Showing papers in "Analysis in 1993"
TL;DR: In this paper, the authors characterize the matrix class (ίίχ ΠΧ, Y) for certain sequence spaces X and Υ, where stx is the set of all statistically convergent sequences defined by a non-negative regular matrix A.
Abstract: We characterize the matrix class (ίίχ ΠΧ, Y) for certain sequence spaces X and Υ , where stx is the set of all statistically convergent sequences defined by a non-negative regular matrix A. AMS-classification: 40A05, 40C05, 40D25, 40F05
220 citations
TL;DR: Laudan and Leplin this article show that the case for underdetermination is triply doomed: one of its premisses is false, the conclusion wouldn't follow even if the premiss were true, and there are no proposals for alternative avenues to the same conclusion.
Abstract: According to Larry Laudan and Jarrett Leplin, it is a received view among philosophers of science that (E) there are empirically equivalent rivals to any scientific theory, and that as a consequence, (U) theory choice is radically underdetermined by all possible evidence (L. Laudan and J. Leplin, 'Empirical Equivalence and Underdetermination', Journal of Philosophy, 88, 1991, pp. 449-72). Laudan and Leplin repudiate this view in its totality: they reject both E and the claim that E entails U. In addition, they seem to suggest that there are no arguments for U that do not employ E as a premiss. Thus the case for underdetermination is triply doomed: one of its premisses is false, the conclusion wouldn't follow even if the premiss were true, and there are no proposals for alternative avenues to the same conclusion.
98 citations
TL;DR: In this article, the authors argue that Kukla's arguments against empirical equivalence and epistemic underdetermination (UD) fail to obtain adequate evidential warrant for any theory, and show that EE is in fact true, and establish UD independently of EE.
Abstract: In 'Empirical Equivalence and Underdetermination' (Journal of Philosophy 88, 1991, pp. 449-73), we argued against the thesis of empirical equivalence (EE') viz. the thesis that every theory has observationally equivalent rivals and against the inference from EE to the thesis of epistemic underdetermination (UD) viz. the thesis that it is impossible to obtain adequate evidential warrant for any theory. Andre Kukla, in 'Laudan, Leplin, Empirical Equivalence and Underdetermination' (ANALYSIS, this issue), attempts (1) to refute our argument against EE, (2) to show that EE is in fact true, and (3) to establish UD independently of EE. In this reply to Kukla, we shall argue that all three of these attempts fail.
78 citations
TL;DR: Contrairement a Crane et Mellor, l'A. affirme qu'on peut definir une vraie, substantive doctrine du physicalisme as mentioned in this paper.
Abstract: Contrairement a Crane et Mellor, l'A. affirme qu'on peut definir une vraie, substantive doctrine du physicalisme
66 citations
TL;DR: In this paper, it was shown that a generalized power series has s-Gevrey index (oo > s > 1) if ζ = Σ Α (, *, ρ ) χ α γ < 6 C[[X,K0,...,Fn]] and ζ is a Puiseux's series.
Abstract: In 1903 E.Maillet proved that a formal solution of an algebraic ordinary differential equation has some Gevrey order 8 < oo. In 1989, B.Malgrange gave a bound of s for convergent ordinary differential equations. Here we extend these results for formal differential equations of Gevrey type. Our method is based in an algorithmic use of the Newton-Puiseux Polygon for differential equations. A.M.S. Classification: 34A05, 34A20, 34A09. 0. Introduction. We say that a formal series / = Σ Α ( , * , ρ ) χ α γ < 6 C[[X,K0 , ...,Fn]] has s-Gevrey index (oo > s > 1) if Let ζ be a generalized power series expansion [14], that is, a formal power series ζ = ΣίΞι 9 u c h that c,· € C, μ,· 6 Q, < μί+ι, and l i m = oo. If μι > η, and / is as above, we define the generalized power series f[z] by We say that ζ is a solution of ( / = 0) if f[z] = 0. In Theorem 1 we prove that if 2 is a solution of ( / = 0) then there is a q € Ν such that ζ € Cfpf1/ ']] , i.e. ζ is a Puiseux's series as it happens in the case / € C[[X, Y]]. »Partially supported by the D.G.I.C.Y.T.
