Jeanne Peijnenburg

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems

We have never entirely agreed with Daniel Cohnitz on the status and rôle of thought experiments. Several years ago, enjoying a splendid lunch together in the city of Ghent, we cheerfully agreed to disagree on the matter; and now that Cohnitz has published his considered opinion of our views, we are glad that we have the opportunity to write a rejoinder and to explicate some of our disagreements. We choose not to deal here with all the issues that Cohnitz raises, but rather to restrict ourselves to three specific points

Various arguments have been put forward to show that Zeno-like paradoxes are still with us. A particularly interesting one involves a cube composed of colored slabs that geometrically decrease in thickness. We first point out that this argument has already been nullified by Paul Benacerraf. Then we show that nevertheless a further problem remains, one that withstands Benacerraf’s critique. We explain that the new problem is isomorphic to two other Zeno-like predicaments: a problem described by Alper and Bridger in 1998 and a modified version of the problem that Benardete introduced in 1964. Finally, we present a solution to the three isomorphic problems

Often, regret implies the wish not to have performed certain actions. In this article I claim that this wish can to some extent be fulfilled: it is possible, in a sense, to influence the character of actions that have already been performed. This possibility arises from combining a first person perspective with an outlook on actions as expressions of tendencies, where tendencies are identified on the basis of a number of actions. The idea is specified within the framework of Carnapian reduction sentences, but this technique is in no sense mandatory: it can be formulated in other vocabularies as well

From 1929 onwards, C. I. Lewis defended the foundationalist claim that judgements of the form 'x is probable' only make sense if one assumes there to be a ground y that is certain (where x and y may be beliefs, propositions, or events). Without this assumption, Lewis argues, the probability of x could not be anything other than zero. Hans Reichenbach repeatedly contested Lewis's idea, calling it "a remnant of rationalism". The last move in this debate was a challenge by Lewis, defying Reichenbach to produce a regress of probability values that yields a number other than zero. Reichenbach never took up the challenge, but we will meet it on his behalf, as it were. By presenting a series converging to a limit, we demonstrate that x can have a definite and computable probability, even if its justification consists of an infinite number of steps. Next we show the invalidity of a recent riposte of foundationalists that this limit of the series can be the ground of justification. Finally we discuss the question where justification can come from if not from a ground

The meaning of mental terms and the status of mental entities are core issues in contemporary philosophy of mind. It is argued that the old Reichenbachian distinction between abstracta and illata might shed new light on these issues. First, it suggests that beliefs, desires and other pro-attitudes that make up the higher mental life are not all equally substantial or real. Second, it conceives the elements of the lower mental life as entities that are inferred from concrete, observable events. As a consequence, it might teach us two lessons: first, to see reliefs in the higher mental map, and second, to acknowledge that qualia are probabilistically inferred rather than directly experienced

It is widely held that the paradox of Achilles and the Tortoise, introduced by Zeno of Elea around 460 B.C., was solved by mathematical advances in the nineteenth century. The techniques of Weierstrass, Dedekind and Cantor made it clear, according to this view, that Achilles’ difficulty in traversing an infinite number of intervals while trying to catch up with the tortoise does not involve a contradiction, let alone a logical absurdity. Yet ever since the nineteenth century there have been dissidents claiming that the apparatus of Weierstrass et al. has not resolved the paradox, and that serious problems remain. It seems that these claims have received unexpected support from recent developments in mathematical physics. This support has however remained largely unnoticed by historians of philosophy, presumably because the relevant debates are cast in mathematical-technical terms that are only accessible to people with the relevant training. That is unfortunate, since the debates in question might well profit from input by philosophers in general and historians of philosophy in particular. Below we will first recall the Achilles paradox, and describe the way in which nineteenth century mathematics supposedly solved it. Then we discuss recent work that contests this solution, reiterating the dissident dogma that no mathematical approach whatsoever can even come close to solving the original Achilles. We shall argue that this dissatisfaction with a mathematical solution is inadequate as it stands, but that it can perhaps be reformulated in the light of new developments in mathematical physics.

Kuipers' model of action explanation is compared, first with that of Anscombe, and then with models in the post-Anscombian tradition. Whereas Kuipers and Anscombe differ on the question of the first-person view, the difference with post-Anscombian writers concerns the so-called intentional statement. Kuipers criticizes the models of both Hempel and von Wright for their lack of an intentional statement. Kuipers' own model seems immune to this criticism, since it contains no less than two intentional statements, a "specific" and an "unspecific" one. I argue that, contrary to appearances, it is not so immune. The call for intentional statements is in fact a call for intentions that are irreducible to beliefs and desires. Kuipers' intentional statements, however, are about intentions that can be so reduced.

It is argued that the recent revival of theakrasia problem in the philosophy of mind is adirect, albeit unforeseen result of the debate onaction explanation in the philosophy of science. Asolution of the problem is put forward that takesaccount of the intimate links between the problem ofakrasia and this debate. This solution is basedon the idea that beliefs and desires have degrees ofstrength, and it suggests a way of giving a precisemeaning to that idea. Finally, it is pointed out thatthe solution captures certain intuitions of bothSocrates and Aristotle.

