Showing papers in "Analysis in 1998"

The Extended Mind

Abstract: Where does the mind stop and the rest of the world begin? The question invites two standard replies. Some accept the intuitive demarcations of skin and skull, and say that what is outside the body is outside the mind. Others are impressed by arguments suggesting that the meaning of our words "just ain't in the head", and hold that this externalism about meaning carries over into an externalism about mind. We propose to pursue a third position. We will advocate an externalism about mind, but one that is in no way grounded in the debatable role of external reference in fixing the contents of our mental states. Rather, we advocate an *active externalism*, based on the active role of the environment in driving cognitive processes.

I am not here now

Abstract: Recorded messages and written notes are a source of befuddlement for the philosopher of language interested in the semantic behaviour of indexical expressions. It is a consequence of certain prima facie harmless premisses that sentences such as 'I am here now' may never be uttered falsely. But this conclusion is at odds with apparently true instances of 'I am not here now', written on a piece of paper or recorded in an answering machine. Assuming that our intuitions on the truth-values of recorded messages are to be trusted, it must be the case that some of the traditional assumptions in the semantics of indexicals ought to be rejected. So, where exactly did the traditional account of 'I', 'here', and 'now' go wrong, and what adjustments are required?

Some series of the zeta and related functions

Abstract: We propose and develop yet another approach to the problem of summation of series involving the Riemann Zeta function (s), the (Hurwitz's) generalized Zeta function (s; a), the Polygamma function (z) (p = 0; 1; 2; ), and the polylogarithmic function Lis(z). The key ingredients in our approach include certain known integral representations for (s) and (s; a). The method developed in this paper is illustrated by numerous examples of closed-form evaluations of series of the aforementioned types; the method developed in Section 2, in particular, has been implemented in Mathematica (Version 3.0). Many of the resulting summation formulas are believed to be new. 1991Mathematics Subject Classi cation. Primary 11M06, 11M35; Secondary 33B15.

A problem for expressivism

Abstract: Language, Truth and Logic added expressivism to the inventory of substantive positions in meta-ethics, and the recent defences of versions of it by Simon Blackburn and Allan Gibbard have enhanced its status as a major position. 1 Ayer presented the doctrine as an improvement on subjectivism – that is, on the doctrine that ethical sentences serve to report attitudes of approval and disapproval – and it is widely supposed to be an internally coherent and interesting position. We argue, however, that there is a serious problem that expressivists, unlike subjectivists, have to face which has not been adequately addressed in the development of the doctrine. Expressivism is a bipartite theory. It holds, first, that ethical sentences lack truth conditions – they are not truth apt, truth assessable etc. – and do not serve to report anything that the speaker believes to be so. And it holds, second, that ethical sentences express certain distinctive pro and con attitudes, and express them without in any sense reporting them: without reporting them even in the broad sense in which ‘The present King of France is bald’ reports the existence of the King as well as his baldness. 2 The first clause is a negative, semantic claim; it denies that ethical sentences have truth conditions. The second is a positive claim: it informs us about the function – that of expressing attitudes – served by ethical sentences. The second, positive clause is supposed to underpin the first, semantic claim in the following sense. If ethical sentences reported the presence of

Vehicles, Contents, Conceptual Structure, and Externalism

Abstract: We all know about the vehicle/content distinction (see Dennett 1991a, Millikan 1991, 1993). We shouldn't confuse properties represented in content with properties of vehicles of content. In particular, we shouldn't confuse the personal and subpersonal levels. The contents of the mental states of subject/agents are at the personal level. Vehicles of content are causally explanatory subpersonal events or processes or states. We shouldn't suppose that the properties of vehicles must be projected into what they represent for subject/agents, or vice versa. This would be to confuse the personal and subpersonal levels.

