Professor P. Bernays has kindly drawn my attention to the fact that the assignment of Godel numbers to formulas described on page 295 of volume I of this Journal, is not correct. Under this assignment, different formulas may obtain the same Godel number and therefore the argument given on page 296 under (i) is not cogent. The correct assignment would give, for the formula considered as an example, the Godel number 28. 320. 514. 782 The correction to be made on (...) page 294, L 20 is obvious. (shrink)

Given an admissible indexing φ of the countable atomless Boolean algebra B, an automorphism F of B is said to be recursively presented (relative to φ) if there exists a recursive function $p \in \operatorname{Sym}(\omega)$ such that F ⚬ φ = φ ⚬ p. Our key result on recursiveness: Both the subset of $\operatorname{Aut}(\mathscr{B})$ consisting of all those automorphisms which are recursively presented relative to some indexing, and its complement, the set of all "totally nonrecursive" automorphisms, are uncountable. This arises (...) as a consequence of the following combinatorial investigations: (1) A comparison of the cycle structures of f and f̄, where f is a permutation of some free basis of B and f̄ is the automorphism of B induced by f. (2) An explicit description of the permutations of ω whose conjugacy classes in $\operatorname{Sym}(\omega)$ are (a) uncountable, (b) countably infinite, and (c) finite. (shrink)

Modern philosophical biology has been dominated by the idea of mechanism. Even the attempts to escape from mechanism, such as the theories of vitalism and holism, covertly assume the mechanistic hypothesis while surrounding it with an aura of mysticism. The mechanistic approach is the result of applying the methods of physics to the realm of biology. The immense prestige of physics has tended to disguise the fact that biology is a science in its own right, with autonomous principles. The purpose (...) of the article is to develop the philosophy of organism, first systematically elaborated by Whitehead, and to seek to demonstrate that organic being is unintelligible without the concept of purposiveness and hence of value. This necessarily leads to the return of metaphysics in the form of metabiology.RésuméLa biologie philosophique moderne est dominée par l'idée de mécanisme. Il n'est pas jusqu'aux tentatives d'échapper au mécanisme, telle par exemple la théorie du vitalisme et celle du holisme, qui n'assument implicitement l'hypothése mécaniste tout en l'entourant d'une aura de mysticisme. La conception mécaniste résulte de l'applicatio n des méthodes de la physique au domaine de la biologie. L'immense prestige de la physique a tendu à déguiser le fait pourtant reel que la biologie est une science qui jouit de sa propre souveraineté et de principes autonomes. Le but de cet article est d'exposer une philosophie de l'organisme élaborée systématiquement par Whitehead pour la premiére fois et de chercher ensuite à démontrer que tout être organique est inintelligible en dehors du concept de finalité et, par conséquent, de valeur. Ceci conduit nécessairement à un renouveau de la métaphysique sous forme de métabiologie. (shrink)