The work by J.H. Conway (1976, ch. 4), Philip Ehrlich (1987, with further references) and others on absolute continua derives much of its philosophical and mathematical interest from its instantiating a more general approach to the foundations of mathematics. This approach focuses on the role of extremality (rnaximality and minimality) assumptions as a part of the basis of mathematical theories. The idea of extremality is potentially much more important than has recently been pointed out in the literature. It is illustrated by the principle of mathematical induction, which can be thought of as an attempt to enforce the requirement of minimality on the models of elementary number theory as well as by Hilbert's Axiom of Completeness (1971), which was calculated to enforce a kind of maximality on the models of axiomatic geometry. (These models were of course intended to be a species of continua.)

Many philosophers, and particularly those of a Kantian stripe, have suspected that claims about the ways the world and its Joints are (in contrast to claims about the joints in our models of the world and the way they are) make little sense. Recently, similar views have gained prominence in the philosophy of science and in cognitive psychology. The demise of the strong distinction between theoretical and observational terms over the past two decades is just one, among many, developments in the philosophy of science which is of a piece with such suspicions. Meanwhile, a great deal of recent theoretical work on the psychology of categorization also affirms the fundamentality of our cognitive constructs in structuring human experience.

Perhaps one of the chief items of pride of mathematical philosophy in the last century and a half is the insight that mathematics is the science of formal structures; as opposed to the traditional view, that ‘the proper and exclusive subject matter of mathematics is…quantity.’ Closely associated with this insight is the distinction between pure mathematics, the beneficiary of the freedom conferred by the new status, and applied mathematics (in the philosopher's rather than the mathematician's sense of the word), which has been sent into philosophical limbo, supposedly under the care of philosophy of empirical science.

These two insights allow us to avoid many embarrassments. Our postulated freedom to adore gods other than Quantity allows us to break the seemingly endless circle of pointless debate, whether or not negative and complex numbers are legitimate quantities; our assumption that mathematical truth is independent of physical truth relieves us of the worry, whether Euclidean or non-Euclidean geometries are legitimate.

Konrad Lorenz suggests that adequate grounds for classifying some behaviors as innate are to be found in the results of what he calls “the deprivation experiment“: ”… the experiment of withholding from the young organism information concerning certain well-defined givens of its natural environment.” (Lorenz 1965, p. 83). Thus, a stickleback fish is deprived of the information that its rival has a red belly. The stickleback is then confronted, for the first time, with a red-bellied rival (or a red-bellied dummy). If that stickleback responds with species-typical rival-fighting behavior, then (according to Lorenz) the experiment has established that the stickleback possesses certain innate information about its natural environment. On the other hand, should the stickleback fail to respond in this way, Lorenz tells us that ”…we should not be justified in asserting that this response is normally dependent on learning.

Unlike some recent authors, Hilary Putnam recognizes that we can not avoid inquiring about the normative force of the principles that guide scientific reasoning. His answer is in terms of values. In presenting his case for “Internal Realism”, he argues that values are presupposed in statements of fact (1981, pp. 128-134). The central thesis in his argument is that truth is not a correspondence with an “unconceptualized reality” and that “the claim that science seeks to discover the truth can mean no more than that science seeks to construct a world picture which, in the ideal limit, satisfies certain criteria of rational acceptability” (p. 130). We adopt these criteria because having a theory which conforms to them is valuable to us; it is part of human flourishing (pp. 133-134).

What is the use of probability theory in the sciences? A common answer to this question is: probability is the conceptual tool for statistics, i.e. for the evaluation of collections of numerical data. This reply, that covers a wide range of applications may be rendered by saying that the calculus of probability is the theory for statistical practice. Under this interpretation, probability is part of scientific method; it belongs to the ‘logic’ of science, i.e. it regulates scientific inference. At most, it says something about the state of justified belief of a scientist, but nothing about the nature of his objects.

If I speak of probability as a theoretical concept, I intend to refer to a different use of probability in the sciences; an explanatory use, or - more cautiously put - a use within the framework of explanatory theories, e.g. in microphysics or evolutionary biology. Compared with the standard application to statistics, this use is exceptional and problematical.

