Ilkka Niiniluoto

Inducibility and epistemic systematization: Rejoinder to Kaufman

In his essay on the theoreticians dilemma argument, Hempel (1958) ad vanced the thesis that, unlike deductive systematization, observational inductive systematization need not be preserved in the course of elimina tion of theoretical terms from scientific theories. Cornman (1972) and independently of Cornman, and in a somewhat different form Sinks (1972) have suggested, however, that the well-known Craigian procedure for the elimination of theoretical terms can be extended by taking into consideration not only the deductive but also the inductive theorems of theories, and that this extended Craigian procedure (let us call it ECP, for short) in a sense guarantees the preservation of observational inductive systematization. In my survey of the extant literature on Hempels thesis of the non eliminability of theoretical terms within inductive systematization (Niini luoto, 1972; see also Niiniluoto, 1973), I claimed that no convincing argu ments have so far been put forward either to defend or to refute it. Against Cornmans suggestion, in particular, I argued that ECP, the proposed extension of the Craigian procedure, has to face a number of problems which seem fatal to Cornmans philosophical purposes. Later, a detailed proof of Hempels thesis has been given in Ch. 9 of Niiniluoto and Tuomela (1973). In his interesting attempt to make precise Cornmans relatively sketchy outline of ECP, Kaufman (this issue, pp. 215-221) argues that while my criticism of Cornman contains one valid conclusion, this conclusion is based on incorrect reasons and does not even count as an argument against ECP. As is shown below, my discussion of ECP contains, indeed, one error (which Kaufman fails to locate). However, neither this error nor Kaufmans paper refutes my conclusion that theoretical terms may be logically indispensable for observational inductive systematization, i.e., that Hempels thesis is valid, and the theoreticians dilemma argu

Theoretical Concepts and Inductive Inference

This work represents an attempt to clarify the role which theoretical concepts may play within inductive scientific inference or inductive systematization. A study is made of some of the possible gains that accrue from the introduction of theories employing new theoretical concepts. We are especially interested in gains for which theoretical concepts are logically indispensable, as they provide us with strong methodological reasons for the introduction and employment of theoretical concepts. We have restricted ourselves to dealing with relatively simple kinds of theories, which may be taken to exemplify theories from the primarily non-quantitative sciences.

Linguistic Variance in Inductive Logic

The technical approach to hypothetico-inductive inference which was developed in the preceding chapters of this book is directly and indirectly relevant to many important problems in the philosophy of science. Some of these problems have already been mentioned above. For example, we showed how theoretical concepts can be desirable and even logically indispensable for the purposes of scientific theorizing. In Chapter 9, we indicated how this can be taken to support scientific realism against methodological instrumentalism - and, of course, against those ‘descriptive’ or ‘positivist’ views which do not allow of open theoretical concepts assuming any role in science.

Corroboration and Theoretical Concepts

One of the central problems in the philosophy of science is the problem of accounting for the support that theories and generalizations receive or may receive. This support may come from various sources, which have two main types. One is empirical information obtained by means of observation and experimentation, and the other is theoretical information obtained from other theories and generalizations belonging to the same nomological network. We call these two types of support observational and theoretical support, respectively.

Piecewise Definable Theoretical Concepts

It has often been claimed that no gain - except possibly one in economy - results from theoretical concepts which are definable, and hence eliminable, by observational terms. Here definition normally means explicit definition. However, these claims do not always hold even for explicit definitions (cf. Chapter VI of Tuomela, 1973). Accordingly, they need not hold true for definitions satisfying the classical criteria of eliminability and noncreativity for definitions. An example of such a strong kind of definition satisfying these criteria is provided by a piecewise definition (see Hintikka and Tuomela, 1970 and Tuomela, 1973 for a discussion of its logical and methodological properties).

Hintikka’s Two-Dimensional Continuum of Inductive Methods

In this study002C Hintikka’s inductive logic will be used as a general framework for discussion of the technical problems of inductive systematization. For later reference, this chapter summarizes some basic results about Hintikka’s two-dimensional continuum of inductive methods.1

Theoretical Concepts and Inductive Explanation

In this chapter, we discuss the inductive explanation of (non-probabilistic) generalizations (or laws) by means of (non-probabilistic) theories. Our general viewpoint is that inductive explanation, and indeed a major part of inductive systematization, is best conceived as information-providing argumentation, but it is argumentation that does not lead to detaching a conclusion from some premises. Thus, for instance, to explain something inductively is to give a certain amount of information relevant to the explanandum. In other words, an explanans is assumed to convey some information concerning the explanandum. The more the explanans carries such relevant information, the better the resulting explanation is. As in this chapter information will generally be measured in terms of probabilities (for instance, by positive relevance), we can alternatively say that within inductive systematization, the explanation of something is stating some propositions inductively relevant to the explanandum.

Inductive Probabilities of Weak Generalizations

In this chapter, we are interested in the question of how the probabilities of weak generalizations of the observational language change when a new predicate is introduced into our language, and, at the same time, our knowledge of the connections of this new predicate to the old vocabulary is applied. The same question for strong generalizations is taken up in the next section. General formulae are calculated for the probabilities of generalizations in Hintikka’s system with λ( w) = w, and some observations and examples of their behaviour are given. For simplicity, we generally consider only the case of one new monadic predicate.

Inductive Probabilities of Strong Generalizations

In Chapter 3, we considered weak generalizations of L(λ), i.e., disjunctions of constituents to the effect that at least certain b Ct-predicates of L(λ) are empty. In this chapter, a study is made of the probabilities of strong generalizations, i.e., constituents of the observational language. (The formulas of Chapter 3 cannot, in general, be applied to this case.)

Towards a Non-Inductivist Logic of Induction

According to the old Aristotelian dictum, one can have knowledge only of the general. In the spirit of this epistemological tradition, philosophers have often emphasized that the proper subject-matter of science includes only those aspects of the world which are, in some sense, invariant, uniform, or regular.1 While the Ancient thinkers were apt to find these uniformities in the unchanging ‘forms’ or ‘essences’ of particular things, the founders of modern natural science sought them in the invariant relations or functional dependences between things and events.2 A common tenet of these views is that science proper studies invariable uniformities which can be expressed by universal laws. It is also generally thought that these laws are explained by more comprehensive and general theories employing characteristic theoretical concepts and postulates. Thus, all genuine scientific knowledge, as it is expressed in theories and laws, should be stated in universal form.