To compute is to execute an algorithm. More precisely, to say that a device or organ computes is to say that there exists a modelling relationship of a certain kind between it and a formal specification of an algorithm and supporting architecture. The key issue is to delimit the phrase of a certain kind. I call this the problem of distinguishing between standard and nonstandard models of computation. The successful drawing of this distinction guards Turing's 1936 analysis of computation against (...) a difficulty that has persistently been raised against it, and undercuts various objections that have been made to the computational theory of mind. (shrink)

The paper describes the evolution of russell's theory of judgment between 1910 and 1913, With especial reference to his recently published "theory of knowledge" (1913). Russell abandoned the book and with it the theory of judgment as a result of wittgenstein's criticisms. These criticisms are examined in detail and found to constitute a refutation of russell's theory. Underlying differences between wittgenstein's and russell's views on logic are broached more sketchily.

In this paper, elementary but hitherto overlooked connections are established between Wittgenstein's remarks on mathematics, written during his transitional period, and free-variable finitism. After giving a brief description of theTractatus Logico-Philosophicus on quantifiers and generality, I present in the first section Wittgenstein's rejection of quantification theory and his account of general arithmetical propositions, to use modern jargon, as claims (as opposed to statements). As in Skolem's primitive recursive arithmetic and Goodstein's equational calculus, Wittgenstein represented generality by the use of free (...) variables. This has the effect that negation of unbounded universal and existential propositions cannot be expressed. This is claimed in the second section to be the basis for Wittgenstein's criticism of the universal validity of the law of excluded middle. In the last section, there is a brief discussion of Wittgenstein's remarks on real numbers. These show a preference, in line with finitism, for a recursive version of the continuum. (shrink)

It is widely assumed that Russell's problems with the unity of the proposition were recurring and insoluble within the framework of the logical theory of his Principles of Mathematics. By contrast, Frege's functional analysis of thoughts (grounded in a type-theoretic distinction between concepts and objects) is commonly assumed to provide a solution to the problem or, at least, a means of avoiding the difficulty altogether. The Fregean solution is unavailable to Russell because of his commitment to the thesis that there (...) is only one ultimate ontological category. This, combined with Russell's reification of propositions, ensures that he must hold concepts and objects to be of the same logical and ontological type. In this paper I argue that, while Frege's treatment of the unity of the proposition has immediate advantages over Russell's, a deeper consideration of the philosophical underpinnings and metaphysical consequences of the two approaches reveals that Frege's supposed solution is, in fact, far from satisfactory. Russell's repudiation of the Fregean position in the Principles is, I contend, convincing and Russell's own position, despite its problems, conforms to a greater extent than Frege's with common sense and, furthermore, with certain ideas which are central to our understanding of the origins of the analytical tradition. (shrink)

When it comes to name-calling, structural realists have heard pretty much all of it. Among the many insults, they have been called ‘empiricist anti-realists’ but also ‘traditional scientific realists’. Obviously the collapse accusations that motivate these two insults cannot both be true at the same time. The aim of this paper is to defend the epistemic variety of structural realism against the accusation of collapse to traditional scientific realism. In so doing, I turn the tables on traditional scientific realists by (...) presenting them with a dilemma. They can either opt for a construal of their view that permits epistemic access to non-structural features of unobservables but then face the daunting task of substantiating a claim that seems to have little hope of being true or they can drop the requirement of epistemic access to non-structural features but then face a collapse to epistemic structural realism. There is thus only one well supported way to be a realist. No wonder then that many traditional scientific realists have over the years expressed views that are strikingly similar to epistemic structural realism. It is high time to let these epistemic structural realists out of the closet. (shrink)

It is occasionally claimed that the important work of philosophers, physicists, and mathematicians in the nineteenth and in the early twentieth centuries made Kant’s critical philosophy of geometry look somewhat unattractive. Indeed, from the wider perspective of the discovery of non-Euclidean geometries, the replacement of Newtonian physics with Einstein’s theories of relativity, and the rise of quantificational logic, Kant’s philosophy seems “quaint at best and silly at worst”.1 While there is no doubt that Kant’s transcendental project involves his own conceptions (...) of Newtonian physics, Euclidean geometry and Aristotelian logic, the issue at stake is whether the replacement of these conceptions collapses Kant’s philosophy into an unfortunate embarrassment.2 Thus, in evaluating the debate over the contemporary relevance of Kant’s philosophical project one is faced with the following two questions: (1) Are there any contradictions between the scientific developments of our era and Kant’s philosophy? (2) What is left from the Kantian legacy in light of our modern conceptions of logic, geometry and physics? Within this broad context, this paper aims to evaluate the Kantian project vis à vis the discovery and application of non-Euclidean geometries. Many important philosophers have evaluated Kant’s philosophy of geometry throughout the last century,3 but opinions with regard to the impact of non-Euclidean geometries on it diverge. In the beginning of the century there was a consensus that the Euclidean character of space should be considered as a consequence of the Kantian project, i.e., of the metaphysical view of space and of the synthetic a priori character of geometry. The impact of non-Euclidean geometries was then thought as undermining the Kantian project since it implied, according to positivists such.. (shrink)

