Bolzano - The Discovery of Objective Propositions (1781-1848)

Kai Froeb2026

This text is a preview of History of the Reception of Hegel, volume I, to be published in 2026 by Reflexivity Press.

Bernard Bolzano is one of the most original—and also one of the longest-overlooked—thinkers of the nineteenth century. His Wissenschaftslehre [Theory of Science] (1837) developed ideas that were decades ahead of their time and were only rediscovered through Husserl, Frege, and analytic philosophy. In the context of the reception of Hegel, Bolzano occupies a peculiar position: he developed an alternative to speculative idealism without engaging in a systematic confrontation with Hegel—a parallel movement of thought that shows that the problems to which Hegel responded also admitted of other solutions.

We treat Bolzano here after Trendelenburg, although his Wissenschaftslehre appeared three years earlier (1837 vs. 1840). The reason is systematic: Trendelenburg articulates the methodological critique of Hegel, Bolzano shows an alternative conception of objectivity, and Lotze makes both motifs connectable for academic philosophy.

11.3.1 Life and Intellectual Position

Bernard Bolzano was born in 1781 in Prague, studied philosophy, mathematics, and theology, and was ordained a priest in 1805. In the same year he received a professorship in the philosophy of religion at the University of Prague. In 1819 he was removed from his office because of allegedly “freethinking” teachings and placed under police surveillance—a fate that forced him to write his major philosophical works outside the academic system.

The Wissenschaftslehre appeared in 1837 in four volumes—in the very decade in which Hegel’s influence reached its peak and the first countermovements set in. Bolzano died in 1848 in Prague, largely unnoticed by the philosophical public.

The Intellectual Context

Bolzano worked in relative isolation from the main currents of German philosophy. He knew Kant, but rejected his transcendental idealism. He took scarcely any notice of Hegel—the Wissenschaftslehre contains no substantial engagement with speculative idealism.

His main influences were:

  • The Leibniz-Wolffian tradition, with its confidence in logical analysis
  • Mathematics, especially the foundational questions of analysis
  • Scholastic logic, which he thought underestimated

Bolzano saw himself as a renewer of logic against what he took to be signs of decay—both the psychologism of the empiricist tradition and the subjectivism of idealist philosophy.

11.3.2 What Bolzano Argues Against: The Awareness of the Problem

The Problem of Psychologism

Bolzano’s main opponent was psychologism—the view that logical laws are descriptions of factual thought processes. This position was widespread in the early nineteenth century, both in the empiricist tradition (which understood logic as part of associationist psychology) and in parts of idealist philosophy (which analyzed thought as an activity of the subject).

Bolzano saw a fundamental confusion here: if logical laws merely describe how people factually think, then:

  • they would be contingent (they could be otherwise)
  • they would be relative (different people could think differently)
  • they would have no normative force (they would not say how one ought to think)
The Problem of Subjective Idealism

Bolzano also opposed every attempt to ground truths in acts of consciousness. Kant’s “Copernican turn”—that objects must conform to our cognition—appeared to him as a path into relativism. If truth depends on the structures of the knowing subject, then there is no longer any objective truth.

Against Fichte and post-Kantian philosophy, Bolzano objected that the self-positing of the I cannot be the foundation of logic. The I posits itself—but according to which laws? These laws must precede self-positing, not follow from it.

The Problem of the Foundations of Mathematics

As a mathematician, Bolzano was confronted with foundational problems in analysis. Concepts such as “infinitesimally small,” “limit,” and “continuity” were used intuitively, but their logical structure was unclear. Bolzano sought a clarification that did not need to rely on intuition or psychology.

11.3.3 What Bolzano Wants to Achieve: The Goals

Bolzano’s program can be summarized in three main goals:

  1. To free logic from psychology: logical laws are not descriptions of thought processes but objective structures that subsist independently of thought.

