In den „Fundamenta praedemonstrabilia“ der Theoria motus abstracti entwickelt Leibniz den Versuch, das Kontinuum als aus grundsätzlich unteilbaren Einheiten in einer Weise aufgebaut zu denken, die seine Kontinuität bewahrt - durch die systematische Unterscheidung der Verhältnisse von ,unum ad infinitum‘ und von ,nullius ad unum‘ versucht er hier Balance zu halten. Zwar komme ich zu dem Ergebnis, daß Leibniz' Auffassung vom Kontinuum in der Theoria motus abstracti letztlich inkohärent bleibt, gleichwohl bildet er Begriffe, die sein weiteres Bemühen, den Zugang zum (...) Unendlich-Kleinen neu zu legen, zum Mittel seiner Lösung des ,labyrinthus de compositione continui‘ gestalten. Im zweiten Teil der Arbeit konfrontiere ich die hier vorgelegte Interpretation der Position von Leibniz einer Deutung, die unlängst Philip Beeley gab. (shrink)

Dieser Artikel konzentriert sich auf zwei der frühesten Schriften aus Leibniz' Pariser Zeit, die „Accessio ad Arithmeticam Infinitorum“ und die „De Minimo et Maximo. De corporibus et mentibus“ , und er beurteilt die Beziehung zwischen den in der AAI angegebenen mathematischen Ergebnissen und dem Wandel in Leibniz' Metaphysik, der in MM und in den damit in Verbindung stehenden Schriften und Briefen zum Ausdruck gebracht wird. Sowohl Leibniz' mathematische Ergebnisse als auch der Wandel seiner Haltung in der Metaphysik können als Resultat (...) einer stärkeren Verpflichtung gegenüber dem Euklidischen Axiom betrachtet werden, daß das Ganze größer ist als der Teil. Indem das Euklidische Axiom eine bedeutendere Rolle in Leibniz' Metaphysik und mathematischer Arbeit einnimmt, bewegt sich Leibniz von der Vorstellung der Zusammensetzung des Kontinuums aus unteilbaren Punkten zu einer Aufgliederung des Kontinuums in unvergleichbar kleine Teile, die in sich selbst kontinuierlich sind. Dieser Wandel führt Leibniz dazu, die Rolle der Identität und eines Kalküls von Teil und Ganzem zu betonen und sich in Richtung einer Vorstellung vom Unbestimmten als eines Unendlichen zu bewegen. (shrink)

This paper rejoins the debate surrounding Thomas Tymockzko’s paper on the surveyability of proof, first published in the Journal of Philosophy, and makes the claim that by attending to certain broad features of modern conceptions of proof we may understand ways in which the debate surrounding the surveyability of proof has heretofore remained unduly circumscribed. Motivated by these historical reflections, I suggest a distinction between local and global surveyability which I believe has the promise to open up significant new advances (...) in the philosophy of mathematics. (shrink)

In der Zeit zwischen 1668 und 1671 ändert Leibniz seine Ansicht zu Bewegung und Körper von dem Standpunkt, Bewegung sei keine essentielle Eigenschaft eines Körpers, zu dem, dass Bewegung den Wesenskern eines Körpers bilde. Dieser Aufsatz will den Prozess analysieren, der diesem Wandel zu Grunde liegt. Die Theoria motus abstracþi wird dabei als vorsichtige Synthese interpretiert, die zwar den Wandel ankündigt, die aber den neuen Standpunkt noch nicht explizit vertritt. Die ausdrückliche Hinwendung zu der Position, Bewegung sei der Wesenskern eines (...) Körpers, wird als Folge davon gesehen, dass Leibniz die Existenz einer unbewegten materia prima verneint; und diese Haltung führt zu einer ausdrücklich phänomenologischen Ableitungsmethode im zweiten Entwurf des Specimen demonstrationum de natura rerum corporearum ex phaenomenis, die mit ihrer Unterscheidung zwischen dem Körper als wandelbar und dem Raum als unwandelbar zu der Schlussfolgerung, Bewegung sei der Wesenskern eines Körpers, führt. (shrink)

