Can some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it can, moreover under conditions that are the same for ten different measures of confirmation. Further we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

Could some evidence confirm a conjunction of two hypotheses more than it confirms either of the hypotheses separately? We show that it might, moreover under conditions that are the same for ten different measures of confirmation. Further, we demonstrate that it is even possible for the conjunction of two disconfirmed hypotheses to be confirmed by the same evidence.

Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.

Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.

An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution (...) that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place. (shrink)

An infinite number of elastically colliding balls is considered in a classical, and then in a relativistic setting. Energy and momentum are not necessarily conserved globally, even though each collision does separately conserve them. This result holds in particular when the total mass of all the balls is finite, and even when the spatial extent and temporal duration of the process are also finite. Further, the process is shown to be indeterministic: there is an arbitrary parameter in the general solution (...) that corresponds to the injection of an arbitrary amount of energy (classically), or energy-momentum (relativistically), into the system at the point of accumulation of the locations of the balls. Specific examples are given that illustrate these counter-intuitive results, including one in which all the balls move with the same velocity after every collision has taken place. (shrink)

A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.

A Zenonian supertask involving an infinite number of identical colliding balls is generalized to include balls with different masses. Under the restriction that the total mass of all the balls is finite, classical mechanics leads to velocities that have no upper limit. Relativistic mechanics results in velocities bounded by that of light, but energy and momentum are not conserved, implying indeterminism. The notion that both determinism and the conservation laws might be salvaged via photon creation is shown to be flawed.

Theo Kuipers describes four kinds of research programs and the question is raised here as to whether string theory could be accommodated by one of them, or whether it should be classified in a new, fifth kind of research program.

Theo Kuipers describes four kinds of research programs and the question is raised here as to whether string theory could be accommodated by one of them, or whether it should be classified in a new, fifth kind of research program.

The notion of probabilistic support is beset by well-known problems. In this paper we add a new one to the list: the problem of transitivity. Tomoji Shogenji has shown that positive probabilistic support, or confirmation, is transitive under the condition of screening off. However, under that same condition negative probabilistic support, or disconfirmation, is intransitive. Since there are many situations in which disconfirmation is transitive, this illustrates, but now in a different way, that the screening-off condition is too restrictive. We (...) therefore weaken this condition to what we call ‘partial’ screening off. We show that the domain defined by partial screening off comprises two mutually exclusive subdomains. In one subdomain disconfirmation is indeed transitive, but confirmation is then intransitive. In the other, confirmation is transitive, but here disconfirmation is once more intransitive. (shrink)

My theme is thought experiment in natural science, and its relation to real experiment. I shall defend the thesis that thought experiments that do not lead to theorizing and to a real experiment are generally of much less value that those that do so. To illustrate this thesis I refer to three examples, from three very different periods, and with three very different kinds of status. The first is the classic thought experiment in which Galileo imagined that he had, by (...) pure thought, demolished Aristoteles' dogma that heavier bodies fall more quickly than light ones. I will show that he was mistaken. The second is the Einstein-Podolsky-Rosen paper purporting to show that quantum mechanics must be incomplete in its domain of application. This thought experiment is a very good one, not because its conclusions are correct, but precisely because it was fruitful, leading to theory and, above all, to a real experiment. Finally I discuss the modern string theory of everything, which, while it is regarded as a physical theory by its instigators, shares some properties of the least successful sort of thought experiment. (shrink)

Time is often said to play in quantum mechanics an essentially different role from position: whereas position is represented by a Hermitian operator, time is represented by a c-number. This discrepancy has been found puzzling and has given rise to a vast literature and many efforts at a solution. In this paper it is argued that the discrepancy is only apparent and that there is nothing in the formalism of quantum mechanics that forces us to treat position and time differently. (...) The apparent problem is caused by the dominant role point particles play in physics and can be traced back to classical mechanics. (shrink)

