This paper makes an important contribution to the ongoing debate over the validity of the psychological construct, ADHD. While not ruling out the possibility that something of value may lie at the core of this diagnosis, the authors articulate a clear set of problems with the research logic that forms the foundation of the disorder itself, reaching the conclusion that there appears to be insuffi cient, valid scientifi c evidence for the demarcation of a coherent and independent disease entity.

David Hilbert's finitistic standpoint is a conception of elementary number theory designed to answer the intuitionist doubts regarding the security and certainty of mathematics. Hilbert was unfortunately not exact in delineating what that viewpoint was, and Hilbert himself changed his usage of the term through the 1920s and 30s. The purpose of this paper is to outline what the main problems are in understanding Hilbert and Bernays on this issue, based on some publications by them which have so far received (...) little attention, and on a number of philosophical reconstructions of the viewpoint (in particular, by Hand, Kitcher, and Tait). (shrink)

In the 1920s, David Hilbert proposed a research program with the aim of providing mathematics with a secure foundation. This was to be accomplished by first formalizing logic and mathematics in their entirety, and then showing---using only so-called finitistic principles---that these formalizations are free of contradictions. ;In the area of logic, the Hilbert school accomplished major advances both in introducing new systems of logic, and in developing central metalogical notions, such as completeness and decidability. The analysis of unpublished material presented (...) in Chapter 2 shows that a completeness proof for propositional logic was found by Hilbert and his assistant Paul Bernays already in 1917--18, and that Bernays's contribution was much greater than is commonly acknowledged. Aside from logic, the main technical contribution of Hilbert's Program are the development of formal mathematical theories and proof-theoretical investigations thereof, in particular, consistency proofs. In this respect Wilhelm Ackermann's 1924 dissertation is a milestone both in the development of the Program and in proof theory in general. Ackermann gives a consistency proof for a second-order version of primitive recursive arithmetic which, surprisingly, explicitly uses a finitistic version of transfinite induction up to www . He also gave a faulty consistency proof for a system of second-order arithmetic based on Hilbert's &egr;-substitution method. Detailed analyses of both proofs in Chapter 3 shed light on the development of finitism and proof theory in the 1920s as practiced in Hilbert's school. ;In a series of papers, Charles Parsons has attempted to map out a notion of mathematical intuition which he also brings to bear on Hilbert's finitism. According to him, mathematical intuition fails to be able to underwrite the kind of intuitive knowledge Hilbert thought was attainable by the finitist. It is argued in Chapter 4 that the extent of finitistic knowledge which intuition can provide is broader than Parsons supposes. According to another influential analysis of finitism due to W. W. Tait, finitist reasoning coincides with primitive recursive reasoning. The acceptance of non-primitive recursive methods in Ackermann's dissertation presented in Chapter 3, together with additional textual evidence presented in Chapter 4, shows that this identification is untenable as far as Hilbert's conception of finitism is concerned. Tait's conception, however, differs from Hilbert's in important respects, yet it is also open to criticisms leading to the conclusion that finitism encompasses more than just primitive recursive reasoning. (shrink)

In 1866 J.C. Maxwell thought he had discovered a Maxwellian demon—though not under that description, of course [1]. He thought that the temperature of a gas under gravity would vary inversely with the height of the column. From this he saw that it would then be possible to obtain energy for work from a cooling gas, a clear violation of Thompson’s statement of the second law of thermodynamics. This upsetting conclusion made him worry that “there remains as far as I (...) can see a collision between Dynamics and thermodynamics.” Later, he derived the Maxwell-Boltzmann distribution law that made the temperature the same throughout the column. However, he continued to think about the relationship between dynamics and thermodynamics, and in 1867, he sent Tait a note with a puzzle for him to ponder. The puzzle was his famous “neat-fingered being” who could make a hot system hotter and a cold system colder without any work being done. Thompson in 1874 christened this being a “demon”; Maxwell unsuccessfully tried to rename it “valve.” However named, the demon’s point was to “show that the second law of thermodynamics has only a statistical validity.” Since that time a large physics literature has arisen that asks a question similar to that asked in theology, namely, does the devil exist? Beginning with Popper, philosophers examining the literature on Maxwell’s demon are typically surprised—even horrified [2,3,4,5,6,7]. As a philosopher speaking at a physics conference exactly 100 yrs after Popper’s birth, I want to explain why this is so. The organizers of this conference instructed me to offend everyone, believers and non-believers in demons. Thus my talk, apart from an agnostic middle section, contains a section offending those who believe they have exorcized the demon and a section offending those who summon demons. Throughout the central idea will be to clearly distinguish the various second laws and the various demons.. (shrink)