My purpose in this talk is to give an overview of the rediscovery of Frege's theorem together with certain of the issues that this rediscovery has raised concerning the evaluation of Frege's logicism—the ‘old doctrine’ of my title.

The contextual definition of the cardinality operator, suggested in §63 of Grundlagen— what, after George Boolos, has come to be known as Hume's principle—asserts

where F ≈ G (the Fs and the Gs are in one-to-one correspondence) has its usual, second order, explicit definition. The importance of this principle for the derivation of Peano's second postulate (‘Every natural number has a successor’) was emphasized by Crispin Wright (1983, §xix) who presented an extended argument showing that, in the context of the system of second-order logic of Frege's Begriffsschrift, Peano's second postulate is derivable from Hume's principle.

In his first philosophy book, Science and Hypothesis, Poincaré gives us a picture which relates the different sciences to different kinds of hypotheses. In fact, as Michael Friedman has pointed out (Friedman 1995), Poincaré arranges this book—chapter by chapter—in terms of a hierarchy of sciences. Arithmetic is the most general of all the sciences because it is presupposed by all the others. Next comes mathematical magnitude, or the analysis of the continuum, which presupposes arithmetic; then geometry which presupposes magnitude; the principles of mechanics which presuppose geometry; and finally experimental physics which presupposes mechanics. Poincaré's basic view was that experiment in science depends on fixing other concepts first. In particular he believed at the time that our concept of space had to be fixed before we could discover truths about the objects in space.

Sometimes themes exist only in the eye of the beholder and emerge from the history of mathematics only with the benefit (or otherwise) of hindsight. There is however at least one issue (no doubt there are others) which was clearly present throughout the foundational debates of the early Twentieth century. It formed the core component of one of the major traditions that grew up as responses to the paradoxes, though the intuition behind it has never been fully articulated nor has it been possible to give a fully fledged mathematical articulation to that intuition. Essentially the central idea is that of ‘indefinite extensibility’ generated by an appropriate form of diagonalisation and it has its fundamental source in Richard's paradox and in particular in Poincaré's response to that paradox.

Of the four great epistemological concerns around which much of the work in the foundations of mathematics this century has concentrated viz the notions of demonstrability, definability, set or class and computability only the latter clearly falls outside the scope of the Richard type reasoning.

Aristotle's De Partibus Animalium (PA) is, if there ever was one, a classic. It consists, at the broadest level, of four books. The first is devoted to articulating (I'm quoting its introduction) “…standards, by reference to which one will judge the manner of the demonstrations <of natural inquiry>, apart from the question of how the truth has it, whether thus or otherwise.” (639al2-15). Books II-IV, on the other hand, are introduced as attempts to provide causal explanations for the facts regarding the parts that belong to the various kinds of animals, facts systematically organized in the Historia Animalium. (646a8-12). This means that Aristotle's De Partibus consists of an introductory book on the philosophy of biological science, and three books of biological science.

Such an arrangement provides the student of this great work an opportunity to explore one of the perennial issues in the history and philosophy of science: the connection between a scientist's theory of science, and his actual scientific practice.

The aim of this paper is to suggest that Galileo's Dialogue may be fruitfully interpreted and evaluated from the viewpoints of methodological judgment and critical reasoning. This approach has significant historical precedents in the readings of Thomas Salusbury and the Port-Royal logicians. This focus on the book's philosophical dimension is not meant to exclude its scientific, historical, rhetorical, and aesthetic dimensions; indeed, such anti-reductionism is suggested by methodological judgment applied at the metalevel; the latter also suggests a criticism of the excessively rhetorical readings prevalent today, as well as viable ways for resolving the problems of hermeneutical pluralism, interpretation versus evaluation, and theory versus practice. Finally, the book's methodological judgment and critical reasoning can be shown to correspond to Galileo's intentions and self-reflections.

The opening paragraphs of Thomas Kuhn's Structure of Scientific Revolutions noted that different kinds of scientific writings have peculiar roles (Kuhn 1962). A textbook written for pedagogical purposes in a well-established scientific field gives a view of the field quite different from the actual history—an actual history that for the most part has to be reconstructed from the writings that originated the field. The originating writings correspond to the period of founding, to revolutionary science, whereas conventionalized textbooks belong to normal science.

This is almost too well known to be rehearsed again. Certain works found a science, like Newton's Opticks or Watson and Crick's original papers on the double-helical structure of DNA; others come in their wake, not just textbooks used for beginners but all the future texts that contribute to the paradigm project embodied in the originals.

