Carnapian inductive logic for Markov chains

Carnap's Inductive Logic, like most philosophical discussions of induction, is designed for the case of independent trials. To take account of periodicities, and more generally of order, the account must be extended. From both a physical and a probabilistic point of view, the first and fundamental step is to extend Carnap's inductive logic to the case of finite Markov chains. Kuipers (1988) and Martin (1967) suggest a natural way in which this can be done. The probabilistic character of Carnapian inductive logic(s) for Markov chains and their relationship to Carnap's inductive logic(s) is discussed at various levels of Bayesian analysis.     

Lakatos's criticism of Carnapian inductive logic was mistaken

In [39], Imre Lakatos influentially argued that Carnapian inductive logic was a degenerate research programme. This paper argues that Lakatos's criticism was mistaken and that, according to Lakatos's own standards, Carnapian inductive logic was progressive rather than degenerate.     

Hypotheses and Inductive Predictions

This paper studies the use of hypotheses schemes in generatinginductive predictions. After discussing Carnap–Hintikka inductive logic,hypotheses schemes are defined and illustrated with two partitions. Onepartition results in the Carnapian continuum of inductive methods, the otherresults in predictions typical for hasty generalization. Following theseexamples I argue that choosing a partition comes down to making inductiveassumptions on patterns in the data, and that by choosing appropriately anyinductive assumption can be made. Further considerations on partitions makeclear that they do not suggest any solution to the problem of induction.Hypotheses schemes provide the tools for making inductive assumptions, but theyalso reveal the need for such assumptions.     

Verification, falsification, and the logic of enquiry

Our starting point is Michael Luntley's falsificationist semantics for the logical connectives and quantifiers: the details of his account are criticised but we provide an alternative falsificationist semantics that yields intuitionist logic, as Luntley surmises such a semantics ought. Next an account of the logical connectives and quantifiers that combines verificationist and falsificationist perspectives is proposed and evaluated. While the logic is again intuitionist there is, somewhat surprisingly, an unavoidable asymmetry between the verification and falsification conditions for negation, the conditional, and the universal quantifier. Lastly we are lead to a novel characterization of realism.     

Revising Carnap’s Semantic Conception of Modality

I provide a tableau system and completeness proof for a revised version of Carnap??s semantics for quantified modal logic. For Carnap, a sentence is possible if it is true in some first order model. However, in a similar fashion to second order logic, no sound and complete proof theory can be provided for this semantics. This factor contributed to the ultimate disappearance of Carnapian modal logic from contemporary philosophical discussion. The proof theory I discuss comes close to Carnap??s semantic vision and provides an interesting counterpoint to mainstream approaches to modal logic. Despite its historical origins, my intention is to demonstrate that this approach to modal logic is worthy of contemporary attention and that current debate is the poorer for its absence.     

Logical Pluralism from a Pragmatic Perspective

This paper presents a new view of logical pluralism. This pluralism takes into account how the logical connectives shift, depending on the context in which they occur. Using the Question-Under-Discussion Framework as formulated by Craige Roberts, I identify the contextual factor that is responsible for this shift. I then provide an account of the meanings of the logical connectives which can accommodate this factor. Finally, I suggest that this new pluralism has a certain Carnapian flavour. Questions about the meanings of the connectives or the best logic outside of a specified context are not legitimate questions.     

From a Continental Point of View: The Role of Logic in the Analytic-Continental Divide

My discussion addresses the differences between analytic and continental philosophy concerning the use of logic and exact reasoning in philosophical practice. These differences are mainly examined in the light of the controversial dominance of Hegel's concept of logic (and theory of concept) in twentieth-century continental philosophy. The inquiry is developed in two parts. In the first (Sections 1-2), I indicate some aspects of the analytic-continental divide, pointing to the role that the topic 'logic and philosophy' plays in it. In the second part (Sections 3-6), I give a short account of the views of logic which are typical of the three main trends of continental philosophy (see Table 1). I also suggest how, with the aid of some typical analytical devices, some continental 'anti-logical' attitudes may be corrected, on their own terms.     