53 citations
46 citations
TL;DR: In this article, the prima facie case for symmetry between the higher and lower orders survives Wright's argument to the contrary, and it is shown that the logic and semantics of such expressions may best be elucidated using an operator, Def, meaning 'definitely'.
Abstract: 1. In [6] Crispin Wright presents an argument with the conclusion that it is higher-order vagueness, rather than vagueness as such, which is paradoxical. A simple manoeuvre removes the threat of paradox to the latter, he claims, and while at first sight this manoeuvre succeeds equally with higher-order vagueness, at second sight it does not. I show here that the prima facie case for symmetry between the higher and lower orders survives Wright's argument to the contrary.1 First, a sketch of his reasoning. A salient feature of a vague expression ('red', say) is that it admits of borderline cases things which are neither definitely red nor definitely not red. The logic and semantics of such expressions may, then, best be elucidated using an operator, Def, meaning 'definitely'. While
35 citations
TL;DR: In this article, the authors argue that the real similarity between the surprise examination and Moore's paradox lies in the students' acceptance of the teacher's announcement not in that announcement itself, and they argue that this yields a solution to the latter paradox that satisfies all reasonable criteria of satisfactoriness.
Abstract: Some commentators have noticed a similarity between a pared down version of the paradox of the surprise examination and Moore's paradox. What they have failed to notice is that the real similarity with Moore lies in the students' acceptance of the teacher's announcement not in that announcement itself. I shall attempt to bring Wittgenstein's little discussed discussion of Moore's paradox to bear on the surprise examination and to argue that this yields a solution to the latter paradox that satisfies all reasonable criteria of satisfactoriness. A variant of the Moore paradox, equally susceptible to the Wittgensteinian treatment, underlies Gregory Kavka's Toxin paradox which, though superficially quite dissimilar to the surprise examination, has been shown by Roy Sorensen to belong in the same family. Since it too falls to the solution here advocated, there is some reason to believe that that solution is powerful and true. The surprise examination paradox goes like this: A teacher, at school's end on Friday, says to her class 'I'm going to give you a surprise examination one day next week'. A bright pupil figures out that next Friday can't be that day since, if no exam is given by close of school on Thursday, there would be only one day left for the exam; students would know this and therefore they would expect the exam that day - it wouldn't be a surprise. But, with Friday ruled out, we can go through the same kind of reasoning to rule out Thursday: by Wednesday evening, with Friday already ruled out as surprise day, only Thursday would remain as possible, so the exam would have to be given on that day; no surprise. A similar line of argument rules out Wednesday, Tuesday and Monday as possible exam days, hence the argument shows that the surprise exam promised by the teacher cannot take place. But then, on, say, Tuesday, the teacher waltzes into the class and dishes out the exam papers. This comes as a great surprise to the students, especially those who regarded the clever student's argument as impeccable. Clearly it's not impeccable. But where does it go wrong?
35 citations
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TL;DR: A cottage industry was created by Gettier's "Is Justified True Belief Knowledge?" as discussed by the authors, which was the most influential paper of modern analytic epistemology, and was followed by a series of arguments against the theory of propositional knowledge.
Abstract: Thirty years ago this journal published the most influential paper of modern analytic epistemology Edmund Gettier's 'Is Justified True Belief Knowledge?' (ANALYSIS 23, 1963, pp. 121-23). In it Gettier refuted a classic theory of propositional knowledge by constructing thought experiments to test the theory. A cottage industry was born. Each response to Gettier was quickly met by a new Gettier-style case. In turn there would be a response to the case, a further Gettier scenario, and a reiteration of the process. The industry's output was staggering. Its literature became so complicated, its thought experiments so baroque, that commonsense was stretched beyond limit. The deep significance of Gettier's work drowned in the resulting cacophony. That significance can be seen by reflecting on two points: first, why the problem arises; and second, how it is to be solved.
