Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set (...) theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science. (shrink)

The current status of explanation worked out by Physics for the Periodic Law is considered from philosophical and methodological points of view. The principle gnosiological role of approximations and models in providing interpretation for complicated systems is emphasized. The achievements, deficiencies and perspectives of the existing quantum mechanical interpretation of the Periodic Table are discussed. The mainstream ab initio theory is based on analysis of selfconsistent one-electron effective potential. Alternative approaches employing symmetry considerations and applying group theory usually require some (...) empirical information. The approximate dynamic symmetry of one-electron potential casts light on the secondary periodicity phenomenon. The periodicity patterns found in various multiparticle systems (atoms in special situations, atomic nuclei, clusters, particles in the traps, etc) comprise a field for comparative study of the Periodic Laws found in nature. (shrink)

A numerical classification was performed on 69 elements with 54 chemicaland physicochemical properties. The elements fell into clusters in closeaccord with the electron shell s-, p- andd-blocks. The f-block elements were not included forlack of sufficiently complete data. The successive periods ofs- and p-block elements appeared in an ovalconfiguration, with d-block elements lying to one side. Morethan three axes were required to give good representation of thevariation, although the interpretation of the higher axes is difficult.Only 15 properties were scorable for (...) the noble gases, but despite thepaucity of properties reflecting chemical reactivity, analysis of the 69elements on these properties still showed the major features seen fromthe full set. (shrink)