Genevieve Lloyd’s Spinoza is quite a different thinker from the arch rationalist caricature of some undergraduate philosophy courses devoted to “The Continental Rationalists”. Lloyd’s Spinoza does not see reason as a complete source of knowledge, nor is deductive rational thought productive of the highest grade of knowledge. Instead, that honour goes to a third kind of knowledge—intuitive knowledge (scientia intuitiva), which provides an immediate, non-discursive knowledge of its singular object. To the embarrassment of some hard-nosed philosophers, intellectual intuition has an (...) affective component; it is a form of love, and ultimately given that human beings are finite modes of God/Nature (Deus sive Natura), it is a form of the intellectual love of God (amor Dei intellectualis). Some philosophers do not know what to make of this mysterious aspect of Spinoza’s philosophy, which is nonetheless firmly anchored in a reading of Part V of the Ethics. Nonetheless, this note will insist with Lloyd’s “Reconsidering Spinoza’s Rationalism” that such doctrine is an integral part of Spinoza’s philosophy. Moreover, it will be shown that Spinoza is well aware of the limitations of reason (ratio) in gaining scientific knowledge of the world and requires intuition precisely because of the inability of reason to represent individuals in their full particularity. Imagination too has a role to play in shaping scientific knowledge, although reason performs a vital critical role in disciplining and liberating the human mind from inadequate imaginary ideas. The result is an interpretation of Spinoza’s epistemology as both rationalist and intuitionist. DOI: 10.1080/24740500.2021.1962652. (shrink)

The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...) reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)

A fallibilist theory of knowledge is employed to make sense of the idea that agents know what they are doing 'without observation' (as on Anscombe's theory of practical knowledge).

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. This paper considers how the doctrine of symbolism and the philosophers' different commitments to the laws of logic, especially the Law of Non-Contradiction (LNC), enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

Coping with everyday life limits the extent of one’s scepticism. It is practically impossible to doubt the existence of the things with which one is immediately engaged and interacting. To doubt that, say, a door exists, is to step back from merely using the door (opening it) and to reflect on it in a detached, theoretical way. It is impossible to simultaneously act and live immersed in situation S while doubting that one is in S. Sceptical doubts—such as ‘Is this (...) really a door?’, ‘Am I really walking?’ — require a reflective withdrawal in thought from the situation at hand. Maintaining sceptical doubt while coping with everyday life requires a split consciousness, a bad faith, with one part of consciousness doubting the existing of things that the other part takes forgranted. For this reason, a sustained lived sceptical doubt is sometimes thought to be impossible. -/- In this article, I examine Wittgenstein's response to scepticism in "On Certainty". I argue that one of his responses is "the response based on action", which is (as other Wittgenstein interpreters have noted) a characteristically pragmatist response. I then evaluate the quality of this pragmatist response to scepticism, noting that actions just as much as representations are susceptible to mis-interpretation. It is argued that despite the insights contained in it, Wittgenstein's contextualism about meaning is inadequate to rescue the Wittgensteinian response to scepticism. (shrink)

G. E. M. Anscombe’s view that agents know what they are doing “without observation” has been met with skepticism and the charge of confusion and falsehood. Simultaneously, some commentators think that Anscombe has captured an important truth about the first-personal character of an agent’s awareness of her actions. This paper attempts an explanation and vindication of Anscombe’s view. The key to the vindication lies in focusing on the role of practical knowledge in an agent’s knowledge of her actions. Few commentators, (...) with the exception of Moran (2004) and Hursthouse (2000), have gotten the emphasis right. The key to a proper interpretation of Anscombe’s views is to explain her claims within the context of her teleological theory of action. The result is a theory ofintentional action that makes self-knowledge of one’s own actions the norm. (shrink)

In chapter 7 of The Varieties of Reference, Gareth Evans claimed to have an argument that would present "an antidote" to the Cartesian conception of the self as a purely mental entity. On the basis of considerations drawn from philosophy of language and thought, Evans claimed to be able to show that bodily awareness is a form of self-awareness. The apparent basis for this claim is the datum that sometimes judgements about one’s position based on body sense are immune to (...) errors of misidentification relative to the first-person pronoun 'I'. However, Evans’s argument suffers from a crucial ambiguity. 'I' sometimes refers to the subject's mind, sometimes to the person, and sometimes to the subject's body. Once disambiguated, it turns out that Evans’s argument either begs the question against the Cartesian or fails to be plausible at all. Nonetheless, the argument is important for drawing our attention to the idea that bodily modes of awareness should be taken seriously as possible forms of self-awareness. (shrink)

