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

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

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

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

Generic structures

In this article ideas from Kit Fine's theory of arbitrary objects are applied to questions regarding mathematical structuralism. I discuss how sui generic mathematical structures can be viewed as generic systems of mathematical objects, where mathematical objects are conceived of as arbitrary objects in Fine's sense

The role played by the South African human rights commission's economic and social rights reports in good governance in South Africa

The preamble of the Constitution of South Africa, 1996 (the Constitution)contains the commitment to, amongst other things, establish a society based on democratic values, social justice and fundamental human rights, lay the foundations for a democratic and open society in which government is based on the will of the people and every citizen is equally protected by law and improve the quality of life of all citizens and free the potential of each person. One of the methods used to achieve these objectives is the inclusion of enforceable socio-economic rights in the Chapter 2 Bill of Rights. Despite numerous debates surrounding the issue of enforceability of socioeconomic rights, it has become evident that these rights are indeed enforceable. Not only does section 7(2) of the Constitution place the state under an obligation to respect, protect, promote and fulfil all rights in the Bill of Rights, including socio-economic rights, but the Constitutional Court has in various decisions passed judgment on issues relating to socio-economic rights, underpinning the fact that these rights are indeed enforceable. The fact that socio-economic rights have been included in the Bill of Rights and are enforceable is, however, not sufficient to achieve the aims set out in the preamble. In order for these rights to be of any value to the people they seek to protect, they need to be implemented. One of the ways in which the implementation of these rights is monitored is by means of the South African Human Rights Commission's annual Economic and Social Rights Reports. The aim of this contribution is to assess these reports and to establish the degree to which they contribute to good governance in South Africa with reference to,inter alia, the constitutional mandate of the South African Human RightsCommission, the reporting procedure and the evaluation of reports

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