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arXiv:2512.06034

Tractatus Quanticum

Niccolò Covoni, Carlo Rovelli

quant-phphysics.hist-phSubmitted Dec 4, 2025• Announced Dec 5, 2025• 0 citations
v1 · Dec 4, 2025v2 · Jan 4, 2026
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Abstract

This is a re-editing, which takes quantum mechanics into account, of Wittgenstein's famous Tractatus. The operation has a playful side in the form, but is a serious attempt to capture possible philosophical implications of the Relational Interpretation of Quantum Mechanics, and formalize the naturalistic third-way between realism and instrumentalism explored by this interpretation.

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16 pages

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This is a re-editing, which takes quantum mechanics into account, of Wittgenstein's famous Tractatus. The operation has a playful side in the form, but is a serious attempt to capture possible philosophical implications of the Relational Interpretation of Quantum Mechanics, and formalize the naturalistic third-way between realism and instrumentalism explored by this interpretation.
This article reads two recent tractatus-style texts - Niccolo Covoni and Carlo Rovelli's Tractatus Quanticus (arXiv:2512.06034) and Mikolaj Sienicki and Krzysztof Sienicki's Tractatus de Conscientia (arXiv:2607.05459) - together with Jenann Ismael and Huw Price's interpretive introduction Against Totalitarianism (arXiv:2601.01070), as parts of what may be called a New Tractatus Program. The program is unified by a single pressure point: the demand for a perspective-free description of reality, whether as a final inventory of facts, a world viewed from nowhere, or a self placed outside the physical order. On the relational interpretation of quantum mechanics, Tractatus Quanticus revises Wittgenstein's opening claim by replacing the world as the totality of facts with the world as what is the case from some perspective. Against Totalitarianism then makes the philosophical stakes of this move explicit by challenging the idea of the world as one closed totality. Tractatus de Conscientia carries the same discipline into the theory of consciousness, where conscious experience is treated neither as a mysterious substance nor as mere behavior, but as an integrated, temporally thick, operationally accessible perspective. Read together, these texts point toward a post-classical philosophy of partiality: reality is not abolished, but de-absolutized; consciousness is not mystified, but constrained by access, coupling, memory, and evidence; and the limits of language become inseparable from the limits of perspective. The article does not claim that relational quantum mechanics is the only viable interpretation of quantum theory. It instead develops the philosophical consequences of the relational reading. Its aim is programmatic rather than demonstrative: it does not prove a new ontology, but organizes a family of arguments around disciplined perspective-dependence.
The new discoveries of QM led to re-assessing, broadening the meanings of many physical concepts, and formulating a new logic that was no longer based on the classical principles of non-contradiction, identity, and causality. Heisenberg considered the classical logic and the conception of language expressed in the Tractatus Logico-Philosophicus inadequate for the understanding of the problems of language with which the physicists of the Copenhagen school had had to deal in order to define the foundations of Quantum Mechanics. On the contrary, he saw in Wittgenstein’s posthumous Philosophical Investigations the key to solving those problems. One may formulate a proportion and state that the use of language described in the Tractatus fits the use of language in Classical Mechanics, as the use of language described in PI fits the use of language in QM. I interpret the reflections of the physicists of the Copenhagen school on the limits of language relative to QM by highlighting how the epistemological revolution of quantum physics shares a conception of language similar to that expressed by late Wittgenstein in PI. I also aim to explain why Heisenberg considered it inappropriate to subsume the propositions and concepts of QM under the rules of the propositional logic of Tractatus. I explain why the philosophy of language expounded in PI, which is based on language games and resemblance families, sheds a light on how and why QM has contributed to renewing existing concepts (such as space, trajectory, observer, etc.) and to formulate a new logic (quantum logic).