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Please note that Rini's lecture is exceptionally scheduled on Tuesday 20 May, 14h, as a joint activity with the Centrum for Logica en Wetenschapsfilosofie (VUB). CANCELED (because of a train strike).
Please note also that all BSLPS lectures are now held -- unless otherwise specified -- at the
Écuries royales / Koninklijke Stallingen
Palais des Académies / Paleis der Academiën
Rue Ducale / Hertogsstraat 1
1000 Bruxelles / Brussel
Archives of 2006-07 lectures are available here.
In this talk I will first present calculi of individuals -- that is, theories for which it is common that they are considered to be nominalistic -- and extensions of them formulated in wider vocabularies: e.g., in a vocabulary which contains topological or geometrical notions. I then address the topic of the proof-theoretic strength of these theories: how much mathematics can be developed in them, and how do they relate to each other? Finally, I want to touch the question whether they still deserve to be classified as nominalistically acceptable theories.
Dans les théories physiques conventionnelles, celles qui sont opératoires aujourd'hui (mécanique classique, physique quantique, relativités restreinte et générale), le principe de causalité, en imposant un ordre entre certains événements, contraint de l'extérieur la façon de représenter le temps. Mais certaines "nouvelles physiques" qui sont à l'ébauche aujourd'hui visent à renverser cette logique en partant de l'idée que la causalité est une donnée première et en tentant de montrer que le temps lisse et continu que nous connaissons est une propriété qui émerge, à une certaine échelle, à partir d'un inframonde dans lequel il n'y a pas de temps prédéfini mais dans lequel se trouvent déjà des événements causalement reliés. Le temps ne serait alors qu'une émanation de la causalité. Nous tenterons de présenter et d'analyser ces différentes démarches.
I will argue, with reference to various central areas of mathematics, that the Gödel Incompleteness Phenomenon remains very remote from the concerns of mathematicians. I will sketch some arguments that PA (First Order Peano Arithnmetic), far from being a weak system, is extremely strong, and well able to accommodate such sophisticated arguments as those going into the Wiles proof of Fermat's Last Theorem. The basic ideas, both philosophical and mathematical, go back to work of Kreisel in the 1950's.
In the literature on the foundations of the special theory of relativity, Malament's theorem on the conventionality of simultaneity has often been taken to settle the issue in a definitive way. Recently, there has been some discussion about some of its premises, but the issue of what it means to claim that simultaneity is conventional has not been addressed and reevaluated. In the talk I will try to show that two issues that in the literature have been so far regarded as independent of each other are connected in the following way: if there is objective relativistic becoming, then simultaneity is conventional.
Evidence for causal claims comes in a variety of forms in the social sciences. The most important of these are evidence of what would have been, evidence of regularities, evidence of certain statistical relations,evidence of connecting mechanisms and evidence of invariant relationships. Social scientists often use evidence from more than one source in order to confirm a single causal hypothesis and sometimes even demand a plurality of evidence in order for a causal hypothesis to be regarded as established. The overall aim of this paper is to provide an analysis of this state of affairs and draw some methodological conclusions. A number of philosophers have recently offered pluralistic perspectives on causation. Here I distinguish epistemic, conceptual and metaphysical versions of pluralism and consider some of the arguments in favour of these. Ignoring metaphysical issues here, I end up with a form of evidential monism but conceptual pluralism about causation in the social sciences.
This paper concerns Gödel’s conception of the reality of mathematical objects. I distinguish three claims (i), (ii), (iii).
(i) “Mathematics describes a non-sensual reality, which exists independently both of the acts and [of] the dispositions of the human mind.”
(ii) “Mathematical objects and facts (or at least something in them) exist objectively and independently of our mental acts and decisions.”
(iii) Mathematics (or something in mathematics) is independent of the specific properties of the human being.
Claim (i) is usually quoted to characterize Gödel’s Platonism. However, relying on the unpublished papers (in particular Gödel’s drafts), I argue that Gödel cannot hold such a strong Platonism after 1954. His position is better described by the two weaker claims, (ii) and (iii). Claims (ii) and (iii) offer two different meanings for the idea of an 'objectivity' of mathematics. I discuss, using as much as possible Gödel’s interpretation of their writings, the position of other mathematicians (Brouwer, Dedekind), or philosophers (Husserl, Lautman), with regard to the three claims (i), (ii) and (iii).
Philosophers of time frequently talk about a tenseless 'is' - for example Tooley's "There are (tenselessly) dinosaurs." A tenseless sentence is supposed not to change its truth value with the passage of time. It's supposed to have its truth value absolutely. But of course we need a semantic analysis of that. This papers looks at what might be involved in such an analysis by looking at the parallel modal case - i.e., by looking at what would be involved in a non-contingent 'is'. I will pay particular attention to the need for tenseless or non-contingent sentences to be incorporated into constructions in tensed and contingent languages with a compositional semantics.