How should one discount utility across time? The conventional wisdom in social science is that one should use an exponential discount function. Such a function is a representation of the axioms that provide a well-defined utility function plus a condition known as stationarity. Yet stationarity doesn’t really have much intuitive normative pull on its own. Here I try to cast it in a normative glow by deriving stationarity from two explicitly normative premises, both suggested by the philosophical thesis of temporal neutralism. Putting the argument in this form helps us better understand exponential discounting and challenges to it.

If categorical equivalence is a good criterion of theoretical equivalence, then it would seem that if some class of mathematical structures is represented as a category, then any other class of structures categorically equivalent to it will have the same representational capacities. Hudetz (2019a) has presented an apparent counterexample to this claim; in this note, I argue that the counterexample fails.

Having noted my intention to improve upon other statistical analyses of causal relatedness by providing theoretical means to distinguish cause and effect without reference to temporality [1], Professor Shrader argues [3] that the alternative model I offer falters “before the same sort of examples he had previously used to assail” these other analyses. Although the assailant seems both to have misunderstood the model in question and to have overestimated the effect of his counterexamples, his objections provide a welcome opportunity for clarification.

Here, we hypothesize that a smooth nongeodesic closed timelike curve is never most efficient with respect to total acceleration if a kink is permitted at the initial (terminal) point. We support our hypothesis in a variety of ways. Most notably, we show Malament's opposing conjecture concerning Gödel space-time to be false.

I develop an account of ecological role functions—the functions of species within ecosystems—that is informed by alternative regime phenomena in ecology. My account is a causal-role theory that includes a counterfactual sensitivity condition. The account tracks and explains a distinction ecologists make between functions and various activities that are not functions. My counterfactual sensitivity condition resolves the liberality problem often attributed to causal-role theories of function while also illuminating the explanatory centrality of role functions within ecology.

The epoch-making revolution that has been taking place in mathematics and physics during the past hundred years is gradually changing our whole conception of reality and of the function of science in regard to it. We have discovered that the “common sense” view of the world which has become ingrained in the feeling-thought habits of Western man, especially since the seventeenth century, contains elements of serious limitation and even an illusion both from the standpoint of immediately intuited experience and from that of demonstrated scientific fact. Moreover, by a long drawn out tortuous process, lasting over many centuries and involving the constant creation and correction of an enormously complicated scientific structure, we have finally arrived at an understanding of what may be the root of our difficulty. It seems that certain peculiarities of the over-all grammatical structure of those languages that have conditioned the feeling-thought world of the West have tended to lead us astray. Their correction, however, has so far been possible only through the invention of new esoteric languages, such as the symbolism of mathematics and the new logic. By means of these “languages of science” modern mathematicians and physicists have at last succeeded in freeing themselves from the shackles of their everyday speech and “common sense” concepts, at least so far as their scientific work is concerned.

The Lorentz-formulae are deduced from three factual statements the physical meaning of which is explained in terms of operations with clocks, light-signals and measuring rods. These statements are:

(1) The time-length of a process is invariant.

(2) The velocity of light is the same in all inertial systems.

(3) The velocity of light is independent of the source.

It is also shown that these statements can be deduced from the Lorentz-formulae. They are the physical content of the latter.

The principle of relativity and the light-principle together, however, contain more physical meaning than the Lorentz-formulae.

Operational definitions are given for all relevant concepts.

This essay considers a mixed-effects modeling practice and its implications for the philosophical debate surrounding reductive explanation. Mixed-effects modeling is a species of the multilevel modeling practice, where a single model incorporates simultaneously two (or even more) levels of explanatory variables to explain a phenomenon of interest. I argue that this practice makes the position of explanatory reductionism held by many philosophers untenable because it violates two central tenets of explanatory reductionism: single-level preference and lower-level obsession.

Most handbooks on statistics and the theory of probability leave the reader in a mysterious tangle of mathematical rules for computing apparently arbitrarily chosen numerical functions. At first sight, then, a treatise on the Logical Foundations of Probability raises hopes that it will be a guide to clarity in these matters. These hopes are strengthened if the reader remembers that the author, Professor Rudolph Carnap of the University of Chicago, is noted for his thesis that philosophy is the study of the logic of science. On the other hand, a first glance into this book may discourage a reader who, though familiar with statistics, is not familiar with modern logic and its notation. For this reason particularly I shall try to give an account of this book that will enable the interested student to form some opinion of its usefulness to him.

Freedom is variability within a system. I venture to give this definition as a natural extension of a series of discussions dealing with what I call materialistic analysis and insight. Objects and such, as I portrayed them, may be analyzed or comprehended as wholes (insighted). The questions were always lurking in my discussion, however, whether an analysis or an insight must be unique, whether it is sharply determined or not, whether it is fixed or variable, whether there are alternative analyses and insights, and whether in some sense one is “free” to choose his analysis or insight. In suggesting these questions, I was not referring to the possible lack of talent of the thinker, who might have a hopelessly single-track mind, but to the objective limitations set by the object being thought about and the observer doing the thinking. I was referring to an emphatically comprehensive freedom, persistently objective although it embraces a so-called “subject.” This freedom I would call materialistic or concrete freedom, and it is this freedom that I wish to discuss. What I call objective includes many things described—carelessly, I believe—as subjective. For better or for worse, I propose to limit the term subjective in connection with freedom to what would be specifically described as purely subjective. The purely subjective notion of freedom would make it absolute, completely arbitrary, infinitely variable, independent of matter as a pure phenomenon of mind, and empirically unverifiable in the sense of being most private. Such freedom I would be unable to discuss were I rash enough to want to do so. Such freedom is personal and mystical and hence not subject to the finite prison of discussion with its bars of language, its narrow bed of fact and its threat of the strait jacket for the prisoner who imagines words to be what they are not to all others. Otherwise, there is no objection to retaining the term “subjective” for the objective behavior of a “subject.” The blend of such subjective factors (arising in subjects) with factors we habitually call objective (arising in objects) I call materialistic. I have no more affection for the purely objective than for the purely subjective. The blend is the thing.

Complex life cycles are common in the eukaryotic world, and they complicate the question of how to define individuality. Using a bottom-up, gene-centric approach, I consider the concept of fitness in the context of complex life cycles. I analyze the fitness effects of an allele (or a trait) on different biological units within a complex life history and how these effects drive evolutionary change within populations. Based on these effects, I attempt to construct a concept of fitness that accurately predicts evolutionary change in the context of complex life cycles.

There is a significant and a too little noted analogy between the histories of the physical and the “mental” sciences—especially psychology—an analogy capable of throwing much light upon the present-day problems of the latter. Some aspects of this analogy have become commonplaces, but others have been almost completely overlooked.

The status of a causal approach to EPR-Bell nonlocal correlations in terms of a counterfactual framework for causation is considered. It is argued that when the relativistic spacetime structure of the events is taken into due account, the adoption of this approach is best motivated by the assumption of a preferred frame of reference, an assumption that seems even more in need of justification than the causal theory itself.

The first aim of science has been analysis. From Leucippus in the fifth century B.C. to Sir Arthur Eddington today, science has tried to reduce nature to simple structural units. For Leucippus the atoms are structurally alike, though they differ in external characteristics, such as size and shape. The aim of physics today is expressed by Sir Arthur Eddington: “The aim of the analysis employed in physics is to resolve the universe into structural units which are precisely alike one another ... so that all variety originates in the structure and not in the elements out of which the structure is built.” To be sure, that is an ideal. In practice we speak of electrons, protons, neutrons. But that does not alter the problem. The question is: Are there such structural units?