34 citations
TL;DR: The Sorites Paradox as discussed by the authors states that the vagueness of a predicate "Fe" consists in there being no sharp distinction between the objects which satisfy it and those which do not.
Abstract: The vagueness of a predicate 'Fe' consists in there being no sharp distinction between the objects which satisfy it and those which do not. Hence, it ought to be possible for there to be objects a and b, where a is F, but b is not F, and a (doubly well-ordered) series of objects 'connecting' a to b such that there is no F-'boundary' between any two adjacent objects in the series. What gives rise to the so-called Sorites Paradox is the thought that, where x' is the next object in such a series after x, the vagueness of 'Fe' ought to imply or even to consist in the truth of the following:
31 citations
TL;DR: The missing explanation thesis as mentioned in this paper states that people are sensitive to how things are: the dispositions are manifested, not at random, and not under inappropriate influences, but dependently on what there is.
Abstract: 1. The missing explanation thesis If someone takes a realist view of the things people are disposed to say in any area of thought or discourse, then that is presumably because he thinks that their dispositions are sensitive to how things are: the dispositions are manifested, not at random, and not under inappropriate influences, but dependently on what there is. As Socrates argued that the gods love the holy because it is holy - and not the other way around - so the realist about a discourse involving a concept C, will hold that, all going well, if participants judge that something is C or have an experience of it as C then that is because it is C, and not the other way around. When all goes well, the participants' judging that something is C or their having an experience of
TL;DR: In this paper, it was shown that only a small class of theories attribute the right linguistic or logical structure to Q if P to provide a compositional account of Q only if P, i.e. an account of the latter's meaning in terms of the meaning of its grammatical components only.
Abstract: Q only if P frequently features in logical and analytical discourse. Any linguistically serious theory of if needs to provide a compositional account of Q only if P, i.e. an account of the latter's meaning in terms of the meaning of its grammatical components only and the conditional Q if P. This paper aims to show, given what is very plausibly the independent meaning of only and the meaning of Q only if P, that only a small class of theories attribute the right linguistic or logical structure to Q if P to provide such an account. Theories must either (i) accept the thesis of conditional excluded middle as valid for conditional logic, or (ii) deny that Q if P expresses a conditional proposition, adopting instead the view that in uttering Q if P, a speaker asserts Q conditionally on P. In addition to this, it is argued that material implication theories, though validating conditional excluded middle, cannot provide the basis for compositional theories of indicative only if. The discussion shall be couched in terms of indicatives, but the results hold equally well for counterfactuals.1
TL;DR: In this paper, it was argued that modes are syntactic items in a language of thought, and one can then go on to explain behaviour via the contents of thoughts (and desires), which has great explanatory power: handles twin-earth problems, names puzzles, vacuous singular thoughts, opacity problems, identity puzzles and a host of other traditional issues in the philosophy of mind and language.
Abstract: man flies' and 'Superman doesn't fly'. Thus, Schiffer gives no reason to think that Floyd violates the principle of rationality that if one is disposed to think something of the form Sa and --Sb then one will be disposed to think -(a = b). Floyd does not have these syntactic strings in his belief box, so he does not flout this maxim. So the neat explanation that modes are syntactic items in a language of thought, survives Schiffer's objections. Armed with this, one can then go on to explain behaviour via the contents of thoughts (and desires). Elsewhere we have argued that this theory has great explanatory power: handles twin-earth problems, names puzzles, vacuous singular thoughts, opacity problems, identity puzzles, and a host of other traditional issues in the philosophy of mind and language. It's a good thing Schiffer is wrong!4
TL;DR: The authors argue that there are (hypothetical) circumstances in which "we" would find utterances of such sentences unnatural and improper but "RTD" (embellished or not) would sanction.
