Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the appropriate foundation for modern mathematics, proof theorists have known for decades that virtually all mainstream mathematics can actually be formalized in much weaker systems which are essentially number-theoretic in nature. Feferman has observed that this severely undercuts a famous argument of Quine and Putnam accordin...

The target of this paper is twofold. The first part develops firstly a very general and abstract topic, by describing what philosophy of logic is, when it is embedded in a genuine philosophical system, and it secondly provides an explanation of the reason why intuitionism, assumed as genuine philosophical system, is in total harmony with the contemporary intuitionistic formal logic. This part e...

Some aestheticians, e.g., Peter Kivy,' are Platonists about pieces of music. They hold that a piece of music is the sound structure indicated by the notation, and that performances are (or, present) tokens of the sound structure, i.e., tokens of a type. Other philosophers, e.g., Jerrold Levinson, deny this; in Kivy's terminology they are anti-Platonists. Levinson holds that the essential charac...

Abstract This chapter examines the Platonizing myths of Dio Chrysostom, Plutarch, and (to a lesser degree) Aelius Aristides, in light our evidence for both philosophical literary-rhetorical reception Plato’s own myths. It argues that, while reflections development Platonism as systematic philosophy can be detected them, it hard may some respects pointless to disentangle this input neatly from r...

It is shown that the problem of source and essence morality most satisfactorily solved on basis metaphysics Platonism. Its concrete implementation in form a fundamental physical theory relational paradigm theoretical physics. A number consequences have been developed from interpretation as transcendent connection person with First Cause being for religious philosophy social ideology.