###### Language in Zhuangzi: How to Say Without Saying?

## Abstract

The paper is concerned with the status of language and its usage in Zhuangzi and how this particular way of viewing and using language can affect our “perception” of Dao. Zhuangzi’s language skepticism is first introduced and possible reasons for Zhuangzi’s mistrust in language are explored. The question is then raised as to why Zhuangzi himself used language to talk about Dao if he mistrusted it. At this point Zhuangzi’s usage of language is discussed in two aspects: the negative aspect and the positive aspect, the latter being the main concern of this paper. The negative aspect is exposed as the denouncing factor of employing (fuzzy) language to undermine (propositional) language while using different techniques (paradox, uncertainty/doubt, mockery, reversal). The positive aspect is explored as twofold: first, putting language and reason to their “proper” limits entails an acquisition of a broader perspective and a more receptive, open state of mind which prepares one for the wordless “perception” of Dao. Second, fuzzy language is presented as capable of “accommodating” silence and emptiness. Doing so it unites silence and speech giving an incredible insight of what Dao is about. An approach taking from both the principles of scholarly analysis and an unrestricted personal experience of the text is employed.

###### Defining Cognitive Logics by Non-Classical Tableau Rules

## Abstract

In the paper we propose a new approach to formalization of cognitive logics. By cognitive logics we understand supraclassical, but non-trivial consequence operations, defined in a propositional language. We extend some paradigm of tableau methods, in which classical consequence Cn is defined, to stronger logics - monotonic, as well as non-monotonic ones - by specific use of non-classical tableau rules. So far, in that context tableaus have been treated as a way of formalizing other approaches to supraclassical logics, but we use them autonomically to generate various consequence operations. It requires a description of the hierarchy of non-classical tableau rules that result in different supraclassical consequence operations, so we give it.

###### The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

## The Analytic Versus Representational Theory of Measurement: A Philosophy of Science Perspective: (Invited Article)

In this paper we motivate and develop the analytic theory of measurement, in which autonomously specified algebras of quantities (together with the resources of mathematical analysis) are used as a unified mathematical framework for modeling (a) the time-dependent behavior of natural systems, (b) interactions between natural systems and measuring instruments, (c) error and uncertainty in measurement, and (d) the formal propositional language for describing and reasoning about measurement results. We also discuss how a celebrated theorem in analysis, known as *Gelfand representation*, guarantees that autonomously specified algebras of quantities can be interpreted as algebras of observables on a suitable state space. Such an interpretation is then used to support (i) a realist conception of quantities as objective characteristics of natural systems, and (ii) a realist conception of measurement results (evaluations of quantities) as determined by and descriptive of the states of a target natural system. As a way of motivating the analytic approach to measurement, we begin with a discussion of some serious philosophical and theoretical problems facing the well-known representational theory of measurement. We then explain why we consider the analytic approach, which avoids all these problems, to be far more attractive on both philosophical and theoretical grounds.

###### The Axiomatization of Propositional Linear Time Temporal Logic

. Temporal Logic and State Systems . Springer-Verlag, 2008. [10] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [11] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133-137, 1999. [12] Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1( 1 ):67-71, 1990. [13] Edmund Woronowicz. Many-argument relations. Formalized

###### The Axiomatization of Propositional Logic

Logic . Wydawnictwo UwB - Bialystok, 1992. [11] Witold Pogorzelski. Notions and theorems of elementary formal logic . Wydawnictwo UwB - Bialystok, 1994. [12] Piotr Rudnicki and Andrzej Trybulec. On same equivalents of well-foundedness. Formalized Mathematics , 6( 3 ):339–343, 1997. [13] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133–137, 1999. [14] Anita Wasilewska. An Introduction to Classical and Non-Classical Logics . SUNY Stony Brook, 2005. [15] Edmund

###### The Properties of Sets of Temporal Logic Subformulas

] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics , 1( 2 ):329-334, 1990. [20] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [21] Andrzej Trybulec. Enumerated sets. Formalized Mathematics , 1( 1 ):25-34, 1990. [22] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1( 1 ):97-105, 1990. [23] Andrzej Trybulec. Defining by structural induction in the positive propositional language

###### Propositional Linear Temporal Logic with Initial Validity Semantics

Mathematics , 19( 2 ):113–119, 2011. doi:10.2478/v10037-011-0018-1. [11] Adam Grabowski. Hilbert positive propositional calculus. Formalized Mathematics , 8( 1 ): 69–72, 1999. [12] Fred Kröger and Stephan Merz. Temporal Logic and State Systems . Springer-Verlag, 2008. [13] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ): 115–122, 1990. [14] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133–137, 1999. [15] Zinaida Trybulec

###### Pseudo-Canonical Formulae are Classical

the positive propositional language. Formalized Mathematics , 8(1):133–137, 1999. [17] Andrzej Trybulec. The canonical formulae. Formalized Mathematics , 9(3):441–447, 2001. [18] Andrzej Trybulec. Classes of independent partitions. Formalized Mathematics , 9(3): 623–625, 2001. [19] Zinaida Trybulec. Properties of subsets. Formalized Mathematics , 1(1):67–71, 1990. [20] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics , 1 (1):73–83, 1990. [21] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics , 1

###### Weak Completeness Theorem for Propositional Linear Time Temporal Logic

functions. Formalized Mathematics , 1( 2 ):329-334, 1990. [24] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics , 1( 1 ):115-122, 1990. [25] Andrzej Trybulec. Enumerated sets. Formalized Mathematics , 1( 1 ):25-34, 1990. [26] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics , 1( 1 ):97-105, 1990. [27] Andrzej Trybulec. Defining by structural induction in the positive propositional language. Formalized Mathematics , 8( 1 ):133-137, 1999