N.B.-In both of these a particular conclusion would

(iii.) Rules of fig. ii. are

fig. iii.,,

The Major Premiss must be

universal.

One of the Premisses must be negative.

The Minor Premiss must be

affirmative.

The conclusion must be particular.

Fig. iv. can be more clearly arranged as fig. i.

(iv.) The moods of fig. iii. are Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison (see p. 124).

In all of these a universal conclusion involves an illicit minor.' So the 3rd fig. only gives particular conclusions. Putting two of the above into words, we get:

All animals sustain life by assimilating food.
All that lives by assimilating food is liable to hunger
All that is liable to hunger may be half famished.
.. All fleas may be half famished.

C=Sustaining life by assimilating food.'
D'Liable to hunger.'

E= 'May be half famished.'

And the Sorites may be resolved as in the cipher-form

APPENDIX C.

TURNING back to p. 103 we find inductive inference put aside. Induction or inductive inference starts from particulars and works towards universals. The process is fully explained under the heading 'What is Science?' (pp. 4 to 13; read carefully) for all science is inductive (p. 184, 'Method'). As deduction has its forms and rules (discovered by Logic), so induction has its forms and rules (discovered by Logic); and we have inductive as well as deductive logic. The mind of man is as carefully controlled in its journey (μé¤odos) from the particular facts up to the universal laws, as it is in its journey from the universal law down to the particular facts. (See illustration, p. 45.) Let us consider :

1. Induction-what it is.

2. The principles upon which induction ultimately depends, as deduction depends upon its principle, p. 113 (A.).1 3. The processes required for induction (observation and experiment).

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4. The methods' in Induction corresponding to the syllogistic laws in Deduction.

This principle of syllogism is founded on the three great laws upon which all deductive reasoning depends (Laws of Thought, p. 160). The principles of inductive inference are not founded upon these three self-evident axioms. Consequently we do not find the same certainty about our conclusions in induction as we have in deduction. For the principles of the syllogism are laws, the violation of which is inconceivable, whereas the principles of induction are laws, whereof the violation is not inconceivable. For the principles of induction are generalisations from experience, and not like those of deduction part of our nature, which we found but did not make.

(1) Induction has been called an argument from the known to the unknown,' or 'generalisation from experience,' or 'inference from particular facts to universals.' (Pp. 4-13 give the process.) For by induction the old man ascends from the particular objects he lets fall to the universal laws of gravity. Most of the laws which deduction brings down to particular facts have been by induction raised from particular facts beforehand. For induction precedes deduction except in cases where the laws were implanted in us by nature, and even then induction in a sense precedes; for by it we find those implanted laws (though we do not make them) before we can bring them down to particular facts.

Now, induction may be thus subdivided (starting with arguments from the known to the known, and working towards arguments from the known to the unknown)1:

In arguing from particular facts to universal laws you may know all the particular facts or you may not. If I say all the officers in the British army weigh more than six stone, after having gone through the Army List, and caused each officer to be weighed, I am not in my calculation stating more

The four subdivisions of perfect induction are arranged according as they resemble more or less closely imperfect induction. Parity of reasoning might almost be called imperfect induction; colligation is nearer than traduction; traduction and 'from known to known' are the pure cases of perfect induction.