Tractatus Quanticum: Quantum Perspectives

• Tractatus Quanticum is a reinterpretation of Wittgenstein’s Tractatus using quantum mechanics, redefining facts as perspective-dependent phenomena.
• It formulates a naturalistic third way between realism and instrumentalism by grounding perspectives in physical states and mutual correlations.
• Employing quantum formalism, the work details how measurement and knowledge arise from interactional facts, challenging the notion of an absolute, perspective-free reality.

Tractatus Quanticum is a 2025 re-editing of Wittgenstein’s Tractatus Logico-Philosophicus that takes quantum mechanics, and specifically Relational Quantum Mechanics (RQM), as its governing framework. It preserves the numbered, aphoristic, self-undermining form of the original while replacing a quasi-absolute logical picture of the world with a relational one: the world is no longer the totality of facts simpliciter, but what is the case from some perspective. Facts, knowledge, and even the self are treated as physically embodied, perspective-relative, and mutually describable within a web of correlations rather than from a view from nowhere (Covoni et al., 4 Dec 2025, Ismael et al., 5 Jul 2026).

1. Origin, model, and textual design

The work presents itself as “a re-editing, which takes quantum mechanics into account, of Wittgenstein’s famous Tractatus.” It is playful in form but serious in aim: to articulate the philosophical implications of RQM and to formalize a “naturalistic third-way between realism and instrumentalism” (Covoni et al., 4 Dec 2025). Its 2026 introduction, “Against Totalitarianism,” explicitly casts itself in a role analogous to Bertrand Russell’s introduction to the original Tractatus, while stressing that the quantum reworking is directed against the idea of the world as a totality and against the idea of a single privileged language or framework (Ismael et al., 5 Jul 2026).

The book is organized into three parts—Synthesis, Short, and Long—thereby mimicking the compressed architecture of Wittgenstein’s original while allowing progressively fuller elaboration. The style remains proposition-based and ladder-like: the argument is meant to be climbed and then, in Wittgensteinian fashion, destabilized from within. Yet the object of destabilization is different. The original Tractatus undermined the possibility of saying the world as a whole; Tractatus Quanticum extends that demolition by arguing that quantum mechanics excludes even the presupposition of a single, perspective-independent world available as a common object of all descriptions (Covoni et al., 4 Dec 2025).

Dimension	Tractatus Logico-Philosophicus	Tractatus Quanticum
Opening world-thesis	“The world is everything that is the case”	“The world is everything that is the case from some perspective”
Literary form	Numbered propositions	Numbered propositions in Synthesis / Short / Long
Philosophical target	Unsayability of the world as a whole	Absence of a perspective-free world and of a privileged language

This structural continuity matters because the later work does not merely borrow Wittgensteinian style. It reenacts the Tractarian method under altered physical assumptions: where the original presupposed a broadly classical background, the new text treats quantum theory as requiring a different conception of fact, objectivity, and logical articulation.

2. Perspective as the primitive category

The central primitive in Tractatus Quanticum is the perspective. A perspective is not primarily mental, phenomenological, or anthropocentric. It is a physical notion: a system, or configuration of systems, defined by sets of commuting variables and embodied in actual correlations. Observers are therefore only a special case. A detector, thermometer, brain, particle, or any system capable of correlating with another can instantiate a perspective (Covoni et al., 4 Dec 2025).

The book’s opening synthesis condenses this position into seven theses, among them: the world is what is the case from some perspective; my knowledge is a particular perspective; perspectives are themselves facts when considered from another perspective; and what we do not have information about must be passed over in silence. These claims relocate epistemology inside physics. Knowledge is not a relation between a detached subject and an independent world; it is a physical configuration of correlations among systems.

This yields one of the work’s characteristic formulas: perspectives are transparent to each other because they are facts. A perspective can be known because it is itself a physical state of affairs for another perspective. The self is therefore not an extra-physical pole standing outside the world. It is a particular recursive organization of facts: a reflective point of knowledge that includes information about itself. The book thereby naturalizes the knower instead of treating subjectivity as an exception to physical description (Covoni et al., 4 Dec 2025).

