In contrast to his views of some years ago Suppes in now convinced that modal concepts are essential to standard scientific talk. Yet he emphasizes two main points: (1) in a majority of cases the modal concepts remain implicit in that talk, and (2) this logic is scarcely used in either theoretical or experimental analysis of empirical phenomena. Furthermore, in dealing with probability and referring in particular to the sample space, he substantially says that modal concepts are left implicit to eliminate excess baggage.

In my opinion the situation emphasized by Suppes and described by him in detail, is quite natural and to be foreseen, up to details: Indeed, first, mathematization is the most important step in the qualitative development of science.

Professors Bressan and Suppes have both argued that modality is of great importance to the philosophy of science. I shall not dispute this, but I shall raise some problems of interpretation, which arise if one considers the possibility of a philosophical retrenchment with respect to the use of modal concepts.

Professor Bressan uses the discussion initiated by Mach's attempted definition of mass as a paradigm example of the use of modal concepts in foundational work in physics. He mentions the modal terms used in informal axiomatizations of mechanics which followed Mach, and explains how mass is defined in his own formalized axiomatic mechanics.

On the other hand, in his book Introduction to Logic, Professor Suppes had said unequivocally that he knew of no problem in philosophy of science to which modality is relevant.

The purpose of this paper is to provide a systematic appraisal of the covering law and statistical relevance theories of statistical explanation advanced by Carl G. Hempel and by Wesley C. Salmon, respectively. The analysis is intended to show that the difference between these accounts is in-principle analogous to the distinction between truth and confirmation, where Hempel's analysis applies to what is taken to be the case and Salmon's analysis applies to what is the case. Specifically, it is argued

1. (a) that statistical explanations exhibit the nomic expectability of their explanandum events, which in some cases may be strong but in other cases will not be;

2. (b) that the statistical relevance criterion is more fundamental than the requirement of maximal specificity and should therefore displace it; and,

3. (c) that if statistical explanations are to be envisioned as inductive arguments at all, then only in a qualified sense since, in particular, the requirement of high inductive probability between explanans and explanandum must be abandoned.

Important revisions and additions to the contemporary objectives of acceptance rules result from construing a theory of warranted inductive inference to presuppose an account of adequate scientific explanations. We conceive the objects of acceptance rules to be the best of competing scientific explanations. Our primary interest is to show how to construct an analysis of competing explanations. Hence our specific investigation concerns the interrelations between the criteria of adequacy for scientific explanations and the definitions of the modes of competition between explanations.

In his book, The Structure of Science, E. Nagel pontifically handed down the judgment that the dispute between scientific instrumentalism and scientific realism resolved into an issue over ‘preferred modes’ of speech. Nagel argued that any realistic interpretation of formulation of a scientific theory could, by an appropriate switch from the material to the formal mode of speech, be converted into an instrumentalistic interpretation. Thus, the basic issue dividing the instrumentalists and realists, i.e., the ontological status of theoretical entities, whether and in what sense they existed and were real, was declared to be a pseudo-issue. In the interim, despite the high interest in the formalization of theories, a movement that could only serve the instrumentalist or neutralist camp, scientific realism, although pronounced dead, has refused to lie down.

A not uncommon conclusion of philosophers studying the conceptual foundations of measurement is that scales of measurement, though subject to requirements of consistency, convenience, and simplicity, are essentially based upon conventions, and thus cannot be said to refer to relationships among existing quantities. Brian Ellis, for example, in one of. the most searching contemporary analyses of measurement concepts, claims that

Some aspects of measurement are clearly conventional in the strong sense of resting on essentially arbitrary agreements. Thus to ask which of the scales of temperature, Centigrade or Fahrenheit, is the ‘true’ scale would be like asking which are the true words for the first three integers - ‘one, two, three’ or ‘eins, zwei, drei’.

Philosophers of Science have long paid lip service to the desirability of distinguishing the questions that arise about the propositions (statements, hypotheses) of a science from those that arise about its concepts (terms, ideas); but hitherto there has been a curious hesitation on their part to explore the consequences of this distinction as far as they will take us. This hesitation is understandable in those writers whose primary commitment is to the methods of mathematicallogic, with its formal analysis of prepositional systems and relations. But it extends also to those, who have no such commitment: e.g. the pragmatists. (Recall William James's confused question, “What makes an idea true?” - as though concepts could be true-or-false, in the way propositions are!)

The account of scientific change and rationality outlined in this paper,. and set out at length in my recent book on Human Understanding, is designed to show how a full understanding of those consequences can help us to move beyond current quandaries in the subject to a more constructive set of philosophical, historical and sociological questions.

If we examine some relatively sophisticated area of science at a particular stage of its development, we find that a certain body of information is, at that stage, taken to be an object for investigation. On a general level, we need only think of the subject-matters called ‘electricity’, ‘magnetism’, ‘light’, or ‘chemistry’; but both within and outside such standard fields, there are more specific examples - such as, for instance, what are taken to be subfields of the preceding subjects. Further, those general subjects themselves are, in many cases, considered to be related in certain ways. (For example, in the nineteenth century, reasons accumulated for believing that electricity, magnetism, chemistry, and light were related, and in such a manner that it was reasonable to search for a common account of all these subjects.)

It is argued that by explicating rationality in terms of benefits balancing or outweighing costs instead of in terms of maximizing or satisficing something, a more adequate view of rationality is obtained.