Many interpreters have noted that §§138–242 of Wittgenstein's Philosophical Investigations is dominated by an attack on a platonist or classical realist conception of rules and meaning. In this paper, I address the lack of clarity that still exists concerning the nature and strength of the arguments in those sections. I argue that Wittgenstein's attack is genuinely compelling if viewed as an intricate reductio ad absurdum argument that runs all the way through §§138–201. On my reading, the well-known regress-of-interpretations argument is (...) merely one stage in the overall reductio and is not sufficient on its own to generate the rule-following paradox. (shrink)

A. P. A. Hutchinson. What's the Point of Elucidation? Metaphilosophy, 2007, vol. 38, no. 5, pages 691-713. Published by and copyright Wiley-Blackwell Publishing. The definitive version of this article is available from http://www.blackwell-synergy.com/.

In this article I examine three ways in which one might interpret Wittgenstein's Philosophical Investigations (PI). In a partial response to Hans‐Johann Glock's article in this journal, I suggest that since publication PI has, broadly speaking, been interpreted in three ways: doctrinal; elucidatory; or therapeutic. The doctrinal interpretation is shown to be, at best, difficult to sustain textually. The elucidatory (standard) interpretation, though seemingly closer to the text, is shown both to implicate Wittgenstein in some unfortunate philosophical commitments and to (...) face a problem of “motivation.” I argue that, correctly understood, any attempt to elucidate in PI is undertaken only in pursuit of the therapeutic goal. I conclude by arguing that the therapeutic interpretation is the only interpretation that can adequately make sense of Wittgenstein's text as a whole and the metaphilosophical remarks in particular. Furthermore, it is the only interpretation that can demonstrate Wittgenstein's continued importance and relevance as a philosopher. (shrink)

Employing Searle’s views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call Cognitive Mathematics and Technical Mathematics respectively. The former type relates to concepts and meanings, logic and sense, whilst the latter relates to algorithms, heuristics, rules and application of various techniques. I claim that an upgrade in the school teaching of Cognitive Mathematics is necessary. The aim is to (...) change the current mentality of the stakeholders so as to compensate for the undue value presently attached to Technical Mathematics, due to advances in technology and its applications, and thus render the two sides of Mathematics equal. Furthermore, I suggest a reorganization/systematization of School Mathematics into a cognitive network to facilitate students’ understanding of the subject. The final goal is the transition from mechanical execution of rules to better understanding and in-depth knowledge of Mathematics. (shrink)