The conceptual consequence is that asking for a fact without a perspective is, on this view, like asking for velocity without a reference frame. The request is not merely difficult to satisfy; it is malformed. What classical metaphysics took to be absolute fact is reinterpreted as a category mistake produced by neglecting the physical embodiment of information.

3. Relative facts, probability, and the quantum formalism

The formal vocabulary of Tractatus Quanticum is deliberately sparse but exact. A fact is written as

$A=a$

where $A$ is a variable and $a$ one of its values. A variable is understood as a way a system manifests itself in interactions. Facts are therefore interactional rather than intrinsic in the classical sense.

In the quantum case, the variables of a system are represented by elements of a non-commutative algebra, and a perspective is associated with an abelian subalgebra of commuting observables. This is the formal expression of the claim that not all variables can simultaneously be factual in the same perspective. If $A$ has spectral decomposition

$A=\sum_a a\,\Pi_a,$

then the probability of value $a$ relative to a given perspective is

$p(a)=\rho(\Pi_a),$

where $\rho$ is the state relative to that perspective. For commuting variables $A$ and $B$,

$A$0

The notion of a relative fact is then sharpened through conditionalization:

$A$1

If $A$2, then $A$3 is factual relative to $A$4. Mutual information provides the operational measure of how one perspective encodes another:

$A$5

Uncertainty is quantified with Shannon entropy,

$A$6

while information content is written as

$A$7

These formulas are not auxiliary decoration. They support the thesis that knowledge is physical information and that objectivity is reconstructed from stable correlation structures rather than from a perspective-independent inventory of properties (Covoni et al., 4 Dec 2025).

The text also highlights an interference schema:

$A$8

even when $A$9. This is used to mark the failure of classical total probability and, with it, the failure of the assumption that all relevant variables possess simultaneously definite values. On this reading, quantum theory is not a theory of hidden absolute facts partially concealed from finite observers; it is a theory in which the very space of factuality is perspective-structured.

4. Anti-totalitarianism, language, and the critique of totality

The companion introduction gives the book’s polemical title—“Against Totalitarianism”—a technical philosophical meaning. The target is not political totalitarianism but the thought that reality is a single complete totality of facts and that there exists one privileged framework capable of capturing it “as it is in itself.” The introduction argues against both the metaphysical image of the world as a total whole and the linguistic image of one essential use of language (Ismael et al., 5 Jul 2026).

Its most compact statement of the new position appears in Proposition 3.7:

“All things stand only in relation to a perspective, and with a shift of perspective, what once appeared as fact may be absent or incompatible with other facts from another perspective.”

This is not subjectivism. “Perspective” does not mean a private consciousness; it means a physical system embedded in relations of interaction and correlation. The relativity of fact is therefore presented as objective, not voluntaristic. There are facts, but they are facts only for systems.

The introduction links this anti-totalitarianism to a second Wittgensteinian turn: the rejection of a single essential function of language. It contrasts the early Tractatus, with its emphasis on proposition and fact, with the later Wittgenstein’s pluralism of language-games. Statements, questions, requests, warnings, and other uses of language are not reducible to one essence. This linguistic pluralism is paired with physical perspectivalism: just as language has no single total function, reality has no single absolute articulation (Ismael et al., 5 Jul 2026).

A further consequence is the collapse of the traditional public/private split. Classical thought preserved a “public” world of objective primary qualities behind the “private” domain of appearance. The introduction argues that quantum mechanics erodes even that middle ground. Once intrinsic, perspective-independent properties are abandoned, neither a hidden objective field nor a hidden subjective field remains as the foundation of experience. What remains is a network of relative facts.

5. Realism, instrumentalism, measurement, and the self

A major ambition of Tractatus Quanticum is to articulate a third way between realism and instrumentalism. It rejects a metaphysics of absolute, perspective-free facts, but it also rejects the conclusion that theory is merely a predictive instrument. The world is real; facts are real; knowledge is real. What is denied is not reality but the idea that reality must be describable from nowhere (Covoni et al., 4 Dec 2025).

