Dummett's intuitionism is not strict finitism

Michael Dummett's anti-realism is founded on the semantics of natural language which, he argues, can only be satisfactorily given in mathematics by intuitionism. It has been objected that an analog of Dummett's argument will collapse intuitionism into strict finitism. My purpose in this paper is to refute this objection, which I argue Dummett does not successfully do. I link the coherence of strict finitism to a view of confirmation — that our actual practical abilities cannot confirm we know what would happen if we could compute impracticably vast problems. But to state his case, the strict finitists have to suppose that we grasp the truth conditions of sentences we can't actually decide. This comprehension must be practically demonstrable, or the analogy with Dummett's argument fails. So, our actual abilities must be capable of confirming that we know what would be the case if actually undecidable sentences were true, contradicting the view of confirmation. I end by considering objections.I especially want to thank Alex George and Philip Kitcher for their help on this paper. I'd also like to thank the members of the Propositional Attitudes Task Force, Jane Braaten, Jay Garfield, Lee Bowie, Murray Kitely and Tom Tymoczko. My thanks also to Peter Godfrey-Smith and the anonymous reviewers of Synthese, one of whom was particularly helpful.     

A comparison of single-subject and traditional statistical designs in steady-state evoked potential research

An experiment was conducted to assess the relationship between level of auditory noise and a measure derived from the steady-state evoked potential (SSEP) called relative transmission time (RTF). The visual stimulus consisted of a 150-fL light that was modulated at 45, 48, or 51 Hz to a depth of 30%. The auditory stimulus was bandpass-limited white noise at 65, 75, or 85 dB, The outcomes of single-subject and group statistical analyses were compared. Neither statistic indicated a significant effect for cross-modal white noise on the SSEP. Whereas the more traditional group approach indicated only large between-subject variability, the single-subject approach clearly indicated deviant data of one of the subjects.     

Systems analysis of the integrative activity of the neuron

This article is aimed at revising the traditional concept of neuronal activity based on preeminence of transmembrane potentials and “electric summation” on the neuron surface. It presents a historical survey of the emergence of the prevailing concept on propagation of potentials alongconductive structures and reveals the psychological situation that determined the transfer of this concept to dendrites and the neuronal soma. Structural and biophysical properties of the neuron which do not permit information propagation along the neuronal membrane without crude distortion are critically discussed in detail.     

Organizational vs retrieval factors in the development of digit span

Three possible sources of memory span growth were tested with a modified version of the digit span task using subjects 6, 8, 11, and 19 years of age. There was no developmental trend in facilitation due to experimenter-imposed organization of the input strings, ruling out simple input-organizational theories. The notion that children are deficient at organizing retrieved information was also found to be untenable. The data support the view that older subjects use more selective retrieval strategies, strategies which are better suited to the encoded material. The largest improvement in retrieval selectivity occurred between sixth grade and college. Recency effects were smaller for the younger subjects than for older subjects, with first graders showing significantly less recency than third graders, sixth graders, and college students. Improved item identification during input may account for this finding.     

A general least squares solution for successive intervals

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.This research was jointly supported in part by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service.