Philosophy and language learning

In this paper, I explore different ways of picturing language learning in philosophy, all of them inspired by Wittgenstein and all of them concerned about scepticism of meaning. I start by outlining the two pictures of children and language learning that emerge from Kripke’s famous reading of Wittgenstein. Next, I explore how social-pragmatic readings, represented by Meredith Williams, attempt to answer the sceptical anxieties. Finally, drawing somewhat on Stanley Cavell, I try to resolve these issues by investigating what characteristically happens to our view of language learning when we do philosophy. The focus throughout is on the relation between the individual (the learning child) and the community (usually represented by the parents), and how that relation is deformed when we operate with a certain philosophical notion of ground.     

Kripke Models,Distributive Lattices,and Medvedev Degrees

We define a variant of the standard Kripke semantics for intuitionistic logic, motivated by the connection between constructive logic and the Medvedev lattice. We show that while the new semantics is still complete, it gives a simple and direct correspondence between Kripke models and algebraic structures such as factors of the Medvedev lattice. Presented by Daniele Mundici     

FINITE MODELS CONSTRUCTED FROM CANONICAL FORMULAS

This paper obtains the weak completeness and decidability results for standard systems of modal logic using models built from formulas themselves. This line of work began with Fine (Notre Dame J. Form. Log. 16:229–237, 1975). There are two ways in which our work advances on that paper: First, the definition of our models is mainly based on the relation Kozen and Parikh used in their proof of the completeness of PDL, see (Theor. Comp. Sci. 113–118, 1981). The point is to develop a general model-construction method based on this definition. We do this and thereby obtain the completeness of most of the standard modal systems, and in addition apply the method to some other systems of interest. None of the results use filtration, but in our final section we explore the connection.     

现代世界观中的意识及其哲学难题

人是具身心智的存在者,其存在方式独特性在于:他既依赖于物理形态的身体,又有存在论上不可还原性的主观性。因此如何在现代世界观中一致且完备地解释和理解人遂成了心智哲学的大问题。如果坚持现代世界观的基本立场一致性,那么对意识的解释和理解不可避免存在着"难问题"所界定的不完备性。人们大致从三个进路来处理不完备性的局面。然而,原则上它们都无法实现一致且完备的要求,因为这里存在一个根本的局限,即不可能通过认识论的方法在两种存在论形式(无和有)之间实现等价转换。尽管在认识论上这是一个悲观的结局,但另一方面它又是积极的,因为它显示了个体经验在存在论上是独一无二的。     

The Causal Closure of Physics: An Explanation and Critique

Bistable, autonomously growing and self‐maintaining dynamical systems possess a new mathematical and applicational aspect: they can switch toward (physical) existence. Larger dynamical systems containing such flip‐flops as subsystems are frequent. The mathematical prototype is a special type of Z₂‐networks, termed a competence automaton. A chemical implementation is the ‘magic soup.’ It constitutes a general model for life‐type evolution processes including economic evolution.     

Escape from Twin Earth: Putnam's 'Logic' of Natural Kind Terms

Many still seem confident that the kind of semantic theory Putnam once proposed for natural kind terms is right. This paper seeks to show that this confidence is misplaced because the general idea underlying the theory is incoherent. Consequently, the theory must be rejected prior to any consideration of its epistemological, ontological or metaphysical acceptability. Part I sets the stage by showing that falsehoods, indeed absurdities, follow from the theory when one deliberately suspends certain devices Putnam built into it , presumably in order to block such entailments. Part II then raises the decisive issue of at what cost these devices do the job they need to do. It argues that - apart from possessing no other motivation than their capacity to block the consequences derived in Part I - they only fulfil this blocking function if they render the theory unable to deal with fiction and related 'make-believe' activities. Part III indicates the affinity Putnam's account has with the classically 'denotative' view of meaning, and thus how its weaknesses may be seen as a variant of the classical weakness of 'denotative' approaches. It concludes that the theory is a conceptual muddle.     

Axiomatizing hybrid products: How can we reason many-dimensionally in hybrid logic?

The aim of this paper is to propose a two-dimensional hybrid logic in order to formalize inferences containing both spatial and temporal propositions. The semantic idea behind the proposal is to name both horizontal and vertical lines in a 2D-plane by two kinds of nominals. This is a generalization of the idea of naming a point in one-dimensional hybrid logic. I give an axiomatization of the proposed two-dimensional hybrid logic and show that it enjoys a general completeness result (called pure completeness) with respect to product Kripke frames. Moreover, in order to capture $T\times W$-frames studied by R.H. Thomason (1984), I introduce the notion of a dependent product frame, which enables us to represent the dependence of space over time. I also give a complete axiomatization of this dependent two-dimensional hybrid logic, and, as a corollary, reveal that a hybridization of $T\times W$-logic enjoys strong completeness.     

Gentzen Calculi for the Existence Predicate

We introduce Gentzen calculi for intuitionistic logic extended with an existence predicate. Such a logic was first introduced by Dana Scott, who provided a proof system for it in Hilbert style. We prove that the Gentzen calculus has cut elimination in so far that all cuts can be restricted to very simple ones. Applications of this logic to Skolemization, truth value logics and linear frames are also discussed.