One Heresy and One Orthodoxy: On Dialetheism, Dimathematism, and the Non-normativity of Logic

Abstract

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

A note on negation inconsistent variants of FDE-negation

“…The value of taking (non-trivial) negation inconsistent logics seriously is vigorously defended by Wansing [21], who also endorses [22] an informational view of logical values (e.g. t interpreted as signifying the support of truth (only) rather than truth (only)) inspired by the reading of the values in FDE by N. Belnap [9,10], and through which (non-trivial) negation inconsistent systems can be seen to support the logico-informational view which he calls dimathematism.…”

Paraconsistency, Evidence and Semantic Incompleteness

“…They only show that the evidence interpretation of LET J is problematic, but nothing prevents that this logic can be interpreted epistemologically in terms of other notions. According to Wansing (2022), logic can be seen as the study of 22 Blasio (2017) provides a nice epistemological interpretation for FDE, where each truth-value of FDE may be interpreted in terms of propositional attitudes of acceptance, rejection, non-acceptance and non-rejection. 23 The non-deterministic character of D'Agostino's proposal is justified in the following passage: "In general, when we are faced with a conjunction A∧B in which A and B are indeterminate, the value of the conjunction may be either informational falsity 0, or informational indeterminacy ⊥, depending on whether or not we hold the additional information that A and B cannot be simultaneously true."…”

Quasi-truth and defective knowledge in science: a critical examination

“…Things become even more difficult in cases where not only the empirical theory is inconsistent, but the underlying logic itself already derives contradictions, while being non-trivial. One can check a discussion of some of such logics in[27,28]. Given that our focus in this paper is on empirical science, we shall not enter in the details of such more radical cases.Manuscrito-Rev.…”