  2. To secure the objectivity of truth: truths are true regardless of whether anyone recognizes them. They are not “in the head” of thinkers, but have their own kind of subsistence.

  3. To clarify the foundations of science: all sciences rest on propositions and their logical relations. A “theory of science” must explicate these foundations.

11.3.4 Bolzano’s Solution: Propositions in Themselves and Ideas in Themselves (Steelman Presentation)

The Central Innovation: “In Itself”

Bolzano’s decisive step is the distinction between the act of thinking and the content of what is thought. When I think “Snow is white,” there is:

  1. My psychic act of thinking (a real event in my consciousness)
  2. The proposition in itself, which is thought (an objective structure not identical with my act)

The proposition “Snow is white” is true—but this truth does not depend on my thinking it. The proposition was true before I thought it and will remain true when I stop thinking. It has, as Bolzano says, a subsistence “in itself.”[1]

Propositions in Themselves

A “proposition in itself” is, for Bolzano:

  • The content of an assertion, abstracted from the act of asserting
  • Neither physical nor psychic—it does not exist in space and time
  • Objective—it is the same for all thinkers
  • True or false in itself—independent of whether anyone recognizes its truth

Bolzano emphasizes: there are infinitely many propositions in themselves, most of which have never been thought by any human being and never will be. The truth “The number 10^100 is greater than 10^99” already held before human beings existed, and would hold even if there were no human beings.

Ideas in Themselves

Analogous to propositions in themselves, there are “ideas in themselves”—the objective contents of concepts. The idea “triangle” is not identical with my psychic act of imagining, but the objective content that is the same across different acts.

Ideas in themselves can be:

  • objectual (there are things falling under them: “tree”)
  • objectless (nothing falls under them: “round square”)

This distinction matters: even objectless ideas are objective contents. “Round square” is a well-determined (if contradictory) concept.

Truths in Themselves

Bolzano calls true propositions in themselves “truths in themselves.” They form an objective realm:

There are truths which no human being knows—indeed, which even God knows only because he is omniscient, not because he creates or produces them. […] It is therefore more correct to say that truths subsist than to say that they exist.[2]

How the Solution Addresses the Problems

From Bolzano’s perspective, the distinction between “in itself” and “thought” resolves all the problems mentioned:

  1. Against psychologism: logical laws are relations between propositions in themselves, not between psychic acts. Logic deals with objective structures, not with brain processes.

  2. Against subjective idealism: truths are not dependent on the knowing subject. They “subsist” regardless of whether and how they are known.

  3. For the foundations of mathematics: mathematical propositions are truths in themselves. Their validity depends not on intuition or construction but on their logical relations.

Derivability

A further central concept is “derivability”: a proposition B is derivable from propositions A₁, A₂, … if every assignment to the variable parts that makes A₁, A₂, … true also makes B true.

This is a precursor of the modern concept of logical consequence—developed decades before Frege and modern logic.

11.3.5 The Internal Contradictions: Immanent Critique

Bolzano’s position is impressively consistent, but it raises questions arising from its own logic.

1. The Ontological Problem: What Does “Subsist” Mean?

Bolzano says: propositions in themselves “subsist,” but they do not “exist.” They are neither physical nor psychic. But what kind of being is this “subsisting”?

Bolzano himself admits this is difficult to explain. He writes: “By the being or existence of propositions in themselves I do not mean being in time or space, not being as actuality, but a being that one calls so only in an improper sense.”[3]

The question remains: if propositions in themselves neither exist nor fail to exist (in the ordinary sense), what ontological status do they then have? Bolzano introduces a new category (“subsisting”) without fully clarifying it.

2. The Epistemic Problem: How Do We Grasp Propositions in Themselves?

If propositions in themselves are neither physical nor psychic, how can we—as physical-psychic beings—grasp them? How does a real act of judgment have access to a non-real proposition in itself?

Bolzano must assume that there is a relation between the psychic act and the objective content. But how is this relation to be conceived? It cannot be causal (propositions in themselves do not act), it cannot be spatial (propositions in themselves have no location).

