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

The focus in this essay will be upon the paradoxes, and foremostly in set theory. A central result is that the librationist set theory £ extension \Pfund $\mathscr{HR}(\mathbf{D})$ of \pounds \ accounts for \textbf{Neumann-Bernays-Gödel} set theory with the \textbf{Axiom of Choice} and \textbf{Tarski's Axiom}. Moreover, \Pfund \ succeeds with defining an impredicative manifestation set $\mathbf{W}$, \emph{die Welt}, so that \Pfund$\mathscr{H}(\mathbf{W})$ %is a model accounts for Quine's \textbf{New Foundations}. Nevertheless, the points of view developed support the view that the truth-paradoxes and (...) the set-paradoxes have common origins, so that the librationist resolutions of the set theoretic paradoxes are at the same time resolutions of the truth theoretic paradoxes. Both the librationist resolutions of the set theoretic paradoxes and the truth theoretic paradoxes have non-trivial philosophical implications: librationist set theories have the consequence that there are no absolutely uncountable sets, and librationist truth theories allow the use of syntactical modalities in ways which circumvent limitations as those of \parencite{Montague1963}, and a truth predicate which is useful for more precise philosophical discourse. (shrink)

We show that we in ways related to the classical Square of Opposition may define a Cube of Opposition for some useful statements, and we as a by-product isolate a distinct directive of being inviolable which deserves attention; a second central purpose is to show that we may extend our construction to isolate hypercubes of opposition of any finite cardinality when given enough independent modalities. The cube of opposition for obligations was first introduced publically in a lecture for the Square (...) of Opposition Conference in the Vatican in May 2014. -/- A COLORFUL ERRATUM: The article Cubes and Hypercubes of Opposition, with Ethical Ruminations on Inviolability, suffered a couple of mishaps when it was published in Logica Universalis, ISSN 1661-8297, 10(2-3), p. 373–376. The worst of them was that the colorful cube was printed in shades of grey, instead of decorating the sides with two transparent sides, and then a red, a yellow, a blue and a green side. The text of the article is not quite understandable because of this mishap, so I avail a colorfully updated version of the original article here. -/- . (shrink)

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. (shrink)

The paper provides some observations that support the view, such as with Nathan Salmon, that we have full substitutivity of coextensional names in belief contexts. Further, the paper notes some consequences for doxastic modalites in an induced Millian logic of belief.

In this dissertation I present a new solution to the renowned Gettier problem. My solution, which in a sense represents a defense of a rather traditional epistemological approach, is based upon a distinction between primary and secondary beliefs. I argue that primary beliefs are known if justified and true, whereas secondary beliefs are known if they are believed on the basis of a known primary belief. Much emphasis is put upon defending this approach against potential objections, but I also draw (...) some epistemological and semantical consequences pertaining to such issues as the nature of epistemological justification, the Lottery Paradox, philosophical skepticism and the semantics of belief contexts. (shrink)

Cartesian skepticism has its roots in classical skepticism and is geared to undermine our confidence even in immediate perceptual statements as `I see things in front of me'. We investigate with some assumptions which have as consequence that Cartesian skepticism is avoided in some contexts. I assume that Gettier style difficulties are not engendered by immediate perceptual statements, and I invoke things in general to not make assumptions in the metaphysics of objects. As Gettier issues are side stepped for such (...) statements as mentioned we have that I know that I see things in front of me if, and only if it is true that I see things in front of me, I am justified in believing that I see things in front of me and I believe that I see things in front of me. We assume epistemological deontologism, so that I am justified in believing something iff I am permitted to believe it. We assume Kant’s Law so that ‘ought’ implies ‘can’. As a matter of fact it is impossible for me to not believe that I see things in front of me; it follows by Kant’s Law that it is not the case that it ought to be the case that I do not believe that I see things in front of me; so I am permitted to believe that I see things in front of me, thence by epistemic deontologism I am justified in believing that I see things in front of me. Even the skeptic may not reasonably deny that it is true that I see things in front of me, and the skeptic does also not deny that I believe that I see things in front of me. Given our assumption that Gettier style difficulties do not apply for immediate perceptual statements it follows that I know that I see things in front of me. Needless to say, but one may challenge some of the assumptions we made to reach an anti skeptical conclusion. One may also explore the viability of extending the approach we have put forth here, and it can be of interest to explore further consequences for epistemology in general. The deontological conception of epistemic justification, e.g. in the version according to which a person is justified in holding p just in the case she is in some sense, normatively permitted to believe that p, has come under attack. According to William Alston, the major defect of epistemic deontologism is that it presupposes doxastic voluntarism, i.e. the view that we have direct voluntary control over whether to believe something or not. But Alston thinks that we have no such direct voluntary control, or rather that we only quite rarely have such control. And given this alleged failure of the prevalence of voluntary control, Alston maintains that "it is futile to discuss whether I am permitted to believe that p at t or whether I would be irresponsible in choosing to believe that p at t.". (shrink)

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.

1st to date [partial yet irrefutable] proof of this creed well-foundedness.

The article includes my contribution to the "Future of Text Initiative" and summarizes a more elabotate article on 'E-text' in The Oxford Researech Encyclopedia Literature from 2018.