Donnellan’s distinction/Kripke’s test

Abstract: 1. Preliminaries In 'Reference and definite descriptions' (1966), Keith Donnellan argued that there were two different uses of definite descriptions: referential and attributive. He went on to suggest that Russell's (1905) Theory of Descriptions was incomplete at best, as it failed to accommodate the referential use. In 'Speaker's reference and semantic reference' (1977), Saul Kripke countered that Donnellan was mistaken in supposing that Russell's Theory was threatened by the referential use. Although definite descriptions could indeed be used referentially, this was (Kripke claimed) a pragmatic, not a semantic fact, and was therefore irrelevant to Russell's (semantic) Theory. In arguing on behalf of this view, Kripke proposed a particular test, the application of which was supposed to show that the referential use of definite descriptions did not disprove, or in any way threaten, Russell's Theory. Kripke thereby attempted to substantiate his claim that Donnellan's Distinction was not a semantically significant one. Kripke's argument against the alleged semantic significance of Donnellan's referential/attributive distinction has considerable intuitive appeal and has, consequently, been endorsed by a number of Russellians.1 Indeed, I agree with Kripke that the mere fact that definite descriptions are used referentially does not undermine Russell's Theory. However, I also believe that the fact that the referential use of definite descriptions is a standard (i.e., statistically common) use of such expressions, does pose a problem for Russell's Theory. When Kripke's Test is applied to the relevant phenomenon - the frequency of the referential use - the results lend credence to Donnellan's claims concerning the inadequacy of Russell's Theory. Although the mere frequency of the referential use does not, by itself, establish that such use is semantically significant, when coupled with various other considerations (to be discussed below), such frequency does indeed support Donnellan's claims about the semantic significance of his distinction. Or so I intend to argue. First, however, I will argue briefly for an alternative (non-Russellian, non-Donnellian) account of the semantics of referentially used definite descriptions. Once I have done this, it will not be difficult to motivate Donnellan's claim that the referential use (given its frequency) does indeed pose a problem for Russell's Theory.

Turing’s O-machines, Searle, Penrose and the brain

Abstract: Analogies offered in the literature include hurricanes, the motion of the planets around the sun, and the digestion of pizza. None of these phenomena is itself computational in nature yet, supposedly, all can be simulated perfectly by a Turing machine (in the sense that the machine can compute descriptions of the phenomena to any desired number of decimal places and on any temporal grid). (2) is Searle's position (1992, 1997).

Agnosticism meets Bayesianism

Abstract: As a result, your credal state cannot really be modeled by a single probability function at all. A better model is provided by a set of such probability functions - what van Fraassen (1990) has called a representor. Each function in your representor agrees with your opinion as far as it goes, but then goes further, precisifying that opinion in some permissible way. (This can be thought of as analogous to the supervaluational approach to vagueness.) According to van Fraassen, your explicit judgments determine which precisifications get admitted into your representor. For example, if you judge that the Democrats are at least as likely to win as not, then for each probability function p that gives 0.5 < p(Democrats win) < 1, and that is consistent with all your other such judgments, p is in your representor. In his highly influential Laws and Symmetry, van Fraassen advocates (a version of) Bayesianism, and also constructive empiricism, an anti-realist position regarding scientific theories according to which 'acceptance of a theory [that postulates unobservables] involves a certain amount of agnosticism, or suspension of belief' (1989: 193). He is thus naturally led to ask whether Bayesianism has the resources to represent agnosticism, and he argues that it does. More than that, he gives an analysis:1 agnosticism is 1 He does not explicitly say that he is giving an analysis of agnosticism, nor explicitly state the analysis, but it is apparent from context that this is exactly what he has in mind. Furthermore, van Fraassen agrees that this is indeed the case (personal

Egalitarianism and the levelling down objection

Abstract: 1. Teleological egalitarians believe that inequality is intrinsically bad.1 Therefore they believe that it is at least in one respect better, if inequality is reduced. It would be in one respect better, for instance, if the worse off are made better off, even if it involves making the better off worse off. In order to make this judgement, we do not need to know the size of the changes to the worse off and to the better off. This is because for an egalitarian, it is in itself better that inequality is reduced. However, inequality can be reduced and even removed by other means than by making the worse off better off. It can be removed by reducing the level of the better off until they reach the level of the worse off, or even by reducing the level of everyone to some (low) level. Even though egalitarians do not need to claim that such reductions are improvements all things considered after all, they may be pluralists they are committed to the claim that these reductions are improvements in one respect. There will then be perfect equality. However, it seems implausible to claim that it is in any way better to secure equality, when doing so involves making some people worse off and no-one better off, or even making everyone worse off. This is the Levelling Down Objection.2