Here arises a problem of mediation structurally similar to the Platonic problem of “methexis” (participation): how can the concrete (the act of thought) participate in the ideal (the proposition in itself)? This question returns in Lotze as “the mediation of validity” and in Frege as the “puzzle” of grasping—and is only systematically addressed by Husserl (through the analysis of intentionality).

3. The Individuation Problem: How Many Propositions Are There?

Bolzano claims there are infinitely many propositions in themselves. But by what criteria are two propositions identical or distinct?

“The morning star is a planet” and “The evening star is a planet”—are these the same proposition or different propositions? Bolzano would say: different propositions (since the ideas “morning star” and “evening star” are different), although they concern the same object.

But then: how finely must one distinguish? Is “2+2=4” the same proposition as “two plus two equals four”? Bolzano gives no complete answer.

4. The Tension Between Objectivity and Relevance

Bolzano claims that the vast majority of truths are never thought. But what value do these never-thought truths have? If they have no influence on anything, are they not then meaningless?

Bolzano would answer: their value lies in their truth itself, not in their effect. But this answer leads to a peculiarly empty concept of truth—truths that merely “subsist,” without ever becoming effective.

11.3.6 Bolzano’s Influence: The Legacy

The Delayed Effect

Bolzano’s Wissenschaftslehre initially remained almost unnoticed. The reasons were manifold:

  • His political fate (removal from office, publication ban)
  • The dominance of German Idealism
  • The size and dryness of the work (four volumes, over 2,000 pages)

Only toward the end of the nineteenth century was Bolzano rediscovered. The line of reception ran through the Brentano school: Franz Brentano knew Bolzano, and his students—especially Kazimierz Twardowski and Anton Marty—brought Bolzano’s ideas into Austrian philosophy. From there they reached:

  • Edmund Husserl, who in the Logical Investigations (1900/01) took up and developed further Bolzano’s distinction between act and content
  • Early analytic philosophy, which recognized in Bolzano a forerunner of its own semantic distinctions
The Connection to Lotze: Parallel Developments

Bolzano’s “propositions in themselves” and Lotze’s “validity” address the same problem: the objectivity of logical structures beyond psychology and metaphysics. The historical relationship between the two is, however, complicated.

No direct adoption: Lotze does not refer to Bolzano’s Wissenschaftslehre in his major works, although it appeared in 1837—six years before Lotze’s first Logik (1843). Frege too, who is often compared to Bolzano, never cites him.[4]

Recognition of similarity: Lotze later did himself acknowledge the kinship of his position with Bolzano’s. In his Kleine Schriften (Vol. III/1, 1891, p. 367), he recognizes the closeness of his conception of validity to Bolzano’s “propositions in themselves.”

The “Bolzano-Lotze thesis”: Scholarship speaks of a “Bolzano-Lotze thesis” regarding the priority of the concept of the proposition. Both thinkers argue that propositions must be the “most essential components of the ideal world”—an insight that Lotze himself criticizes Plato for not having sufficiently taken into account.[5]

Husserl’s key role: Husserl testifies that Lotze’s logic gave him the “key” to understanding Bolzano’s conception and to developing the concept of “ideal meaning.” The two parallel traditions—Bolzano and Lotze—converge in Husserl.[6]

The differences nevertheless remain significant:

  • Bolzano is more ontologically explicit: he speaks of a distinct “subsistence” of propositions
  • Lotze is more mediating: he attempts to connect the sphere of validity with a teleological world order
  • Bolzano is mathematically oriented: his examples come from logic and mathematics
  • Lotze is oriented toward value philosophy: he also includes aesthetic and ethical values
  • Bolzano does not present his objectivism as an interpretation of Plato, while Lotze does precisely this
The Legacy of the Problems

The problems Bolzano left behind became the starting point for later developments:

  • Husserl developed the theory of intentionality to solve the epistemic problem: consciousness is “directed at” contents—this is its essential structure.
  • Frege spoke of a “third realm” of thoughts and called the grasping of them “puzzling”—without offering a solution.
  • Analytic philosophy tended to bracket the ontological questions and concentrate on the logical structures.

