Material Points and Formal Concepts in the Early Wittgenstein

Material Points and Formal Concepts in the Early Wittgenstein

I Introduction

In an influential article, Gerd Grasshoff has argued for the identification of the objects in Wittgenstein's Tractatus¹ with the ultimate constituents of reality in Heinrich Hertz's Principles of Mechanics. Grasshoff's interpretation is based on two interrelated claims: (1) The specific determination of the objects in the world and the relation among them is the primary theme in Wittgenstein's early philosophy, because it is the primary theme for Hertz.² (2) Wittgenstein did not assume the existence of simple objects on purely logical grounds without having specific examples of simple objects in mind, because Hertz did not do this.³ The first of these claims tries to remedy what Grasshoff calls the 'thematic' misunderstanding of the Tractatus, the second what he calls the 'elementary' (or 'logicistic') misunderstanding, and both together are intended to revise what he calls the 'biographical' misunderstanding that ascribes to Frege and Russell a more significant influence on the early Wittgenstein than to Hertz.⁴

Indeed, to interpret Tractarian objects as Hertzian objects is suggested by TLP 6.3431, where Wittgenstein says that the laws of physics 'indirectly speak about the objects of the world.' Moreover, in TLP 6.3432, Wittgenstein adds that mechanics mentions not 'particular material points' but 'some points or other.'⁵ This suggests that material points — one kind of the entities that play a fundamental role in Hertz's mechanics — belong to the simple objects in the technical sense of the Tractatus. Obviously, Wittgenstein is little concerned with the details of the technical apparatus of Hertz's Principles of Mechanics. As David Keyt has pointed out, material points, for Hertz, display internal complexity and, hence, according to the terminology of the Tractatus, are states of affairs rather than objects.⁶ Nevertheless, as Grasshoff has argued, another kind of entities in Hertz's mechanics, the so-called 'mass particles' [Massenteilchen], do not suffer from this difficulty.

Does the obvious affinity between Hertz's and Wittgenstein's ultimate constituents of reality imply that, for Wittgenstein, the ontology of Hertzian objects has an epistemological priority over his logic? I agree that, contrary to logicistic interpretations, Wittgenstein's early views on simple objects and their concatenations should not be seen as derived from his views on names and their combinations into propositions. In this sense, there is no epistemological priority of logic over ontology.⁷ However, contrary to the physicalistic interpretation, neither does the ontology of Hertzian objects have a priority over logic for the early Wittgenstein. Wittgenstein's early views on names and their combinations should not be seen as derived from his views on simple objects and states of affairs. Rather, the conceptual structure of Wittgenstein's early philosophy should be seen as a net of mutually interdependent concepts, in which neither logical nor ontological concepts can be defined independently of each other. As I argue, this conceptual structure is captured by Wittgenstein's characterization of the concept of object as a 'formal concept'. Moreover, I claim that only by taking into account this conceptual structure can we be led to an understanding of the analogy Wittgenstein sees between his own view of the method of logic and the method of Hertz's mechanics.

II Hertz on 'Pseudo-Pictures'

Wittgenstein's earliest remarks on Hertz do not directly concern two issues that have received wide attention in the recent literature, viz. the influence of Hertz's idea of scientific sentences as pictures on Wittgenstein's picture theory of language,⁸ and the influence of Hertz's conception of clarification as eliminating 'idling wheels' from language on Wittgenstein's view of elucidation.⁹ Rather, they address the analogy between the role of construction in logic and the role Hertz ascribes to construction in mechanics. In an entry in the Notebooks 1914-1916, after discussing the...