Keeping Track of the Time: Emending the Counterfactual Analysis of Causation

Abstract: I will focus on the most well developed analysis, David Lewis's (1973, 1986a) version, although the emendation that I suggest can be modified and applied to other counterfactual analyses.' The analysis for deterministic causation states that for any two actual, distinct events c and e, e depends counterfactually on c iff, had c not occurred, e would not have occurred.2 Causation is the ancestral of counterfactual dependence: c causes e iff there is a chain of counterfactual dependencies running from c to e. The probabilistic version of the analysis (1986a: 175-84) states that e depends probabilistically on c iff, given c, there is a chance x of e's occurring, and if c were not to occur, there would be a chance y of e's occurring, where x is much greater than y. Causation is again taken as the ancestral, this time of probabilistic dependence, so c causes e iff there is a chain of probabilistic dependencies running from c to e. The chance of the effect's occurring is assessed immediately after the cause occurs, and the truth value of the counterfactual at each step is evaluated based upon that chance.

Compact traces in weighted Sobolev spaces

Abstract: We study trace operators νν·''(Ω;υο,υι) -> L(dQ,;w) in weighted Sobolev spaces for sufficiently regular unbounded domains Ω C M N with noncompact boundary. We show that under certain conditions on the weight functions V0,Vi ,w, this operator is compact. This result is then used to prove existence of a nontrivial solution of a semilinear elliptic equation with nonlinear boundary condition in an unbounded domain. AMS-Classification (1991): 46 E 35, 35 J 65

Field’s programme: some interference

Abstract: The Quine/Putnam Indispensability Argument says that, since our best scientific theories unavoidably quantify over abstract objects, and since we have good reasons for believing our best scientific theories, we have good reasons for believing in the existence of abstract objects (Putnam 1971). Field has attacked the first premiss of this argument: he suspects that scientific theories can be formulated so that they do not quantify over abstract objects (Field 1980, 1985a). He defends this claim by providing nominalistic reformulations of two physical theories: Euclidean three-dimensional geometry and Newtonian gravitational theory. Although it does not immediately follow from this that modern physical theories can be nominalistically reformulated, Field sees no reason to suppose that the techniques used in his nominalistic reformulations could not be extended and developed to cover these theories. Field says we should prefer his reformulations for two reasons. Firstly, there is simply the consideration of nominalism: the new formulations of scientific theories are not committed to abstract objects, the old formulations are.1 Secondly, Field argues that, independently of the issue of nominalism, the reformulations have superior explanatory power to the old ones (Field 1980, Ch. 5). In this paper I shall argue that (1) aside from nominalism, Field's reformulations have the same unattractive features Field pins on the platonistic ones; (2) though his reformulations are nominalist, they are nevertheless still ontologically unparsimonious; and (3) Field has failed to show that certain aspects of scientific practice can be captured in his reformulations.

Great harms from small benefits grow: how death can be outweighed by headaches

Abstract: Suppose that a very large number of people, say one billion, will suffer a moderately severe headache for the next twenty-four hours. For these billion people, the next twenty-four hours will be fairly unpleasant, though by no means unbearable. However, there will be no side-effects from these headaches; no drop in productivity in the work-place, no lapses in concentration leading to accidents, no unkind words spoken to loved ones that will later fester. Nonetheless, it is clearly desirable that these billion people avoid the headaches. Even though the headaches are moderate, they are impervious to pain-killing drugs, acupuncture, transcendental meditation, and just about any other remedy. In fact, there is only one way in which the headaches can be avoided. In a remote South American village, a young woman, Agnes, is suffering from a fever. A simple dose of antibiotics will save her life, otherwise she will die. If, and only if, she dies, the billion headaches will be prevented. You just happen to be passing through the village, in full knowledge of the circumstances. Although not a doctor (and therefore not bound by codes of professional ethics, Hippocratic oaths, etc.), you possess the requisite dose of antibiotics, for which you have no other use, and which will become useless, if not used in the next two hours. What ought you to do? Our ordinary moral intuitions tell us that you ought to save Agnes's life, even though this leaves a billion people unprotected from twenty-four hours of moderate headache. We think it is worse that one person die than that a billion suffer moderate headaches. In fact, many, perhaps most, people would agree to an even stronger claim:

