mortal persons, no difficult deductive process is necessary; but in many cases the required resemblances can only be indirectly established by a train of inductive and deductive processes.
Thus, suppose the syllogism to be 'All arsenic is poisonous.' In this case probably the minor premise would itself require to be established by a syllogistic process thus: Whatever substance gives certain chemical tests is arsenic; this substance gives these tests; therefore this substance is arsenic. Here, therefore, we have two syllogisms, and the major term of each is an induction. In the deductive sciences the processes of induction and deduction are numerous and complicated. It must be noted that even the most deductive sciences start from inductions, and that even the axioms of mathematics are inductions from the evidence of our senses.
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