This book charts the shape of future philosophical investigation by posing the question: "What is the Matrix?" Guided by the example of the Matrix film trilogy, the author examines issues ranging from simulation, proof and action to value, culture and mythology, offering a progressively deeper diagnosis of modern philosophical conditions. In contrast to the contemporary focus upon cognitive science and a commitment to the distinction between appearance and reality, this book helps readers to explore the argument that such abstractions are (...) inevitably displaced by a more concrete distinction between dreaming and waking, with the Matrix as the real and only world we inhabit. Researchers and scholars will find this work an engaging and enlightening examination of reality, via the medium of popular culture and film. (shrink)

New light is shed on Leibniz’s commitment to the metaphysical priority of the intensional interpretation of logic by considering the arithmetical and graphical representations of syllogistic inference that Leibniz studied. Crucial to understanding this connection is the idea that concepts can be intensionally represented in terms of properties of geometric extension, though significantly not the simple geometric property of part-whole inclusion. I go on to provide an explanation for how Leibniz could maintain the metaphysical priority of the intensional interpretation while (...) holding that logically the intensional and the extensional stand in strictly inverse relation to each other. (shrink)

This book addresses the philosophy of Kant and the poetry of Shelley as historical starting points for a new way of thinking in the modern age. Fusing together critical philosophy and visionary poetry, Bassler develops the notion of visionary critique, or paraphysics, as a model for future philosophical endeavor. This philosophical practice is rooted in the concept of the indefinite power associated with the sublime in both Kant and Shelley’s work, to which the notion of the parafinite or indefinitely (...) large is extended in this book. (shrink)

In The Principles of Mathematics Revisited Jaakko Hintikka proposes nothing less than “to prepare the ground for the next revolution in the foundations of mathematics”. Hintikka’s proposal involves a rejection, inter alia, of the views that ordinary first-order logic is the basic elementary logic and that axiomatic set theory is a natural framework for theorizing about mathematics.

The second volume of Jaakko Hintikka’s selected papers brings together essays from the decade 1986–96 concerning an often tacit distinction between “two competing overall views concerning our relationship to our language”. The first of these Hintikka characterizes as the view of language as lingua universalis, a single universal medium of communication; the second view, of language as calculus ratiocinator, is not meant to indicate that language is a “mere play with symbols” but rather that language “can be re interpreted like (...) a calculus”. (shrink)

I maintain that quantum mechanics is fundamentally about a system of N particles evolving in three-dimensional space, not the wave function evolving in 3N-dimensional space.

Sometimes we learn what the world is like, and sometimes we learn where in the world we are. Are there any interesting differences between the two kinds of cases? The main aim of this article is to argue that learning where we are in the world brings into view the same kind of observation selection effects that operate when sampling from a population. I will first explain what observation selection effects are ( Section 1 ) and how they are relevant (...) to learning where we are in the world ( Section 2 ). I will show how measurements in the Many Worlds Interpretation of quantum mechanics can be understood as learning where you are in the world via some observation selection effect ( Section 3 ). I will apply a similar argument to the Sleeping Beauty Problem ( Section 4 ) and explain what I take the significance of the analogy to be ( Section 5 ). Finally, I will defend the Restricted Principle of Indifference on which some of my arguments depend ( Section 6 ). (shrink)

How do temporal and eternal beliefs interact? I argue that acquiring a temporal belief should have no effect on eternal beliefs for an important range of cases. Thus, I oppose the popular view that new norms of belief change must be introduced for cases where the only change is the passing of time. I defend this position from the purported counter-examples of the Prisoner and Sleeping Beauty. I distinguish two importantly different ways in which temporal beliefs can be acquired and (...) draw some general conclusions about their impact on eternal beliefs. (shrink)