Bayesian Agnosticism and Constructive Empiricism

Abstract: 1. How should the traditional doxastic attitude of agnosticism be represented in a Bayesian framework? In Laws and Symmetry, Bas van Fraassen proposes that agnosticism be represented as having a certain type of vague opinion. A Bayesian with no vague opinions assigns sharp subjective probabilities to all propositions in a domain of discourse. A Bayesian with vague opinions represents his opinions not by a single probability function, but by a set of probability functions. The probability given to a proposition H is an interval [x, y] iff [x, y] is the smallest closed interval containing the probabilities assigned to H by members of that set. Van Fraassen (1989: 194) gives a general analysis of Bayesian agnosticism when he implicitly suggests that a Bayesian is agnostic about a proposition iff her opinion about the proposition is represented by an interval with zero as the lower limit.1

Sampling expansions for discrete transforms and their relationship with interpolation series

Abstract: Kramer's sampling theorem gives us the possibility to reconstruct integral transforms from their values at sequences of real numbers. It is known that this theorem includes the Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem, and that many Kramer-type expansions can be written in forms of Lagrange-type interpolation series. Here we introduce a discrete version of Kramer's theorem and prove that the discrete theorem is equivalent to Kramer's theorem. The WSK sampling theorem is shown to be included in the new theorem. Moreover, the relationship between the sampling expansions of the discrete transforms and the interpolation expansions is discussed. 1991 Mathematics Subject Classification: 39A12 and 41A05.

Carleson type measure characterization of Qp spaces

Abstract: B denotes the open unit ball in C \" , 5 the unit sphere and H(ß) the collection of all holomorphic functions in B. Let Aut(ß) denote the group of biholomorphic automorphisms of B. For a 6 B, is the Möbius transformation of B which satisfies tfiaiz) eAut(ß) , VJ<.(0) = a, ipa(a) = 0 and ^p'^ = ^Pa, see 2.2 of [8]. Let V f ( z ) = V ( / o denote the invariant gradient of / , see [6], where V = • • •, gl^). we say / € Qp for 0 < p < oo if

Predetermination and tense probabilism

Abstract: Dorothy Edgington (1995), following suggestions in Adams 1975 and Skyrms 1981, has argued for a unified treatment of conditionals according to which all conditionals express conditional probabilities and disparities of assertability between indicatives and counterfactuals are explained as the result of tense differences. Call this doctrine 'Tense Probabilism'. In this paper I argue that Tense Probabilism is untenable. Tense Probabilism is motivated as follows. Let's say we believe that Oswald was acting alone so that we accept (1), but reject (2):

Orthogonal rational functions and interpolatory product rules on the unit circle. I. Recurrence and interpolation

Abstract: Let R be the space of rational functions with poles among f k ; 1= k g 1 k=0 with 0 = 0 and j k j < 1, k 1. We consider sequences fR n g 1 n=0 of nested subspaces with 1 n=0 R n = R. This rst part will be concerned with the construction of two distinct orthogonal bases for R. We derive an intertwined recurrence relation for these orthogonal functions which appear as denominators of certain continued fractions. By contraction of these continued fractions, these recurrences are decoupled. It is explained how, with the given problem, one can associate two sequences of interpolation data and it is shown that the approximants of the continued fractions interpolate these data in a multipoint Pad e sense. In part II, interpolatory quadrature rules which are exact for all f 2 R n are constructed and their convergence is discussed as n ! 1.

