Sets and Probability

In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets

Iterated reflection principles over full disquotational truth

Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by finitely iterated reflection at strong compositional truth theories. In the context of classical logic it is incoherent to adopt an initial truth theory in which A and 'A is true' are inter-derivable. In this article we show how in the context of a weaker logic, which we call Basic De Morgan Logic, we can coherently start with such a fully disquotational truth theory and arrive at a strong compositional truth theory by applying a natural uniform reflection principle a finite number of times

Cantorian Infinity and Philosophical Concepts of God

It is often alleged that Cantor’s views about how the set theoretic universe as a whole should be considered are fundamentally unclear. In this article we argue that Cantor’s views on this subject, at least up until around 1896, are relatively clear, coherent, and interesting. We then go on to argue that Cantor’s views about the set theoretic universe as a whole have implications for theology that have hitherto not been sufficiently recognised. However, the theological implications in question, at least as articulated here, would not have satisfied Cantor himself

Truth and Existence

Halbach has argued that Tarski biconditionals are not ontologically conservative over classical logic, but his argument is undermined by the fact that he cannot include a theory of arithmetic, which functions as a theory of syntax. This article is an improvement on Halbach's argument. By adding the Tarski biconditionals to inclusive negative free logic and the universal closure of minimal arithmetic, which is by itself an ontologically neutral combination, one can prove that at least one thing exists. The result can then be strengthened to the conclusion that infinitely many things exist. Those things are not just all Gödel codes of sentences but rather all natural numbers. Against this background inclusive negative free logic collapses into noninclusive free logic, which collapses into classical logic. The consequences for ontological deflationism with respect to truth are discussed

Hypatia's silence. Truth, justification, and entitlement.

Hartry Field distinguished two concepts of type-free truth: scientific truth and disquotational truth. We argue that scientific type-free truth cannot do justificatory work in the foundations of mathematics. We also present an argument, based on Crispin Wright's theory of cognitive projects and entitlement, that disquotational truth can do justificatory work in the foundations of mathematics. The price to pay for this is that the concept of disquotational truth requires non-classical logical treatment

A HUMAN RIGHTS-BASED APPROACH TO POVERTY REDUCTION: THE ROLE OF THE RIGHT OF ACCESS TO MEDICINE AS AN ELEMENT OF THE RIGHT OF ACCESS TO HEALTH CARE

The prevention and treatment of infectious diseases remain among the greatest challenges faced by today's developing countries. The World Health Organisation estimates that about one-third of the world's population lacks access to essential medicine, a fact which, according to the United Nations, directly contradicts the fundamental principle of health as a human right. According to the World Summit for Social Development, poor health and illness are factors that contribute to poverty, while the adverse effects of illness ensure that the poor become poorer. A lack of access to health care, amongst other rights, (including access to medicines as an element thereof) aggravates poverty. The most important provision in international law relating to the right to health is article 12 of the United Nations International Covenant on Economic, Social and Cultural Rights. Article 12(1) of this Covenant provides a broad formulation of the right to health in international law, while article 12(2) prescribes a non-exhaustive list of steps to be taken in pursuit of the highest attainable standard of health. Article 12(2), in particular, illustrates the role that adequate access to medication plays in the right of access to health care. The United Nations Committee on Economic, Social and Cultural Rights has explicitly included the provision of essential drugs as a component of the right to health care, thereby emphasising the causal link between the lack of access to essential medicines and the non-fulfilment of the right of access to health care. As with all socio-economic rights, the resource implications of the realisation of the right to health has the result that states cannot be expected to immediately comply with its obligations in respect thereof. Instead, article 2(1) of the International Covenant on Economic, Social and Cultural Rights and the General Comments of the Committee on Economic, Social and Cultural Rights place obligations on states to take deliberate, concrete and targeted steps towards expeditious and effective full realisation of the right to health, including access to medication. The measures taken to do so must, according to General Comment 3, embrace the concept of the minimum core obligation (the minimum core in relation to medicines being access to essential medicines, at the very least). In this article it is argued that adequate access to essential medicines, as an element of the right of access to health care, could contribute to the reduction of poverty. This is done by firstly discussing the human rights-based approach to poverty reduction, whereafter attention is turned to access to medicines as an element of the right to health, with specific focus on obligations in terms of the International Covenant on Economic, Social and Cultural Rights. Finally, the role of access to medicines in reducing poverty is considered. The article concludes that poverty constitutes an infringement on human rights and will not be eradicated without the fulfilment of human rights, including the right to health. The adequate fulfilment of peoples' rights of adequate access to essential medicines will enable them to achieve a higher level of well-being, thereby reducing the level of poverty which they experience. Both the right of access to health care and to essential medicines – a crucial component thereof – thus have a significant role to play in a state's poverty reduction strategies

Infinitesimal Probabilities

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general.publishe

The Coexistence of Contradictory Properties in the Same Subject According to Aristotle

In Metaphysics, Book Gamma, Aristotle argues that he who asserts a contradiction is committed to a rejection of degrees. On the other hand, though, Aristotle claims that there can be no intermediary situation in-between pure or entire truth or existence and utter, complete falseness or nonexistence. Such a combination of views can be rendered noncontradictory at best through objectionable manoeuvres. Although Aristotle accepts that two contrary properties can be both present in the same object to some extent, he is, in order to keep clear of contradictions, bound to regard intermediary situations as something irreducibly different from both extremes.Peer reviewe