Doing and Showing

The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a mathematical theory consists of a set of axioms and further theorems deduced from these axioms according to certain rules of logical inference. Thus the usual notion of axiomatic method is inadequate and needs a replacement.Comment: 54 pages, 2 figure

Mathematics and language

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes that we view mathematics as a system of conventions and norms that is designed to help us make sense of the world and reason efficiently. Like any designed system, it can perform well or poorly, and the philosophy of mathematics has a role to play in helping us understand the general principles by which it serves its purposes well

the primacy of use over naming

In Philosophical Investigations, Wittgenstein proposed the notion of meaning that accounts for the large variety of contexts in which we apply the term “meaning”. This paper agreement with the manner in which Wittgenstein enhance his conception of meaning emphasizing his methodology of observation and description of particular cases. By applying a descriptive approach, Wittgenstein demonstrated that meaning of the term does not reside in physical or mental objects as well as in its correlations. As a result of contrasting denotative theory as well as the correspondence theory of meaning and recognizing the inadequacy of the accounts of meaning, he has proposed earlier in his Tractatus. But in later work, he has suggested that only one conception of meaning which could not be invalidated, at least for a large class of cases. This is none other than the notion of meaning which is regarded as public in nature. Consequently, the meaning of a term is not its denotation but its “use” in the language. Hence, by upholding the slogan i.e., “meaning is use” here I want to illustrate the supremacy of use over “naming” concerning to Wittgenstein’s Tractatus and Philosophical Investigations

Values based practice and authoritarianism

Values based practice (VBP) is a radical view of the place of values in medicine which develops from a philosophical analysis of values, illness and the role of ethical principles. It denies two attractive and traditional but misguided views of medicine: that diagnosis is a merely factual matter and that the values that should guide treatment and management can be codified in principles. But, in the work of KWM (Bill) Fulford, it goes further in the form of a radical liberal view: that the idea of an antecedently good outcome should be replaced by that of a right process. That however leads to a dilemma as to whether it can account for its own normative status. Given that difficulty, why might one adopt the radical version? I sketch a possible motive drawing on Rorty’s rejection of authoritarianism which replaces objectivity with solidarity as the aim of judgement. But I argue that, nevertheless, this does not justify the rejection of the more modest particularist version of VBP

A Critique of Saul Kripke's "Wittgenstein on Rules and Private Language"

In Wittgenstein on Rules and Private Language, Saul Kripke presents a controversial skeptical argument, which he attributes to Wittgenstein’s interlocutor in the Philosophical Investigations [PI]. The argument purports to show that there are no facts that correspond to what we mean by our words. Kripke maintains, moreover, that the conclusion of Wittgenstein’s so-called private language argument is a corollary of results Wittgenstein establishes in §§137-202 of PI concerning the topic of following-a-rule, and not the conclusion of an independently developed argument in §§243ff of PI, as most commentators take it to be. In this work, I assess Kripke’s skeptical argument both in its own right, and as an interpretation of the rule-following sections of PI. In its own right, I try to show that it is critically flawed. However, as an interpretation of the rule-following sections of PI, I try to show that it is essentially correct. I do this by showing that Kripke’s interpretation squares with and supports the meta-philosophical framework developed by Wittgenstein in §§107-136 of PI, which immediately precedes his remarks on following-a-rule. (Oct 16, 2008. Committee: Paul Horwich, Galen Strawson, Stephen Neale, Michael Levin

Parikh and Wittgenstein

A survey of Parikh’s philosophical appropriations of Wittgensteinian themes, placed into historical context against the backdrop of Turing’s famous paper, “On computable numbers, with an application to the Entscheidungsproblem” (Turing in Proc Lond Math Soc 2(42): 230–265, 1936/1937) and its connections with Wittgenstein and the foundations of mathematics. Characterizing Parikh’s contributions to the interaction between logic and philosophy at its foundations, we argue that his work gives the lie to recent presentations of Wittgenstein’s so-called metaphilosophy (e.g., Horwich in Wittgenstein’s metaphilosophy. Oxford University Press, Oxford, 2012) as a kind of “dead end” quietism. From early work on the idea of a feasibility in arithmetic (Parikh in J Symb Log 36(3):494–508, 1971) and vagueness (Parikh in Logic, language and method. Reidel, Boston, pp 241–261, 1983) to his more recent program in social software (Parikh in Advances in modal logic, vol 2. CSLI Publications, Stanford, pp 381–400, 2001a), Parikh’s work encompasses and touches upon many foundational issues in epistemology, philosophy of logic, philosophy of language, and value theory. But it expresses a unified philosophical point of view. In his most recent work, questions about public and private languages, opportunity spaces, strategic voting, non-monotonic inference and knowledge in literature provide a remarkable series of suggestions about how to present issues of fundamental importance in theoretical computer science as serious philosophical issues

A self-study course in FORTRAN programming. Volume 1 - Textbook

Self study textbook for course in FORTRAN programming - Vol.