11.3.7 Bolzano and Hegel: Parallel Worlds

Bolzano and Hegel worked in the same period on related problems without entering into dialogue with one another. This non-dialogue is instructive.

What Both Share
  • The conviction that logic deals with objective structures, not mere habits of thought
  • The rejection of empiricist psychologism
  • The interest in systematic completeness
What Separates Them

| Aspect | Bolzano | Hegel | |——–|———|——-| | Ontology | Propositions “subsist” statically | Concepts “develop” dialectically | | Method | Analytic-definitional | Dialectical-speculative | | Truth | Timeless, independent of cognition | In process, self-recognizing | | Contradiction | To be avoided | Productively sublated |

The Question of Mediation

Hegel’s logic attempts to mediate the objectivity of logical structures with their genesis in thought. The categories “develop”—they are not simply given, but arise through the self-movement of the concept.

Bolzano does without this mediation. Propositions in themselves simply “subsist”—how they come to be recognized by us remains a subordinate problem.

The question is: is Bolzano’s renunciation of mediation an advantage (clarity, rigor) or a disadvantage (an unexplained gulf between thinking and what is thought)?

11.3.8 What Is to Be Learned from Bolzano

The Legitimate Concern

  1. The distinction between act and content: there is a real difference between the psychic process of thinking and what is thought. This distinction is fundamental and must be defended against any psychologism.

  2. The objectivity of logical structures: logical relations hold independently of whether anyone recognizes them. “2+2=4” was not true only once someone discovered it.

  3. The rigor of analysis: Bolzano’s effort toward precise definitions and clear distinctions is a model of philosophical work.

What Must Be Transformed

  1. The static “subsisting” must be related to the activity of cognizing. Propositions do not simply “subsist” somewhere—they show themselves in the exercise of thought.

  2. The gulf between act and content must be bridged. A theory of intentionality (as in Husserl) or a theory of conceptual mediation (as in Hegel) is needed.

  3. The isolation of truths must be overcome. Truths that never become effective are philosophically unsatisfying. The question of the relevance of truth for life must not be bracketed out.

The Formulation of the Task

Bolzano has shown that logical structures are objective. The question he leaves behind is: how does this objectivity relate to the subjectivity of cognition?

This question leads directly to Husserl’s phenomenology—and it leads back to Hegel, whose logic attempts precisely this mediation: not static “subsisting,” but the living self-unfolding of the concept.

  1. Bolzano, Wissenschaftslehre (1837), Vol. 1, § 19. ↩︎

  2. Bolzano, Wissenschaftslehre (1837), Vol. 1, § 25. ↩︎

  3. Bolzano, Wissenschaftslehre (1837), Vol. 1, § 19, note. ↩︎

  4. Cf. Künne, Wolfgang, “Bernard Bolzano,” in: Stanford Encyclopedia of Philosophy (2022). The fact that Lotze and Frege do not cite Bolzano is broadly documented in the scholarship. On the history of reception, see also Simons, Peter, Philosophy and Logic in Central Europe from Bolzano to Tarski (1992). ↩︎

  5. Cf. Beyer, Von Bolzano zu Husserl (1996), on the “Bolzano-Lotze thesis” regarding the priority of the concept of the proposition. Lotze criticizes Plato for not having “impressed upon himself” that propositions “must be the most essential components of the ideal world”—a criticism that Bolzano shares (Wissenschaftslehre, § 48). ↩︎

  6. Husserl, Articles sur la logique, ed. J. English, Paris 1975, p. 216: Lotze’s logic gave him the “clé” (the key) to understanding Bolzano’s conception. ↩︎