Abstract: One of Strawson's objections to Russell's theory of descriptions (RTD) is that what are intuitively natural and correct (i.e., true) utterances of sentences involving incomplete (definite) descriptions come out false by RTD. Russellians have responded, not by challenging Strawson's view that these uses are natural and correct, but by embellishing RTD to accommodate these uses. I pursue an alternative line of attack: I argue that there are (hypothetical) circumstances in which "we" would find utterances of such sentences unnatural and improper but "RTD" (embellished or not) would sanction. So, RTD clashes with ordinary language, as Strawson suggests.
TL;DR: The authors show that van Inwagen's metaphysics is not consistent with what ordinary people mean when, in everyday life, they say things like "There are two chippendale chairs in the room" or "there are rocks that weigh over a ton".
Abstract: 1. Philosophical theories that convict ordinary discourse of metaphysical error tend to be viewed with suspicion. It is true that some philosophers present their metaphysical claims as error theories theories that imply that ordinary language incorporates metaphysical mistakes. However, many who advocate what appear to be revisionary metaphysical theories prefer to present them as consistent with ordinary discourse. An extreme example of this reconciling tendency is to be found in Peter van Inwagen's recent Material Beings.' The central tenet of van Inwagen's metaphysics is that there are no tables, chairs, rocks, stars, or any other visible material objects except living organisms. Yet he maintains that this theory is consistent with what ordinary people mean when, in everyday life, they say things like 'There are two chippendale chairs in the room' or 'There are rocks that weigh over a ton'. This apparently outrageous thesis is defended by an appeal to the metaphysical neutrality of ordinary language. Van Inwagen holds that the everyday utterances are sufficiently free of metaphysical commitment to be insulated from conflict with his metaphysical denial of the existence of chairs, rocks, etc. (pp. 1-2, 98-107, 112-13, 129-31). I do not agree with van Inwagen's metaphysical theory2, but it is a separate issue whether he is right in claiming for the ordinary language statements a metaphysical neutrality that would allow them to be true even if his metaphysical theory were correct. In this paper, I shall challenge this claim. First, I shall show that van Inwagen must say that although ordinary discourse 'about' chairs, stars, rocks, etc., is not systematically mistaken, it is systematically misleading as to its ontological commitments. Secondly, I shall argue that this radical thesis is not supported by the analogies to which van Inwagen appeals in his attempt to reconcile his metaphysics with popular usage.
TL;DR: The rejection of (PAP) does not require rejection of the Kantian principle that 'ought' implies 'can' as discussed by the authors, and the rejection of PAP does not imply rejection of this principle.
Abstract: Harry Frankfurt is well-known for his argument, in [1], against the Principle of Alternate Possibilities: "(PAP) A person is morally responsible for what he has done only if he could have done otherwise." In [2], pp. 95-96, he argues that the rejection of (PAP) does not require rejection of the Kantian principle that 'ought' implies 'can': "(K) An agent S has a moral obligation to perform [not to perform] an act A only if it is within S's power to perform [not to perform] A."
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TL;DR: Pettit's definition of physicalism as discussed by the authors involves four claims, two about entities and two about laws, which are in tension with one another, with the result that his definition does not avoid the dilemma.
Abstract: Philip Pettit [4] accepts this challenge, and responds with a definition of physicalism which he thinks avoids the dilemma. Pettit's definition of physicalism involves four claims, two about entities, two about laws. Claims 1 and 3, concerning the existence of microphysical entities and microphysical laws, should not be questioned. Claims 2 and 4 are what make Pettit's theory physicalist: 2 says that microphysical entities constitute everything, 4 says that microphysical laws govern everything. I shall argue that the various ways Pettit offers of understanding these claims are in tension with one another, with the result that his definition does not avoid the dilemma posed in [3]. Claim 2 says that (A) everything empirical is composed out of microphysical entities, and that (B) no two things can differ without differing microphysically. Pettit rightly says that (A) would be denied by a dualist who holds that immaterial minds inhabit the empirical world but are not composed of anything. Fair enough; Mellor and I exaggerated when we said that there is no question of physicalism whatsoever: there is the question of whether this sort of dualism is true.