A consensus has recently emerged concerning the role of values in scientific inquiry. The idea that science is value-laden has been elaborated by writers as diverse as Kuhn, McMullin, Hempel, Putnam, Laudan, Feyerabend, Scriven, and Graham.1 Although they all agree that values, value judgment, and evaluation play an important role in science, their emphases and their arguments are different. In fact, I believe that enough work has been done, and enough issues have been raised, that it is becoming increasingly useful and instructive to discuss and explore further the main issues that divide this group of thinkers.

One of these issues is whether it is advisable to treat as a value any type of controversial position, such as belief in God or the thesis of metaphysical materialism; some writers do this, but it is questionable whether it is useful to mix together such disparate items.2

Any plausible treatment of human knowledge must acknowledge two shapers of opinion: the psychological and the social. The formation of almost any belief, even the mere perception of familiar objects or recollection of recent events, involves the execution of a complex array of mental operations or computations. So the psychological component in belief-formation is ubiquitous. The social component, while not quite ubiquitous, is almost as crucial. A large proportion of the mature cognizer's beliefs are acquired from others; and typically the vehicles of acquisition — public language, and internal techniques for assessing the claims of others — are themselves socially or culturally acquired. Scientists, of course, are no different in these fundamental respects. They too are cognizers with human brains, and they work in professional communities. Their beliefs result from use of their psychological equipment, and from the scientific lore and methodology that is largely indebted to interpersonal training and communication.

Epistemology has been socialised. Cognitive and social interactions between observers are now as important as their interventions into the course of nature. This contrasts with traditional views of how we get natural facts into our discourse about nature. These assumed the efficacy of individual observers’ causal interactions with the natural world, making their interactions with other observers irrelevant. Kant’s conclusion that empirical access depends also upon our concepts did not challenge the individualistic character of the epistemology of science. Observers’ agreement about their observations showed that each individual can have independent perceptual access to one and the same world.

Historical and sociological studies of science show that social and procedural aspects of observation in the laboratory make an essential contribution to consensus about observations (see Knorr-Cetina and Mulkay (1983) and Gooding (1985a).

The first published paper on pulsars was entitled, by its five co-authors, “Observation of a Rapidly Pulsating Radio Source”. (Hewish, et al. 1968). The publication of this paper preceded by some months the coining of the word ‘pulsar’ to refer to such pulsating radio sources. Does it seem odd to talk of observing pulsars? It might seem so since much effort has subsequently gone into identifying pulsars with optically visible stars using conventional light, not radio, telescopes. We can say that the moons of Jupiter are observable since either we can see them through a telescope or, at some future date, astronauts will be able to travel close enough to Jupiter to see its moons without visual aids.

Goldman has offered a novel conception of epistemology, or, to use his terminology, epistemics. Although the project is complex and terminologically intricate, the central point that sets it apart from traditional epistemology is his conception of the objects of epistemic evaluation. Goldman claims that the objects of epistemic evaluation include not merely the beliefs a person holds and the relation of these beliefs to the evidence, but the processes and methods that are used in arriving at the beliefs. Processes and methods are epistemically commendable, on Goldman's view, to the extent that they reliably produce true beliefs, where “truth” is defined independently of epistemic norms. It is the role of the cognitive and social sciences to identify the processes and methods that are to be evaluated; the cognitive and social sciences thus have an essential role to play in epistemology, though they can by no means replace it.

When attempting to introduce new ideas it is usually best to provide an exemplar which demonstrates, in a particular case, the usefulness of those ideas. It is also occasionally helpful to talk about why the new ideas might be useful. Given limited space, one cannot do both. I have chosen here to talk about the use of cognitive models in the philosophy of science, leaving the exhibition of their usefulness for other occasions.

Now if one is just going to talk about something rather than exhibit its potential, it is best not to be too general or abstract. After all, the objective is to convince one's audience that one has something to offer. Few people, including even philosophers, are easily convinced by generalities or abstractions. So I will begin by sketching an account of how I personally came to the conclusion that the cognitive sciences provide models that are useful to the philosopher of science.