On How We Know What there is

Abstract: ed away. This argument fails. In the state-of-affairs metaphysic that Armstrong commends, particulars and universals are both but gutted remnants (Armstrong 1978a: 110, 1983: 84, 1989a: 43, 1993: 230). Particulars, like universals, occur only as the constituents of states of affairs. They are not given independently of their occurrence in states of affairs but are arrived at by a process of 'abstraction'. Particulars are what remain of a state of affairs once its other constituents have been abstracted away (Armstrong 1989b: 96, 1993: 433, 1997: 123). A particular, just like a universal, is a state-of-affairs type, the constituent that is common to all the state of affairs that contain it. Consequently, Armstrong's conception of universals as unsaturated provides no support, and a fortiori no a priori support, for (CP). Given a prior characterisation of particulars, Armstrong's conception could be applied to identify universals as those entities which remain once the particulars in a state of affairs have been abstracted away. But unless that characterisation served to distinguish particulars from universals, this method would be ineffective since it would not be possible to determine which constituents of a state of affairs are particulars, rather than universals, and require to be abstracted away in order to isolate the universal in a state of affairs. This just shows that Armstrong's conception, rather than This content downloaded from 207.46.13.146 on Tue, 23 Aug 2016 05:07:19 UTC All use subject to http://about.jstor.org/terms ON HOW WE KNOW WHAT THERE IS 3 5 providing grounds for supposing that there is a particular-universal distinction, simply presupposes that such a distinction exists. It remains unclear just what sort of a priori justification (CP) could possess. At any rate, (CP) suffers intrinsic defects that prevent it delivering a particular-universal distinction a priori. First, given that necessarily equivalent states of affairs are identical, (CP) cannot distinguish a priori all particulars from all universals.4 (CP), if true, distinguishes particulars and universals that occur in atomic states of affairs. But it is epistemically possible that some universals occur only in molecular states of affairs. For example, it may be that the world is infinitely complex and contains only conjunctive universals (whose conjuncts are conjunctive, and so on ad infinituum).s The state of affairs in which each conjunctive universal occurs (F&G(a)) is necessarily equivalent to, and therefore identical with, some molecular states of affairs (F(a)&G(a)). Conjunctive universals do not occur in atomic state of affairs. Consequently, (CP) cannot distinguish particulars from these universals a priori. Second, (CP) is flawed in the way that all counting principles are. In 'lower-order' states of affairs, particulars instantiate universals. In 'higherorder' states of affairs, universals instantiate further universals. Higherorder states of affairs have been posited (by Armstrong and others) for a variety of purposes, including that of providing an account of natural laws.6 The epistemic possibility of such states of affairs undermines (CP)'s claim to be a priori. Contra (CP), higher-order states of affairs are atomic but contain more than one universal and no particulars (e.g. N(F,G), where N is a dyadic universal relating the universals F and G). The epistemic possibility of higher-order states of affairs undermines the claim of any counting principle to be a priori. For any counting principle which distinguishes particular and universal by determining the relative proportion of particulars and universals that go to make up states of affairs will fail if there are states of affairs which lack any particulars to be counted. This difficulty may be avoided by supposing that particulars and universals are arranged in a hierarchy of orders (where particulars are 0-order 4 Armstrong 1997: 133-34, endorses this identity criteria for states of affairs. s See Armstrong 1997: 31-33 and Oliver 1992: 95-96. Even if there are atomic states of affairs there may be other reasons for admitting complex universals (as emergent properties say) that do not figure as their constituents (Armstrong 1978b: 35, 1989a: 113, 1997: 27-28, 33, and, Tooley 1987: 123-29. If so, (CP) fails. Mellor 1995: 19699, argues against the possibility of any complex universals. 6 See Armstrong 1983: 88-92, 1997: 223-30, Tooley 1997: 67-91, and Mellor 1995: 208-9. Higher-order universals are posited for other purposes. See Armstrong 1978b: 134-141, Bigelow 1988: 38-100, Bigelow and Pargetter 1990: 38-92, and, Fales 1990:233-43. This content downloaded from 207.46.13.146 on Tue, 23 Aug 2016 05:07:19 UTC All use subject to http://about.jstor.org/terms

