We discuss some ways in which topos theory (a branch of category theory) can be applied to interpretative problems in quantum theory and quantum gravity. In Sec.1, we introduce these problems. In Sec.2, we introduce topos theory, especially the idea of a topos of presheaves. In Sec.3, we discuss several possible applications of topos theory to the problems in Sec.1. In Sec.4, we draw some conclusions.

Foucault’s critique of early modern political theory aimed at displacing sovereignty as the principle of intelligibility of power. In the genealogical literature since Foucault, sovereignty has become a residual category lacking analytic specificity, largely displaced by governance, in turn equated with politics. We argue that Foucault and the Foucauldians have not understood that the flourishing of governance has presupposed a symbolic regime with a division of knowledge-power-law characteristic of the democratic sovereign. The conflation of governance with politics, together with the (...) sliding of sovereignty under governance, has left Foucauldians unable to diagnose the dangers present in varying possible sovereignty-governance configurations. (shrink)

We may be at the brink of a Kuhnian paradigm shift when it comes to the categorical classification system of mental disorders. Reviewing more than 30 years of critical literature on the categorical classification of personality disorders, Kueger, Hopwood, Wright, and Markon conclude that the Diagnostic and Statistical Manual of Mental Disorders is "fundamentally broken". Just before, the director of the National Institute of Mental Health declared that the institute will no longer support research that is based on DSM categories.The (...) critique on the categorical system of mental disorders consists of several arguments that are briefly mentioned as they have been... (shrink)

Let be a recursive structure, and let R be a recursive relation on . Harizanov isolated a syntactical condition which is necessary and sufficient for to have recursive copies in which the image of R is r.e. of arbitrary r.e. degree. We had conjectured that a certain extension of Harizanov's syntactical condition would be necessary and sufficient for to have recursive copies in which the image of R is ∑α0 of arbitrary ∑α0 degree, but this is not the case. Here (...) we give examples illustrating some restrictions on the possible ∑α0 degrees. In these examples, the image of R cannot be ∑α0 of degree d unless d possesses an “α-table”. (shrink)

This paper explores Plato and Aristotle 's responses to the pre-Socratic philosopher Parmenides, who paradoxically said that there is no such thing as non-being, and no such things as change. I argue that Plato’s response would have been good enough to defeat the claim in a debate, thereby remedying the political aspects of the Parmenides problem. However, Aristotle ’s answer is required to answer some additional philosophical and scientific aspects. Plato's Sophist is a very difficult dialogue to understand; seeing it (...) in light of Aristotle 's discussion of the same topic helps to explain the complexities of what his teacher Plato wrote. (shrink)

Despite the importance of the Judgement of Paris in the story of the Trojan War, theIliadhas only one explicit reference to it. This occurs, rather out of the blue, in the final book of the poem in a dispute among the gods about the treatment of Hector's body (24.25–30). Achilles keeps dragging the body around behind his chariot, but Apollo protects it with his golden aegis (24.18–21). Apollo then speaks among the gods and attacks the conduct of Achilles (24.33–54), claiming (...) at the end that he offends the dumb earth (24.54). Other gods too have their concerns about what is going on, and they keep trying to get Hermes to snatch the body away (24.23–4). The three most powerful divine enemies of Troy, however, Hera, Poseidon and Athena, will have none of this. They remain as hostile to Troy and Priam and his people as they ever were, and it is in this context that the Judgement of Paris is mentioned:ἔνθ' ἄλλοις μὲν πᾶσιν ἑήνδανɛν, οὐδέ πoθ' Ἥρῃοὐδὲ Ποσɛιδάων' οὐδὲ γλαυκώπιδι κούρῃ,ἀλλ' ἔχον ὥς σϕιν πρῶτον ἀπήχθɛτο Ἴλιος ἱρὴκαὶ Πρίαμος καὶ λαὸς Ἀλɛξάνδρου ἕνɛκ' ἄτης,ὃς νɛίκɛσσɛ θɛάς, ὅτɛ οἱ μέσσαυλον ἵκοντο,τὴν δ' ᾔνησ' ἥ οἱ πόρɛ μαχλοσύνην ἀλɛγɛινήν.(24.25–30)And this was pleasing to all the others, but never to Heranor to Poseidon, nor to the flashing-eyed maiden,but they remained hostile to sacred Ilios as in the beginning,and to Priam and to his people, because of Alexander's folly,he who insulted the goddesses when they came to his inner courtyardand praised her who provided his grievous lust. (shrink)

The measurement of food intake has long been used to describe ‘adaptation’ to low energy intakes in certain tropical peoples. However, the methods available to quantify food intake are unlikely to reflect accurately real energy intakes in free living peoples. Alternatively, estimating energy expenditure shows some promise—particularly the measurement of basal metabolic rate . The BMR may be measured effectively in males, but females show wide intra-individual variation in BMR during their menstrual cycle, which makes BMR measurements more difficult to (...) interpret in the context of adaptation. The use of double-labelled water may be the only method suitable to quantify and define ‘adaptation’ to low intakes in women. (shrink)

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose ‘configuration space’ (or history-theory analogue) is the set of objects Ob(Q) in a category Q. We develop a scheme based on constructing (...) an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold Q ≃ G/H, where G and H are Lie groups. In particular, we choose as the analogue of G the monoid of “arrow fields” on Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the ‘category quantisation monoid’, we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over Ob(Q). For the example of a category of finite sets, we construct an explicit representation structure of this type. (shrink)

In den bisherigen Auseinandersetzungen hat der Schriftsteller eine besondere Hierarchie des Denkens angewandt, nämlich ontologisch... anthropologisch... pädagogisch. Ontologisches Denken in der Pädagogik ist heutzutage an der Tagesordnung. Die Fundamentalpädagogik soll in der ersten Linie eine Ontologie der Erziehung sein: “Als Strukturanalyse der Seinsweise von Erziehung erscheint die Erziehungsphilosophie also zunächst Ontologie der Erziehung...”27 Fundamentalpädagogik als ontologisch-anthropologische Pädagogik ist daher eine Suche nach ontischen Strukturen als Seinsbedingungen für das In-Erscheinung-Treten des Pädagogischen. Klafki erklärt, dass es dem Pädagogen als Wissenschaftler der Seinsweise (...) von Erziehung unmöglich ist, wissenschaftliche Aussagen zu geben, wenn sie nicht fortfliessen aus einer ontologischen Bestimmung der Erziehungswirklichkeit: “Es gibt kein pädagogisches Sein ohne pädagogisches Denken, aber auch kein pädagogisches Denken, das abgelöst wäre vom pädagogischen Sein.”28 In diesem pädagogischen Aufsatz hat der Schriftsteller einen Versuch gemacht, pädagogische Kategorien und Kriterien ontologisch-anthropologisch zu fundieren. (shrink)

Recent interest in ethical pluralism derives from Isaiah Berlin's reflections on the writings of Vico and Herder and their opposition to the views of the Enlightenment. I begin with two quotations from Berlin: It is not relativism. Members of one culture can, by the force of imaginative insight, understand … the values, the ideals, the forms of life of another culture or society, even those remote in time or space. They may find these values unacceptable, but if they open their (...) minds sufficiently they can grasp how one might be a full human being, with whom one could communicate, and at the same time live in the light of values widely different from one's own, but which nevertheless one can see to be values, ends of life, by the realisation of which men could be fulfilled. (shrink)