Objective interpretations of probability are usually discussed in two varieties: frequency and propensity accounts. But there is a third, neglected possibility, namely, probabilities as deriving from ranges in suitably structured initial state spaces. Roughly, the probability of an event is the proportion of initial states that lead to this event in the space of all possible initial states, provided that this proportion is approximately the same in any not too small interval of the initial state space. This idea can also (...) be expressed by saying that in the types of situations that give rise to probabilistic phenomena we may expect to find an initial state space such that any "reasonable" density function over this space leads to the same probabilities for the possible outcomes. This "method of arbitrary functions" was introduced by Poincaré, studied and extended by Hopf and more recently by Eduardo Engel, Jan von Plato and Michael Strevens. The natural-range, or method-of-arbitrary-functions approach to probabilities is usually treated as an explanation for the occurrence of probabilistic patterns, whereas I examine its prospects for an objective interpretation of probability, in the sense of providing truth conditions for probability statements that do not depend on our state of mind or information. The main objection to such a proposal is that it is circular, i.e. presupposes the concept of probability, because a measure on the initial state has to be introduced, and density functions over the space are considered. I try to argue that this objection can be successfully met. (shrink)
A proposal for an objective interpretation of probability is introduced and discussed: probabilities as deriving from ranges in suitably structured initial-state spaces. Roughly, the probability of an event on a chance trial is the proportion of initial states that lead to the event in question within the space of all possible initial states associated with this type of experiment, provided that the proportion is approximately the same in any not too small subregion of the space. This I would like to (...) call the “natural-range conception” of probability. Providing a substantial alternative to frequency or propensity accounts of probability in a deterministic setting, it is closely related to the so-called “method of arbitrary functions”. It is explicated, confronted with certain problems, and some ideas how these might be overcome are sketched and discussed. (shrink)
Der Aufsatz stellt einige Überlegungen zu internalistischen Lösungsversuchen für das sog. Gettier-Problem an. Dieses Problem besteht darin, daß die klassische Definition von Wissen als gerechtfertigte wahre Meinung unzureichend ist. Ausgehend von naheliegenden Ideen, die an wohlbekannten Beispielen scheitern, unterbreite ich einen eigenen Vorschlag zur Lösung des Problems. Anschließend diskutiere ich den prominenten Ansatz von Keith Lehrer und zeige seine Unzulänglichkeit, aber auch, wie er modifiziert werden kann, um eine befriedigende Lösung des Gettier-Problems zu ergeben. Externalistische Analysen des Wissensbegriffs, die als (...) das entscheidende Kriterium für Wissen ansehen, daß die fragliche Meinung in der richtigen Weise durch den entsprechenden Sachverhalt verursacht ist, werden in diesem Aufsatz nicht behandelt.The subject of this article are internalistic solutions of the Gettier problem. The problem is that the traditional definition of knowledge as justified true belief is unsatisfying. Starting from natural proposals to solve the problem, which are refuted by well-known counterexamples, I arrive at a suggestion of my own. Then I discuss the prominent solution of Keith Lehrer and show that it is unsatisfactory, but also, how it can be modified to yield a correct analysis of knowledge. Externalistic solutions to the problem, which demand that the belief in question be caused in some appropriate way to count as knowledge, are not discussed in this paper. (shrink)
A conception of probability that can be traced back to Johannes von Kries is introduced: the “Spielraum” or range conception. Its close connection to the so-called method of arbitrary functions is highlighted. Possible interpretations of it are discussed, and likewise its scope and its relation to certain current interpretations of probability. Taken together, these approaches form a class of interpretations of probability in its own right, but also with its own problems. These, too, are introduced, discussed, and proposals in response (...) to them are surveyed, some of which also go back to von Kries. (shrink)
In diesem Aufsatz gebe ich eine Darstellung und kritische Bewertung der sog. Propensity-Theorie der Wahrscheinlichkeit. Diese konzipiert Wahrscheinlichkeiten als reale „Neigungen“ oder „Tendenzen“ experimenteller Arrangements zur Hervorbringung bestimmter Resultate. Damit gibt sie Wahrscheinlichkeitsaussagen eine objektive, ontologische Interpretation. Ihre Konkurrenten in diesem Feld sind die Häufigkeitstheorie, der zufolge sich Wahrscheinlichkeitsaussagen auf relative Häufigkeiten, und die Symmetrieauffassung, der zufolge sie sich auf Symmetrieverhältnisse beziehen. Ich diskutiere kurz und grundsätzlich diese Alternativen und versuche zu verdeutlichen, wie sie von selbst zur Propensity-Theorie hinführen, um (...) diese dann ausführlicher zu thematisieren. Dabei erweist sich, dass die Konzeption von Wahrscheinlichkeiten als Tendenzen in der Wirklichkeit die merkwürdige Konsequenz hat, dass dadurch Entitäten mit einer normativen Kraft eingeführt werden, die nicht näher erläutert werden kann. Es ergibt sich, dass bisher keine wirklich befriedigende Konzeption objektiver Wahrscheinlichkeiten vorliegt. (shrink)
New varieties of libertarianism connect not only free will and moral responsibility to indeterminism, but also agency and choice as such. In this paper, the author highlights what seems to be an embarrassment for all libertarian accounts, but especially for the ones just mentioned. The problem is brought out by clear cases of decisions in which there are strong and rather obvious reasons for one of the options and only relatively weak ones in favour of the alternatives. It is hard (...) to insist that there be indeterminism even in such cases. Either it has no significant role to play, which means that libertarianism is in effect largely abandoned, or it has a purely negative role, being linked to some serious and thoroughgoing defect in the agent’s rationality. Thus, a dilemma for libertarians arises, which the author spells out in the text. Furthermore, he argues that some versions of compatibilism face essentially the same difficulty. (shrink)
Contractualism, the view that morality is to be grounded on an hypothetical agreement among rational agents, is a very plausible conception for the justification of morality under modern circumstances. No metaphysical assumptions are made, morality is supposed to be erected on undisputed, minimal foundations. However, contractualists generally underestimate or downplay the degree to which their idea allows to convert might into right. This is shown exemplarily by an examination of the conceptions of David Gauthier and Peter Stemmer. A more realistic (...) variety of contractualism would admit that, depending on contingent circumstances, idiosyncratic or massively discriminating moral principles can easily be part of the hypothetical agreements. (shrink)
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