Philosopherd have long stressed a distinction between theory justification and theory discovery based on a belief that justification and discovery are essentially different processes. What makes these two processes essentially different, it was assumed, is that the process of justification is guided by criteria which are expressable as rules, while the processes involved in discovery are not rule-guided. Moreover and perhaps more importantly, it was assumed that tha rules for justification are discoverable a priori by rationalistic logical analysis but an account of discovery, whatever it turns out to be like, will be describable only a posteriori.

This paper is a summary of my oral presentation at PSA 86. Since that presentation was in turn a summary of views that will appear in great detail elsewhere (Thagard forthcoming), I shall be very brief here. My aim is to outline how computational models can provide the same benefits to the philosophy of science that they currently provide to cognitive psychology. I shall begin by situating an enterprise that I call computational philosophy of science in relation to the more familiar fields of historical philosophy of science, artificial intelligence, and cognitive psychology. After some general remarks about the use of computational models, I shall describe a particular model of problem solving and learning that has been used to simulate the discovery and justification of the wave theory of sound.

J.J.C. Smart says that instrumentalism makes it “surprising that the world should be such as to contain these odd and ontologically disconnected phenomena…. Is It not odd that the phenomena of the world should be such as to make a purely instrumental theory true? On the other hand, if we interpret the theory in a realist way, then we have no need for such a cosmic coincidence…. A lot of surprising facts no longer seem surprising….” (Smart 1963, p. 39).

Intuitively Smart seems right. The instrumentalist, who believes the observational consequences of some theory, but eschews any commitment to the theory itself, ends up believing something far less plausible than the realist, who can account for those consequences in terms of the theory.

A recent article in Philosophy of Science by Andrew Lugg (1985), revives interest once again in Johannes Kepler’s so-called “discovery” of the laws of planetary motion. Typically, as if by some recurring philosophical instinct, it focuses on Kepler’s finally settling on the ellipse for planetary orbits--the first of his three laws. There is a fascination with the limiting shape of what is still taken to be the scope of the Sun’s sovereign domain, rather than with the second, or, even more rarely, the third law. Ever since the famous debate between John Stuart Mill and William Whewell, philosophers and historians have been drawn to this notable advance in early modern science--in what Kepler himself calls his “war on Mars” (the planet itself named after the “god” of war).

Michael Faraday (1791-1867) was a productive, historically significant, figure who has served as the subject of several recent attempts to construct a cognitive model of the nature of scientific thinking (Gooding, 1985; Nersessian, 1984; Tweney, 1985a; in press). Of particular interest in the present context is the relation of such an analysis to the broader issue of the role of cognitive accounts in the philosophy of science. In accord with Giere's call for a ‘cognitive realism,’ I believe there are substantial philosophical implications that stem from one overriding characteristic of Faraday's work, namely his reliance on procedural ways of thinking. By procedural, I mean thinking which is rooted in specific activities whether concrete or abstract. As will become clear, my use of this term places me at odds with those psychologists, like Piaget, who regard concrete thought as different in kind and less powerful than formal thought. While it is indeed different in kind, it is not less powerful.

Ever since Aristotle, the philosophy of science has had two clearly delineated components: (a) conceptual foundations and (b) methodology. These rather closely correspond to what one might call the metaphysical and the epistemic bases of scientific knowledge. Both branches of philosophy of science have co-existed for a long time. If anything, methodology has usually tended to predominate over foundations.

Recently, however, methodology has come onto hard times and, since the 1960s especially, it has come in for considerable abuse. Some of that abuse is doubtless well-deserved. Much of traditional methodology made assumptions about the nature of scientific inference which simply cannot be sustained.

What Daniel Hausman has called “the simple criticism of economic theory”1 is succinctly conveyed by the following passage: “We know full well not only that commodities are not infinitely divisible (which is only intended as a simplification), but businessmen do not always attempt to maximize profits and that the preferences of consumers are not always transitive. ‘Businessmen maximize profits’ and ‘a consumer’s preferences are transitive’ are fundamental economic ‘laws’. How can economists rationally accept a theory which is so full of falsehoods?” (1981a, p. 382). In a recent paper Hausman considers several defenses of neoclassical microeconomics against the simple criticism. One of them is the modal view which Hausman initially characterizes in the, following admittedly vague and ambiguous manner: “Microeconomic general statements are modal (counter-factual) claims.