Suppose q is some proposition, and let P(q) = v0 (1) be the proposition that the probability of q is v0.1 How can one know that (1) is true? One cannot know it for sure, for all that may be asserted is a further probabilistic statement like P(P(q) = v0) = v1, (2) which states that the probability that (1) is true is v1. But the claim (2) is also subject to some further statement of an even higher probability: P(P(P(q) = v0) = v1) = v2, (3) and so on. Thus, an infinite regress emerges of probabilities of probabilities, and the question arises as to whether this regress is vicious or harmless. Radical probabilists would like to claim that it is harmless, but Nicholas Rescher (2010), in his scholarly and very stimulating Infinite Regress: The Theory and History of Varieties of Change, argues that it is vicious. He believes that an infinite hierarchy of probabilities makes it impossible to know anything about the probability of the original proposition q: unless some claims are going to be categorically validated and not just adjudged probabilistically, the radically probabilistic epistemology envisioned here is going to be beyond the prospect of implementation. . . . If you can indeed be certain of nothing, then how can you be sure of your probability assessments. If all you ever have is a nonterminatingly regressive claim of the format . . . the probability is .9 that (the probability is .9 that (the probability of q is .9)) then in the face of such a regress, you would know effectively nothing about the condition of q. After all, without a categorically established factual basis of some sort, there is no way of assessing probabilities. But if these requisites themselves are never categorical but only probabilistic, then we are propelled into a vitiating regress of presuppositions.

This book is the second of two volumes devoted to the work of Theo Kuipers, a leading Dutch philosopher of science. Philosophers and scientists from all over the world, thirty seven in all, comment on Kuipers’ philosophy, and each of their commentaries is followed by a reply from Kuipers. The present volume is devoted to Kuipers’ neo-classical philosophy of science, as laid down in his Structures in Science . Kuipers defends a dialectical interaction between science and philosophy in that he views philosophy of science as a meta-science which formulates cognitive structures that provide heuristic patterns for actual scientific research, including design research. In addition, Kuipers pays considerable attention to the computational approaches to philosophy of science as well as to the ethics of doing research. Thomas Nickles, David Atkinson, Jean-Paul van Bendegem, Maarten Franssen, Anne Ruth Mackor, Arno Wouters, Erik Weber & Helena de Preester, Eric Scerri, Adam Grobler & Andrzej Wisniewski, Alexander van den Bosch, Gerard Vreeswijk, Jaap Kamps, Paul Thagard, Emma Ruttkamp, Robert Causey, Henk Zandvoort comment on these ideas of Kuipers, and many present their own account. The present book also contains a synopsis of Structures in Science. It can be read independently of the first volume of Essays in Debate with Theo Kuipers, which is devoted to Kuipers’ From Instrumentalism to Constructive Realism

This book is the first of two volumes devoted to the work of Theo Kuipers, a leading Dutch philosopher of science. Philosophers and scientists from all over the world, thirty seven in all, comment on Kuipers' philosophy, and each of their commentaries is followed by a reply from Kuipers. The present volume focuses on Kuipers' views on confirmation, empirical progress, and truth approximation, as laid down in his From Instrumentalism to Constructive Realism (Kluwer, 2000). In this book, Kuipers offered a synthesis of Carnap's and Hempel's confirmation theory on the one hand, and Popper's theory of truth approximation on the other. The key element of this synthesis is a sophisticated methodology, which enables the evaluation of theories in terms of their problems and successes (even if the theories are already falsified), and which also fits well with the claim that one theory is closer to the truth than another. Ilkka Niiniluoto, Patrick Maher, John Welch, Gerhard Schurz, Igor Douven, Bert Hamminga, David Miller, Johan van Benthem, Sjoerd Zwart, Thomas Mormann, Jesús Zamora Bonilla, Isabella Burger & Johannes Heidema, Joke Meheus, Hans Mooij, and Diderik Batens comment on these ideas of Kuipers, and many present their own account. The present book also contains a synopsis of From Instrumentalism to Constructive Realism. It can be read independently of the second volume of Essays in Debate with Theo Kuipers, which is devoted to Kuipers' Structures in Science (2001).

We have earlier shown by construction that a proposition can have a welldefined nonzero probability, even if it is justified by an infinite probabilistic regress. We thought this to be an adequate rebuttal of foundationalist claims that probabilistic regresses must lead either to an indeterminate, or to a determinate but zero probability. In a comment, Frederik Herzberg has argued that our counterexamples are of a special kind, being what he calls ‘solvable’. In the present reaction we investigate what Herzberg means by solvability. We discuss the advantages and disadvantages of making solvability a sine qua non , and we ventilate our misgivings about Herzberg’s suggestion that the notion of solvability might help the foundationalist.