In a recent article, Christopher Ormell argues against the traditional mathematical view that the real numbers form an uncountably infinite set. He rejects the conclusion of Cantor’s diagonal argument for the higher, non-denumerable infinity of the real numbers. He does so on the basis that the classical conception of a real number is mys- terious, ineffable, and epistemically suspect. Instead, he urges that mathematics should admit only ‘well-defined’ real numbers as proper objects of study. In practice, this means excluding as (...) inadmissible all those real numbers whose decimal expansions cannot be calculated in as much detail as one would like by some rule. We argue against Ormell that the classical realist account of the continuum has explanatory power in mathematics and should be accepted, much in the same way that "dark matter" is posited by physicists to explain observations in cosmology. In effect, the indefinable real numbers are like the "dark matter" of real analysis. (shrink)

Online philosophy seminar notes, for virtual conference on the Aristotelian philosophy of mathematics, hosted by University of Geneva (organiser Ryan Miller), June 15, 2023.

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)

This paper is on Aristotle's conception of the continuum. It is argued that although Aristotle did not have the modern conception of real numbers, his account of the continuum does mirror the topology of the real number continuum in modern mathematics especially as seen in the work of Georg Cantor. Some differences are noted, particularly as regards Aristotle's conception of number and the modern conception of real numbers. The issue of whether Aristotle had the notion of open versus closed intervals (...) is discussed. Finally, it is suggested that one reason there is a common structure between Aristotle's account of the continuum and that found in Cantor's definition of the real number continuum is that our intuitions about the continuum have their source in the experience of the real spatiotemporal world. A plea is made to consider Aristotle's abstractionist philosophy of mathematics anew. (shrink)

We show how an epistemology informed by cognitive science promises to shed light on an ancient problem in the philosophy of mathematics: the problem of exactness. The problem of exactness arises because geometrical knowledge is thought to concern perfect geometrical forms, whereas the embodiment of such forms in the natural world may be imperfect. There thus arises an apparent mismatch between mathematical concepts and physical reality. We propose that the problem can be solved by emphasizing the ways in which the (...) brain can transform and organize its perceptual intake. It is not necessary for a geometrical form to be perfectly instantiated in order for perception of such a form to be the basis of a geometrical concept. (shrink)

Does Cantorian set theory alter our intuitive conception of number? Yes. In particular, Cantorian set theory revises our intuitive conception of when two sets have the same size (cardinal number). Consider a variant of Galileo’s Paradox, which notes that the members of the set of natural numbers, N, can be put in one-to-one correspondence with the members of the set of even numbers, E.

Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...) Georg Cantor (1845-1918) says that between the realm of the finite and the absolute infinite, there is an intermediate realm partaking in properties in a certain sense of both the finite and the infinite: the transfinite realm. Like the finite, the transfinite realm is a realm of mathematical objects, numbers, and knowledge. Like the absolute infinite, the transfinite is a form of infinity insofar as transfinite sets and numbers transcend any finite number. Echoing Cusanus and neo-Platonism, Cantor says that the transfinite sequence of all ordinals is a symbol of the absolutely infinite, that is, God. Moreover, Cantor envisioned his transfinite set theory (Mengenlehre) as providing the analytical methods and techniques necessary for a comprehensive, organic, non-reductive description of nature, a Naturphilosophie. Thus Cantor’s novel mathematics is presented as part of a long tradition, to which Cusanus, Bruno, Spinoza, Leibniz and others belong, in which the infinity and infinite character of organic life forms is appreciated, and is in some sense a mirror or symbol of the divine. The doctrine of symbolism and their different approach to the laws of logic present in both the work of Cusanus and Cantor enables these thinkers to articulate a transcendental apophatic approach to divinity. (shrink)

This is a grant proposal for a research project conceived and written as a Research Associate at UNSW in 2011. I have plans to spin it into an article.

This is a grant proposal written as a post-doctoral application for MQRF at Macquarie University in 2009. As I did so much research for it, I have plans to spin it into an article. I note with pleasure the increased relevance of this kind of research given developments such as Neuralink and ChatGPT.

