The unique role of the second derivative of position with respect to time in classical mechanics is investigated. It is indicated that mechanics might have been developed around other order derivatives. Examples based on $\overset \ldots \to{x}$ and $\overset....\to{x}$ are presented. Kirchhoff's argument for using ẍ is given and generalized.

The fundamental tenet of modern empiricism is the view that all non-analytic knowledge is based on experience. Let us call this thesis the principle of empiricism. [1] Contemporary logical empiricism has added [2] to it the maxim that a sentence makes a cognitively meaningful assertion, and thus can be said to be either true or false, only if it is either (1) analytic or self-contradictory or (2) capable, at least in principle, of experiential test. According to this so-called empiricist criterion (...) of cognitive meaning, or of cognitive significance, many of the formulations of traditional metaphysics and large parts of epistemology are devoid of cognitive significance--however rich some of them may be in non-cognitive import by virtue of their emotive appeal or the moral inspiration they offer. Similarly certain doctrines which have been, at one time or another, formulated within empirical science or its border disciplines are so contrived as to be incapable of test by any conceivable evidence; they are therefore qualified as pseudo- [p. 42:] hypotheses, which assert nothing, and which therefore have no explanatory or predictive force whatever. This verdict applies, for example, to the neo-vitalist speculations about entelechies or vital forces, and to the "telefinalist hypothesis" propounded by Lecomte du Noüy. (shrink)

Reminiscences of Peter, by P. Oppenheim.--Natural kinds, by W. V. Quine.--Inductive independence and the paradoxes of confirmation, by J. Hintikka.--Partial entailment as a basis for inductive logic, by W. C. Salmon.--Are there non-deductive logics?, by W. Sellars.--Statistical explanation vs. statistical inference, by R. C. Jeffre--Newcomb's problem and two principles of choice, by R. Nozick.--The meaning of time, by A. Grünbaum.--Lawfulness as mind-dependent, by N. Rescher.--Events and their descriptions: some considerations, by J. Kim.--The individuation of events, by D. Davidson.--On properties, by (...) H. Putnam.--A method for avoiding the Curry paradox, by F. B. Fitch.--Publications (1934-1969) by Carl G. Hempel (p. [266]-270). (shrink)

The so-called "non-commutativity" of probability kinematics has caused much unjustified concern. When identical learning is properly represented, namely, by identical Bayes factors rather than identical posterior probabilities, then sequential probability-kinematical revisions behave just as they should. Our analysis is based on a variant of Field's reformulation of probability kinematics, divested of its (inessential) physicalist gloss.

In the thesis I criticize the project of showing that the primary qualities mentioned in a special "scientific" or "objective" conception of the world enjoy a status that secondary qualities do not, and suggest how the appeal of such a distinction might be overcome. ;Descartes argued that we erroneously ascribe illusory "secondary" qualities to the world. In the painting analogy of the First Meditation I identify a line of reasoning that has been previously overlooked yet is crucial to the success (...) of Descartes's project. I show why Descartes's explanation of how we come to have the supposedly erroneous beliefs is unacceptable, and that contemporary accounts of so-called projective error fail for similar reasons. These failures suggest that an explanation of the thoughts we do have cannot succeed without appeal to more than the limited resources Descartes took to be available. ;Pursuing this suggestion I examine alternatives to the form of anti-skeptical reasoning of the painting analogy. I develop a modified transcendental strategy that resembles aspects of Davidson's treatment of error, while respecting the realism that motivates the project in question. I argue that beliefs about the colors of objects, for example, are systematically related and that the attribution of systematic disagreement cannot be justified. This shows that the systematic error Descartes claimed to find in our ordinary judgements is not fully intelligible. ;Finally I survey some contemporary alternatives to Descartes's account. Many dispositional analyses of qualities aim to revise our ordinary understanding of these qualities, thus taking for granted a prior demonstration of the distinction in question. I argue that no non-revisionary dispositional analysis of these qualities can succeed. I show that the notion of "anthropocentricity" is irrelevant to the project. Lastly I consider accounts that characterize primary qualities by their explanatory power. Previous arguments show that identifying some objects as possessing certain qualities is a condition of identifying beliefs as beliefs about those qualities. I end with a lesson about the limits of the explanatory power of a special austere conception of the world. (shrink)

Can a man intend to do the impossible? That is, can a man undertake to do some action, A—and not merely to come as close as possible to doing A with the hope that the doing of A will result—when he believes he has no chance of doing A?

