Using Carnap’s concept explication, we propose a theory of concept formation in mathematics. This theory is then applied to the problem of how to understand the relation between the concepts formal proof and informal, mathematical proof.

Accounts of the evolutionary past have as much in common with works of narrative history as they do with works of science. Awareness of the narrative character of evolutionary writing leads to the discovery of a host of fascinating and hitherto unrecognized problems in the representation of evolutionary history, problems associated with the writing of narrative. These problems include selective attention, narrative perspective, foregrounding and backgrounding, differential resolution, and the establishment of a canon of important events. The narrative aspects of (...) evolutionary writing, however, which promote linearity and cohesiveness in conventional stories, conflict with the underlying chronicle of evolution, which is not linear, but branched, and which does not cohere, but diverges. The impulse to narrate is so great, however, and is so strongly reinforced by traditional schemes of taxonomic attention, that natural historians have more often abandoned the diverging tree than they have abandoned the narrative mode of representation. If we are to understand the true nature of the evolutionary past then we must adopt tree thinking, and develop new and creative ways, both narrative and non-narrative, of telling the history of life. (shrink)

The "Darwinian revolution" remains an acceptable phrase to describe the change in thought brought about by the theory of evolution, provided that the revolution is seen as occurring over an extended period of time. The decades from the 1790s through the 1850s are at the focus of this article. Emphasis is placed on the issue of species extinction and on generational shifts in opinion.

Too often C. S. Peirce’s theory of signs is used simply as a classificatory scheme rather than primarily as a heuristic framework (that is, a framework designed and modified primarily for the purpose of goading and guiding inquiry in any field in which signifying processes or practices are present). Such deployment of his semeiotic betrays the letter no less than the spirit of Peirce’s writings on signs. In this essay, the author accordingly presents Peirce’s sign theory as a heuristic framework, (...) attending to some of the most important ways that it might serve to facilitate a semeiotic investigation of our legal practices. He pays close attention to the ways the topics of history, formalism, reductionism, and generality become, from a Peircean perspective, salient features of legal studies. (shrink)

This well-written volume is an introduction, not to world history, but to the special genre of "Big History," as the subtitle indicates. Christian and his fellow big historians, reacting against popular scepticism toward "master narratives," seek to create a new class of grand works that incorporate not only the history of human society, but also of the Earth, its life, and the universe as a whole. Specialists in any of the fields covered by the volume may find rough spots in (...) the treatment of topics they know well, but given the scope of the effort I think it is fair to regard this as something like the first edition of a continuing work. Later editions would be strengthened—as would the Big History movement as a whole—by explicitly incorporating some discussion of teleological reasoning in science, and by deploying clear distinctions between processes that are teleomatic (such as star formation), teleonomic (such as organismal development), and classically teleological (such as intentional behaviour on the part of humans). In "Maps of Time," David Christian has given us a book full of interesting facts, and with ideas to argue for and against in every chapter. It should provoke lively discussion across a whole range of academic disciplines. (shrink)