Kepler’s achievements are well known and can be stated succinctly, or so it seems. Yet he was a complex thinker who responded in unusual ways to many intellectual currents in astronomy and other disciplines. To set Kepler in his intellectual context I offer a few preliminary remarks on the historical development and the inner logic of the derivations of his laws of planetary motion and sketch some of his theological and methodological commitments that affected his astronomical arguments.

1. Kepler’s contribution to astronomy consists in his three laws: the first two laws (the ellipse and the Area Law) that were derived...

In his important and influential book,How Experiments End, Peter Galison (1987) discusses how scientists decide when a given experiment is finished, and when the supposed fact that it purports to establish can be accepted as fact, and not a mistaken reading of the apparatus, not a result of a malfunctioning piece of equipment, not a misinterpretation of a given observation, and so on. This epistemological question, the transition between individual observations, individual runs of a complex experiment, and the experimental fact that they are supposed to establish is a matter of some discussion in the recent literature in the...

Several closely related methodological themes from Newton were central to the transformation of natural philosophy into natural science as we now know it. These themes continue to be exemplified in research in gravitational physics. One such theme is an attempt to turn theoretical questions into ones that can be answered empirically by measurement. Another is an ideal of empirical success according to which a successful theory has its parameters accurately measured by the phenomena it purports to explain. A third is that phenomena are to be projectable generalizations that fit open-ended bodies of data. All of these themes play an...

According to Einstein’s son-in-law and biographer, Rudolf Kayser, portraits of three figures hung on the wall of Einstein’s Berlin study in the late 1920s: Michael Faraday, James Clerk Maxwell, and Arthur Schopenhauer (Reiser-Kayser 1930, 194).¹ One can guess why Faraday and Maxwell, the inventors of field theory, were there. But I have long been puzzled about what Schopenhauer was doing in this august company.

Something else puzzled me as well. From what source did Einstein draw the idea of “spatiotemporal separability,”—that a non-null spatiotemporal separation is a sufficient condition for the individuation of physical systems and their states, an...

Constructive mathematics takes many forms, representing a variety of philosophical perspectives, but a common thread has been a dissatisfaction with the platonist commitments of classical analysis and set theory and the desire to provide an epistemically more secure alternative. But by what standard can the adequacy of any such alternative be judged? Apart from a priori philosophical principle, surely we are well advised to take seriously Hermann Weyl’s dictum that “it is the function of mathematics to be at the service of the natural sciences” (Weyl 1949, 61). For if a proposed constructivist framework should prove incapable of recovering portions...

In this essay I describe the present state of affairs infundamentaltheoretical physics, as I see it, with particular regard to the recent evolution of the notions of space and time. I believe that we are going through a period of profound confusion, in which we lack a general coherent picture of the physical world capable of embracing what, or at least most of what, we have learned about it. The “fundamental scientific view of the world” of the present time is characterized by an astonishing amount of perplexity, and disagreement, about what time, space, matter, and causality are....

A number of famous stories in the physical literature start out by supposing the state of the world at any given instant can be completely described by means of a quantum-mechanical wave function, and that the linear quantum-mechanical equations of motion amount to a true and complete account of the evolutions of those wave-functions in time. These stories have absurd endings. That those sorts of stories end up that way has come to be called the measurement problem.

The sharpest and clearest of those stories, I think, is the one about Wigner’s friend (1961).

Let me remind you of it....

Similarities between preparations and measurements make it easy to suppose that something like the measurement problem also plagues preparation procedures. Both measurements and preparations are typically modeled as interactions: A system is measured when it interacts with a measuring deviceMand as a resultMexhibits the outcome of the measurement; a systemOis prepared when it interacts with a preparation device and as a result ends up in the state to be prepared. Both are interactions that are supposed to leave one of the interacting systems in a particular state: BecauseMis supposed to exhibit the...

In this essay I show that there is essentially only one way to solve the measurement problem of quantum mechanics. I show how to construct all possible modal interpretations of quantum mechanics that solve the measurement problem formally in a certain sense. One such interpretation is Bohm’s (1952) hidden-variable theory, and all other modal interpretations are hidden-variable theories that preserve the dynamics of quantum mechanics. So a modal interpretation in the sense I propose is a type of Bohmian theory.

The essay is divided into three subsections. In the first I discuss the relation between classical and quantum mechanics by...