The term ‘classic’ runs a risk that all our terms of approbation face in these inflationary times, the risk, that is, of losing its ability to mark off singular works of human achievement. A “classic” today might be anything from a horse-race to a hairstyle. But it was not always so. There is some debate about the origins of the term (“of the highest class”? “books for class use”?), but it long ago came to designate those works of Greek and Latin literature that for centuries shaped the education of young Western Europeans. These books were held up not only as models of literary accomplishment but also as sources of moral and social wisdom. Though they were composed in ages long past, their resonance was still felt in the present. And so the broader sense developed of a significant literary work of the past that still in one way or another speaks to us today.

Traditional philosophy of science concentrated on logic and methodology, dismissing psychology and sociology as irrelevant (except for the context of discovery). Recent movements to ‘naturalize’ philosophy of science have reinstated psychological and social factors repudiated by the tradition, but these two types of factors have mostly been addressed independently and by different authors. Most cognitive approaches (e.g., Thagard 1989a, 1992; Churchland 1989) pursue the microcognition of science in abstraction from the social, and most sociologists of science ignore, post pone, or reject cognitive explanations of science (Latour and Woolgar 1986, 280). More recently, however, several philosophers of science have urged a blending of the cognitive and the social (Thagard 1993, in press, Solomon 1992, 1994a, 1994b, Kitcher 1993, Giere 1988), and this paper has a similar thrust. I shall not endorse a reduction of the social to the psychological, but a substantial overlap or intermingling of the two.

Philosophers are particularly susceptible to the temptation to produce what Donna Haraway calls a “TOE (=a Theory of Everything)” (Haraway 1994). Many of us like to integrate the methods and results of different disciplines, discern underlying unity in bifurcations and thereby—so we think—get closer to a single, true, representation of the universe. Proposals to integrate cognitive and social models of scientific change have come from philosophers—and not from historians, sociologists, feminist critics, anthropologists, rhetoricians or semioticians of science. The proposals are also responses to the growing influence of sociologists of science (e.g. Collins, Latour, Shapin, Woolgar) who have taken stands on epistemological matters, formerly the province of philosophers. It is common among sociologists of science to reject all proposals to integrate cognitive and social accounts, as well as to reject all cognitive accounts: Bruno Latour's famous moratorium on cognitive studies of science (Latour 1987, 247) is one example of this.

In 1979, Dr. J. Robin Warren of the Royal Perth Hospital in Australia discovered bacteria in the biopsies of stomach tissue taken from patients with digestive complaints. His colleague Dr. Barry Marshall followed up on Warren's work and found the bacteria in many patients with stomach inflammation and peptic ulcers (Marshall and Warren 1984). When Marshall claimed at a medical conference that bacteria are the principal cause of peptic ulcers, his remarks were rejected as preposterous. It was widely believed that the human stomach's caustic gastric juices made it too antiseptic for bacteria to survive for long. Moreover, alternative explanations of the principal cause of ulcers were available, focusing on excess acidity and emotional stress. Stung by rejection of his theory and failure of animal experiments, Marshall resorted in 1984 to drinking the bacteria himself, and underwent endoscopy and biopsy to show that his stomach had indeed become inflamed (Monmaney 1993).

When reading the papers of Solomon, Thagard and Goldman, I observed their framing doing considerable explicit and implicit work. Framing, a visual metaphor, stimulated me to respond with images of one kind or another. These should allow readers to visualize more issues and propositions than an argumentive format could have pinned down in the limited space available.

Figure 1 conveys how the three papers seem to me to frame the issue of integrating the cognitive and social: Scientists’ beliefs are the focal phenomena, within three nested boxes of factors surrounding them: thinking (reasoning etc.); cognition (information input and processing); and social (interaction among agents). (The other objects and lines will be explained in due course.) These factors are referred to as influences, something outside that gets into beliefs (1). The authors then argue about which set of influences is strongest or how to think about the factors “intermingling,” “overlapping,” “interacting.”.

The Human Genome Project (henceforth HGP) arouses strong feelings. Enthusiasts view it as the culmination of the extraordinary progress of molecular biology during the past half century and as the beginnings of a revolutionized biology and medicine (Gilbert 1992, Caskey 1992). Detractors charge that it is wasteful, misguided, and pregnant with possibilities for social harm (Lewontin 1992, Hubbard and Wald 1993). In a short paper it is plainly impossible to explore all the sources of disagreement. My aim will be to consider the debate about the purely scientific merit of the HGP, to sketch the nature of the short-term issues which the project raises, and, finally, to identify what I take to be the deepest and most difficult questions.

The official goals of the HGP are to map and sequence the human genome, and the genomes of other organisms (so-called “model organisms”).

Newborn screening for the genetic disease phenylketonuria (PKU) is generally considered the greatest success story of applied human genetics. Paradoxically, it is invoked both by those who stress the value and those who emphasize the limitations of genetic medicine.

