Cocchiarella’s Formal Ontology and the Paradoxes of Hyperintensionality

This is a critical discussion of Nino B. Cocchiarella’s book “Formal Ontology and Conceptual Realism.” It focuses on paradoxes of hyperintensionality that may arise in formal systems of intensional logic.

Strong Completeness Theorems for Weak Logics of Common Belief

We show that several logics of common belief and common knowledge are not only complete, but also strongly complete, hence compact. These logics involve a weakened monotonicity axiom, and no other restriction on individual belief. The semantics is of the ordinary fixed-point type.     

Looking for Whitehead

Saul Kripke in his revolutionary and influential series of lectures from the early 1970s (later published as the book Naming and Necessity) famously resurrected John Stuart Mill's theory of proper names. Kripke at the same time rejected Mill's theory of general terms. According to Kripke, many natural kind terms do not fit Mill's account of general terms and are closer to proper names. Unfortunately, Kripke and his followers ignored key passages in Mill's A System of Logic in which Mill enunciates a sophisticated and detailed theory of natural kind terms that anticipates and is in some ways superior to Kripke's.     

A Modal Logic for Discretely Descending Chains of Sets

We present a modal logic for the class of subset spaces based on discretely descending chains of sets. Apart from the usual modalities for knowledge and effort the standard temporal connectives are included in the underlying language. Our main objective is to prove completeness of a corresponding axiomatization. Furthermore, we show that the system satisfies a certain finite model property and is decidable thus.     

Paradigm Terms: The Necessity of Kind Term Identifications Generalized

Standard Kripke-Putnam semantics is widely taken to entail that theoretical identifications like ‘Brontosauruses are Apatosauruses’ or ‘Gold is ⁷⁹Au’ are necessary, if true. I offer a new diagnosis as to why this modal consequence ensues. Central to my diagnosis is the concept of a paradigm term. I argue that modal and epistemic peculiarities that are commonly considered as distinctive of natural kind expressions are in fact traits that are shared by paradigm terms in general. Philosophical semantics should broaden its focus from natural kind expressions to paradigm terms.     

Gentzen-Type Methods for Bilattice Negation

A general Gentzen-style framework for handling both bilattice (or strong) negation and usual negation is introduced based on the characterization of negation by a modal-like operator. This framework is regarded as an extension, generalization or re- finement of not only bilattice logics and logics with strong negation, but also traditional logics including classical logic LK, classical modal logic S4 and classical linear logic CL. Cut-elimination theorems are proved for a variety of proposed sequent calculi including CLS (a conservative extension of CL) and CLS_cw (a conservative extension of some bilattice logics, LK and S4). Completeness theorems are given for these calculi with respect to phase semantics, for SLK (a conservative extension and fragment of LK and CLS_cw, respectively) with respect to a classical-like semantics, and for SS4 (a conservative extension and fragment of S4 and CLScw, respectively) with respect to a Kripke-type semantics. The proposed framework allows for an embedding of the proposed calculi into LK, S4 and CL.     

Thomas Kuhn's Misunderstood Relation to Kripke-Putnam Essentialism

Kuhn's ‘taxonomic conception’ of natural kinds enables him to defend and re-specify the notion of incommensurability against the idea that it is reference, not meaning/use, that is overwhelmingly important. Kuhn's ghost still lacks any reason to believe that referentialist essentialism undercuts his central arguments in SSR – and indeed, any reason to believe that such essentialism is even coherent, considered as a doctrine about anything remotely resembling our actual science. The actual relation of Kuhn to Kripke-Putnam essentialism, is as follows: Kuhn decisively undermines it – drawing upon the inadequacies of such essentialism when faced with the failure of attempts to instantiate in history or contemporaneously its ‘thought-experiment’ – and leaves the field open instead for his own more ‘realistic’, deflationary way of thinking about the operation of ‘natural kinds’ in science. This revised version was published online in August 2006 with corrections to the Cover Date.