TL;DR: The knowledge argument for the existence of qualia is one strategy which condenses the issue of physicalism and consciousness sufficiently precisely to force Dennett to face his opponent directly.
Abstract: Daniel Dennett's philosophical method in Consciousness Explained could be described as the Jericho method. He believes that if he marches around a philosophical problem often enough, proclaiming what are, plausibly, relevant scientific truths, the problem will dissolve before our eyes. In so far as he is inviting us to adopt a new way of looking at things, this method is quite appropriate. It does mean, however, that moments of direct philosophical argument are rare, and are to be cherished when found. The knowledge argument for the existence of qualia is one strategy which condenses the issue of physicalism and consciousness sufficiently precisely to force Dennett to face his opponent directly. When he does face this argument head on his response is unconvincing. This matters, because if he cannot cope with the knowledge argument then his more indirect ways of 'deconstructing' our notion of consciousness must be futile. Dennett considers the argument in Jackson's famous 'what Mary didn't know' form. Mary knows everything that a completed physical science could tell her about the physical processes involved in visual perception, including colour perception, but has never been allowed to perceive colour, only black and white. If she is finally allowed to perceive colours she will discover something she previously did not know, namely what colour and seeing colour are like. As she previously knew everything physical and relevant, the new knowledge must relate to something non-physical. Dennett's response is that if we take seriously the premiss that Mary knew everything there was to know about the physical processes, then the conclusion that she would gain new knowledge on being allowed to see colour does not follow. He continues the story as follows.
TL;DR: In this article, it is argued that there is a sense in which the dichotomy between classical mathematics and anti-realism cannot really be confined to the level of the classical continuum or the real line, and that it must also penetrate to the theory of the natural numbers.
Abstract: Within the foundations of mathematics it is traditional to see the irreconcilability of realism and constructivism as emerging, at least in its starkest form, at the level of the classical continuum or the real line. However I argue here that there is a sense in which the dichotomy between classical mathematics and anti-realism cannot really be confined to the level of the continuum, for there is a strong argument that it must also penetrate to the level of the theory of the natural numbers. This can be brought out most effectively by looking at some recent work on the consistency of the formal system implicit in Frege's Grundlagen (Boolos [1], [2], [3] and Wright [23]) and, in particular, a defence of a version of number theoretic logicism by Wright. This will be contrasted with a recent attack also by Wright ([24], pp. 131-37), but in the spirit of Dummett's anti-realism on the coherence of Cantor's famous diagonal argument ([6], [7]) for the existence of an uncountable set, viz. the continuum, which is surely the primary distinctive result of set theory. What Wright attacks here is the notion of an arbitrary subset of natural numbers, a notion that seems to be needed for us to be able to claim that there is in fact an uncountable set. Yet it is precisely this notion which is crucial to the non-contradictory reconstruction of Fregean logicism which Wright wants to defend as being plausible and thus at least coherent. Thus it seems that, either the argument against Cantor shows that the modern logicist account of arithmetic is incoherent along with the Cantorian conception of the classical continuum, incomplete as it may be; or the attack on the latter fails. The point here is of general interest and is not just an ad hominem argument against Wright, for his position is unusual and challenging in that it tries to combine logicism (admittedly of a sophisticated form) about the natural numbers with constructivism of a very radical kind about the real numbers. This is very much against the general tradition in the philosophy of mathematics which sees as the only viable position constructivism for both or neither. I shall argue that this middle way is incoherent and this for rather deep and general reasons.
TL;DR: The notion of sortal universal is one which conveys not only a criterion for application for its instances, but also a criterion of identity for them, in the terminology of Dummett [3], pp. 73ff.
