II. PROPOSITIONS AND IMMEDIATE INFERENCE. 13. What is meant by (1) the Conversion, and (2) the Contra-position of a proposition? Apply these processes, as far as admissible, to the following:-- (a) All invertebrates have cold blood. (b) Some cold-blooded animals are not invertebrates. (c) No wingless birds are songsters. (d) Some winged birds are not songsters. What can you infer from (a) and (b) jointly, and what from (c) and (d) jointly? [S] 14. "The author actually supposes that, because Professor Fawcett denies that all wealth is money, he denies that all money is wealth." Analyse the differences of opinion implied in the above passage. [S] 15. Take any universal affirmative proposition; convert it by obversion (contraposition); attach the negative particle to the predicate, and again convert. Interpret the result exactly, and say whether it is or is not equivalent to the original proposition. [S] 16. What information about the term "solid body" can we derive from the proposition, "No bodies which are not solids are crystals"? [S] 17. Discuss the proposal to treat all propositions as affirmative. 18. Convert the proposition "A is probably B." What information does the proposition give us concerning B? [S] 19. Show in how many ways you can deny the following assertions: All cathedral towns are all cities; Canterbury is the Metropolitan see. [S] 20. Explain the nature of a _hypothetical_ (or conditional) proposition. What do you consider the radical difference between it and a categorical? [S] 21. What is the function of the _copula_? In what different manners has it been treated? [S] 22. Convert "A killed C unjustly"; "All Knowledge is probably useful"; "The exception proves the rule"; "Birds of a feather flock together." [S] 23. What is modality? How are modals treated by (a) formal logic and (b) by the theory of induction? [S] 24. What is the subject of an impersonal proposition? Give reasons for your answer. [S] 25. Is the categorical proposition sufficiently described as referring a thing or things to a class? [S] 26. Enumerate the cases in which the truth or falsity of one proposition may be formally inferred from the truth or falsity of another. Illustrate these cases, and give to each its technical name. [S] 27. Illustrate the relation of Immediate Inferences to the Laws of Thought. 28. Explain what is meant by (a) Symbolic Logic; (b) the Logic of Relatives. Describe some method of representing propositions by means of diagrams; and indicate how far any particular theory of the import of propositions is involved in such representation. [S] 29. Explain the exact nature of the relation between two _Contradictory_ propositions; and define Conversion by Contraposition, determining what kind of propositions admit of such conversion. Give the contradictory and the contrapositive of each of the following propositions:-- (a) All equilateral triangles are equiangular;