Librationist cum classical set theories

A librationist set theoretic system \Pfund, which is inter alia geared to deal with set theoretic paradoxes in new ways, is developed. It descends from work in a semantic setting, for truth, initiated by by Kripke, Herzberger and Gupta. \Pfund \ extends the author's contribution in Librationist closures of the paradoxes in Logic and Logical Philosophy 21(4), 323-361, 2012. It is shown that \Pfund \ provides an interpretation of a set theory published by D. Scott in More on the axiom of extensionality, in Bar-Hillel et alia, Essays on the foundations of mathematics, North-Holland Publishing Company, 1961, 115-131. Given this, \Pfund \ also obtains an interpretation of ZFC vi results of von Neumann on regularity in 1929, and G\"odel on the Axiom og Choice in 1938. However, \Pfund \ offers alternative ways to include choice and regularity by means of principles which are informative, and natural. \Pfund \ retains the idea, of Bj{\o}rdal 2012, that the set theoretic universe is countable. But the set within which ZF is interpreted "believes" that there are sets which are not countable. The situation can be resolved much as by Skolem, though one need not suggest that the notion of 'set' is imprecice: for the bijection from the set of finite von Neumann ordinals to the full universe is itself not a member of a classical set theory

All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument

A metaphysical system engendered by a third order quantified modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D, and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are D we in Section 2 derive the thesis (40) that all properties are D or some individual is G. In Section 3 theorems 1 to 3 suggest a sufficient kinship to Gödelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Gödel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a fixed point analysis is used as diagnosis so that atheists may settle for the minimal fixed point. Theorem 3 shows it consistent to postulate theistic fixed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g, then necessarily all objects which are G are identical with g. The impredicative origin of D suggests weakened Gaunilo-like objections that offer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we finesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts `God’ allow thorough indifference as to whether God exists or not

Recursionist Theories of Knowledge

A recursive definition of knowledge is proposed, to deal with Gettier style difficulties, and provide a framework for a variety of epistemologies

Humean cum Counterfactual Skepticism and Epistemological Deontologism

We present a strategy to avoid versions of Humean and counterfactual skepticism based upon a deontologist theory of justification, a partial guideline for how to side step Gettier problems for certain statements and the assumption that certain statements are compelling. As an upshot the threats of Humean skeptical arguments disappear for some subjects and classes of statements