It is a simple premise and yet, at the same time, an article of faith—a faith that the future would be better than the past.
The fact is that the uniformity of nature stands to induction as the axioms of syllogism do to syllogism; they are not premises, but conditions of inference, which ordinary men use spontaneously, as was pointed out in Physical Realism, and afterwards in Venn's Empirical Logic. The axiom of contradiction is not a major premise of a judgment: the dictum de omni et nullo is not a major premise of a syllogism: the principle of uniformity is not a major premise of an induction.
Another important conception connected with the preceding is the infinity of philosophy, which arises out of history and is as it were a reflection from history, varying at every moment and always solving a problem by placing alongside its solution the premise of a new history and therefore of a new problem and a new philosophy.
For in the latter case we possess, according to Hume, no standard of equivalence other than that supplied by immediate observation, and consequently transition from one premise to another by way of reasoning must be, in geometrical matters, a purely verbal process.
But one premise can only reproduce itself in another form, e.g.
Induction and deduction differ still more, and are in fact opposed, as one makes a particular premise the evidence of a universal conclusion, the other makes a universal premise evidence of a particular conclusion.
In indicating specifically, too, the case of conclusion from a copulative major premise with a disjunctive minor, Herbart seems to have suggested the cue for Sigwart's exposition of Bacon's method of exclusions.
Roman bricks appear in its fabric, and premise a Roman station in the vicinity.
Each inference contains three terms. In syllogistic inference the subject of the conclusion is the minor term, and its predicate the major term, while between these two extremes the term common to the two premises is the middle term, and the premise containing the middle and major terms is the major premise, the premise containing the middle and minor terms the minor premise.
Not that these inferences require us to believe, or assume, or premise or formulate this principle either in general, or in its applied forms: the premises are all that any inference needs the mind to assume.
As we see from Lotze's own defence, the conclusion cannot be drawn without another premise or premises to the effect that " S, Q, R, are /, and is the one real subject of M."
This is like Aristotle's inductive syllogism in the arrangement of terms; but, while on the one hand Aristotle did not, like Wundt, confuse it with the third figure, on the other hand Wundt does not, like Aristotle, suppose it to be practicable to get inductive data so wide as the convertible premise, " All S is M, and all M is S," which would at once establish the conclusion, " All M is P."
The "infinity" of the premise is an infinity of subdivisions of a distance which is finite; the "infinity" of the conclusion is an infinity of distance.
Analogical and inductive inference alike begin with a particular premise containing one or more instances; but the former adds a particular premise to draw a particular conclusion, the latter requires a universal premise to draw a universal conclusion.
Even so, however, it starts from a particular premise which only contains many instances, and leaves room to doubt the universality of its conclusions.
In point of fact, he analysed it into premises, but then analysed a premise into terms, which he divided into subject and predicate, with the addition of the copula " is " or " is not."
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.
In rising, however, from particular to universal inference, induction, as we have seen, adds to its particular premise, S is P, a universal premise, every M is similar to S, in order to infer the universal conclusion, every M is P. This universal premise requires a universal conception of a class or whole number of similar particulars, as a condition.
The general idea of all men or the combination that the idea of all men is similar to the idea of particular men would not be enough; the universal premise that all men in fact are similar to those who have died is required to induce the universal conclusion that all men in fact die.
With regard to inference, he remarked that a universal judgment means by " all," not every individual we know, but every individual absolutely, so that, when it becomes a major premise, we know therein every individual universally, not individually, and often do not know a given individual individually until we add a minor premise in a syllogism.
On the one hand, having reduced categorical judgments to an existential form, Brentano proposes to reform the syllogism, with the results that it must contain four terms, of which two are opposed and two appear twice; that, when it is negative, both premises are negative; and that, when it is affirmative, one premise, at least, is negative.
Sigwart, indeed, has missed the essential difference between the categorical and the hypothetical construction of syllogisms. In a categorical syllogism of the first figure, the major premise, " Every M whatever is P," is a universal, which we believe on account of previous evidence without any condition about the thing signified by the subject M, which we simply believe sometimes to be existent (e.g.
Aristotle, indeed, was as well aware as German logicians of the force of convertible premises; but he was also aware that they require no special syllogisms, and made it a point that; in a syllogism from a definition, the definition is the middle, and the definitum the major in a convertible major premise of Barbara in the first figure, e.g.: The interposition of an opaque body is (essentially) deprivation of light.
Whately, on the other hand, proposed an inductive syllogism with the major suppressed, that is, instead of the minor premise above, he supposed a major premise, " Whatever belongs to A, B, C magnets belongs to all."
Reduction he defines as " the framing of possible premises for given propositions, or the construction of a syllogism when the conclusion and one premise is given."
Hence induction cannot be reduced to Aristotle's inductive syllogism, because experience cannot give the convertible premise, " Every S is M, and every M is S "; that "All A, B, C are magnets " is, but that " All magnets are A, B, C " is not, a fact of experience.
A deduction is often like an induction, in inferring from particulars; the difference is that deduction combines a law in the major with the particulars in the minor premise, and infers syllogistically that the particulars of the minor have the predicate of the major premise, whereas induction uses the particulars simply as instances to generalize a law.
As we have seen, Jevons, Sigwart and Wundt all think that induction contains a belief in causation, in a cause, or ground, which is not present in the particular facts of experience, but is contributed by a hypothesis added as a major premise to the particulars in order to explain them by the cause or ground.
Really, we first experience that particular causes have particular effects; then induce that causes similar to those have effects similar to these; finally, deduce that when a particular cause of the kind occurs it has a particular effect of the kind by synthetic deduction, and that when a particular effect of the kind occurs it has a particular cause of the kind by analytic deduction with a convertible premise, as when Newton from planetary motions, like terrestrial motions, analytically deduced a centripetal force to the sun like centripetal forces to the earth.
In all induction the universal is the conclusion, in none a major premise, and in none the ground of either the being or the knowing of the particulars.
Bradley seems to suppose that the major premise of a syllogism must be explicit, or else is nothing at all.
The form of the syllogism is therefore: A is B Major premise C is A Minor „ .'.
No term may be distributed in this conclusion which was not distributed in the premise in which it occurs.
If either premise is particular, the conclusion must be particular .3 2 The following mnemonic hexameter verses are generally given (first apparently in Aldrich's Artis logicae rudimenta) to aid in remembering these moods.
The kind of reasoning which his view of virtuous conduct requires is one in which the ultimate major premise states a distinctive characteristic of some virtue, and one or more minor premises show that such characteristic belongs to a certain mode of conduct under given circumstances; since it is essential to good conduct that it should contain its end in itself, and be chosen for its own sake.
Let us premise, however, that the portions mentioned in the 9th edition of the Ency.
The major premise of syllogism, says the Pyrrhonist, is established inductively from the particular ' 'Errt4 opcc. = " in " as in i raywyi 7, inductio, and - 40pa = - ferentia, as in 8eoopa, differentia.
A premise that has the utmost universality consistent with this view can clearly be of no service for the establishment of a proposition that has gone to the making of it.
In applying this principle of similarity, each of the three processes in its own way has to premise both that something is somehow determined and that something is similar, and by combining these premises to conclude that this is similarly determined to that.
But deduction, starting from a premise about all the members of a class, compels a conclusion about every and each of necessity.
Like induction, it starts from a particular premise, containing one or more examples or instances; but, as it is easier to infer a particular than a universal conclusion, it supplies particular conclusions which in their turn become further particular premises of induction.
But the premise is not that conception; it is a belief that there is a whole number of particulars similar to those already experienced.