One of the main challenges faced by Russell's theory of judgement was to provide a satisfactory account of judgement that was not committed to the existence of true, false, or non-existent complex entities such as Meinongian objectives. In the study of the Russell-Wittgenstein debate on that theory, scholars never considered the idea that Wittgenstein might not have followed Russell on that issue. In this article. I address that question and hold, first, that problems raised by Russell's theory of judgement find (...) their solution in the picture theory. Then, I show that Wittgenstein hesitated for a long period of time in theNotebooksbetween a version of his solution which is committed to the existence of possible (non-existing) complex entities and one which is not. Finally, I argue that he did, along with Meinong, go for a committing version in theTractatus. (shrink)

Philosophy has four forms: wonder, faith, doubt and scepticism. These are not separate categories, but separate ideal possibilities. Modern academic philosophy has fallen, for several centuries, into an error: which is the error of supposing that philosophy is only what I call doubt. Philosophy may be doubt: indeed, it is part of my argument that this is undeniably one element of, or one possibility in, philosophy; but doubt is only one of four points of the compass. In this essay I (...) indicate the nature of each point of the compass as it has been found in the history of philosophy. (shrink)

Bertrand Russell’s conception of philosophy evolved dramatically in 1911 — the year he fell in love with Lady Ottoline Morrell. For many years Russell had been an ardent advocate of the view that philosophers ought to look for truths that are certain. The co-author of Principia Mathematica altered his commitment to certainty in philosophy in 1911. An analysis of his published views and correspondence from this time strongly suggests that the radical transformation was induced by an epiphany brought about by (...) his emotional entanglement with his lover. (shrink)

Unification of natural science and social science is a centuries-old, unmitigated debate. Natural science has a chronological advantage over social science because the latter took time to include many social phenomena in its fold. History of science witnessed quite a number of efforts by social scientists to fit this discipline in a rational if not mathematical framework. On the other hand a tendency among some physicists has been observed especially since the last century to recast a number of social phenomena (...) in the mould of events taking place in physical world and governed by well-known systems and equations of physics. It necessitated the introduction of social physics as a new inter-disciplinary subject. Obviously this attempt is aimed at explaining hitherto unsolved or highly debated issues of social science. Physicists are showing special interest on problems on economics, ranging from some topics of normative economics to the movement of prices of derivatives. Statistics has been widely used in these attempts and at least two sub-disciplines of the subject, namely, stochastic process and time series analysis deserve special mention. All these research activities gave birth to another inter-disciplinary subject named as econophysics. Interestingly, global financial crisis of 2007–08 has revived the need of determination of prices of derivatives in a more accurate manner. This article adumbrates a sketch of the theoretical synthesis between physics and economics and the role played by statistics in this process. (shrink)

Abstract Studies of irrationality in cognitive psychology have usually looked at areas where humans might be expected to be rational, yet appear not to be. In this paper the other extreme of human irrationality is examined: the delusion as it occurs in psychiatric illness. A parallel is suggested between the delusion as an aberration of cognition and some illusions which result from aberrations within optics. It is argued that, because delusions are found predominantly within certain limited areas of cognitive functioning, (...) they may represent a form of mental aberration which may tell us something about the abstract properties of mind. Possible implications of this model for several areas of cognitive science are discussed. (shrink)

