Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

I sitt berömda bevis för tidens overklighet påstod McTaggart att det sätt händelser tycks skifta position i tiden från framtid till nutid och till förfluten tid, innebär en motsägelse. Vad McTaggart egentligen menade har varit föremål för en livlig debatt ända sedan beviset först publicerades 1908. Beviset består av två delar. I den första argumenterar McTaggart för att ingenting kan förändras förutom genom att övergå från framtid till förfluten tid. I den andra argumenterar han för att en sådan övergång innebär (...) en motsägelse och att det därför inte kan finnas någon förändring överhuvudtaget, vilket i sin tur innebär att det heller inte finns någon tid. De flesta filosofer är i dag eniga om att McTaggart har fel, men oeniga om på vilket sätt han har fel. Olika filosofer förkastar olika delar av beviset, beroende på om de har vad som kallas en A- eller B-uppfattning av tiden. De som har en A-uppfattning förnekar att tid förstådd som övergång från framtid till förfluten tid är motsägelsefull. De som har en B-uppfattning förnekar att en övergång från framtid till förfluten tid är nödvändig för förändring, men håller med om att sådan övergång är motsägelsefull. Det är min uppfattning att denna oenighet beror på att McTaggarts argument från första början blivit missuppfattat, av både A- och B-teoretiker. Av någon anledning har det alltid betraktats som ett självständigt argument, ett som är oberoende av det ontologiska system McTaggart förespråkade. Jag föreslår ett nytt sätt att förstå hur han menade att tiden är motsägelsefull. Ett sätt som tar hans ontologiska system som utgångspunkt. (shrink)

Philosophically, the study of argumentation is important because it holds out the prospect of an interpretation of rationality. For this we need to identify a transcendent perspective on the argumentative interaction. We need a normative theory of argumentation that provides an answer to the question: should the hearer accept the argument of the speaker. In this article I argue that formal logic implies a notion of transcendence that is not suitable for the study of argumentation, because, from a logical point (...) of view, argumentation ’disappears from sight‘. We should therefore not expect formal logic to provide an interesting interpretation of the rationality intrinsic in argument and discussion. (shrink)

Conventional approaches to consciousness assume that our current science tells us within tolerable limits what physical nature is. Because nature so understood cannot explain consciousness as we seem to experience it ourselves, explaining consciousness becomes a problem. One solution is to rethink what consciousness is so that it becomes the sort of thing our current natural science could in principle explain. Whitehead takes the opposite approach, using the existence of consciousness as a clue to what nature must be if it (...) can generate something like consciousness. The justification for this approach can be found in Whitehead’s implicit indictment of descriptive phenomenology. According to Whitehead, the seemingly insoluble problem of explaining consciousness naturalistically is an artifact created by the assumption that consciousness faithfully samples the world, when in fact it obscures the very aspects of nature that are indispensable to understanding how anything, including consciousness itself, could emerge through a physical process. (shrink)

Michael Tooley presents a major new philosophical theory of the nature of time, offering a powerful alternative to the traditional "tensed" and recent "tenseless" accounts of time. He argues for a dynamic conception of the universe, in which past, present, and future are not merely subjective features of experience. He claims that the past and the present are real, while the future is not. Tooley's approach accounts for time in terms of causation. He therefore claims that the key to understanding (...) the dynamic nature of the universe is to understand the nature of causation. Time, Tense, and Causation is a landmark treatment of one of the oldest and most perplexing intellectual problems, and will be fascinating reading for anyone interested in the character of time. (shrink)

No-futurists ('growing block theorists') hold that that the past and the present are real, but that the future is not. The present moment is therefore privileged: it is the last moment of time. Craig Bourne (2002) and David Braddon-Mitchell (2004) have argued that this position is unmotivated, since the privilege of presentness comes apart from the indexicality of 'this moment'. I respond that no-futurists should treat 'x is real-as-of y' as a nonsymmetric relation. Then different moments are real-as-of different times. (...) This reunites privilege with indexicality, but entails that no-futurists must believe in ineliminably tensed facts. (shrink)

We care not only about what experiences we have, but when we have them too. However, on the B-theory of time, something’s timing isn’t an intrinsic way for that thing to be or become. Given B-theory, should we be rationally indifferent about the timing per se of an experience? In this paper, I argue that B-theorists can justify time-biased preferences for pains to be past rather than present and for pleasures to be present rather than past. In support of this (...) argument, I appeal to the doctrine of temporal parts or “four-dimensionalism” for short. When held in conjunction with a certain evaluative principle about whose experiences matter, four-dimensionalism reconciles B-theory with some time-biased preferences. (shrink)

The paper presents and defends a metadoxastic view on (intentional) consciousness that is novel in four respects: (1) It is motivated both by Husserl’s dynamic approach, which looks upon mental acts as momentary components of certain cognitive structures – “dynamic intentional structures” – in which one and the same object is intended throughout a period of time (during which the subject’s cognitive perspective upon that object is constantly changing) and by his conception of consciousness in terms of internal time-consciousness (temporal (...) awareness). (2) It combines a dispositionalist higher-order judgment theory about the structure of (intentional) consciousness with the claim that the contents of these judgments are such that they can be expressed by essentially indexical sentences containing the temporal indexical “now,” thus accommodating the basic role of internal time-consciousness. (3) It is immune against the “objection from lack of mental concepts” raised, e.g., by Dretske against any higher-order representation theory, as it employs counterfactuals in the framework of a disjunctive account of (intentional) consciousness. (4) It explains the unity of consciousness at a time as well as across time. (shrink)

