On a formal account of science: Hertz’s influence on the early Wittgenstein and the non-metaphysical approach to science

João Vitor Ferrari

This work aims at presenting a way through which certain formal traits of the Tractarian conception of language could be interpreted as leading to an anti-metaphysical approach to science. My central claim is that the formalism regarding the natural sciences in the Tractatus prevents from raising metaphysical puzzles, namely, issues about the “ultimate structure of reality” and the natural laws that supposedly describe the behaviour of its constituents. I consider that these puzzles stem from a metaphysical approach to science, which the Tractatus avoids.

Focusing on one of the core ideas that underlie the early Wittgenstein’s account of language, i.e., the notion of logical form, I aim at shedding light on the Tractarian view on science firstly by highlighting Hertz’s influence on the philosopher. To this purpose I explore briefly a possible parallel between Hertz’s and Wittgenstein’s picture-theories: the similarity between the role of dynamical models’ degrees of freedom in modelling systems and that of logical form in depicting reality, respectively. Although the notations brought by the Principles of Mechanics and the Tractatus include fundamental elements, i.e., material points and simple objects, and at first glance may seem as if they were providing symbols for metaphysical entities that stand for reality’s ultimate substratum, I claim that, within the notation of dynamical models and Tractatrian analysis, these primitives should rather be interpreted as purely formal – they do not perform primary roles. That is to say, mechanical systems are not reducible to the behaviour of material points, for these are a formal expedient and do not stand for external ultimate entities; likewise, the sense of sentences does not depend on the existence of simple objects and the significance of their names, for the very use of language already plays this primary role. Therefore the question about the existence of these primitives in reality is avoided. This is pivotal in understanding how the Principles and the Tractatus are not committed to the metaphysical task of giving an account of such thing as the ultimate structure of reality.

I examine subsequently what the centrality of the logical form achieves in the sentences that describe the traits and limits of science (4.11n e 6.3n). By reducing the scope of the idea of necessity to logic and thus denying that there are necessarily true depictions, I argue that the Tractatus sets restrictions to a metaphysical approach to the laws of nature. For laws and principles do not describe reality’s structure. Instead, they work as instructions for constructing propositions that will, correctly or not, depict phenomena, showing thus the logical forms that propositions within the same representational system share. In this sense, both newtonian and hertzian mechanics enable constructing descriptions of reality – their differences, though, lie in the manner whereby they bring the description to an unitary form, since their fundamental principles show distinct logical forms. That is to say, the laws within a system do not depict any sort of underlying structure of reality when enabling the construction of true propositions, for they merely treat of the respective notation that they belong to and not of the phenomena they seek to describe (6.35).

Thus I claim that the outcome of the formal traits of the Tractatus is the non-commitment to a metaphysical view on science, in opposition to the traditional realist interpretations. That does not mean the Tractatus denies realism – after all, reality is what decides ultimately whether propositions hold or not; but only that science should not aim at attaining something deeper than reality itself.