Carruthers (2000; 2005) provides a general defence of reductive representationalism about phenomenal consciousness while critiquing first-order theories of the sort proposed by Baars (1988), Tye (1995), Dennett (2001), and others (thereby motivating a form of higher-order account). The present paper defends first-order theories against that attack.

We expand the notion of resplendency to theories of the kind T + p↑, where T is a first-order theory and p↑ expresses that the type p is omitted. We investigate two different formulations and prove necessary and sufficient conditions for countable recursively saturated models of PA. Some of the results in this paper can be found in one of the author’s doctoral thesis [3].

This paper presents a theory of informative communications among agents that allows a speaker to communicate to a hearer truths about the state of the world; the occurrence of events, including other communicative acts; and the knowledge states of any agent — speaker, hearer, or third parties — any of these in the past, present, or future — and any logical combination of these, including formul...

In a recent meta-analysis, Khemlani & Johnson-Laird (2012) showed that the conclusions drawn by human reasoners in psychological experiments about syllogistic reasoning are not the conclusions predicted by classical first-order logic. Moreover, current cognitive theories deviate significantly from the empirical data. In this paper we show how human syllogistic reasoning can be modelled under th...

We prove a set-theoretic version of Hájek, Paris and Shepherdson’s theorem [HPS00] as follows: The set ω of natural numbers must contain a non-standard natural number in any natural Tarskian semantics of Cà L0(ω), the set theory with comprehension principle within à Lukasiewicz’s infinitevalued predicate logic. The key idea of the proof is a generalization of the derivation of Moh Shaw-Kwei’s p...

We give a presentation of the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan [12]. We limit our attention to a simple major subclass of V -minimal theories of the form ACVF S , that is, the theory of algebraically cl...

It is shown by a purely syntactic argument how the completeness of resolution in type theory implies the consistency of type theory with axioms of extensionality, descriptions, and infinity. In this system the natural numbers are defined, and Peanos Postulates proved; indeed, classical analysis and much more can be formalized here. Nevertheless, Godels results show that the completeness of reso...