Talk: Jan Wolenski (Krakow)
Generalized Logical Square of Modalities and Its Philosophical Applications
Modalities play import ant role in many philosophical investigations and debates. So-called alethic modalitie, that is, necessity, possibility, impossibility, accidentality are the paradigm of the modal-variety. The qualification “alethic” refers to truth. Thus, we have necessary truth, etc. However, we have also epistemic, deontic, ontological, causal, doxastic, etc. modalities; always truth as such can be considered as a modality. Is there a common logic valid for all modalities? Logical square for modalities, introduced by Aristotle, plays this role. Such rules as necessity implies possibility or necessity excludes impossibility hold for all kinds of modalities (the concept of truth simpliciter leads to some problems). The square can be extended to other diagrams, in particular, hexagon and octagon. Take alethic modalities as an example. Necessary truth (A is necessary) implies truth simpliciter (A is true), the latter entails possible truth (A is possible). Now, there is a problem whether truth implies its necessity (the Leibniz question). If we take “A is true” it entails A, but the reverse dependence is somehow problematic. Obligation (A is obligatory) does not entail actuality (A obtains) and reversely. According to the classical definition of knowledge “x knows that A” implies “A is true”, but this dependence is dubious, due to the Gettier problem.
Hume argued that is does not entail ought. One can state a generalized Hume’s thesis and argue that no deontic modality entails actuality and reversely. The question is whether the Hume thesis can be generalized to other modalities. The answer that epistemic and doxastic modalities behave similarly as deontic ones is plausible. If we analyse ontological modalities, some interesting conclusions arise, for instance, concerning determinism. Consider “F (a fact) is determined” as a counterpart of necessity. Determinism is defined as saying that everything is determined, but it must be understood as the thesis that everything is necessary or impossible. Moreover, it is so-called radical determinism. Moderate determinism says that something is determined and something is not (accidental). Radical indeterminism – that everything is not determined, moderate indeterminism – that something is determined and something is not. A surprising conclusion is that there is no logical difference between moderate determinism and moderate indeterminism.