There was a time when it seemed that we understood determinism. If a system of differential equations had a unique solution for a given set of boundary and initial conditions, then the entire future evolution of the system in question was thereby determined. In a deterministic world, despite the complexities and vagaries of large scale observation, predictability was guaranteed, at least in principle. Beneath these surface generalizations there was a world of order and clarity whose workings could be gleaned by controlled experiment and observation. In such a world, chance lay only on the surface of things, the result of...

Feynman made this comment in 1964, at a time when the prospects for a grand unified theory of absolutely everything looked particularly bleak. But even if such a theory is vouchsafed to us, I will suggest, physics will still exhibit disunity. Or rather, it will exhibit disunities, for disunity comes in various forms. In this essay I will examine three kinds of disunity, without claiming that my list is exhaustive. At each stage of the discussion, the topic of unity and disunity will be intertwined with another: the use of models in physics. In the central part of the essay...

LetX₁,X₂,X₃, … denote a sequence of observations of a phenomenon (for example, the successive letters in an encrypted text, the successive species observed in a previously unexplored terrain, the success or failure of an experimental surgical procedure). In the classical Johnson-Carnap continuum of inductive methods (Johnson 1932, Carnap 1952), the outcomes that can occur are assumed to be ofT< ∞ possible types or species that are known and equiprobable prior to observation. If, in a sample ofn, there aren₁outcomes of the first type,n₂of the second, and so on, then (under appropriate...

Among my most treasured professional memories is the semester Wilfrid Sellars and I were colleagues. The two of us met an afternoon a week to discuss basic philosophical issues. Fueling that highly productive series of discussions¹ was the shared belief that philosophy of science was that branch of epistemology and metaphysics concerned with our most sophisticated forms of knowledge. Thus, any separation of philosophy of science from epistemology and metaphysics was artificial. That vision seems largely to have disappeared. A recent citation analysis of the epistemology and philosophy of science literatures (Kreuzman 1990) indicates only the most minimal concern with...

Although Kuhn published a paper in 1964 arguing for an important function for thought experiments in science, his fellow philosophers did not find this topic all that interesting until recently. Of the papers, books and anthologies that have appeared in the last half dozen years, most deal with thought experiments in science, primarily physics (Gooding 1990, 1993; Brown 1991, 1993; Nersessian 1993; Hacking 1993). However, a few also deal with thought experiments in philosophy, especially the philosophy of science (Wilkes 1988; Hull 1989; Horowitz and Massey 1991; Sorenson 1992). To my way of thinking, philosophers have done an excellent job...

The problem of sorting out “real” or “natural” properties is as old as philosophy itself. Thus in Plato’sStatesman(287c), the Stranger, in talking to young Socrates about dividing up the arts so as to separate the kingly art, says: “Let us divide them according to their natural divisions as we would carve a sacrificial victim. For we must in every case divide into the minimum number of divisions that the structure permits” (Greek translations come from Hamilton and Cairns 1963).

And Socrates, inPhaedrus(265d, e), talks of two procedures which we might now call synthesis and analysis. “The...

This billiard ball collides with that billiard ball on a certain billiard table, setting the second ball in motion. This is singular causation. Hume used the case as a paradigm of singular causation, and a very good paradigm it is.

But what is iton the side of the objectsthat makes this a case of causation? As we know, analytical philosophers have long been enslaved by Hume’s idea (or what is generally taken to be Hume’s idea) that, setting aside the elements of contiguity and succession which mayor may not be essential, there is nothing in the sequence which...

When Clyde, wanting to get to Chicago, turns north because he thinks that is the way to Chicago, it is surely obvious that what he believes — thatthatis the way to Chicago — explains, or helps explain, why he turns north. If we speak of what is believed as the meaning of the belief (treating referential differences as differences in meaning), then

(1) When beliefs figure in the explanation of behavior, it is their meaning (whatis believed) that explains, or helps explain, why the behavior occurs.

Though not everything we do is explained by what we believe...

I come to the topic of explanations involving rationality as a philosopher of science rather than a philosopher of mind. Nowadays, that is perilous, given that the philosophy of mind has become such a powerful export-oriented philosophical economy. Indeed, these exports have been a source of novelty in some otherwise fairly quiet corners of the philosophical globe — perhaps most notably in the philosophy of social science. Although this might be seen as the reawakening of old disputes, we should not underrate the extent to which these issues are now susceptible to more sophisticated and compelling formulations. I don’t think...