Two approaches to natural kinds

Philosophical treatments of natural kinds are embedded in two distinct projects. I call these the philosophy of science approach and the philosophy of language approach. Each is characterized by its own set of philosophical questions, concerns, and assumptions. The kinds studied in the philosophy of science approach are projectible categories that can ground inductive inferences and scientific explanation. The kinds studied in the philosophy of language approach are the referential objects of a special linguistic category—natural kind terms—thought to refer directly. Philosophers may hope for a unified account addresses both sets of concerns. This paper argues that this cannot be done successfully. No single account can satisfy both the semantic objectives of the philosophy of language approach and the explanatory projects of the philosophy of science approach. After analyzing where the tensions arise, I make recommendations about assumptions and projects that are best abandoned, those that should be retained, and those that should go their separate ways. I also recommend adopting the disambiguating terminology of “scientific kinds” and “natural kinds” for the different notions of kinds developed in these different approaches.

     

A logic for epistemic two-dimensional semantics

Epistemic two-dimensional semantics is a theory in the philosophy of language that provides an account of meaning which is sensitive to the distinction between necessity and apriority. While this theory is usually presented in an informal manner, I take some steps in formalizing it in this paper. To do so, I define a semantics for a propositional modal logic with operators for the modalities of necessity, actuality, and apriority that captures the relevant ideas of epistemic two-dimensional semantics. I also describe some properties of the logic that are interesting from a philosophical perspective, and apply it to the so-called nesting problem.     

Metaphysical analyticity and the epistemology of logic

Recent work on analyticity distinguishes two kinds, metaphysical and epistemic. This paper argues that the distinction allows for a new view in the philosophy of logic according to which the claims of logic are metaphysically analytic and have distinctive modal profiles, even though their epistemology is holist and in many ways rather Quinean. It is argued that such a view combines some of the more attractive aspects of the Carnapian and Quinean approaches to logic, whilst avoiding some famous problems.     

Philosophy of Science: Interfaces between Logic and Knowledge Representation

Abstract

In this inaugural lecture I offer, against the background of a discussion of knowledge representation and its tools, an overview of my research in the philosophy of science. I defend a relational model-theoretic realism as being the appropriate meta-stance most congruent with the model-theoretic view of science as a form of human engagement with the world. Making use of logics with preferential semantics within a model-theoretic paradigm, I give an account of science as process and product. I demonstrate the power of the full-blown employment of this paradigm in the philosophy of science by discussing the main applications of model-theoretic realism to traditional problems in the philosophy of science.

I discuss my views of the nature of logic and of its role in the philosophy of science today. I also specifically offer a brief discussion on the future of cognitive philosophy in South Africa. My conclusion is a general look at the nature of philosophical inquiry and its significance for philosophers today.     

论牟宗三哲学中的易学研究

牟宗三的易学研究为的是从易学中发见与解析中国哲学、中国思想,旨在抉发中国的玄学与道德哲学,而不是作一种历史的研究。他从哲学上为《周易》的解释提供了一个逻辑符号论的模型,为中国古典思想的现代诠释作出了首开先河的有益尝试;他对易学的“实在论的价值论”或“超越的内在”的价值论的诠释,与康德、维特根斯坦关于道德世界的“超越的外在论”不同;他对易之道德世界的分析与解释也是极其形式化的逻辑的。在这些分析与解释中,《周易》的“逻辑世界”或“符号世界”变成了语义的价值世界,或者说,作为“数理物理”世界的《周易》变成了价值论的道德世界。无论是在叙述方式,或内容的阐释与解析上,牟氏的这项研究都是十分新颖的,为国内所未有。但是,牟氏的易学研究只是他学思的开端起步,相对于他的逻辑研究来说,易学研究构成了他的哲学思想发展进路的前逻辑起点,而非逻辑起点,具有形式的象征意义。     

Nothing More or Less than Logic: General Logic, Transcendental Philosophy, and Kant's Repudiation of Fichte's Wissenschaftslehre

In this paper I lay the foundations for an understanding of one of Fichte's most neglected and least understood texts: the late lecture course on Transcendental Logic. I situate this work in the context of Fichte's lifelong struggle with the problem of understanding the relation between logic and philosophy – a problem that I show to figure centrally both in Fichte's own revolutionary thinking and in his response to Kant's notorious denunciation of the Wissenschaftslehre. By attending to this context we can understand Fichte's philosophical ambitions in the late lectures: a critique of particular doctrines of general logic; a critique of the conception of thought presupposed both by the traditional logic and by Kant himself; and a new conception of the relation between logic and the philosophical theory of experience. This revised version was published online in June 2006 with corrections to the Cover Date.     