When we use secure computer systems, we engage with carefully orchestrated and ordered interactions called “security ceremonies”, all of which exist to assure security. A great deal of attention has been paid to improving the usability of these ceremonies over the last two decades, to make them easier for end-users to engage with. Yet, usability improvements do not seem to have endeared end users to ceremonies. As a consequence, human actors might subvert the ceremony’s processes or avoid engaging with it. (...) Here, we consider whether beautification could be one way of making ceremonies more appealing. To explore beautification in this context, we carried out three studies. Study 1 surveyed 250 participants to derive a wide range of potential dimensions of “beautiful ceremonies”. These statements were sorted into dominant themes and converted into statements, which fed into the second study, with 309 respondents, to reveal the dominant dimensions constituting beauty. Study 3 asked 41 participants to carry out a Q-sort, which revealed the ways that people combine the identified dimensions when characterising security ceremonies as “beautiful”. These studies have allowed us to pin down the perceived dimensions of beauty in the context of security ceremonies, and also to understand how people combine these dimensions in different ways in judging security ceremonies to be beautiful, confirming the old adage of beauty being “in the eye of the beholder”. We conclude by highlighting the constraints imposed by the overarching requirement for security to be maintained in the face of any usability improvements and beautification endeavours. (shrink)

In this article, I pay special expository attention to two pieces of philosophically relevant Wittgenstein–Russell correspondence from the period leading up to the ultimate demise of Russell's Theory of Knowledge manuscript (in June 1913). This is done in the hopes of shedding light on Wittgenstein's notoriously obscure criticisms of Russell's multiple relation theory of judgement. I argue that these two pieces of correspondence (the first, a letter from Wittgenstein to Russell dated January 1913, and the second, a letter from Russell (...) to Ottoline Morrell, reporting a tense confrontation with Wittgenstein on 26 May 1913) each refer to what is more or less the same approach to problems concerning the unity and well-formedness of propositions or judgements. However, the view advanced in Wittgenstein's January letter to Russell nevertheless differs in a key respect from the view of Russell's referred to in the May letter to Morrell. The difference involves Wittgenstein's incorporating qualities and relations as unsaturated parts of the copulae of atomic complexes, where these copulae are in turn conceived as logical forms. Because such an approach to logical form (and more specifically, to relations) was philosophically unpalatable to Russell, he undertook an alternative theoretical correction in the context of his 1913 Theory of Knowledge manuscript. This theoretical correction was discussed with Wittgenstein during the tense confrontation on 26 May, and involved deploying a supplemental significance constraint on judgements. It was this significance constraint on judgements, moreover, which was the ‘premiss’ alluded to by Wittgenstein in the context of a June 1913 letter to Russell, wherein he claims to express his objection to Russell's theory ‘exactly.’. (shrink)

When it comes to name-calling, structural realists have heard pretty much all of it. Among the many insults, they have been called ‘empiricist anti-realists’ but also ‘traditional scientific realists’. Obviously the collapse accusations that motivate these two insults cannot both be true at the same time. The aim of this paper is to defend the epistemic variety of structural realism against the accusation of collapse to traditional scientific realism. In so doing, I turn the tables on traditional scientific realists by (...) presenting them with a dilemma. They can either opt for a construal of their view that permits epistemic access to non-structural features of unobservables but then face the daunting task of substantiating a claim that seems to have little hope of being true or they can drop the requirement of epistemic access to non-structural features but then face a collapse to epistemic structural realism. There is thus only one well supported way to be a realist. No wonder then that many traditional scientific realists have over the years expressed views that are strikingly similar to epistemic structural realism. It is high time to let these epistemic structural realists out of the closet. (shrink)

For logicians and metaphysicians curious about the evolution of Russell's logic from The Principles of Mathematics to Principia Mathematica, no volume of the Collected Papers of Bertr...

While thrusting the importance of knowledge, Bertrand Russell highlights one special utility of it, i.e., knowledge promotes a widely contemplative habit of mind; and such knowledge, he terms ‘useless’. For Russell, the habit of contemplation is the capacity of rationalized enquiry which enables individuals to consider all questions in a tentative and impartial manner, frees them from dogmas and encourages the expression of a wide diversity of views. Besides ‘useless’ knowledge, Russell admits the importance of ‘useful’ knowledge too, but his (...) appreciation for the intrinsic value of ‘useless’ knowledge more than the extrinsic value of ‘useful’ one brings to light the significance of knowing, i.e., to know is to know something for its own sake. Pursuit of such knowledge is possible only in case of ‘useless’ knowledge; and not in case of ‘useful’ one. Highlighting contemplative habit of mind as the greatest advantage of ‘useless’ knowledge, Russell says that such habit, in order to get accelerated, has to be guided by education; but education without freedom cannot perform the job. To be free, according to Russell, means, to be free from the forces of tradition; and also from the tyranny of one’s own passions. Freedom is thus seen to be the cardinal force in fostering contemplative habit, and is closely found to have been associated with ‘useless’ knowledge. In the present paper, by highlighting the nature of contemplative habit of mind, I have argued that ‘useless’ knowledge has to be appreciated more than ‘useful’ knowledge. Moreover, I have shown why freedom in education has to be considered a necessity for accelerating habit of contemplation. (shrink)

