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)

In Pure Inductive Logic, the rational principle of Predicate Exchangeability states that permuting the predicates in a given language L and replacing each occurrence of a predicate in an L-sentence phi according to this permutation should not change our belief in the truth of phi. In this paper we study when a prior probability function w on a purely unary language L satisfying Predicate Exchangeability also satisfies the principle of Unary Language Invariance.

In Portraits of American Philosophy, eight of America's most prominent philosophers offer autobiographical narratives that remind us that the life of a scholar is both a tale of personal struggle and an adventure in ideas.

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)

Shortly before his death in 1934, the British historian of chemistry, A. N. Meldrum, published two lengthy articles on Lavoisier's early career in science. After a careful investigation of the collection of manuscripts at the Académie des Sciences in Paris and in light of a detailed and penetrating analysis of Lavoisier's published work, Meldrum concluded that as a youth, Lavoisier was concerned with chemistry only to the extent that he found it useful for his mineralogical and geological researches. Lavoisier began (...) his career as a mineralogist; he became a chemist only in 1772, the “crucial year” when he turned his attention to chemical theory for its own sake and started his famous course of experiments on the nature of combustion and fixed air. Although some details—notably concerning Lavoisier's early education and geological work—have been added to this account since Meldrum's time, the broad conclusions of Meldrum's study are still generally accepted by historians of the chemical revolution. (shrink)

Postnatally, heart muscle cells almost completely lose their ability to divide, which makes their loss after trauma irreversible. Potential repair by cell grafting or mobilizing endogenous cells is of particular interest for possible treatments for heart disease, where the poor capacity for cardiomyocyte proliferation probably contributes to the irreversibility of heart failure. Knowledge of the molecular mechanisms that underly formation of heart muscle cells might provide opportunities to repair the diseased heart by induction of (trans) differentiation of endogenous or exogenous (...) cells into heart muscle cells. We briefly review the molecular mechanisms involved in early development of the linear heart tube by differentiation of mesodermal cells into heart muscle cells. Because the initial heart tube does not comprise all the cardiac compartments present in the adult heart, heart muscle cells are added to the distal borders of the tube and within the tube. At both distal borders, mesodermal cell are recruited into the cardiac lineage and, within the heart tube, muscular septa are formed. In this review, the relative late additions of heart muscle cells to the linear heart tube are described and the potential underlying molecular mechanisms are discussed. BioEssays 26:248–261, 2004. Wiley Periodicals, Inc. (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.

L’article examine la reprise que le « prince des Averroïstes » Jean de Jandun fait de cette phrase délicate d’Averroès, tirée de son Grand Commentaire du De anima d’Aristote : « forte igitur philosophia invenitur in maiori parte subiecti in omni tempore ». On cherche à montrer par l’analyse des textes que l’interprétation du maître ès arts s’écarte radicalement de la pensée du Cordouan qu’il prétend suivre. Tandis qu’Averroès suppose l’existence continue d’au moins un philosophe dans le monde, Jean de (...) Jandun, rejetant comme irréaliste l’idée d’un homme parfait en qui s’incarnerait tout le savoir, et tributaire d’une erreur de traduction arabo-latine qui donne « sujet » pour « lieu », soutient qu’il n’y a chaque fois de perfection que si l’on totalise tous les savoirs particuliers des différents penseurs en activité sur la terre. Autrement dit, la philosophie est parfaite, certes, mais il n’y a pas de philosophe parfait. C’est coniunctim que la science est achevée, et non pas divisim. Un tel constat, qui rapproche l’analyse de Jean de celle menée par Dante au début de sa Monarchia, permet deux révisions : d’une part, l’idée d’un « averroïsme » latin réactionnaire, se contentant de répéter les paroles du maître, est à revoir ; d’autre part, cela signifie qu’il n’y a pas chez Jean les bases théoriques de l’idéal éthico-intellectualiste dont l’historiographie moderne assure qu’il en fut le champion parisien. (shrink)

Everywhere the 1990s have been characterized by an odd mixture of ideological triumphalism-Fukuyama's "end of history" being only the crassest example-and of ideological uncertainty-can there be, should there be, a "third way"? For all its pretensions to universality, the "New World Order" has never lost a fragility in appearance. Students of historiography can scarcely be surprised to learn that an uneasiness over the present and future has in turn frequently entailed uncertainty about the past and particularly about those parts of (...) the past which had seemed most able to give clear and significant "lessons."One evident example is the history of what in my Explaining Auschwitz and Hiroshima I called the "long" Second World War, that is, that crisis in confidence in the relationship between political and economic liberalism and the nation-state which, by the end of 1938, had left only Britain, France, the Low Countries, and Scandinavia as in any sense preserving those "liberal" freedoms which had spread across Europe since 1789. In this article, I briefly review the most recent difficulties World War II combatant societies have had in locating a usable past in the history of those times. However, my major focus is on the specific case of Italy, very much a border state in the Cold War system, and today the political home of an "Olive Tree" and a "Liberty Pole" whose historical antecedents and whose philosophical base for the future are less than limpid. 1990s Italian historians thus give very mixed messages about the Fascist past; these are the messages I describe and decode. (shrink)