Some philosophers have claimed that it is meaningless or paradoxical to consider the probability of a probability. Others have however argued that second-order probabilities do not pose any particular problem. We side with the latter group. On condition that the relevant distinctions are taken into account, second-order probabilities can be shown to be perfectly consistent. May the same be said of an infinite hierarchy of higher-order probabilities? Is it consistent to speak of a probability of a probability, and of a (...) probability of a probability of a probability, and so on, {\em ad infinitum}? We argue that it is, for it can be shown that there exists an infinite system of probabilities that has a model. In particular, we define a regress of higher-order probabilities that leads to a convergent series which determines an infinite-order probability value. We demonstrate the consistency of the regress by constructing a model based on coin-making machines. (shrink)

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

The classical electrodynamics of point charges can be made finite by the introduction of effects that temporally precede their causes. The idea of retrocausality is also inherent in the Feynman propagators of quantum electrodynamics. The notion allows a new understanding of the violation of the Bell inequalities, and of the world view revealed by quantum mechanics. Published in The Universe, Visions and Perspectives, edited by N. Dadhich and A. Kembhavi, Kluwer Academic Publishers, 2000, pages 35-50.

So far no known measure of confirmation of a hypothesis by evidence has satisfied a minimal requirement concerning thresholds of acceptance. In contrast, Shogenji’s new measure of justification (Shogenji, Synthese, this number 2009) does the trick. As we show, it is ordinally equivalent to the most general measure which satisfies this requirement. We further demonstrate that this general measure resolves the problem of the irrelevant conjunction. Finally, we spell out some implications of the general measure for the Conjunction Effect; in (...) particular we give an example in which the effect occurs in a larger domain, according to Shogenji justification, than Carnap’s measure of confirmation would have led one to expect. (shrink)

This book is open access under a CC BY 4.0 license. This book addresses the age-old problem of infinite regresses in epistemology. How can we ever come to know something if knowing requires having good reasons, and reasons can only be good if they are backed by good reasons in turn? The problem has puzzled philosophers ever since antiquity, giving rise to what is often called Agrippa's Trilemma. The current volume approaches the old problem in a provocative and thoroughly contemporary (...) way. Taking seriously the idea that good reasons are typically probabilistic in character, it develops and defends a new solution that challenges venerable philosophical intuitions and explains why they were mistakenly held. Key to the new solution is the phenomenon of fading foundations, according to which distant reasons are less important than those that are nearby. The phenomenon takes the sting out of Agrippa's Trilemma; moreover, since the theory that describes it is general and abstract, it is readily applicable outside epistemology, notably to debates on infinite regresses in metaphysics. The book is a potential game-changer and a must for any advanced student or researcher in the field. (shrink)

A major objection to epistemic infinitism is that it seems to make justification impossible. For if there is an infinite chain of reasons, each receiving its justification from its neighbour, then there is no justification to inherit in the first place. Some have argued that the objection arises from misunderstanding the character of justification. Justification is not something that one reason inherits from another; rather it gradually emerges from the chain as a whole. Nowhere however is it made clear what (...) exactly is meant by emergence. The aim of this paper is to fill that lacuna: we describe a detailed procedure for the emergence of justification that enables us to see exactly how justification surfaces from a chain of reasons. (shrink)

Today it is generally assumed that epistemic justification comes in degrees. The consequences, however, have not been adequately appreciated. In this paper we show that the assumption invalidates some venerable attacks on infinitism: once we accept that epistemic justification is gradual, an infinitist stance makes perfect sense. It is only without the assumption that infinitism runs into difficulties.