We introduce the notion of "semi-r.e." for subsets of ω, a generalization of "semirecursive" and of "r.e.", and the notion of "weakly semirecursive", a generalization of "semi-r.e.". We show that A is weakly semirecursive iff, for any n numbers x 1 ,...,x n , knowing how many of these numbers belong to A is equivalent to knowing which of these numbers belong to A. It is shown that there exist weakly semirecursive sets that are neither semi-r.e. nor co-semi-r.e. On the (...) other hand, we exhibit nonzero Turing degrees in which every weakly semirecursive set is semirecursive. We characterize the notion "A is weakly semirecursive and recursive in K" in terms of recursive approximations to A. We also show that if a finite Boolean combination of r.e. sets is semirecursive then it must be r.e. or co-r.e. Several open questions are raised. (shrink)

It is shown that for every nonzero r.e. degree c there is a linear ordering of degree c which is not isomorphic to any recursive linear ordering. It follows that there is a linear ordering of low degree which is not isomorphic to any recursive linear ordering. It is shown further that there is a linear ordering L such that L is not isomorphic to any recursive linear ordering, and L together with its ‘infinitely far apart’ relation is of low (...) degree. Finally, an analogue of the recursion theorem for recursive linear orderings is refuted. (shrink)

We establish a probabilized version of modus tollens, deriving from p(E|H)=a and p()=b the best possible bounds on p(). In particular, we show that p() 1 as a, b 1, and also as a, b 0. Introduction Probabilities of conditionals Conditional probabilities 3.1 Adams' thesis 3.2 Modus ponens for conditional probabilities 3.3 Modus tollens for conditional probabilities.

1. Object of this note . In his lively essay, “Between Analytic and Empirical,” , Mr. J. W. N. Watkins challenges the empiricist identification of synthetic statements with empirical ones by arguing that there exists an important class of statements which are synthetic, i.e. not analytically true or false, and yet not empirical. I find Mr. Watkins's arguments very stimulating, but I do not think they provide a sound basis for his contention. In the present note, I wish to indicate (...) what seem to me the principal flaws in Mr. Watkins's reasoning, and to make some additional comments on the issues raised by his discussion. (shrink)

Genuine religion always involves the worship of what is genuinely ultimate. Religion, worship, and ultimate reality are thus indissolubly related. The task of reflective thought in this domain is to distinguish what is sound from what is spurious in religion; to characterise the meaning of religious devotion; and to attempt to articulate the nature of the ultimate reality to which men's worship is directed.

It has often been recommended that the differing probability distributions of a group of experts should be reconciled in such a way as to preserve each instance of independence common to all of their distributions. When probability pooling is subject to a universal domain condition, along with state-wise aggregation, there are severe limitations on implementing this recommendation. In particular, when the individuals are epistemic peers whose probability assessments are to be accorded equal weight, universal preservation of independence is, with a (...) few exceptions, impossible. Under more reasonable restrictions on pooling, however, there is a natural method of preserving the independence of any fixed finite family of countable partitions, and hence of any fixed finite family of discrete random variables. (shrink)

Garber (1983) and Jeffrey (1991, 1995) have both proposed solutions to the old evidence problem. Jeffrey's solution, based on a new probability revision method called reparation, has been generalized to the case of uncertain old evidence and probabilistic new explanation in Wagner 1997, 1999. The present paper reformulates some of the latter work, highlighting the central role of Bayes factors and their associated uniformity principle, and extending the analysis to the case in which an hypothesis bears on a countable family (...) of evidentiary propositions. This extension shows that no Garber-type approach is capable of reproducing the results of generalized reparation. (shrink)

1. The problem. The concept of confirmation of an hypothesis by empirical evidence is of fundamental importance in the methodology of empirical science. For, first of all, a sentence cannot even be considered as expressing an empirical hypothesis at all unless it is theoretically capable of confirmation or disconfirmation, i.e. unless the kind of evidence can be characterized whose occurrence would confirm, or disconfirm, the sentence in question. And secondly, the acceptance or rejection of a sentence which does represent an (...) empirical hypothesis is determined, in scientific procedure, by the degree to which it is confirmed by relevant evidence. (shrink)