We propose a model mechanism for the initiation and spatial positioning of teeth primordia in the alligator, Alligator mississippiensis. Detailed embryological studies by Westergaard and Ferguson have shown that jaw growth plays a crucial role in the developmental patterning of the tooth initiation process. Based on biological data we develop a dynamic patterning mechanism, which crucially includes domain growth. The mechanism can reproduce the spatial pattern development of the first seven teeth primordia in each half jaw of A. mississippiensis. The (...) results for the precise spatio-temporal sequence compare well with experiment. Simulation of the model also predicts that certain transplantations can alter the spatial sequence of teeth primordia initiation. (shrink)

This chapter contains sections titled: The Tractatus and rules of logical syntax From logical syntax to philosophical grammar Rules and rule‐formulations Philosophy and grammar The scope of grammar Some morals.

This book translates into English ten influential articles and extracts from books about Homer written in German over the past fifty years. The work of prestigious scholars such as Wolfgang Schadenwaldt, Karl Reinhardt, and Hermann Fraenkel are represented. These key works, which cover such topics as similes, the end of the Odyssey, the adventures of Odysseus, the meeting of Hector and Andromache, ring-composition, the Telemachy, and Homeric social life will now become easily accessible for the first time to teachers and (...) scholars in the English-speaking world. An accompanying introduction develops the arguments in the light of contemporary scholarly concerns. (shrink)

This chapter contains sections titled: Following a rule Practices and techniques Doing the right thing and doing the same thing Privacy and the community view On not digging below bedrock.

This chapter contains sections titled: Setting the stage Leitmotifs External guidelines Necessary propositions and norms of representation Concerning the truth and falsehood of necessary propositions What necessary truths are about Illusions of correspondence: ideal objects, kinds of reality and ultra‐physics The psychology and epistemology of the a priori Propositions of logic and laws of thought Alternative forms of representation The arbitrariness of grammar A kinship to the non‐arbitrary Proof in mathematics Conventionalism.

This chapter contains sections titled: Is a language necessarily shared with a community of speakers? Innate knowledge of a language Robinson Crusoe sails again Solitary cavemen and monologuists Private languages and ‘private languages’ Overview.

This chapter contains sections titled: The scaffolding of facts The role of our nature Forms of life Agreement: consensus of human beings and their actions.

This chapter contains sections titled: Initial compass bearings Accord and the harmony between language and reality Rules of inference and logical machinery Formulations and explanations of rules by examples Interpretations, fitting and grammar Further misunderstandings.

This chapter contains sections titled: The continuation of the Early Draft into philosophy of mathematics Hidden isomorphism A common methodology The flatness of philosophical grammar.