On the Proof Theory of the Modal mu-Calculus

We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as a corollary. Presented by Heinrich Wansing     

Complexity of the Universal Theory of Modal Algebras

Studia Logica - We apply the theory of partial algebras, following the approach developed by Van Alten (Theor Comput Sci 501:82–92, 2013), to the study of the computational...     

Object Theory and Modal Meinongianism

In this paper, we compare two theories, modal Meinongianism (MM) and object theory (OT), with respect to several issues that have been discussed recently in the literature. In particular, we raise some objections for MM, undermine some of the objections that its defenders raise for OT, and we point out some virtues of the latter with respect to the former.     

Spinoza's Proof of Necessitarianism

This paper consists of four sections. The first section considers what the proof of necessitarianism in Spinoza's system requires. Also in the first section, Jonathan Bennett's (1984) reading of lpl6 as involving a commitment to necessitarianism is presented and accepted. The second section evaluates Bennett's suggestion how Spinoza might have been led to conclude necessitarianism from his basic assumptions. The third section of the paper is devoted to Don Garrett's (1991) interpretation of Spinoza's proof. I argue that Bennett's and Garrett's interpretations of Spinoza's necessitarianism have shortcomings which justify an attempt to offer an alternative proof. In the proof given in the fourth section, it is argued that Spinoza derived necessitarianism from the conjunction of the following principles: (i) necessary existence of the substances; (ii) substance-property ontology; (iii) superessentialism; and (iv) the 'no shared attribute'thesis.     

Spinoza's theory of knowledge

This paper is a discussion of which kinds of knowledge Spinoza himself employs in developing the system of the Ethics. The problem is raised by Professor D. Savan and further discussed by G. H. R. Parkinson. The thesis is (1) that no occurrence of the first kind of knowledge is to be found in the Ethics (against Parkinson), (2) that the main part of the analysis in the Ethics is conducted on the level of the second kind of knowledge (in agreement with Parkinson), and (3) that the third kind of knowledge occurs frequently and plays a most important role in the Ethics (in part against Parkinson). The relation between knowledge and language, the distinction between two types of imagination, or two ways of imagining things, the translation of knowledge of modes of extension into knowledge of the mind, and the relation between the second and third kind of knowledge are main parts of the argument. The third kind of knowledge derives its significance in the Ethics from the definitions and axioms, particularly in Part 1. These definitions and axioms form the basis of the whole system of the Ethics, and at least some of them, it is suggested, belong to the third kind of knowledge.     

Consistency Theory for the General Nonparametric Classification Method

Psychometrika - Parametric likelihood estimation is the prevailing method for fitting cognitive diagnosis models—also called diagnostic classification models (DCMs). Nonparametric concepts...     

Proof Theory for Functional Modal Logic

We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \(\mathord {\sim }\mathord {\Box }A\equiv \mathord {\Box }\mathord {\sim }A\). We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.     

Ethical Theory,Completeness &; Consistency

This paper argues that many leading ethical theories are incomplete, in that they fail to account for both right and wrong. It also argues that some leading ethical theories are inconsistent, in that they allow that an act can be both right and wrong. The paper also considers responses on behalf of the target theories.     

Spinoza's Thinking Substance and the Necessity of Modes

How should ‘the physical’ be defined for the purpose of formulating physicalism? In this paper I defend a version of the via negativa according to which a property is physical just in case it is neither fundamentally mental nor possibly realized by a fundamentally mental property. The guiding idea is that physicalism requires functionalism, and thus that being a type identity theorist requires being a realizer‐functionalist. In §1 I motivate my approach partly by arguing against Jessica Wilson's no fundamental mentality constraint. In §2 I set out my preferred definition of ‘the physical’ and make my case that physicalism requires functionalism. In §3 I defend my proposal by attacking the leading alternative account of ‘the physical,’ the theory‐based conception. Finally, in §4 I draw on my definition, together with Jaegwon Kim's account of intertheoretic reduction, to defend the controversial view that physicalism requires a priori physicalism.     

Consciousness in Spinoza's Philosophy of Mind

Spinoza's philosophy of mind is thought to lack a serious account of consciousness. In this essay I argue that Spinoza's doctrine of ideas of ideas has been wrongly construed, and that once righted it provides the foundation for an account. I then draw out the finer details of Spinoza's account of consciousness, doing my best to defend its plausibility along the way. My view is in response to a proposal by Edwin Curley and the serious objection leveled against it by Margaret Wilson and Jonathan Bennett.     

Correction to: Complexity of the Universal Theory of Modal Algebras

Studia Logica - In the original publication of the article, the authors name were abbreviated as “D. Shkatov” and “C. J. Van Alten”. However it should be “Dmitry...     

The Simple Consistency of Naive Set Theory using Metavaluations

The main aim is to extend the range of logics which solve the set-theoretic paradoxes, over and above what was achieved by earlier work in the area. In doing this, the paper also provides a link between metacomplete logics and those that solve the paradoxes, by finally establishing that all M1-metacomplete logics can be used as a basis for naive set theory. In doing so, we manage to reach logics that are very close in their axiomatization to that of the logic R of relevant implication. A further aim is the use of metavaluations in a new context, expanding the range of application of this novel technique, already used in the context of negation and arithmetic, thus providing an alternative to traditional model theoretic approaches.     

On an Intuitionistic Modal Logic

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4). The novelty of this paper is that we place particular importance on the natural deduction formulation of IS4— our formulation has several important metatheoretic properties. In addition, we study models of IS4— not in the framework of Kirpke semantics, but in the more general framework of category theory. This allows not only a more abstract definition of a whole class of models but also a means of modelling proofs as well as provability.     

斯宾诺莎对圣经的历史批判与诠释

斯宾诺莎的<神学政治论>,在圣经诠释历史上堪称是里程碑式的著作.他通过质疑作为真理之标准与公众法律之来源的圣经,倡导思想、言说与著述的自由.他对圣经研究最具原创性的贡献,并不在于其探求真理所坚持的理性主义标准,而在于对圣经文本自身及其内容所进行的历史理解.本文将简介斯宾诺莎对圣经诠释的历史批判方法,并兼及述评.     

On the Consistency of Q-Matrix Estimation: A Rejoinder

This rejoinder responds to the commentary by Liu (Psychometrika, 2015) entitled “On the consistency of Q-matrix estimation: A commentary” on the paper “A general method of empirical Q-matrix validation” by de la Torre and Chiu (Psychometrika, 2015). It discusses and addresses three concerns raised in the commentary, namely the estimation accuracy when a provisional Q-matrix is used, the consistency of the Q-matrix estimator, and the computational efficiency of the proposed method.