In this paper, I provide a novel approach to the issue of religious diversity: I reject classical pluralist approaches to the issue, such as John Hick’s, and argue that their attempts to construe commonalities between the religions are contrived. The reason that they attempt to find commonalities at all costs is that they presuppose a bivalent notion of truth according to which that which is different is false. I suggest that, in order to get a robust theory on religious diversity (...) off the ground, we should rely on the notion of justification rather than that of bivalent truth. Justification is pluralizable, dependent upon the circumstances, whereas bivalent truth is not. Armed with a pluralizable notion of justification, we can acknowledge that other religious beliefs are genuinely different without necessarily being false: They can be justified, given the circumstances a believer of a different religion is in. Perceiving religious differences in this way allows to liberate the interreligious dialogue from the pressure to find commonalities between religions at all costs, to respect the religious Other in her Otherness, and to ‘mirror’ one’s own religion in light of other religions. (shrink)

In this paper, I argue that the cleavage between the theory of reference and the theory of meaning, which under the influence of Quine has dominated a large part of the philosophy of language of the last fifty years, is based on a misrepresentation of Tarski's achievement and on an overestimation of the scope and value of disquotation. In particular, I show that, if we accept Davidson's critique of disquotation, the same kind of reasons that Quine offered in opposition to (...) the Carnapian theory of meaning also apply, mutatis mutandis, to the Tarskian theory of reference. (shrink)

In 1967, after a talk Deleuze gave to the Society of French Philosophy, Ferdinand Alquiéé expressed concern during the question and answer session that perhaps Deleuze was relying too heavily upon science and not giving adequate attention to questions and problems that Alquiéé took to be distinctively philosophical. Deleuze responded by agreeing with Alquiéé; moreover, he argued that his primary interest was precisely in the metaphysics science needs rather than in the science philosophy needs. This metaphysics, Deleuze argues, is to (...) be done ‘‘in the style of Whitehead’’ rather than the style of Kant, and in developing this metaphysics Deleuze draws heavily on Spinoza. The present essay examines this Deleuzian-Spinozist metaphysics done in the style of Whitehead, the ‘‘metaphysics science needs’’, drawing on the writings of David Hume and Bruno Latour in the process. This discussion will in turn enable us to situate Deleuze's metaphysics in relation to contemporary debates concerning speculative realism and correlationism, and especially Quentin Meillassoux's critique of the latter. Our conclusion will be that the kind of metaphysics Deleuze pursues is neither correlationist nor straightforwardly realist, but rather charts a course between realism and anti-realism. (shrink)

Philosophers have responded to McTaggart’s famous argument for the unreality of time in a variety of ways. Some of those responses are not easy to evaluate, since they involve, for example, sometimes murky questions concerning whether a certain infinite regress is or is not vicious. In this paper I set out a response that has not, I think, been advanced by any other author, and which, if successful, is absolutely clear-cut. The basic idea is simply that a tensed approach to (...) time can avoid McTaggart’s contradiction, and can also avoid any regress, vicious or otherwise, by specifying the times at which events have different tensed properties in a tenseless fashion — namely, by using dates. This answer to McTaggart’s argument is, however, open to four important objections. The first objection is that my answer to the second part of McTaggart’s argument is incompatible with something that McTaggart takes himself to have proved in the first part of his argument — the claim, namely, that “there can be no change unless some propositions are sometimes true and sometimes false.” The second objection is that the sentences that I claim can be used to specify when an event has a given tensed property do not in fact do so, since they turn out to be purely tenseless sentences. The third objection is that the sentences in question make use of tenseless verbs, and that it is not in fact possible to make sense of such verbs. The fourth and final objection is that it is not really possible to specify, in tenseless terms, when an event has a given tensed property, since dates have to be analyzed using the relation of temporal priority, and that relation, in turn, must be analyzed in terms of the tensed properties of pastness, presentness and futurity, so that the purportedly tenseless specification is implicitly tensed. I argue, however, that none of these four objections can be sustained. (shrink)

All change involves temporal variation of properties. There is change in the physical world only if genuine physical magnitudes take on different values at different times. I defend the possibility of change in a general relativistic world against two skeptical arguments recently presented by John Earman. Each argument imposes severe restrictions on what may count as a genuine physical magnitude in general relativity. These restrictions seem justified only as long as one ignores the fact that genuine change in a relativistic (...) world is frame-dependent. I argue on the contrary that there are genuine physical magnitudes whose values typically vary with the time of some frame, and that these include most familiar measurable quantities. Frame-dependent temporal variation in these magnitudes nevertheless supervenes on the unchanging values of more basic physical magnitudes in a general relativistic world. Basic magnitudes include those that realize an observer's occupation of a frame. Change is a significant and observable feature of a general relativistic world only because our situation in such a world naturally picks out a relevant class of frames, even if we lack the descriptive resources to say how they are realized by the values of basic underlying physical magnitudes. (shrink)

