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[This diagram exhibits not the argument itself, but the facts which the statements of the argument might collectively represent.? Hence, if an inference by added determinant is to be valid, the determinant added must have precisely the same application in both cases. Its application must not vary with the significance of the term it qualifies. The following inference by added determinant is perfectly valid :

A St. Bernard is a dog.

Therefore a hungry St. Bernard is a hungry dog.

8. Examine the inference :

'All judges are lawyers.

Therefore a majority of judges is a majority of lawyers.'

This is a fallacious instance of a kind of inference (miscalled immediate) usually known as Inference by Complex Conception. Here the subject and predicate are made determinants of a third expression. Here again the validity of the inference depends on the unambiguous fixity in the application of this third expression. The following inference 'by complex conception' is valid:

Oranges are fruit.

Therefore a barrel of oranges is a barrel of fruit.

But fallacy arises so soon as the expression (like the word 'majority' in the given example) is used in a relative, adjustive sense, varying in its import with the words that determine it.

VII.

THE SIMPLE CATEGORICAL SYLLOGISM.

(i.) Formal Preliminary (ch. xxi.).

(ii.) The Rules of the Syllogism-The Valid Forms (ch. xxii.).

(iii.) Exercises on the Structure of the Syllogism (ch. xxiii.).

(iv.) The Analysis of Syllogisms, and the Reduction of Arguments into

Syllogistic Form (ch. xxiv.).

(v.) Uses and Characteristics of the Four Figures-The Special Rules

(ch. xxv.).

(vi.) The Dicta (ch. xxvi.).

(vii.) The Problem of Reduction (ch. xxvii.).

(viii.) Unorthodox Syllogisms (ch. xxviii.).

1

CHAPTER XXI.

VII. (i.) FORMAL PRELIMINARY.

INSTEAD of considering the valid inferences which, with the help of the Principles of Consistency and Identity, or an assumed disjunction, we can make from some one given proposition, let us now take two propositions, and see what can be inferred from these taken together.

It is not, of course, possible to draw a conclusion from any given pair of propositions. Thus, from the two propositions

All bullfinches are birds,
All flounders are fishes,

no conclusion can be drawn. We might suppose that the conclusion 'All flounders are-not bullfinches' legitimately followed, but this is not the case. To render that conclusion logically sound, a further premiss would be required-namely, the statement 'All fishes are-not birds.'

To put the matter more generally, nothing can be inferred from the premisses 'All S1's are P1's' and 'All S2's are P2's' unless another premiss is given which states some connexion between P1's and Pa's. This is the central postulate involved in Aristotle's great discovery of the Syllogism, for his discovery essentially consisted in finding out that, if a conclusion is to be logically drawn from a pair of given propositions, these must include a common element, i.e., they must contain a common term. Thus, from the two statements

All birds are vertebrates,
All bullfinches are birds,

where the two ideas 'vertebrates' and 'bullfinches' are connected through the mediating link 'birds,' we at once infer the conclusion 'All bullfinches are vertebrates.'

We may say, then, that a conclusion can be drawn from two premisses, only when the premisses have a common term. The common term is called the Middle Term. The terms related through the Middle Term are known as the Major and the Minor Term respectively.

* The propositions from which the conclusion is drawn are technically known as premisses, propositiones præmissæ.

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