This is a copy of the presentation given at the "Workshop on Agency and Distributed Cognition" at Macquarie University, March 2012. What is noteworthy about this piece of work is that (i) it is a very early foray into the pedagogy, ontology, and epistemology of virtual worlds (it's 2012, way before David Chalmers' book "Reality+" in 2022); and (ii) it was my first foray into "social epistemology" beyond the standard "S knows that p" epistemology, drawing on Vygotskian collaborative approaches to (...) learning and teaching, moving beyond analytic philosophy into educational research. Finally, (iii) there's a hyperlink to the actual virtual world in Unity3D created by a cross-disciplinary team of researchers from Sydney University and Macquarie University for the purposes of teaching scientific inquiry. (shrink)

It is argued that there are ways of individuating the objects of perception without using sortal concepts. The result is an moderate anti-sortalist position on which one can single out objects using demonstrative expressions without knowing exactly what sort of thing those objects are.

Do actual infinities exist or are they impossible? Does mathematical practice require the existence of actual infinities, or are potential infinities enough? Contrasting points of view are examined in depth, concentrating on Aristotle’s ancient arguments against actual infinities. In the long 19th century, we consider Cantor’s successful rehabilitation of the actual infinite within his set theory, his views on the continuum, Zeno's paradoxes, and the domain principle, criticisms by Frege, and the axiomatisation of set theory by Zermelo, as well as (...) Zermelo’s assertion of the primacy of potential infinity in mathematics. (shrink)

This thesis proposes that an account of first-person reference and first-person thinking requires an account of practical knowledge. At a minimum, first-person reference requires at least a capacity for knowledge of the intentional act of reference. More typically, first-person reasoning requires deliberation and the ability to draw inferences while entertaining different 'I' thoughts. Other accounts of first-person reference--such as the perceptual account and the rule-based account--are criticized as inadequate. An account of practical knowledge is provided by an interpretation of GEM (...) Anscombe's account in her landmark monograph "Intention". (shrink)

According to Quine’s indispensability argument, we ought to believe in just those mathematical entities that we quantify over in our best scientific theories. Quine’s criterion of ontological commitment is part of the standard indispensability argument. However, we suggest that a new indispensability argument can be run using Armstrong’s criterion of ontological commitment rather than Quine’s. According to Armstrong’s criterion, ‘to be is to be a truthmaker (or part of one)’. We supplement this criterion with our own brand of metaphysics, 'Aristotelian (...) realism', in order to identify the truthmakers of mathematics. We consider in particular as a case study the indispensability to physics of real analysis (the theory of the real numbers). We conclude that it is possible to run an indispensability argument without Quinean baggage. (shrink)

This is a book review of Karen Armstrong's "The Spiral Staircase", the autobiography of a historian of religion. -/- To cite this article: Newstead, Anne. Compassion, Not Belief [Book Review] [online]. Quadrant, Vol. 49, No. 6, June 2005: 88-89. Availability: <http://search.informit.com.au/documentSummary;dn=203690937218529;res=IELLCC> ISSN: 0033-5002. [cited 06 Dec 12].

This is a very short book review of a recent volume on the philosophy of Gareth Evans with special attention to work on first-person reference.

This is a book review of Oppy's "Philosophical Perspectives on Infinity", which is of interest to those in metaphysics, epistemology, philosophy of science, mathematics, and philosophy of religion.

This paper reports on an ongoing ARC Discovery Project that is conducting design research into learning in collaborative virtual worlds (CVW).The paper will describe three design components of the project: (a) pedagogical design, (b)technical and graphics design, and (c) learning research design. The perspectives of each design team will be discussed and how the three teams worked together to produce the CVW. The development of productive failure learning activities for the CVW will be discussed and there will be an interactive (...) demonstration of the project's CVW. (shrink)

This paper presents the intelligent virtual animals that inhabit Omosa, a virtual learning environment to help secondary school students learn how to conduct scientific inquiry and gain concepts from biology. Omosa supports multiple agents, including animals, plants, and human hunters, which live in groups of varying sizes and in a predator-prey relationship with other agent types (species). In this paper we present our generic agent architecture and the algorithms that drive all animals. We concentrate on two of our animals to (...) present how different parameter values affect their movements and inter/intra-group interactions. Two evaluations studies are included: one to demonstrate the effect of different components of our architecture; another to provide domain expert validation of the animal behavior. (shrink)