Adam Elga takes the Sleeping Beauty example to provide a counter-example to Reflection, since on Sunday Beauty assigns probability 1/2 to H, and she is certain that on Monday she will assign probability 1/3. I will show that there is a natural way for Bas van Fraassen to defend Reflection in the case of Sleeping Beauty, building on van Fraassen’s treatment of forgetting. This will allow me to identify a lacuna in Elga’s argument for 1/3. I will then argue, however, (...) that not all is well with Reflection: there is a problem with van Fraassen’s treatment of forgetting. Ultimately I will agree with Elga’s 1/3 answer. David Lewis maintains that the answer is 1/2; I will argue that cases of forgetting can be used to show that the premiss of Lewis’s argument for 1/2 is false. (shrink)

Cian Dorr (2002) gives an argument for the 1/3 position in Sleeping Beauty. I argue this is based on a mistake about Sleeping Beauty's epistemic position.

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object an item which does not have a position in space and time but which exists. (Philosophers have nominated such things as numbers, sets, and propositions to this category. The need to posit such entities has been discussed and disputed for at least 2400 years.).

We give an analysis of the Monty Hall problem purely in terms of confirmation, without making any lottery assumptions about priors. Along the way, we show the Monty Hall problem is structurally identical to the Doomsday Argument.

Bayesian models typically assume that agents are rational, logically omniscient and opinionated. The last of these has little descriptive or normative appeal, however, and limits our ability to describe how agents make up their minds (as opposed to changing them) or how they can suspend or withdraw their opinions. To address these limitations this paper represents the attitudinal states of non-opinionated agents by sets of (permissible) probability and desirability functions. Several basic ways in which such states of mind can be (...) changed are then characterised and compared with those found in AGM style models of attitude revision. Finally these models are employed to describe how agents make up their mind when deliberating. (shrink)

The Carter-Leslie Doomsday argument, as standardly presented, relies on the assumption that you have knowledge of your approximate birth rank. I demonstrate that the Doomsday argument can still be given in a situation where you have no knowledge of your birth rank. This allows one to reply to Bostrom's defense of the Doomsday argument against the refutation based on the idea that your existence makes it more likely that many observers exist.

underpinning of the cognitive sciences. I argue, however, that it often fails to provide adequate explanations, in particular in conjunction with competence theories. This failure originates in the idealizations in competence descriptions, which either ?block? the cascade, or produce a successful cascade which fails to explain cognition.

This paper uses the framework of Popper and Miller's work on axiom systems for conditional probabilities to explore Adams' thesis concerning the probabilities of conditionals. It is shown that even very weak axiom systems have only a very restricted set of models satisfying a natural generalisation of Adams' thesis, thereby casting severe doubt on the possibility of developing a non-Boolean semantics for conditionals consistent with it.

I argue against several extant views (Rolston, etc) about the value of endangered species. I argue that the best way to defend a non-anthropocentric view about the value of endangered species is to appeal to the intrinsic value of biological diversity.

Colin Howson (1995 ) offers a counter-example to the rule of conditionalization. I will argue that the counter-example doesn't hit its target. The problem is that Howson mis-describes the total evidence the agent has. In particular, Howson overlooks how the restriction that the agent learn 'E and nothing else' interacts with the de se evidence 'I have learnt E'.

This paper reconstructs and evaluates the representation theorem presented by Ramsey in his essay 'Truth and Probability', showing how its proof depends on a novel application of Hölder's theory of measurement. I argue that it must be understood as a solution to the problem of measuring partial belief, a solution that in many ways remains unsurpassed. Finally I show that the method it employs may be interpreted in such a way as to avoid a well known objection to it due (...) to Richard Jeffrey. (shrink)

Insurers draw on sophisticated models for the probability distributions over losses associated with catastrophic events that are required to price insurance policies. But prevailing pricing methods don’t factor in the ambiguity around model-based projections that derive from the relative paucity of data about extreme events. I argue however that most current theories of decision making under ambiguity only partially support a solution to the challenge that insurance decision makers face and propose an alternative approach that allows for decision making that (...) is responsive to both the evidential situation of the insurance decision maker and their attitude to ambiguity. (shrink)

Time Time is what clocks measure. The three key features of time are that it orders events in sequence one after the other; it specifies how long any event lasts; and it specifies when events occur. Yet despite 2,500 years of investigating time, many issues about it are unresolved. Here is a list of the […].

