Logic and Existence: Timothy Williams

The paper defends the intelligibility of unrestricted quantification. For any natural number n , 'There are at least n individuals' is logically true, when the quantifier is unrestricted. In response to the objection that such sentences should not count as logically true because existence is contingent, it is argued by consideration of cross-world counting principles that in the relevant sense of 'exist' existence is not contingent. A tentative extension of the upward Löwenheim–Skolem theorem to proper classes is used to argue that a sound and complete axiomatization of the logic of unrestricted universal quantification results from adding all sentences of the form 'There are at least n individuals' as axioms to a standard axiomatization of the first-order predicate calculus.
Of the many questions on which logic is neutral, one is usually supposed to be this: 'How many individuals are there?' On the alternative view defended below, truths about the number of individuals are logically true. They are not contingent logical truths, for it is not contingent what individuals there are.     

Logic And Existence: Ian Rumfitt

Frege's logicism in the philosophy of arithmetic consisted, au fond , in the claim that in justifying basic arithmetical axioms a thinker need appeal only to methods and principles which he already needs to appeal in order to justify paradigmatically logical truths and paradigmatically logical forms of inference. Using ideas of Gentzen to spell out what these methods and principles might include, I sketch a strategy for vindicating this logicist claim for the special case of the arithmetic of the finite cardinals.     

Leibnizian Identity and Paraconsistent Logic

The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity does amount to. Then, I argue that Priest's semantic definition of identity is not Leibnizian. Finally, I offer a semantics characterization of identity in paraconsistent logic that is truly Leibnizian. I demonstrate that the correct formalization of Leibnizian identity in paraconsistent logic also validates substitutivity of identicals and transitivity of identity.     

Model Existence in Non-Compact Modal Logic

Predicate modal logics based on Kwith non-compact extra axioms are discussed and a sufficient condition for the model existence theorem is presented. We deal with various axioms in a general way by an algebraic method, instead of discussing concrete non-compact axioms one by one.     

非严格弗雷格自由逻辑

莱曼(S.Lehmann)的1994年的论文从三值逻辑角度处理语言中的空词项。弗雷格认为句子的所指是真值,包含空词项的句子缺乏所指,而只有涵义,那么这样的句子不真也不假。莱曼的文章刻画了弗雷格这一思想,但有两点不尽人意之处:其一、对量词进行特殊处理,使得量词公式是二值的;其二,把包含空词项的复合句一概归于第三值。针对上述两点,本文以一度衍推系统为基础,在语义上,以偏解释函数为基础构造了一个非严格弗雷格中性自由逻辑表列系统,使得量词公式是三值的,同时使得一部分包含空词项的复合公式或真或假。     

Actual Existence, Identity and Ontological Priority

The paper first distinguishes ontological priority from epistemological priority and unilateral ontic dependence. Then explications of ontological priority are offered in terms of the reducibility of the actual existence or identity of entities in one ontological category to the actual existence or identity of entities in another. These explications lead to incompatible orders of ontological priority for individuals, properties of individuals and states of affairs. Common to those orders is, however, that the primacy of the category of individuals is abandoned. This primacy is challenged in the paper also by epistemological arguments, and an onto-anthropological explanation is offered for the very common but false idea that individuals are ontological prior to all other kinds of entities. Finally ontological priority is discussed with respect to a fully specified system of ontological categories. This revised version was published online in August 2006 with corrections to the Cover Date.     

Quasi-Truth,Supervaluations and Free Logic

The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free logic and supervaluations), and apply the resulting approach to accommodate semantic paradoxes.     

Proto-Semantics for Positive Free Logic

This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of non-existing objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized truth non unlike the notion of truth at world found in modal logic. A model theory is developed, establishing compactness, interpolation (implying a strong form of Beth definability), and completeness (with respect to a particular axiomatization).     

Identity in Mares-Goldblatt Models for Quantified Relevant Logic

Journal of Philosophical Logic - Mares and Goldblatt (The Journal of Symbolic Logic, 71(01), 163–187, 2006) provided an alternative frame semantics for two quantified extensions of the...     

稳定集与自认知逻辑评述

一 问题的提出 自省能力是人类区别于其他一般动物的重要性质之一,也是哲学思考得以可能和发展的基础.     

State-of-affairs Semantics for Positive Free Logic

In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain–outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since logically equivalent statements do not always have the same extension according to it. Finally, it is argued that in such a semantics all statements of a certain language for PFL are state-of-affairs-related extensional as well as salva extensione extensional, even though their salva veritate extensionality fails.     

认知逻辑研究述评

认知逻辑的英文表述是epistemic logic,而episteme的意思就是知识的意思.因此从字面上来理解,认知逻辑就是有关知识的逻辑.然而,现在我们看到的认知逻辑已经从知识扩充到了信念,甚至涉及到更多的认识论概念,换一种宽泛的说法就是形式认知(formal epistemology).这一点充分体现在对认知逻辑的定义或描述上.