Over the past decade, teaching and learning in virtual worlds has been at the forefront of many higher education institutions around the world. The DEHub Virtual Worlds Working Group (VWWG) consisting of Australian and New Zealand higher education academics was formed in 2009. These educators are investigating the role that virtual worlds play in the future of education and actively changing the direction of their own teaching practice and curricula. 47 academics reporting on 28 Australian higher education institutions present an (...) overview of how they have changed directions through the effective use of virtual worlds for diverse teaching and learning activities such as business scenarios and virtual excursions, role-play simulations, experimentation and language development. The case studies offer insights into the ways in which institutions are continuing to change directions in their teaching to meet changing demands for innovative teaching, learning and research in virtual worlds. This paper highlights the ways in which the authors are using virtual worlds to create opportunities for rich, immersive and authentic activities that would be difficult or not possible to achieve through more traditional approaches. (shrink)

Refus des philosophies de l'histoire, des " sciences sociales ", de la philosophie politique... c'est à partir d'un événement - " 1933 " - que Hannah Arendt construit, patiemment, rigoureusement, une réflexion sur la politique. Tous ses textes contribuent à cette entreprise cohérente depuis Les origines du totalitarisme. Et cette entreprise même, qui conteste la tradition, s'appuie sur un effort pour la relire à nouveaux frais, depuis les leçons de la démocratie grecque jusqu'à Kant et aux Révolutions américaine et française. (...) Ainsi, s'élabore une pensée de la cité, du mal, du conflit et de la responsabilité. (shrink)

Zusammenfassung In der soziologischen Diskussion spielen Begriff und Konzept der Inklusion – verstanden als umfassende Teilhabe aller Gesellschaftsmitglieder – aktuell eine große Rolle. Gleichzeitig gibt es eine entsprechende Konjunktur in den politischen, medialen und pädagogischen Diskursen. Über das Bildungssystem hinaus, wo Inklusion vor allem mit Blick auf die schulische Erziehung behinderter Kinder diskutiert wird, ist der Inklusionsgedanke auch in anderen Lebensbereichen, etwa im Sport oder Arbeitsleben, von Bedeutung. Insgesamt fällt auf, dass die soziologische Theorie und die gesellschaftliche Diskussion zwar lose (...) aufeinander verweisen, bisher jedoch kaum systematisch verbunden sind. Dabei ist von komplexen Wechselwirkungen zwischen den verschiedenen Diskursen auszugehen. In einem ersten Zugriff rekonstruiert der Beitrag den Inklusionsbegriff in genealogischer Perspektive, um dessen Umformungen und Umcodierungen sichtbar zu machen. Im zweiten Teil wird ein dispositivanalytischer Ansatz entwickelt, mit dessen Hilfe die Rationalitäten, Technologien, Institutionen und Subjektivierungen untersucht werden können, die Inklusion als ein hegemoniales Leitkonzept der Gegenwart formieren. (shrink)

Waters aries that the demands of indigenous bio-prospecting programs need to be considered against the needs of indigenous communities. Issues of sovereignty and rights to self-determination need to be resolved in the context of negotiating bio-prospecting plans. By setting out clear guidelines and priorities, as determined through the eyes and values of indigenous peoples, indigenous communities may have an opportunity to participate in the global sharing of biomedical information and healing for all our relations. Before any projects get underway, however, (...) social, political, and legal issues ought to be settled so that informed decision can be made on the part of indigenous communities to partake of the invitation to bio-prospecting, or not. (shrink)

Although non-profit organisations typically have high representation of females on their boards, relatively little is known about the effects of gender diversity in these organisations particularly in relation to financial management. In this archival study, resource dependency theory and agency analysis are combined to provide theoretical insight and empirical analysis of gender diversity on effective financial management in member-governed, community financial institutions. The investigation is possible due to the unique characteristics of the organisational form and region being examined—credit unions in (...) Northern Ireland. The sector has not been subject to external regulation on board gender, yet a wide array of gender mix on boards ranging from 100 % male to 100 % female are in existence. In addition, effective financial management is crucial to their survival and their ability to meet member objectives. Boards with higher female representation exhibit superior financial management first, in respect of loan book quality in the period of austerity following the financial crisis and second when measured against return on assets. (shrink)