It has now been over twenty years since Elizabeth Prior, Robert Pargetter, and Frank Jackson (1982) published their classic paper on dispositions, in which they defend the following theses: (1) The Distinctness Thesis: Each disposition is distinct from its base. (2) The Impotence Thesis: Dispositions are causally impotent.1..

Are we acquainted with the self in experience? It may seem so. After all, we tend to be confident in our own existence. A natural explanation for this confidence is that the self somehow shows up in experience. Yet philosophers in both the Eastern and Western philosophical traditions have been sceptical of self-acquaintance. Despite centuries of debate, the matter remains controversial. But the persistence of this dispute is puzzling. Why can we not simply settle this question by introspection? Here, many (...) philosophers hold that the self is elusive. Hence, to address this question we need to use a more indirect method. To this end, philosophers have turned to pathologies of self-awareness such as depersonalization and thought insertion to argue for self-acquaintance, a strategy I label the Pathology Argument. In this paper, I criticize the Pathology Argument on the grounds that we can better explain the symptoms of these disorders without appeal to self-acquaintance. (shrink)

This article reveals a tension between a fairly standard response to "liar sentences," of which -/- (L) Sentence (L) -/- is not true is an instance, and some features of our natural language determiners (e.g., 'every,' 'some,' 'no,' etc.) that have been established by formal linguists. The fairly standard response to liar sentences, which has been voiced by a number of philosophers who work directly on the Liar paradox (e.g., Parsons [1974], Kripke [1975], Burge [1979], Goldstein [1985, 2009], Gaifman [1992, (...) 2000]), Glanzberg [2004], Azzouni [2006], and others), but can also be heard from philosophers who do not work directly on that paradox, is that liar sentences do not express propositions. Call this the "No Proposition View" (hereafter NPV). Evidently, the belief that liar sentences do not express propositions is a deeply held intuition. As the previously mentioned tension will reveal, there is reason to worry about whether this deeply held intuition can be sustained. (shrink)

This paper delves into McTaggart’s metaphysical account of reality without time, and compares and contrasts McTaggart’s account with the account of reality given by modern physics. This comparison is of interest, because there are suggestions from contemporary physics that there is no time at the fundamental level. Physicists and philosophers of physics recognize that we do not have a good understanding of how the world could be such that time is unreal. I argue that, from the perspective of one who (...) is trying to understand modern physics, McTaggart’s metaphysical views do provide some insight into how reality can be timeless at the fundamental level, but the insight that they provide is limited. (shrink)

How should our beliefs change over time? Much has been written about how our beliefs should change in the light of new evidence. But that is not the question I’m asking. Sometimes our beliefs change without new evidence. I previously believed it was Sunday. I now believe it’s Monday. In this paper I discuss the implications of such beliefs for philosophy of language. I will argue that we need to allow for ‘dynamic’ beliefs, that we need new norms of belief (...) change to model how they function, and that this gives Perry’s (1977) two tier account the advantage over Lewis’s (1979) theory -/- . (shrink)

This chapter discusses the metaphysical view referred to by Harry Silverstein as “four-dimensionalism,” but referred to in this chapter as “eternalism.” In contrast to presentism, eternalism posits that purely past and purely future objects and events exist. If a person goes out of existence at the moment of death, the problem arises as to how death is bad for its victim. According to Silverstein, this problem arises from the truth of the “Values Connect with Feelings” thesis, according to which it (...) must be possible for someone to have feelings about a thing in order for that thing to be bad for that person. The badness of death may entail eternalism, but it is for an entirely different reason. Eternalism must be true in order for there to be a time at which death is bad for its victim. These two conflicting views are discussed in this chapter. (shrink)

It is argued that, given certain reasonable premises, an infinite number of qualitatively identical but numerically distinct minds exist per functioning brain. The three main premises are (1) mental properties supervene on brain properties; (2) the universe is composed of particles with nonzero extension; and (3) each particle is composed of continuum-many point-sized bits of particle-stuff, and these points of particle-stuff persist through time.