Abstract: It is tempting to regard the natural numbers 1, 2, 3, 4, ... as abstract objects (cf. Wright [10]). Suppose we yield to the temptation: still we may ask whether they are abstract particulars (individuals) or sorts (kinds). Sorts are universals (more specifically, 'sortal' as opposed to 'characterizing' universals: cf. Strawson [9], p. 168), and so necessarily abstract rather than concrete entities. (A sortal universal is one which conveys not only a criterion of application for its instances, but also a criterion of identity for them, in the terminology of Dummett [3], pp. 73ff.). Some familiar examples of sorts are the natural kinds horse, oak tree and proton, but there are also artefactual kinds (such as table and knife) and abstract kinds that is, kinds of abstract objects, such as the mathematical kinds ellipse and set. Natural number is likewise itself an abstract kind, but the question now at issue is whether it is a kind of abstract particulars (as is the abstract kind set) or a kind of sorts (kinds). If the natural numbers are sorts or kinds, what are they sorts or kinds of? The most plausible answer is that they are kinds of sets (and thus kinds of abstract particulars).' For instance, the number 2 would be the kind of two-membered sets (pairs), so that, for example, the two-membered sets {London, Paris} and {Napoleon, Wellington) would both be twos, in precisely the same sense that London and Paris are both cities and Napoleon and Wellington are both men. Of course, 'The set {London, Paris) is a two' is hardly idiomatic English. But then, ordinary idiomatic English has few resources for explicit talk about sets anyway, so we should not be surprised. Even so, it may be doubted whether ordinary ways of talking about number provide any support at all for the proposal now under scrutiny. On the contrary, I think they do. Consider a simple arithmetical statement of addition, such as '2 + 2 = 4', and consider how one typically teaches a child to see the truth of such a statement. One typically displays a pair of objects fingers, say then another such pair, brings the members of the two pairs into proximity and requests the child to count them all. To accompany the procedure one says 'Two, plus another two, make ...' and the child says (we hope) '... four'. It is crucial, of course, that we really do have two twos on display! But this very language ('another two', 'two
TL;DR: In this article, the authors embed PWA in a 'pragmatic' account of intentional states: desiring P is being disposed to perform actions that would tend to make P obtain in a world in which one's beliefs, whatever they are, were true.
Abstract: obtain at a world w, if and only if w is a member of (the set) P. PWA provides intuitively compelling accounts of necessity, contingency, and impossibility. Conjunction and disjunction are representable as intersection and union. We can say that P entails Q just when P c Q, thereby explaining why the objects of thought stand in entailment relations; and it turns out that P entails Q just when the material conditional (P :D Q) is a necessary truth. Kripke's [11] account of names as rigid designators fits well with PWA. And following Stalnaker [18], one can embed PWA in a 'pragmatic' account of intentional states: desiring P is being disposed to perform actions that would tend to make P obtain in a world in which one's beliefs, whatever they are, were true; believing P is being disposed to perform actions that would tend to satisfy one's desires, whatever they are, in a world in which P and one's other beliefs were true.' This account has
TL;DR: In this paper, a matrix method Frobenius is proposed to construct generalized power series solutions of implicit second order differential systems of the type t A(t) X\"(t), B(t, C(t)), X''(t)) + t B't, X'(t)+ t C't), X ''(t)' + t A''(T), B´t), C´t) = 0, where T is the analytic matrix function in some interval |t|
Abstract: In this paper, a matrix method Frobenius is proposed to construct generalized power series solutions of implicit second order differential systems of the type t A(t) X\"(t) + t B(t) X'(t) + C(t) X(t) = 0, where A(t), B(t), C(t) are analytic matrix functions in some interval |t|
Journal Article•
TL;DR: The authors discusses the structure of the four discourses of Lacan and discusses their general structure, commenting on the four terms and the four places they occupy, and makes some remarks specifically about two of the discourses, the discourse of the master and the university.