PKU screening is often cited as a model for genetic medicine and as a precedent for those who favor the expansion of genetic tests (Azen 1991, 35; Scriver 1991; Bishop and Waldholz 1990, 18-19). But even those skeptical of most screening programs tend to describe this program in sunny terms (Natowicz and Alper 1991, 387-89; Nelkin and Tancredi 1989, 160). The near-consensus on the success of PKU screening is explained by the variety of interests the example serves. Untreated phenylketonuria results in severe mental retardation and behavioral disorders. But if it is identified in the newborn, the disease is treatable through a special diet.

In the Museum of Science and Technology in San Jose, California, there is a display dedicated to advances in biotechnology. Most prominent in the display is a double helix of telephone books stacked in two staggered spirals from the floor to the ceiling twenty five feet above. The books are said to present the current state of our knowledge or the eurcaryotic genome: the primary sequences of DNA polynucleotides for the gene products which have been discovered so far in the twenty years since cloning and sequencing the genome became possible.

In order to grasp what is problematical about the human genome project (HGP), I want you to hold on to this image of a stack of phone books, or rather two stacks, helictical in shape. Imagine that each of the phone books about the size of the Manhattan white pages, and that the two stacks of phone books reach up a mile and a half into the sky.

Traditionally, philosophy of science has focused on the product of science: the scientific hypothesis, principle, law, or more grandiosely, the theory. Using logician's license I'll think of hypotheses and theories as ‘little’ and ‘big’ (or ‘weak’ and ‘strong’) propositions. The tradition spoke of the product as (scientific) knowledge; the more recent phrase “current scientific opinion” carries the same connotation of uniqueness. For this to make sense, something is required: a proposition must be capable of being true or false, capable of being fully believed or disbelieved (and if you like, known).

Probabilism requires us to look at every aspect of science in a new way. In his radical brand of probabilism, Richard Jeffrey told us to reconceptualize knowledge as 'probable knowledge’ and propositions as ‘probasitions’—and never to resolve doubt but simply to quantify it, keeping all possibilities in play.

Richard Jeffrey advocates fallibilism in the form of radical probabilism. Degrees of belief are the objects of prime interest to epistemology and it is rarely plausible that they should take the extreme form of certainty. In particular the creation of certainties by the process of belief change by conditionalization is not necessary:

Pluralism is usually opposed to realism. That's why realists tend to affirm reductionism, even if only the lapsed reductionism of supervenience. It is no accident that postmoderns talk about the different worlds we live in. The realist is bent upon one world with one history, and that is the history for the sciences to tell about it, albeit with different degrees of precision, for different purposes and different points of view. The opposition between realism and pluralism is multiplied when the domains of different theories float about as in the balloon image of the relation of the sciences (Figure 1) and when no combination of fields can together supply a set of descriptions in terms of which at least one baseline history can be told. But the opposition is not necessary.

In both philosophical writing on science and scientific practice itself there has been a long standing interest in theories and explanatory frameworks that unify various phenomena. In the history of physics the most successful theories are often those that supposedly show how diverse effects can be understood as aspects of a single underlying principle or cause. For example, Maxwell's electrodynamics unified electromagnetism and optics by providing a theoretical demonstration that light and electromagnetic waves have the same velocity and are manifestations of the same kind of process. More recently in the 1970's Glashow, Weinberg and Salam produced a unified description of both electromagnetic and the weak interactions. This electroweak theory successfully describes electromagnetic interactions as well as data from a variety of electroweak processes including scattering and number of different particle collisions.

Most discussion of the unity of science has concerned what might be called vertical relations between theories: the reducibility of biology to chemistry, or chemistry to physics, and so on. In this paper I shall be concerned rather with horizontal relations, that is to say, with theories of different kinds that deal with objects at the same structural level. Whereas the former, vertical, conception of unity through reduction has come under a good deal of criticism recently (see, e.g., Dupré 1993), horizontal unity has generally been conceded to be an important goal. The most pressing questions about horizontal unification arise in the study of human behavior. Numerous sciences including psychology, economics, anthropology, sociology, and parts of biology, attempt to provide explanations of human behavior. It is possible that some of these sciences may be able to coexist peacefully or even cooperatively.

The discipline of biological taxonomy is rife with philosophical controversies. One of them is particularly relevant to the topic of this symposium, namely the question of taxonomic unity. Should biologists aim for a single correct classification of the world's organisms or should they allow a plurality of equally correct classifications?

For those with little or no background in evolutionary biology, the suggestion of taxonomic pluralism might seem odd. Don't introductory biology texts as well as television nature shows suggest that there is a single correct way to sort the world's organisms? They do, but that advertised agreement masks a number of controversies that have raged in biology since Darwin's time. Consider the question of how to sort organisms into species. Currently there are no less than seven prominent definitions of the species category (Ereshefsky 1992a).