Timm Lampert

The Problem of Validity Proofs

In philosophical contexts, logical formalisms are often resorted to as a means to render the validity and invalidity of informal arguments formally transparent. Since Oliver (1967) and Massey (1975), however, it has been recognized in the literature that identifying valid arguments is easier than identifying invalid ones. Still, any viable theory of adequate logical formalization should at least reliably identify valid arguments. This paper argues that accounts of logical formalization as developed by Blau (1977) and Brun (2004) do not meet that benchmark. The paper ends by suggesting different strategies to remedy the problem.

Underdetermination and provability: a reply to Olaf Müller

ABSTRACT Newton claims to have proven the heterogeneity of light through his experimentum crucis. However, Olaf Müller has worked out in detail Goethe’s idea that one could likewise prove the heterogeneity of darkness by inverting Newton’s famous experiment. Müller concludes that this invalidates Newton’s claim of proof. Yet this conclusion only holds if the heterogeneity of light and the heterogeneity of darkness is logically incompatible. This paper shows that this is not the case. Instead, in Quine’s terms, we have two logically compatible theories based on mutually irreducible theoretical terms. From a Quinean point of view, this does no harm to the provability of the corresponding statements.

Wittgenstein's ab-Notation: An Iconic Proof Procedure

This paper systematically outlines Wittgensteins ab-notation. The purpose of this notation is to provide a proof procedure in which ordinary logical formulas are converted into ideal symbols that identify the logical properties of the initial formulas. The general ideas underlying this procedure are in opposition to a traditional conception of axiomatic proof and are related to Peirces iconic logic. Based on Wittgensteins scanty remarks concerning his ab-notation, which almost all apply to propositional logic, this paper explains how to extend his method to a subset of first-order formulas, namely, formulas that do not contain dyadic sentential connectives within the scope of any quantifier.

Psychophysical and Tractarian Analysis

This paper argues for a physicalistic interpretation of Wittgensteins Tractatus Logico-Philosophicus. Wittgensteins general conception of world and language analysis is interpreted and exemplified in relation to the historical background of the psychophysical analysis of sense data and, in particular, color analysis. Three of his main principles of analysisthe principle of independence, the context principle and the principle of atomismare interpreted and justified on the background of physicalism. From his proof of color exclusion in the Tractatus, it is shown that Wittgenstein had a detailed conception of how philosophy should fulfil the task of distinguishing between sense and nonsense using physicalistic presuppositions.

Iconic Logic and Ideal Diagrams: The Wittgensteinian Approach.

This paper provides a programmatic overview of a conception of iconic logic from a Wittgensteinian point of view (WIL for short). The crucial differences between WIL and a standard version of symbolic logic (SSL) are identified and discussed. WIL differs from other versions of logic in that in WIL, logical forms are identified by means of so-called ideal diagrams. A logical proof consists of an equivalence transformation of formulas into ideal diagrams, from which logical forms can be read off directly. Logical forms specify properties that identify sets of models (conditions of truth) and sets of counter-models (conditions of falsehood). In this way, WIL allows the sets of models and counter-models to be described by finite means. Against this background, the question of the decidability of first-order-logic (FOL) is revisited. In the last section, WIL is contrasted with Peirce’s iconic logic (PIL).