Indeterminism and indeterminacy

Abstract: 1. E. J. Lowe claims that quantum physics provides examples of ontic indeterminacy, of vagueness in the world. Any such claim must confront the Evans-Salmon argument to the effect that the notion of ontic indeterminacy is simply incoherent (Evans 1978, Salmon 1981: 243-46). Lowe argues that a standard version of the Evans-Salmon argument fails quite generally (Lowe 1994). Harold Noonan (1995) has outlined a non-standard version of the argument, but Lowe argues that this non-standard version fails for specifically quantum mechanical reasons (Lowe 1997). He claims that it is perfectly coherent to suppose that his quantum case is an example of ontic indeterminacy. I will not discuss Lowe's objection to the standard Evans-Salmon argument. Instead, I will argue that Lowe's quantum-mechanical objection to the non-standard Evans-Salmon argument fails. Whilst he posits quantum indeterminacy, Lowe fails to take seriously the implications of any such indeterminacy. I will argue that it is, after all, incoherent to claim ontic indeterminacy in the situation he describes.

Positivity of basic sums of ultraspherical polynomials

Abstract: We determine the maximum ränge of A for the positivity of sums n 53 /-<\\ii\\ ' where C^(x) is the ultraspherical polynomial of degree n and order A. k=o ^ki^) This result resolves a problem posed by Szegö thirty five years ago. AMS 1991 Classification numbers: Primary 33C45 33C55, Secondary 42C05.

Problems with Late Preemption

Abstract: In response to counterexamples involving late preemption, David Lewis (1986) revised his original (1973) counterfactual analysis of causation to include the notion of quasi-dependence. Jonardon Ganeri, Paul Noordhof and Murali Ramachandran (199 8 ) argue that their ‘PCA*-analysis’ of causation solves the problem of late preemption and is superior to Lewis’s analysis. I show that neither quasi-dependence nor the PCA*-analysis solves the problem of late preemption.

Reflections on Putnam, Wright and brains in vats

Abstract: (Putnam, and following him Crispin Wright, has 'I am a BIV' where 'Snow is white' occurs in the formulation in the text. What difference does this make? There are three points to be made. (1) Replacement of 'Snow is white' by 'I am a BIV' would make no difference to the soundness of the argument. (2) It would, however, guarantee the argument's availability for first-personal rehearsal by any philosophically knowledgeable reader of this paper, independently of the contingencies of his linguistic resources whether, that is, he be an Alaskan Eskimo or Saharan Arab. (Saharan Arabs are hereby permitted to replace 'Snow is white' throughout the text by 'Palm trees are green'.) (3) Replacement of 'Snow is white' by 'I am a brain in a vat' would enable the conclusion of the argument to be expressed as the claim that the sceptic's position is self-refuting (as, indeed, Putnam does express it), or, as Crispin Wright puts it, absaud. But, as Wright in effect notes towards the end of his paper, so long as the argument refutes the sceptic, that is enough, self-refutation is merely the icing on the cake.) (A)-(C) is an argument for the conclusion that I am not a BIV. The sceptic's claim is that I cannot know that I am not (since I cannot know this without empirical investigation hereafter 'a.p.' and cannot know it with empirical investigation). To get an argument whose conclusion is in explicit contradiction with the sceptic's claim we can restate Putnam's argument as follows:

David Lewis on indicative and counterfactual conditionals

Abstract: It may seem hard to imagine an argument more decisive than this, but, in fact, without considerable further argument not provided by Lewis, it does not establish what it is intended to establish. The argument is directed against the view, briefly alluded to, that indicative and counterfactual conditionals do not differ in their structure as conditionals, but differ only in giving different indications concerning the truth value of the antecedent, i.e., indicative conditionals express no commitment concerning the truth value of the antecedent whereas counterfactuals express a commitment to the falsehood of the antecedent.2 Lewis holds that this view cannot be correct because it is possible to find pairs of conditionals which are otherwise the same except that one is indicative, the other counterfactual, where the indicative conditional is probably true, but the counterfactual conditional may well be false. If that is right and Lewis's specimen pair of conditionals is intended to show that it is right then, as Lewis concludes, there must be more to the difference