Galileo claimed inconsistency in the Aristotelian dogma concerning falling bodies and stated that all bodies must fall at the same rate. However, there is an empirical situation where the speeds of falling bodies are proportional to their weights; and even in vacuo all bodies do not fall at the same rate under terrestrial conditions. The reason for the deficiency of Galileo’s reasoning is analyzed, and various physical scenarios are described in which Aristotle’s claim is closer to the truth than is (...) Galileo’s. The purpose is not to reinstate Aristotelian physics at the expense of Galileo and Newton, but rather to provide evidence in support of the verdict that empirical knowledge does not come from prior philosophy.Author Keywords: Author Keywords: Aristotle; Galileo; Thought experiments; Falling bodies. (shrink)

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. (shrink)

A characteristic of contemporary analytic philosophy is its ample use of thought experiments. We formulate two features that can lead one to suspect that a given thought experiment is a poor one. Although these features are especially in evidence within the philosophy of mind, they can, surprisingly enough, also be discerned in some celebrated scientific thought experiments. Yet in the latter case the consequences appear to be less disastrous. We conclude that the use of thought experiments is more successful in (...) science than in philosophy. (shrink)

As is well known, implication is transitive but probabilistic support is not. Eells and Sober, followed by Shogenji, showed that screening off is a sufficient constraint for the transitivity of probabilistic support. Moreover, this screening off condition can be weakened without sacrificing transitivity, as was demonstrated by Suppes and later by Roche. In this paper we introduce an even weaker sufficient condition for the transitivity of probabilistic support, in fact one that can be made as weak as one wishes. We (...) explain that this condition has an interesting property: it shows that transitivity is retained even though the Simpson paradox reigns. We further show that by adding a certain restriction the condition can be turned into one that is both sufficient and necessary for transitivity. (shrink)

A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the total mass of all the balls is finite. Classical mechanics leads to the conclusion that momentum, but not necessarily energy, must be conserved. Relativistic mechanics, on the other hand, implies that energy and momentum conservation are always violated. Quantum mechanics, however, seems to rule out the Zeno configuration as an inconsistent system.

Eells and Sober proved in 1983 that screening off is a sufficient condition for the transitivity of probabilistic causality, and in 2003 Shogenji noted that the same goes for probabilistic support. We start this paper by conjecturing that Hans Reichenbach may have been aware of this fact. Then we consider the work of Suppes and Roche, who demonstrated in 1986 and 2012 respectively that screening off can be generalized, while still being sufficient for transitivity. We point out an interesting difference (...) between Reichenbach’s screening off and the generalized version, which we illustrate with an example about haemophilia among the descendants of Queen Victoria. Finally, we embark on a further generalization: we develop a still weaker condition, one that can be made as weak as one wishes. (shrink)

Like many discussions on the pros and cons of epistemic foundationalism, the debate between C. I. Lewis and H. Reichenbach dealt with three concerns: the existence of basic beliefs, their nature, and the way in which beliefs are related. In this paper we concentrate on the third matter, especially on Lewis’s assertion that a probability relation must depend on something that is certain, and Reichenbach’s claim that certainty is never needed. We note that Lewis’s assertion is prima facie ambiguous, but (...) argue that this ambiguity is only apparent if probability theory is viewed within a modal logic. Although there are empirical situations where Reichenbach is right, and others where Lewis’s reasoning seems to be more appropriate, it will become clear that Reichenbach’s stance is the generic one. We conclude that this constitutes a threat to epistemic foundationalism.Keywords: Epistemic foundationalism; Probability; Clarence Irving Lewis; Hans Reichenbach. (shrink)

Quantum electrodynamics is a time-symmetric theory that is part of the electroweak interaction, which is invariant under a generalized form of this symmetry, the PCT transformation. The thesis is defended that the arrow of time in electrodynamics is a consequence of the assumption of an initial state of high order, together with the quantum version of the equiprobability postulate.

