The duality between congruence lattices of semilattices, and algebraic subsets of an algebraic lattice, is extended to include semilattices with operators. For a set G of operators on a semilattice S, we have \ \cong^{d} {{\rm S}_{p}}}\), where L is the ideal lattice of S, and H is a corresponding set of adjoint maps on L. This duality is used to find some representations of lattices as congruence lattices of semilattices with operators. It is also shown that these congruence lattices (...) satisfy the Jónsson–Kiefer property. (shrink)

We propose two principles of inductive reasoning related to how observed information is handled by conditioning, and justify why they may be said to represent aspects of rational reasoning. A partial classification is given of the probability functions which satisfy these principles.

We argue that the simplicity condition on a probability function on sentences of a predicate language L that it takes only finitely many values on the sentences of any finite sublanguage of L can be viewed as rational. We then go on to investigate consequences of this condition, linking it to the model theoretic notion of quantifier elimination.

In this paper, we study the lower semilattice of NP-subspaces of both the standard polynomial time representation and the tally polynomial time representation of a countably infinite dimensional vector space V∞ over a finite field F. We show that for both the standard and tally representation of V∞, there exists polynomial time subspaces U and W such that U + V is not recursive. We also study the NP analogues of simple and maximal subspaces. We show that the existence of (...) P-simple and NP-maximal subspaces is oracle dependent in both the tally and standard representations of V∞. This contrasts with the case of sets, where the existence of NP-simple sets is oracle dependent but NP-maximal sets do not exist. We also extend many results of Nerode and Remmel concerning the relationship of P bases and NP-subspaces in the tally representation of V∞ to the standard representation of V∞. (shrink)

Here we discuss the challenge posed by self-organization to the Darwinian conception of evolution. As we point out, natural selection can only be the major creative agency in evolution if all or most of the adaptive complexity manifest in living organisms is built up over many generations by the cumulative selection of naturally occurring small, random mutations or variants, i.e., additive, incremental steps over an extended period of time. Biological self-organization—witnessed classically in the folding of a protein, or in the (...) formation of the cell membrane—is a fundamentally different means of generating complexity. We agree that self-organizing systems may be fine-tuned by selection and that self-organization may be therefore considered a complementary mechanism to natural selection as a causal agency in the evolution of life. But we argue that if self-organization proves to be a common mechanism for the generation of adaptive order from the molecular to the organismic level, then this will greatly undermine the Darwinian claim that natural selection is the major creative agency in evolution. We also point out that although complex self-organizing systems are easy to create in the electronic realm of cellular automata, to date translating in silico simulations into real material structures that self-organize into complex forms from local interactions between their constituents has not proved easy. This suggests that self-organizing systems analogous to those utilized by biological systems are at least rare and may indeed represent, as pre-Darwinists believed, a unique ascending hierarchy of natural forms. Such a unique adaptive hierarchy would pose another major challenge to the current Darwinian view of evolution, as it would mean the basic forms of life are necessary features of the order of nature and that the major pathways of evolution are determined by physical law, or more specifically by the self-organizing properties of biomatter, rather than natural selection. (shrink)

While cetaceans clearly show social learning in a wide variety of contexts, to label this as hides more than it reveals: we need a taxonomy of culture to tease apart the differences rather than hiding them in a catch-all category.

The sixteen essays contained in this book were all written independently of each other and date back over a considerable period of time to 1956. Most of the essays have been previously published and are reprinted here with little or no change or additions. Only two were specially written for this volume. All but two deal with the theoretical as distinct from the practical dimensions of science. The two exceptions are a set of reflections on the morality of the atomic (...) bombing of Japan in World War II and an essay which sketches a framework for the consideration of issues in nursing as a practical discipline. (shrink)

In the paper I offer a brief sketch of one of the sources of utilitarianism. Our biological ancestry is a matter of fact that is not altered by the way we describe ourselves. With philosophical theories it is otherwise. Utilitarianism can be described in ways that make it look as if it is as old as moral philosophy – as J. S. Mill thought it was. For my historical purposes, it is more useful to have an account that brings out (...) what is specific about Benthamism and its descendants. Let us try to make do with the following. First, utilitarianism asserts that the fundamental requirement of morality is that we are to maximize good, for everyone and not just for the agent. This basic principle presupposes that it makes sense to think of aggregating goods to make a total, and of comparing amounts of good thus aggregated. Second, the good to be brought about is located in feelings of pleasure, and the evil to be avoided in feelings of pain. These feelings have inherent value or disvalue regardless of how they are caused to exist and regardless of their own consequences. Third, all moral principles can be derived from the requirement that good be maximized. The principles involved in evaluating agents as well as in giving moral direction to action are nothing but applications of the basic principle. (shrink)

J. B. Schneewind's "The Invention of Autonomy" has been hailed as a major interpretation of modern moral thought. Schneewind's narrative, however, elides several serious interpretive issues, particularly in the transition from late medieval to early modern thought. This results in potentially distorted accounts of Thomas Aquinas, Hugo Grotius, and G. W. Leibniz. Since these thinkers play a crucial role in Schneewind's argument, uncertainty over their work calls into question at least some of Schneewind's larger agenda for the history of ethics.

One usually identifies a particular collection of geometric objects with the models of general relativity. But within this standard collection lurk ‘physically unreasonable’ models of spacetime. If such models are ruled out, attention can be restricted to some sub-collection of ‘physically reasonable’ models which can be considered a variant theory of general relativity. Since we have yet to identify a privileged sub-collection of ‘physically reasonable’ models, it is helpful to think of ‘general relativity’ in a pluralistic way; we can study (...) a collection of such ‘physically reasonable’ collections of models. (shrink)