Marian Przełęcki

On model theoretic approach to empirical interpretation of scientific theories

In his interesting article Model Theory and Empirical Interpretation of Scientific Theories i Raimo Tuomela gives a detailed presentation and critical discussion of the account of empirical interpretation of scientific theories outlined in my monograph The Logic of Empirical Theories 2. His criticism is directed not only against certain particular features of that account, but also against some basic assumptions underlying it as well as the very kind of general approach to the problem. This is the reason why I want to add a few comments rejoinders and explanations to the discussion. For it is my contention that the general approach to the problem of empirical interpretation exemplified in my monograph is basically sound and well suited for the purpose it is intended to serve. At the same time, I think that its concrete realization propounded in the monograph may rightly be considered unsatisfactory and inadequate in some respects, though I do not plead guilty of all the shortcomings brought up by my critic. The general approach to the problem of empirical interpretation presented in the monograph is set in the model theoretic framework. In particular, the interpretation of a given language is identified with a model theoretic entity a model ~ of language L. ~[Yt assigns to each non-logical constant of L a suitable set theoretic entity as its denotation. Thus, e.g., a one-place predicate of L is interpreted by ~ as denoting a certain set of objects from the universe of L. Such a concept of interpretation is nothing peculiar to the model theoretic approach. It is shared by most semantical theories of, say, Carnaps type. Hence if it is exposed to some criticism so are its more traditional versions. Now, it is obvious that interpretation so conceived, viz. identified with denotation, does not embrace all that is included in the meaning of an expression. But it seems to embrace enough of it to deserve the name ofinterpretation. Interpretation understood in this way is all that is needed in order to define the concept of truth for any genuine first-order language. It is true that it is an extensional interpretation only, but it is exactly exten-

Empirical Meaningfulness of Quantitative Statements

The main object of our analysis is Suppes’s well-known criterion of empirical meaningfulness for quantitative statements proposed in Suppes (1959), and our main purpose is to show this criterion to be a particular instance of some general criterion of empirical meaningfulness applicable to arbitrary statements. Such a criterion has been put forward in Przelecki (1969). It is based on the same fundamental idea that underlies Suppes’s criterion: a connection between meaningfulness and invariance in truth value of a given statement. The criterion is applicable to all empirical languages that can be formalized within first-order predicate logic.

Conceptual Continuity Through Theory Changes

The present paper, meant as a contribution to “theory of rational science development”,1 is concerned with the nature of conceptual changes characteristic of certain types of theory change. Some kind of conceptual continuity has usually been considered to be a necessary prerequisite of rational science development. That view, however, has been seriously questioned in recent years. The argumentation runs, roughly, as follows. Let T 1 and T2 be two successive theories. Interpretation (sense and reference) of their specific terms is said to depend on the very theories in question. As the theories differ in what they say about their terms, the interpretation of the latter appears to be different within the two theories. In the case of mutually incompatible theories, their languages are claimed to be not intertranslatable, and their specific terms “incommensurable”. But this seems to exclude the possibility of a logical comparison and rational choice between the two theories. To treat them as “rival”, we have to regard them as speaking, partly at least, about the same subject-matter. And this seems to presuppose some kind of “commensurability” of their conceptual frameworks. The main aim of the following analysis is to supply some arguments in favour of a certain version of the “commensurability” thesis. Changes in interpretation of a theory’s terms, occurring in the process of its development, may involve both changes in their sense and in their reference.

On Identifiability in Extended Domains

For the sake of the present discussion, by definability I shall understand what is usually called the explicit (or syntactic) definability; by identifiability — the implicit (or semantic) definability. I shall restrict myself to considering empirical theories which can be formalized in first-order logic. As it is known, with regard to such theories these two concepts coincide. A term t is definable in a theory T if it is identifiable in it. That is to say, a definition of t is a theorem of T if the interpretation of the remaining terms in any model of T fixes uniquely the interpretation of t. That is why all cases of nonidentifiability considered thus far are always connected with some kind of non-definability. A concept is not identifiable only if it is not definable; e.g. if it is governed by some postulate weaker than an explicit definition (a conditional, or piecewise, or partial definition — to mention the typical cases). In what follows, I wish to call attention to some other kind of non-identifiability and its characteristic sources. Non-identifiability of this kind is not connected with non-definability. It appears as a result of some looser conception of a theory’s interpretation. On the standard approach, any extension of a given language has as its semantic counterpart a suitable expansion of the language’s structures. But there seem to be cases where an extension of language is connected not only with expanding its structures, but also with extending their domains. This seems to be the case when an observational language is being extended by introducing into it certain types of theoretical terms. In such cases the correspondence between definability and identifiability mentioned above does not apply any longer. Being definable in a given theory, a theoretical concept is not identifiable in the theory’s models — if these are structures with extended domains.

On the Concept of Genotype

Woodger’s book: “Biology and Language” constitutes a great achievement in his attempts at constructing a precise and adequate language for genetics. In the conceptual structure outlined there the concept of genotype occupies an important place and most of the remaining concepts are introduced with its help. The definition of genotype as proposed by Woodger is interesting not only for geneticists. It deserves special attention of all concerned with problems of general methodology. Genotype is usually considered a “theoretical concept” appearing at the highest level of genetical theory. It is said to denote the genetic constitution of an organism, specified by reference to genes — entities which are not accessible to direct observation. Woodger treats genotype as an “elementary concept” belonging to the lowest level of genetical system. His definition of genotype is couched in terms of directly observable things, properties and relations. It does not make use of the much disputed concept of gene. On the contrary, the latter is defined with the help of the former. Woodger’s concept of genotype — a theoretical concept defined explicitly on the observational level — calls for a careful examination, which may throw light on some difficult problems connected with the relation between theory and observation. In what follows I am not trying to give a full analysis of Woodger’s definition. I should like rather to point out one peculiar feature which it seems to share with all definitions of the same kind, i.e., definitions of theoretical concepts in terms of observable entities.

A Model-Theoretic Approach to Some Problems in the Semantics of Empirical Languages

Model theory may be regarded as a modern form of logical semantics. It deals with relations between languages and what these languages speak about, i.e. with typical semantical relations. What is characteristic of the model-theoretic approach might be briefly put as follows: it is a theory of the relations between formalized languages and their models. All languages studied in model theory are formalized ones, and the fragments of reality they speak about are conceived of as certain set-theoretic entities called models (structures, relational systems). The model-theoretic investigations have thus far been restricted to mathematical languages almost exclusively. But this seems to be an unjustifiable limitation. Empirical — that is, non-mathematical — languages also seem to constitute a proper object of the model-theoretic studies. Any empirical language can be formalized — if need be. And that what it speaks about may always be thought of as a certain model; the set-theoretic concept of model is broad enough to cover all fragments of reality.

Ethical Aspects of Non-Ethical Theories

Publisher Summary Ethical aspects of scientific theories may be defined in various ways. It is one sense only of this notion that is going to be discussed in the chapter. Because the proper object of moral valuations seem to be human actions (and, derivatively, human agents), it is not theories themselves, but rather the acts of propounding a theory that may be morally evaluated. In the case of non-ethical theories, including all the scientific ones, the act of propounding such a theory seems to be, in itself, a morally neutral action. If it is morally judged, it is so in regard to its connection with some other kind of action of an explicitly moral character. The chapter presents assumptions concerning the logical character of ethical statements and some remarks on their methodological status. They reflect a certain general view of the structure of ethical systems. The chapter discusses the connection between the hypothesis of the heritability of intelligence and the ethical ideal of social justice.