Read again in light of the current French social conflict around the part-time theater and cinema workers, the book by L. Boltanski and E. Chiapello, Le nouvel esprit du capitalisme, seems to have been quite prescient when describing work as organized store and more through short-term projects. But the lack of social security in this system is supposed by the authors to conte front the artist-critics who were interested mostly in individual freedom and expressivity, store than from the infrastructural organization (...) of capitalism. Solutions are sought by analogy with the rides that protect salaried workers, particularly the idea of a guaranteed income or social wage. (shrink)

Que l’éthique ait pu soutenir le capitalisme n’est pas une idée nouvelle : on la trouve déjà chez Marx, puis chez Weber qui analyse les « affinités électives » entre l’éthique protestante et l’esprit du capitalisme. Il semble cependant qu’aujourd’hui, on assiste à un phénomène qui relèverait d’une « économisation » du concept d’éthique. Le lieu de « production » de l’ « éthique » paraît bien être la sphère économique elle-même, et notamment l’entreprise qui en serait l’un des principaux (...) vecteurs de diffusion. C’est en ce sens que l’on parlera d’ « offre éthique ». Si l’éthique en « s’économisant » s’adresse à l’individu en tant qu’être de besoin, ne va-t-elle pas devenir, au même titre que les biens culturels , un bien marchand ? L’entreprise est-elle fondée à produire une éthique économique ?The support provided by ethics to capitalism is not new : the idea was expressed by Marx, then by Weber analyzing the « elective affinities » between protestant ethics and the spirit of capitalism. Nevertheless, it seems that, in the contemporary period, another phenomenon is appearing : the « economization » of the concept of ethics. From now on, ethics would be produced by the economic sphere itself, and particularly by business. In such a configuration, the question raised are the following ones : is this evolution leading to a « marketization » of ethics parallel to the one put in evidence by Arendt concerning the cultural goods ? Is business legitimate to produce an economic ethics ? (shrink)

Name der Zeitschrift: Kierkegaard Studies Yearbook Jahrgang: 2016 Heft: 1 Seiten: 39-50.

Deux préjugés ont grevé la réception de l'œuvre d'Arendt, en particulier en France. L'un : que l'étude des " origines du totalitarisme " et de sa nature (comme modèle politique portant bien au-delà du prototype nazi) ne définirait pas seulement le point de départ de ses questions, mais en bornerait les enjeux. L'autre : qu'à travers les étapes et les détours d'une pensée de la politique et de l'histoire contemporaines, elle n'aurait tendu qu'à rejoindre la tradition philosophique (la méditation sur (...) " la vie de l'esprit "). Convoquant tour à tour l'analyse des révolutions, la critique du travail et du mouvement ouvrier, le questionnement sur la publicité, la société du spectacle et la capacité de juger, le présent ouvrage entend restituer ce qui fait l'originalité de la réflexion d'Arendt sur l'histoire et la politique. Il la replace dans la lignée de Machiavel, de Montesquieu et de Tocqueville, dans la confrontation déterminante avec Marx, dans l'opposition constante à la philosophie politique. Justifiant la posture non-philosophique qu'elle n'a cessé de revendiquer. Démontrant par là même quel bénéfice réel la philosophie peut tirer d'une provocation qui l'expose à la puissance sauvage de l'événement, et à l'étonnement qu'il doit susciter. (shrink)

En accompagnement de la reprise des fouilles, nous présentons de nouvelles données relatives aux trois monuments les plus occidentaux de la terrasse de la Marmaria, obtenues à l’occasion de l’inventaire des blocs hors œuvre, présents sur le site, et d’une relecture des sources textuelles antiques. La fonction d’hestiatorion de SD 44 est ainsi confirmée. Une nouvelle datation est proposée pour l’édifice de calcaire SD 43 dont l’architecture ne correspond pas à celle d’un temple, mais plutôt à celle d’une salle d’assemblée. (...) La date de la tholos SD 40 est également abaissée, ce qui la met en relation avec le Philippéion d’Olympie. Ces acquis auront à être précisés par la poursuite de l’étude architecturale, mais ils invitent déjà à réévaluer la place que la Macédoine des Argéades tenait à Delphes. (shrink)