Quine’s ideological debacle

In two papers in the mid-seventies, Quine has discussed an ontological deba-cle, the reduction of ontology to an ontology of pure sets only. This debacle, which weakened Quine’s interest in ontology, is the natural outcome of on-tological relativity, or, more precisely, the proxy-function argument. It is ex-plained how Quine unavoidably came to this conclusion. Moreover, it is ar-gued that the result is even more damaging for Quine’s philosophy than has hitherto been assumed. It is shown that in addition to an ontological debacle, there is an ideological debacle, reducing the ideology (lexicon) of science to the ideology of set theory. The ideological debacle results from applying ex-tensional substitution of predicates within a scientific theory that is reinter-preted by means of proxy-functions to a theory with a set-theoretic ontology. Though Quine has recognized the possibility of an ideological debacle, his rebuttal is unconvincing. As a result, his tenet of extensionalism is under heavy pressure

A physicalist reinterpretation of ‘phenomenal’ spaces

This paper argues that phenomenal or internal metrical spaces are redundant posits. It is shown that we need not posit an internal space-time frame, as the physical space-time suffices to explain geometrical perception, memory and planning. More than the internal space-time frame, the idea of a phenomenal colour space has lent credibility to the idea of internal spaces. It is argued that there is no phenomenal colour space that underlies the various psychophysical colour spaces; it is parasitic upon physical and psychophysical colour spaces. The argumentation is further extended to other sensory spaces and generalised quality spaces. © Springer 2006

The conceptual basis of numerical abilities: One-to-one correspondence versus the successor relation

In recent years, neologicists have demonstrated that Hume's principle, based on the one-to-one correspondence relation, suffices to construct the natural numbers. This formal work is shown to be relevant for empirical research on mathematical cognition. I give a hypothetical account of how nonnumerate societies may acquire arithmetical knowledge on the basis of the one-to-one correspondence relation only, whereby the acquisition of number concepts need not rely on enumeration (the stable-order principle). The existing empirical data on the role of the one-to-one correspondence relation for numerical abilities is assessed and additional empirical tests are proposed. In the final part, it is argued that the fact that the successor relation and the one-to-one correspondence relation can play independent roles in number concept acquisition may be a complication for testing the Whorfian hypothesis