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. (shrink)

A thoughtful look at mission, built around one of the most familar texts from the New Testament: 'God so loved the world that he gave his only Son, that whoever believes in him should not perish but have eternal life'. The book is based on the idea that mission should be central to everything we do. Atkinson argues that, just as God's giving of his Son sprang out of his desire to save the world, the function of the church today (...) is to pass on God's love to those around us. His book considers how Christians can., with this renewed emphasis on love, be active in mission in the world today. (shrink)

When the Parrondo effect was discovered a few years ago (Harmer and Abbott 1999a, 1999b), it was hailed as a possible mechanism whereby, in a kind of collaboration of failure, losing strategies could be combined to yield profit. The precise relevance of the Parrondo effect to natural and social phenomena is however still unclear. In this paper we give specific examples, first in the artificial setting of a gambling machine, and then in more natural applications to genetics and to environmental (...) policies. This last example touches questions of rational behaviour and expected utility in a novel setting. (shrink)

After recalling proofs of the Bell inequality based on the assumptions of separability and of noncontextuality, the most general noncontextual contrapositive conditional probabilities consistent with the Aspect experiment are constructed. In general these probabilities are not all positive.

This minicourse on quantum mechanics is intended for students who have already been rather well exposed to the subject at an elementary level. It is assumed that they have surmounted the first conceptual hurdles and also have struggled with the Schrödinger equation in one dimension.

The coupled Dyson-Schwinger equations for the gluon and ghost propagators in QCD are shown to have solutions that correspond to a unique running coupling that has a nite infrared xed point and the expected logarithmic decrease in the ultraviolet. The infrared coupling is large enough to support chiral symmetry breaking and quarks are not con ned, but they cannot be isolated.

The resistance between two arbitrary nodes in an infinite square lattice of identical resistors is calculated. The method is generalized to infinite triangular and hexagonal lattices in two dimensions, and also to infinite cubic and hypercubic lattices in three and more dimensions. © 1999..

An eight parameter family of the most general nonnegative quadruple probabilities is constructed for EPR-Bohm-Aharonov experiments when only 3 pairs of analyser settings are used. It is a simultaneous representation of 3 Bohr-incompatible experimental configurations valid for arbitrary quantum states.

De meesten van ons kunnen zich moeiteloos beelden uit hun schooljaren voor de geest halen. Dikwijls zijn die beelden vaag en fragmentarisch, maar herkenbaar genoeg: het jongetje met het ziekenfondsbrilletje, het meisje met de afgezakte kousen, de onderwijzeres met de grote ruiten rok. Wie begiftigd is met een sterke auditieve verbeelding (en oud genoeg) kan zelfs weer horen hoe de schoolbel klingelde of hoe de kroontjespennen over het papier krasten. Sommigen zijn zelfs in staat om zich geuren te herinneren, of (...) aanrakingen, of de smaak van madeleine-koekjes gedoopt in lindebloesemthee. (shrink)

Nonlocality in quantum mechanics does not follow from nonseparability, nor does classical stochastic independence imply physical independence. In this paper an explicit proof of a Bell inequality is recalled, and an analysis of the Aspect experiment in terms of noncontextual, but indefinite weights, or improper probabilities, is given.

A recent claim that in quantum chromodynamics in the Landau gauge the gluon propagator vanishes in the infrared limit, while the ghost propagator is more singular than a simple pole, is investigated analytically and numerically. This picture is shown to be supported even at the level in which the vertices in the Dyson- Schwinger equations are taken to be bare. The gauge invariant running coupling is shown to be uniquely determined by the equations and to have a large finite infrared (...) limit. S0556-2821 98 04421-X.. (shrink)

A nonlinear integrodifferential equation is solved by the methods of S-matrix theory.

The Michelson-Morley experiment suggests the hypothesis that the two-way speed of light is constant, and this is consistent with a more general invariance than that of Lorentz. On adding the requirement that physical laws have the same form in all inertial frames, as Einstein did, the transformation specializes to that of Lorentz.

Even if two testimonies in a criminal trial are independent, they are not necessarily more trustworthy than one. But if they are independent in the sense that they are screened off from one another by the crime, then two testimonies raise the probability of guilt above the level that one testimony alone could achieve. In fact this screening-off condition can be weakened without changing the conclusion. It is however only a sufficient, not a necessary condition for concluding that two witnesses (...) are better than one. We will discuss two different conditions, each of them necessary as well as sufficient, and we conclude that one of them is slightly better than the other. (shrink)

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. (shrink)