Thomas Hofweber

Cardinality arguments against regular probability measures aim to show that no matter which ordered field ℍ we select as the measures for probability, we can find some event space F of sufficiently large cardinality such that there can be no regular probability measure from F into ℍ. In particular, taking ℍ to be hyperreal numbers won't help to guarantee that probability measures can always be regular. I argue that such cardinality arguments fail, since they rely on the wrong conception of the role of numbers as measures of probability. With the proper conception of their role we can see that for any event space F, of any cardinality, there are regular hyperreal-valued probability measures.

An under-explored intermediate position between traditional materialism and traditional idealism is the view that although the spatiotemporal world is purely material, minds nonetheless have a metaphysically special place in it. One such intermediate position is that minds must exist, by metaphysical necessity, in any material world, and thus a mindless material world is impossible. This position, labeled The Subjectivity Thesis by Anton Friedrich Koch, was defended by him with an intriguing, purely metaphysical argument that is largely neglected in the contemporary debate. This paper is a critical examination of Koch’s argument, as well as of the larger position it would lead to

An under-explored intermediate position between traditional materialism and traditional idealism is the view that although the spatiotemporal world is purely material, minds nonetheless have a metaphysically special place in it. One way this can be is via a special role that subjects have in the metaphysics of material objects. Some metaphysical aspect of material objects might require the existence of subjects. This would support that minds must exist if material objects exist and thus that a mindless material world is impossible. This view, labeled the subjectivity thesis by Anton Friedrich Koch, was defended by him with an intriguing, purely metaphysical argument connected to the individuation of material objects in space and time. The present paper hopes to make progress on assessing the viability of such a position. It starts by critically examining Koch's argument for the subjectivity thesis, as well as similar arguments that give minds a central place in the metaphysics of material objects via considerations about identity and difference. It then compares these ideas to similar ones in the philosophy of time, and concludes with an outlook on whether such a position is viable and what needs to be done to fill the gaps unearthed along the way

On the one hand they seem to be quite obviously truth conditionally equivalent, but on the other hand they seem to be about different things. Whereas (1) is about Jupiter and its moons, (2) is about numbers. In particular, the word ‘four’ appears in (1) in the position of an adjective or determiner, whereas it seems to be a name for a number in (2). Furthermore, (2) appears to be an identity statement claiming that what two number terms stand for is the same thing. Several authors have proposed answers to this puzzle, including Frege, by either pinning the issue on the nature of numbers, pretense, fictionalism, or the nature of reference, but all these proposals agreed that (2) is an identity statement and that in it ‘four’ is a name for an object. In [Hofweber, 2007] I argued that (2) is not an identity statement and that ‘four’ in (2) is not a name for an object. The argument for it was this: When we look at what role (2) has in actual communication we can see that (2) has a focus effect on a discourse that arises from the syntax without special intonation