Syntax without Abstract Objects Nominalizing the Theory of Concatenation

Nominalists deny the existence of abstract objects. In view of the notoriously shadowy and intractable character of the latter, the formers’ thesis certainly has a strong initial appeal to anyone sharing even the least bit of a naturalistic bent. But even though many philosophers nowadays do exhibit this inclination, the vices and virtues of nominalism remain a live issue in contemporary debates. The reason for this is that proponents of nominalism with regard to some sort of alleged entity are usually seen to carry the burden of proof; it is expected that they demonstrate how one can actually get by without the entities in question. A philosopher who claims that, e.g., numbers do not exist, immediately has to face the fact that talk of numbers is ubiquitous in virtually any serious scientific endeavor. Since most nominalists show the broadly naturalistic tendencies I alluded to, this philosopher will normally be very reluctant to call for a grand revision of entrenched scientific practices on the grounds of her philosophical position. Accordingly, she will have to come up with methods of systematically reconstructing or reinterpreting portions of science seemingly committed to numbers in a way that eventually renders them ontologically innocuous, whilst retaining as many of the benefits as possible. Wether or not nominalists can fulfill this task satisfactorily is the question that keeps fuelling the debate despite the prima facie plausibility of nominalism. There is no universally agreed-upon methodology that gets applied in such discussions. Sometimes nominalistic proposals are introduced in a very informal way that does not make it all too easy to assess their respective merits. I believe, however, that it is possible to give rock solid arguments in favor or against certain nominalistic Of course this is a rather dubious sweeping statement. Versions of nominalism have been proposed that have no bearing whatsoever on the abstract-concrete distinction. I will not get into any of these in this paper. Instead I shall take the rejection of abstract objects as the defining criterion for being a nominalist. For a simple example that also served as an inspiration for this paper, cf. [Quine(1980), p.117], where it is ‘shown’ how a theory of (abstract) lengths might be reduced to a theory of physical objects.