33.  Illustrate the process called ‘change of Relation.’

III.  SYLLOGISM AND MEDIATE INFERENCE.

34.  What is a Syllogism?  Find, without reference to the mnemonic verses, in what different ways it is possible to prove syllogistically the conclusion No S is P; and show the equivalence between these different ways. [S]

35.  From what points of view can the syllogism be regarded

    (1) as being, (2) as not being, a petitio principii? [S]

36.  What are the figures of syllogism?  For what kind of arguments are they severally adapted? [S]

37.  What is meant by Mood and Figure?  How can the validity of a Mood be tested?  Should there be four Figures or three? [S]

38.  Construct syllogisms in Camenes, Datisi and Baroco, and reduce them to the corresponding moods of the first figure.

39.  Explain the meaning of “ostensive” and “indirect” Reduction.  Show that any Mood of the second Figure may be reduced in either way.

40.  Show that A cannot be proved except in the First Figure.  Express the following reasoning in as many syllogistic figures as you can:  Some theorists cannot be trusted, for they are unwise. [S]

41.  Discuss the possibility of reducing the argument a fortiori to the syllogistic form. [S]

42.  Can a false conclusion be reached through true premises, or a true conclusion through false premises?  Give reasons for your answer. [S]

43.  Can we under any circumstances infer a relation between X and Z from the premises—­

    Some Y’s are X’s
    Some Y’s are Z’s? [S]

44.  Take an apparent syllogism subject to the fallacy of negative premises, and inquire whether you can correct the reasoning by converting one or both of the premises into the affirmative form. [S]

45.  Enumerate the faults to which a syllogism is liable, giving instances of each. [S]

46.  State any Enthymeme, and expand it into (1) a Syllogism, (2) an Epicheirema, (3) a Sorites; and give in each case the technical name of the Mood or Order that results.

47.  State any Disjunctive Syllogism, and change it (1) into a Hypothetical, (2) into a Categorical; and discuss the loss or gain, in cogency or significance involved in this process.

48.  Can the Syllogism be treated as merely a consequence of the “Laws of Thought”?  If not, why not; and what else does it imply?

49.  Prove that with three given propositions (of the forms A., E., I., O.) it is never possible to construct more than one valid syllogism. [C]

50.  Distinguish between a Constructive and a Destructive Hypothetical Syllogism; and show how one may be reduced to the other. [C]

IV.  INDUCTION, ETC.

51.  What constitutes a Valid Induction?  Distinguish it from a legitimate hypothesis. [S]