This stance also reconfigures the measurement problem. The paper says that the “mis-named measurement problem” is fundamentally a mismatch of perspectives. What appears from one perspective as a definite fact can appear from another as a continuous change in correlations or mutual information. “Measurement” is not elevated to a primitive epistemic miracle; it is treated as an ordinary physical interaction that leaves traces and restructures information. The specialness of measurement is thus derivative, not fundamental.

The same strategy is applied to consciousness. The self is described as “the reflective point of a knowledge that includes information about itself,” and personal knowledge is identified with a physical configuration of the brain. The point is not eliminativist reduction but deflation: the first-person perspective is no longer mysterious once perspectives in general are recognized as physical facts for other perspectives. What becomes impossible is not subjectivity, but an absolute third-person perspective outside every perspective (Covoni et al., 4 Dec 2025).

The work also emphasizes circularity as constitutive rather than vicious. Perspectives are described from other perspectives, which are themselves describable from still others. There is no final external foundation from which the total structure can be surveyed non-circularly. The text explicitly states that “There is nothing wrong with circularity.” This is one of its clearest departures from foundationalist metaphysics and one of its most direct inheritances from the Tractarian practice of philosophical demolition.

Finally, the book places its perspectivalism across multiple descriptive layers—physical, chemical, biological, functional, psychological, social—while insisting that these layers are not separate ontological worlds. They are approximate descriptions of the same physical reality, possibly employing different logical spaces or explanatory regimes. The result is a naturalized pluralism rather than a hierarchy crowned by one final idiom.

6. Place within contemporary quantum-foundational debates

Within recent quantum-foundational literature, Tractatus Quanticum belongs to a wider effort to move beyond atomism, separability, and classical actualism, but its vocabulary is distinctively Wittgensteinian and relational. A useful comparison is “On the Relative Nature of Quantum Individuals,” which likewise rejects the inherited particle ontology and defines a quantum individual as a minimal relational set of powers and potentia within a given degree of complexity; there too individuality is “objectively relative,” though formulated through invariance of bases and factorizations rather than through perspectival facts in the RQM sense (Ronde et al., 2024).

Other neighboring proposals pursue different ontological lexicons. “Taking Heisenberg’s Potentia Seriously” interprets quantum theory through res potentia and res extensa, treating measurement as actualization of real but non-actual possibilities (Kastner et al., 2017). Hartle’s “Quantum Mechanics of Individual Systems” shifts the focus to individual systems and treats the state vector as shorthand for true, false, and indefinite propositions, with Born probabilities derived as infinite-ensemble frequencies (Hartle, 2019). “Computational Complexity and the Nature of Quantum Mechanics” instead reads quantum theory as a computationally constrained generalization of Bayesian probability, locating the classical/quantum divide in polynomial-time certifiability of nonnegativity (Benavoli et al., 2019). “The physics and metaphysics of the conceptuality interpretation of quantum mechanics” proposes yet another non-objectual ontology, interpreting quantum entities as conceptual entities and entanglement as meaning-connection (Aerts et al., 2023).

From the standpoint articulated by Muller, an interpretation of quantum mechanics is not mere semantic gloss but an extension of minimal QM by added ontology, vocabulary, and truth-conditions (Muller, 2014). On that criterion, Tractatus Quanticum is best understood as an interpretive intervention rather than a literary pastiche. It adds substantive claims about what facts are, what knowledge is, how perspectives function, and why quantum mechanics blocks the aspiration to an absolute inventory of properties.

Its distinctive contribution lies in combining four claims that are often separated in the literature: that perspectives are physical rather than mental; that facts are real but only relative; that language and logic themselves are not perspective-free; and that the philosophical temptation toward totality is undermined not only by Wittgensteinian quietism but by quantum theory itself. In that sense, Tractatus Quanticum is less a commentary on Wittgenstein than a quantum reoccupation of the Tractarian form: the world remains factual, but factuality has become irreducibly relational.