Categoricity and Consistency in Second-Order Logic

We analyse the concept of a second-order characterisable structure and divide this concept into two parts—consistency and categoricity—with different strength and nature. We argue that categorical characterisation of mathematical structures in second-order logic is meaningful and possible without assuming that the semantics of second-order logic is defined in set theory. This extends also to the so-called Henkin structures.     

First- and Second-Order Logic of Mass Terms

Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.     

二阶扩展逻辑的复杂性与表达能力

本文研究了在所有有穷结构上SO．HORN＊,SO—HORNτ和SO-HORNτ的表达能力。我们证明了SO-HORNτ,SO—HORN＊τ和FO（LFP）的表达能力是一致的,SO—HORN＊是SO-HORNτ的一个严格子逻辑。为了证明这一结果,我们提出了DATALOG＊程序,DATALOGτ程序以及它们的分层版本S-DATALOG＊程序利S-DATALOGτ程序。我们证明了在所有有穷结构上DATALOGτ和S-DATALOGτ是等价的,并且DATALOG。足DATALOGτ的一个严格子逻辑。最后我们还用两种方法证明了SO-HORN的一个扩展版本SO—EHORNτ逻辑可以在所有有穷结构有有结构上刻画co—NP。     

Modal Deduction in Second-Order Logic and Set Theory - II

In this paper, we generalize the set-theoretic translation method for poly-modal logic introduced in [11] to extended modal logics. Instead of devising an ad-hoc translation for each logic, we develop a general framework within which a number of extended modal logics can be dealt with. We first extend the basic set-theoretic translation method to weak monadic second-order logic through a suitable change in the underlying set theory that connects up in interesting ways with constructibility; then, we show how to tailor such a translation to work with specific cases of extended modal logics.     

A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic

This paper responds to criticism of the Kripkean account of logical truth in first-order modal logic. The criticism, largely ignored in the literature, claims that when the box and diamond are interpreted as the logical modality operators, the Kripkean account is extensionally incorrect because it fails to reflect the fact that all sentences stating truths about what is logically possible are themselves logically necessary. I defend the Kripkean account by arguing that some true sentences about logical possibility are not logically necessary.     

Completeness of Second-Order Intuitionistic Propositional Logic with Respect to Phase Semantics for Proof-Terms

Journal of Philosophical Logic - Girard introduced phase semantics as a complete set-theoretic semantics of linear logic, and Okada modified phase-semantic completeness proofs to obtain normal-form...     

A Defense of Egalitarianism

Recently in this journal, Michael Huemer has attempted to refute egalitarianism. His strategy consists in: first, distinguishing between three possible worlds (one with an equal distribution of well-being, one with an unequal distribution at every moment but with an equal distribution overall, and one with an unequal distribution at every moment as well as overall); second, showing that the first world is equal in value to the second world; third, dividing the second and third worlds into two temporal segments each, then showing that none of the temporal segments possesses greater moral value than any other, thereby demonstrating that the second and third worlds as a whole are equal in value; and finally, concluding that none of the three worlds has more value than any other. The present article rebuts Huemer’s critique of egalitarianism first, and most importantly, by showing that his core argument rests upon an equivocation, and second, by refuting his supplementary arguments.     

A Defense of Emergence

I defend a physicalistic version of ontological emergence; qualia emerge from the brain, but are physical properties nevertheless. First, I address the following questions: what are the central tenets of physicalistic ontological emergentism; what are the relationships between these tenets; what is the relationship between physicalistic ontological emergentism and non-reductive physicalism; and can there even be a physicalistic version of ontological emergentism? This discussion is merely an attempt to clarify exactly what a physicalistic version of ontological emergentism must claim, and to show that the view is at least coherent. I then defend the view from objections, for example, Kim’s (Philos Stud 95:3–36, 1999) attempt to apply a version of his exclusion argument to ontological emergentism. I conclude by offering a positive argument for the view: given certain empirical evidence concerning the organization of the brain, physicalism might have to endorse ontological emergentism to avoid epiphenomenalism.     

Second-Order Schedules

The rules which define the formal specifications of simple schedules of reinforcement have also been used to develop more complex schedules. Within these “second-order” schedules, previously neutral stimuli acquire various degrees of behavioral control. This paper describes some of the experiments used to determine the nature of this control.

     

图式逻辑:哲学逻辑的一个新分支

逻辑研究有效推理,判定其有效的依据是结论所传达的信息与前提所传达的信息之间的必然关系,而传达这些信息的媒介不一定就是语言。日常推理是运用语句、图形甚至声音、气味等多种信息进行的多模态推理,对这些多模态表示系统和推理的研究已经成为心灵哲学、认知科学、心理学、教育学、数学、逻辑学和计算机科学等领域的交叉地带。自从