The paper provides an interpretation of Wittgenstein’s claim that a mathematical proof must be surveyable. It will be argued that this claim specifies a precondition for the applicability of the word ‘proof’. Accordingly, the latter is applicable to a proof-pattern only if we can come to agree by mere observation whether or not the pattern possesses the relevant structural features. The claim is problematic. It does not imply any questionable finitist doctrine. But it cannot be said to articulate a feature (...) of our actual usage of the word ‘proof’. The claim can be dissociated, however, from two tenable doctrines of Wittgenstein, namely that proofs can be used as paradigms for corresponding proof concepts and that a proof is not an experiment. (shrink)

The central claim of this thesis is that concepts, the components from which cognitively significant truth evaluable content (thought) is composed, are unstructured entities an account of whose individuation makes no essential reference to other concepts in the possession of the thinking subject or to any particular means by which the reference of the concept is identified by the thinking subject. This position is called Conceptual Atomism and contrasts with Inferential Role Semantics, according to which concepts are individuated by their (...) inferential roles or their conditions of warranted application. The structure of the argument is as follows. Firstly, a principle called the Transparency Principle is developed. This places constraints on the individuation of concepts across differing contexts. The Transparency Principle is then used to show that Inferential Role Semantics is false because it cannot provide a satisfactory account of cognitive dynamics; that is, of the conditions under which a concept is retained through changes in the epistemic state of the subject over a period of time. A version of Conceptual Atomism is then defended and it is shown that this theory yields the correct individuation of concepts. According to this theory the concepts of an individual subject are individuated in terms of referential episodes, episodes of ongoing reference to an object or property during which it is diachronically transparent to the subject that the same thing is being referred to. The more general notion of a referential practice is then used to account for the sharing of concepts by more than one person. Finally, a novel account of the thoughts expressed using indexical terms is defended in order to show that indexicals present no counterexample to Conceptual Atomism. This account of indexical thoughts is of some consequence in its own right. (shrink)

The apparent 'flow' of time is one of its most mysterious features, and one which discomforts both scientists and philosophers. One of the most striking assaults upon it is McTaggart's argument that the idea of temporal flow is demonstratively incoherent. In this paper I first urge that the idea of temporal flow is an important part of our intuitive understanding of time, underpinning several of our notions about rationality and time. Second, I try to undercut McTaggart's argument by showing that (...) it is not temporal flow which is illusory but rather the vicious regress McTaggart saw in that idea. A steadfast clinging to the notion of now, along with an analysis of McTaggart's argument reveals that the regress halts after but two steps. (shrink)

In this thesis I present a phenomenological investigation of our experience of time – of things as they fall within time – and suggest that something important goes missing in recent debates. This is the notion of a point of view. I believe that articulating the sense in which we have a point of view in time, and what this is a point of view upon, is crucial to an account of how things are for an experiencing subject. In the (...) first chapter, I elucidate the specious present. I argue that theorists appeal to the specious present under two guises without explicitly distinguishing between them; yet these two conceptions are not identical, while one entails the other the reverse is not true. In the second chapter I defend an appeal to the specious present against proponents of what I refer to as snapshot models of temporal experience. I argue that perceptual experience minimally presents something of some non-zero temporal extent as such. In the third chapter I discuss how we are to characterise experience over intervals of time of a greater extent than the specious present. I offer a proposal on which a subject is invariably presented with a positive temporal extent, with this interval marking the partition between the past and the future for the subject. In the fourth chapter I compare and contrast our experience of objects and events, and our experiential point of view in space and in time. Among other things, I argue that getting right how things are for the subject requires an appeal to the subject’s asymmetrical awareness of times either side of the specious present. In fifth and final chapter I demonstrate that appeal to an experiencing subject’s tensed temporal perspective can explain the sense in which time seems to pass. (shrink)

By way of their genre, inaugural lectures are condensed and rather broad since they are addressed to a mixed audience. The following theses develop and defend my thoughts on the ‘justified religiou...

Though there are many analogies between time and space, there appear to be three commonplace yet deeply perplexing features of time that reveal it to be quite unlike space. These can be called ‘orientation’, ‘flow’ and ‘presence’. By orientation I mean that there is a direction to time, a temporal order between events which is not merely a reflection of how they are observed (what McTaggart 1908/1968 labelled the B-series time). Assertions that objects stand in spatial relations, such as to (...) the left of, or above, or to the north of explicitly depend upon the position from which they are asserted or upon arbitrary, conventionally established spatial frameworks. There is nothing intrinsic about them; the objects involved are, so to speak, indifferent to them. Temporal relations are not like that – times are not just arranged along, as it were, a line but are successive along that imaginary line. Whether one event is before or after another is not (altogether) dependent upon how, or from where, they are viewed. Nature appears to respect temporal orientation, as enshrined in the laws of thermodynamics, though it remains a deep mystery exactly how the temporally symmetric basic laws of physics ground strongly asymmetric temporal processes (see Sklar 1993). (shrink)