3.1 Bolzano’s understanding of the matter—Some classic views: Aquinas, Kant and Wittgenstein—Lewis’ criticism—Rapports between our cognition and the world: a question of justification—Rejection of an anthropocentric position—Varieties of intelligence. 3.2 The lack of a comprehensive perceptual apparatus or integration scheme in animals – Knowing and simple being acquainted with—Challenging the canonicity of the human intellect through an extended conception of knowledge: difference between knowledge proper and knowledge*—Sosa on metaphorical knowledge attributions—The manifold correspondences and truths that a multispecies perspective entails—Notion of agreement structure: parallels with Davidson’s “conceptual scheme”. 3.3 Correspondence and relativism—Kant on the “thing in itself”: its unknowability—Why correspondism is inconsistent: aspectual and full knowledge—Bolzano contra Kant—The shortcomings of transcendental schematism—Bolzano’s “propositions in themselves”: consequences of this view. 3.4 How a proposition in itself works—Our mental impressions include many more details than what is propositionally synthesized—The Aristotelian concepts of “substance”, “accident” and “form”: the circumstance of there existing accidents of accidents—Processes of differentiation—Phrasing and propositional instantiation—Helmholtz’s “unconscious inferences”—The primacy of the world over any subjectivism. 3.5 Bolzano’s “truths in themselves” and the performativity of our judgments—Knowledge as an acknowledgement of truth: the bedrock that resists all correspondences—Tragesser on Bolzano and Frege.