11. Explain opposition. 12. Give the Square of Opposition. 13. Give the statement summarizing the relations of contraries; of contradictories; of subcontraries; of subalterns. 14. Give the table showing the effect of the truth of the several propositions upon the other propositions. 15. How is a particular proposition usually to be interpreted in logic? What is the usual colloquial usage of the word some? 16. What is transformation of propositions? 17. What knowledge do we start from in transformation? 18. How many distinct ways of transforming are there? What is the additional way and how related to these two? 19. Explain obversion. 20. What parts of the proposition are affected in obversion? 21. Explain conversion. 22. What parts of the proposition are affected in conversion? 23. What is the aim of conversion? 24. State the rule governing distribution in conversion. 25. Name and explain two types of conversion. 26. Explain contraversion, naming in their proper order the steps of which it consists. 27. What names are given to the original and the derived propositions in each of the processes of transformation. 28. To what propositions is obversion applicable? conversion by limitation? simple conversion? contraversion? 29. Why cannot O be converted? Why cannot I be contraverted? Why is E not usually contraverted? 30. Give the table showing the processes applicable to the several propositions and the results obtained. 31. What are the reasons for transforming propositions? EXERCISES ON CHAPTER VIII 1. Attach to the following propositions the letters indicating their logical character (A, E, I, or O), and place above the terms the signs (+ or -) indicating their distribution. (a) Some men are honest. (b) No self-seeking politicians are patriotic. (c) Some sheep are not white. (d) All women are lovers of the beautiful. (e) Fixed stars are suns. (f) No mental defectives are eligible to serve in the regular army. 2. Be prepared to explain fully, either verbally or by a figure (circles may be used to represent the concepts, being made to overlap partially, being disconnected, or one containing the other), the knowledge given respecting each of the terms in the above propositions in relation to the other. 3. State the contrary, contradictory, and subalternate of the following: (a) All animals are breathers of oxygen. (b) No plants are sentient. 4. State the contradictory, subcontrary, and subalternans of the following: (a) Some insects are nocturnal. (b) Some birds are not flying animals. 5. Make your own example of each of the four propositions, and state the several propositions opposed to each. 6. Assuming each of the four propositions to be false, indicate in a table arranged like that on page 100 what would be the effect on the truth or falsity of the other three. 7. Obvert the following propositions: (a) All reptiles are cold-blooded vertebrates. (b) Some reptiles are not vertebrates with legs. (c) No caterpillars are true worms. (d) Some vertebrates are animals which breathe by gills. 8. Convert as many of the propositions given in Exercise 7 as you think it possible to convert. 9. Contravert all the propositions given in Exercise 7 that you deem contravertible. 10. Take each of the propositions given in Exercise 7 and transform it by all the processes you think applicable to it, showing all steps in logical order. 11. Make your own example of each of the four propositions, and apply to it all possible processes of transformation, indicating by the appropriate symbol all propositions formed, and showing all steps in logical order. 12. Reduce the four following propositions to their simplest logical form, and then determine the logical relation between them (six such relations exhaust the problem, viz., 1 to 2, 1 to 3, 1 to 4, 2 to 3, 2 to 4, 3 to 4; you should be able to pass by transformation from one to the other, or else to show that no such relation is possible): (1) All substances which are material possess gravity. gravity. (4) Some substances which do not possess gravity are immaterial. PART IV. DEDUCTIVE INFERENCE CHAPTER IX.-GENERAL NATURE OF THE INFERENTIAL PROCESSES AND THE GENERAL PRINCIPLES OF DEDUCTIVE INFERENCE 57. NATURE OF INFERENCE.-What are we to understand by logical inference? This is the problem that confronts us now that the language forms, terms and propositions, are understood. Inference from a logical stand-point is the process of passing from one judgment to a related judgment, so that the latter becomes better established as a truth by our consciousness of its connection with the former. It is this consciousness of connection or relation upon which the validity of a logical inferring process depends. We feel and perceive the connection. There can be no doubt that this feeling of relatedness is an essential part of logical inference, for in it lies that emotional attitude toward the situation without which logic would have no force to win assent to the true as distinguished from the false. Inference has two forms, Induction and Deduction. Though generally treated in logic as though they were distinct, from the view-point of modern psychology they are essentially one and the same. Induction or inductive inference is that phase in which the judgments gain in generality, or, as is often said, pass from the less general (or particular) to the more general. Deduction or deductive inference is that phase in which the judgments lose in generality, or, to put it in the usual form, pass from the more general to the less general (or particular). Induction is mainly a process of organizing experiences into the form of accepted truth called by the general name of knowledge, whereas deduction is mainly a process of applying the organized or formulated knowledge which induction furnishes to future instances of experiences which are recognized as the same. But all application aids in completer organization; hence deduction is essential to the full and perfect organization of the knowledge which induction gathers piecemeal and puts into form. Furthermore, every instance of a deductive process of inference means that the generalization has been increased; hence deduction implies induction. Thus it appears that organization and application of knowledge proceed hand in hand-that the inductive and deductive modes of inference are only phases or aspects of one and the same mental functionthat power of the mind which makes the experienced the indispensable agency in further experiencing, the known the essential precondition for apprehending the unknown. In logical inference, therefore, the mind is seen to function inductively-deductively, and not in either way to the complete exclusion of the other. Despite this fact, we shall have to treat the processes as though they existed independently of each other. And we shall apply ourselves to deduction first, because it shows the closest connection with the proposition and |