Home – Home – Jornals – Philosophy of Sciences 2025 number S5

The subject-matter of investigation is the nontrivial modal-logic problem of equivalence of de-dicto and de-re types of modalities. The target - explicating, exact formulating and adding the precisely formulated principle of equivalence of the modality-types as a new proper philosophy axiom scheme to the multimodal axiomatic system of formal philosophy Φ+∃. The scientific novelty : for realizing the target, the already published formal axiomatic theory Φ+∃ has been transformed into a qualitatively different logically formalized multimodal axiomatic system called Φ^DR due to manifest taking into an account and systematical dealing with the different modality types called de-dicto and de-re. For accomplishing the transformation, (1) definitions of the alphabets of artificial object-language and meta-language of Φ+∃ have been changed: new symbols Ω^D and Ω^R standing for perfection-modalities (belonging to the types D and R, respectively) have been included into the alphabet of metalanguage of Ф^DR; (2) in Φ^DR, one new axiom-scheme (containing the new symbols Ω^D and Ω^R) has been added to the set of axiom-schemes of Φ+∃; (3) by means of the artificial language of Φ^DR, a precise formulation of the principle of equivalence of the modality-types de-dicto and de-re is given, and the concrete epistemic condition, under which the equivalence principle is valid, is defined. For the first time, a nontrivial multimodal interpretation is given for the traditional formal logic square of opposition and hexagon. Also, for the first time, these geometric figures have been utilized for visual modeling a system of formal-axiological relations among qualitatively different de-re - perfection-modalities as evaluation-functions.