In the nineteenth and twentieth centuries many mathematicians referred to intuition as the indispensable research tool for obtaining new results. In this essay we will analyse a group of mathematicians who interacted with Luitzen Egbertus Jan Brouwer in order to compare their conceptions of intuition. We will see how to the same word “intuition” very different meanings corresponded: they varied from geometrical vision, to a unitary view of a demonstration, to the perception of time, to the faculty of considering concepts (...) that habitually occur in our thinking separately. Furthermore, we will discover that these different meanings had a philosophical, very relevant counterside: they passed from a racial characterization of mathematics to a pluralistic view of it. (shrink)

In the first part ("Determination"), I consider different notions of determination, contrast and compare modal with non-modal accounts and then defend two a-modality theses concerning essence and supervenience. I argue, first, that essence is a a-modal notion, i.e. not usefully analysed in terms of metaphysical modality, and then, contra Kit Fine, that essential properties can be exemplified contingently. I argue, second, that supervenience is also an a-modal notion, and that it should be analysed in terms of constitution relations between properties. (...) In the second part ("A Theory of Truthmaking"), I first review the literature on ontological commitment, and argue that the notion of truthmaking is better suited to play its explanatory rôle. I then argue that we should take truthmaker theory seriously, and that we should provide actual truthmakers for all truths there are. In the last chapter of this part, I review Armstrong's truthmaker theories and argue that they are unsatisfactory. I generalise my criticism to an argument against truthmaker necessitarianism, the view that truthmakers necessarily make true the truths they are truthmakers of. In the third part ("Properties and their Kind(s)"), I discuss qualitative determination. I present and endorse the truthmaker argument for universals, and defend universalism against friends of tropes, states of affairs and facts. I then give a novel characterisation of the important class of intrinsic properties, building on Lewis' work. With a workable notion of intrinsicness at hand, I argue that relations are ontologically – but not "ideologically" – dispensable: qualitative determination in general is a matter of intrinsic structure. In the future, I plan to add two parts and to publish my thesis as a book: In the fourth part ("Exemplification"), I argue for the existence of an exemplification relation tying universals and particulars together. I derive theoretical benefits from this relation by providing adverbialist theories of modality and tense and identify exemplification with a type of parthood. In the fifth part ("Qua qua qua"), I investigate the curious and interesting ontological category of so-called "qua-objects" (Picasso-as-a-painter, for example) and argue that they exist, are not identical with transworld indidivuals or modal parts and that they provide (contingent) truthmakers for all true predications. (shrink)

Dieser Band versammelt Beiträge zu den drei klassischen Disziplinen der Philosophie – dem Wahren, dem Guten, dem Schönen. Ihre Autoren zeichnet aus, dass sie aus dem akademischen Umfeld Michael Sukales zu seiner Zeit am Institut für Philosophie an der Carl-von-Ossietzky-Universität Oldenburg stammen. Ihm ist dieses Buch zum Abschied von seiner aktiven Lehrtätigkeit in Oldenburg gewidmet. Die thematische Vielfalt der enthaltenen Texte spiegelt die Bandbreite seines philosophischen Schaffens wider.

This article is a critical analysis of the most important assumptions of Chantal Mouffe’s political philosophy, along with its original categories such as agonism, radical democracy and hegemony. The sources of her concept are indicated and certain difficulties that the author falls into are distinguished. The thread that is considered central to this philosophy, with the most profound practical consequences, is an attempt to demonstrate the futility of a liberal doctrine that values consensus and deliberation and proclaims an apology for (...) individualism and rationalism. Mouffe’s diagnosis strikes at the most important liberal values with the intention of discrediting them although she tries to creatively adopt others, such as pluralism. She proposes a new paradigm, much fairer than existing ones, because it does not negate the conflictive nature of politics. Does an agonist dispute and radical democracy really have a chance to undermine liberal axiology? Are we dealing with a breakthrough in thinking about politics? (shrink)