Tibor Norbert Papp

Transcendental Logic (TL) offers a mathematisation of the unsayable background-reality (noumenal domain, N-domain) that underlies the logical models (phenomenal domain, P-domain). According to TL, the N-domain is unsayable not because it is unstructured or inaccessible, but because its structure is governed by the laws of orthomodular logic. In contrast, the P-domain represents reality as a structure of clearly distinct units of meaning; thus, its structure is governed by the laws of classical bivalent logic. This immediately raises two questions: on what basis does TL claim that the N-domain is governed by orthomodular logic, and into what kind of structure the N-domain is organised? The answer lies in TL’s philosophical roots – namely, in Béla Weissmahr’s transcendental metaphysics. His central logical method is dialectic, which governs both the structure of the N-domain and the N-P relation. The structure of the N-domain is analogia entis (the analogy of Being): a dynamic network of analogical-dialectical relations among beings. TL argues that Weissmahr’s dialectic can be expressed in orthomodularity (a dialectical pair is a pair of non-commuting elements), and thus formalises analogia entis as the structure of the N-domain. In Weissmahr’s spirit, TL argues that the dynamic-analogical relations among beings store the information later articulated in the P-domain as structured meaning. The act of this articulation is what TL calls univocalisation. Importantly, TL does not conceive of univocalisation as an act of cognition performed by a particular cogniser. Rather, TL understands univocalisation as the articulation capability of the relational structure itself – independent of any subject or agent. This article does not present the whole of TL, but only its philosophical and algebraic underpinnings. One of its central achievements is the distinction between two interpretations of analogia entis – a structural one and a respective one – and the exposition of their internal relation. In this context, respectivity refers to the algebraic formalisation of the relations among beings as determined by a particular respect. It provides the basis for both relational information storage and univocalisation. The corresponding theorems and proofs are presented in the Appendix. TL thus occupies a new position on the map of logical inquiry. It does not investigate the inferential or linguistic norms of valid reasoning, but rather how meaning is univocalised from the underlying N-domain – understood as analogia entis.