Stephen Yablo

Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains

….it [is] wholly irrational to regard as doubtful matters that are perceived clearly and distinctly by the understanding in its purity, on account of mere prejudices of the senses and hypotheses in which there is an element of the unknown.Descartes, Geometrical Exposition of the MeditationsSubstance dualism, once a main preoccupation of Western metaphysics, has fallen strangely out of view; today’s mental/physical dualisms are dualisms of fact, property, or event. So if someone claims to find a difference between minds and bodies per se, it is not initially clear what he is maintaining. Maybe this is because one no longer recognizes ‘minds’ as entities in their own right, or ‘substances.’ However, selves - the things we refer to by use of ‘I’ - are surely substances, and it does little violence to the intention behind mind/body dualism to interpret it as a dualism of bodies and selves. If the substance dualist’s meaning remains obscure, that is because it can mean several different things to say that selves are not bodies.

Mental causes are threatened from two directions: from below, since they would appear to be screened off by lower-order, e.g., neural states; and from within, since they would also appear to be screened off by intrinsic, e.g., syntactical states. A principle needed to parry the first threat -causes should be proportional to their effects- appears to leave us open to the second; for why should unneeded extrinsic detail be any less offensive to proportionality than excess microstructure? I say that the second threat relies on a perversion of proportionality that would lay waste to all causal relations

[Stephen Yablo] The usual charge against Carnap's internal/external distinction is one of 'guilt by association with analytic/synthetic'. But it can be freed of this association, to become the distinction between statements made within make-believe games and those made outside them-or, rather, a special case of it with some claim to be called the metaphorical/literal distinction. Not even Quine considers figurative speech committal, so this turns the tables somewhat. To determine our ontological commitments, we have to ferret out all traces of nonliterality in our assertions; if there is no sensible project of doing that, there is no sensible project of Quinean ontology. /// [Andre Gallois] I discuss Steve Yablo's defence of Carnap's distinction between internal and external questions. In the first section I set out what I take that distinction, as Carnap draws it, to be, and spell out a central motivation Carnap has for invoking it. In the second section I endorse, and augment, Yablo's response to Quine's arguments against Carnap. In the third section I say why Carnap's application of the distinction between internal and external questions runs into trouble. In the fourth section I spell out what I take to be Yablo's version of Carnap. In the last I say why that version is especially vulnerable to the objection raised in the second

Here is Frege in Foundations of Arithmetic, § 64:The judgment 'Line a is parallel to line b', in symbols: ab, can be taken as an identity. If we do this, we obtain the concept of direction, and say: 'The direction of line a is equal to the direction of line b.' Thus we replace the symbol by the more generic symbol =, through removing what is specific in the content of the former and dividing it between a and b. We carve up the content in a way different from the original way, and this yields us a new concept.Something important is going on in this passage. But at the same time it borders on incoherent. For Frege is saying at least the following:'dir(a ) = dir(b )' has the same content as 'ab'reflecting on that ..