Abstract: Discusses the structure of the four discourses of Lacan. It firstly discusses their general structure, commenting on the four terms and the four places they occupy. Secondly, it makes some remarks specifically about two of the discourses, the discourse of the master and the discourse of the university, leaving aside the two remaining discourses, the discourse of the analyst and the discourse of the hysteric.
TL;DR: McGinn argues that moral perfection is neither an idealistic nor supererogatory goal but one required by ordinary morality as discussed by the authors, and that moral perfect is a matter of completeness.
Abstract: Colin McGinn argues that moral perfection is neither an idealistic nor supererogatory goal but one required by ordinary morality. ('Must I be Morally Perfect?', ANALYSIS 52, 1992, pp. 32-34.) In his view you are morally perfect if you always keep on the right side of the moral law, invariably doing what is right and never doing what is wrong. At first sight this seems too anaemic a conception of perfection in the moral sphere, for an agent who not only acted rightly but had some saintly or heroic conduct to his credit would appear to be nearer the ideal suggested by the word 'perfect'. But, as McGinn implies, the notion of perfection is ill-defined if it embraces such supererogatory conduct as well. Perfection is a matter of completeness. However good a dancer or a philosopher you encounter you can always conceive of a better one; similarly, however morally estimable the life of a particular saint or hero you can always imagine a more estimable one. So the notion of a perfect saint is as ill-defined as the notion of a perfect dancer. On the other hand we can talk intelligibly of a perfect circle or a perfect series of calculations because there are definable limits involved. So if we are to make use of any notion of moral perfection it had better be construed on the lines McGinn proposes, as a matter, so to speak, of getting one's moral sums right. His principle does, perhaps, need some amendment, because there are times when we are justified in bringing about wrong, knowingly if not intentionally, for the greater good, as when we can attend to some unexpected but more urgent matter, say helping the victims of an accident, only by letting someone down. The obligation to compensate or at least make some form of reparation or apology in such cases shows that the justified act is a wrong none the less. So I am inclined to amend McGinn's principle to refer to unjustified wrong, but I will not press the point here. On each occasion, we ought morally to do what is right and avoid (unjustified) wrong: so let us grant that we ought morally to be perfect in McGinn's sense, or at least as nearly perfect as we are able to be. But it is another question whether we should want to be perfect, or whether we should have perfection as a goal. Compare the examinee taking a maths test or the author reading the proofs of a weighty book on mathematical logic. The examinee and the author would both prefer the outcome where they make no mistakes: but should they want perfection or have perfection as a goal? If wanting necessarily involves a propensity to try to achieve the desired object, the extreme effort required to achieve perfection may make
TL;DR: In this paper, the problem of finding the earliest unexpected inspection day for a class visit was considered, and it was shown that the earliest expected inspection is impossible due to the paradox of the surprise examination paradox.
Abstract: Now that you have settled into your new post, I am required to evaluate your teaching performance. The semester is well under way, so the sooner this is done, the better. If we were being scientific about sampling your teaching, the class observation would be a surprise inspection. Thus reason dictates that the visit should occur on the first day that you do not believe it will occur. But on reflection, this is an impossible demand. Could I give the inspection next Monday? No, because you would realize that Monday is the first available unexpected day. What about the next class on Tuesday? Well the previous elimination would make Tuesday the first available unexpected day. Hence, it falls prey to the previous reasoning. And indeed, parallel reasoning would eliminate all of the remaining days. Hence, the earliest unexpected inspection is impossible. Since we hired you in a buyer's market, you have obviously noted the resemblance to the surprise examination paradox. But you may have not noticed that the elimination proceeds in the reverse direction. It is odd that such a reversal could be effected by substituting a definite description ('The event will occur on the first unexpected day') for an existential generalization ('The event will occur on an unexpected day'). But that's logic for you. Thus I am compelled to take refuge in philosophy department's custom of asking you to propose a day for the class visit.