Aristotle in Prussian Gymnasiums: Why the Texts of the Ancient Philosopher Became Popular for Teaching Logic

During the nineteenth century, German philosophy developed from a type of general knowledge to an academic discipline at the university. Changes across disciplines to the philosophy of science and psychological surveys created new challenges for the place and purpose of philosophy in the educational system. The content of logic courses for secondary schools (Gymnasiums) was centred on the dissociation of nature and the scale of logic.In this paper, I will examine a number of projects for teaching philosophy at the secondary school level from new humanism to reduce philosophical to philological concerns about different projects offered by Niethammer, Hegel and Herbart. Then, I will focus on the most successful – Adolf Trendelenburg’s Elements of Aristotle’s Logic (1st edition of 1836). This work is a compilation of the logical texts of Aristotle, and for as long as sixty years, it was an official textbook in Prussian secondary schools. The aim of the paper is to show how the rethinking of Aristotle’s heritage affected the theoretical and ideological expectations of propaedeutic courses and transformed the image of logic as a philosophical discipline.     

On the Special Logic Thesis in Chinese Philosophy

I address the problem of whether philosophy can be international by its claim to represent rationality, hence universality. I argue in favor of this claim by focusing on the special logic thesis in Chinese philosophy. This thesis holds that a different type of logic must be used when studying the Chinese texts. I argue at length against the special logic thesis by examining the problem of human nature in the Confucian philosophers Mencius, Hsün Tzu and Kao Tzu. I show how their arguments can be reconstructed as inductive analogical arguments and as deductive argument. I then broaden the notion of the logic of argumentation into a discussion of metaphysical anti-essentialism and underdetermination in order to resolve the problem of human nature and also to show how the same types of logical analysis (more generally construed) can be applied to the arguments from these Confucian philosophers. Under my treatment, Kao Tzu, somewhat surprisingly, turns out to provide the most insight.     

Emergence of Information Transfer by Inductive Learning

We study a simple game theoretic model of information transfer which we consider to be a baseline model for capturing strategic aspects of epistemological questions. In particular, we focus on the question whether simple learning rules lead to an efficient transfer of information. We find that reinforcement learning, which is based exclusively on payoff experiences, is inadequate to generate efficient networks of information transfer. Fictitious play, the game theoretic counterpart to Carnapian inductive logic and a more sophisticated kind of learning, suffices to produce efficiency in information transfer.     

第八次中国逻辑大会综述

“第八次中国逻辑大会”于2008年10月31日至11月3日在大津召开,全国逻辑学界200余位代表出席了会议。中国逻辑大会由中国逻辑学会土办,每四年召开一次。本次人会听取和审议了中国逻辑学会第7届常务理事会工作报告;     

How Tolerant Can You Be? Carnap on Rationality

In this paper I examine a neglected question concerning the centerpiece of Carnap's philosophy: the principle of tolerance. The principle of tolerance states that we are free to devise and adopt any well‐defined form of language or linguistic framework we please. A linguistic framework defines framework‐internal standards of correct reasoning that guide us in our first‐order scientific pursuits. The choice of a linguistic framework, on the other hand, is an ‘external’ question to be settled on pragmatic grounds and so not itself constrained by these (framework‐internal) standards. However, even if choosing a framework is a practical matter, we would nevertheless expect the process of framework selection to be subject to rational norms. But which norms might those be? And where do they come from? I begin by showing that these questions are crucial to the success of Carnap's entire philosophical project. I then offer a response on behalf of the Carnapian which guarantees the rationality of the process of framework selection, while remaining true to Carnap's firm commitment to tolerance.     

Philosophy of Science: What One Needs to Know

This introduction to the philosophy of science offers an overview of the major concepts and developments in contemporary theories of science. Strengths and weaknesses of deductive, inductive, and falsificationist models of science are considered. The "Received View" in the theory of science is contrasted with Kuhn's paradigms and Feyerabend's "anything goes," leading to an examination of the merits of a research program–based approach. After touching on the sociology of science, postmodernism, and the feminist critique, the article concludes with a summary, in six theses, of the implications for religion/science.     

Analogy and exchangeability in predictive inferences

An important problem in inductive probability theory is the design of exchangeable analogical methods, i.e., of exchangeable inductive methods that take into account certain considerations of analogy by similarity for predictive inferences. Here a precise reformulation of the problem of predictive analogy is given and a new family of exchangeable analogical methods is introduced.Firstly, it is proved that the exchangeable analogical method introduced by Skyrms (1993) does not satisfy the best known general principles of predictive analogy. Secondly, Skyrms's approach — consisting of the usage of particular hyper-Carnapian methods, i.e., mixtures of Carnapian inductive methods — is adopted in the design of a new family of exchangeable analogical methods. Lastly, it is proved that such methods satisfy an interesting general principle of predictive analogy.