PART V.CLASS-LOGIC, AND ADDUCTION.
1.Subsumptive or Nominal.
3.Classes of Classes.
1.First Order Hierarchies.
2.Second Order Hierarchies.
2.The Russell Paradox.
4.Other Types of Probability.
2.Structure of Theories.
1.The Scientific Method.
Summary of findingsin the chapters of this part:
Part V.The Logics of Classification and of Adduction.These two topics were lumped together, without intent to imply a close relation between them. They are fields of logic which derive from the previous, though important in themselves. There are many significant innovations in our treatments of class-logic. The novelty in our treatment of adduction lies in its modal orientation.
43. We saw that class-logic takes terms ‘nominally’, in a way distinct from the subsumptive approach of Aristotelean forms. However, classes and classes of classes are easily defined with reference to Aristotelean forms; and the features, immediate inferences, and deductive arguments of forms with such terms are readily derivable from these definitions.
44. We distinguished classes and classes of classes as two separate ‘orders’ of classes, each with its own though parallel ‘hierarchy’ of classes. The relational aspect of these concepts was stressed, when we sought to clarify their extreme manifestations.
45. We analyzed the concept of self-membership both conceptually and with reference to examples, and found it wanting. We then considered the famous Russell Paradox, and demonstrated that the solution of the problem lay in the concept of permutation (rather than in issues of membership), whose ontological significance was also clarified.
46. Adduction is the general method by which we induce the logical probability of any information. We discussed its well-known form of argument, which is similar to apodosis, only with less established premises and/or conclusions. We showed how it provides and weights evidence, and thus validated it. We also discussedde-readduction.
47. We looked into the psychology of theorizing, described the structures of theories and various criteria we use in making them, and we suggested ways theories may be more purposefully formed and tested.
48. We described in formal terms the scientific method of judging between theories, but also indicated the pragmatic compromises that are often called for, and how theories may gradually be changed. Theories with exclusive empirically-tested predictions were granted formal certainty.
49. Under the heading of Synthetic Logic, we advocated a healthy skepticism and flexibility, which transcends rigidly formal standards of theory-evaluation — an open-mindedness to more far-fetched hypotheses which are not definitely disproved.