Limits of Abductivism About Logic

Abstract

I argue against abductivism about logic, which is the view that rational theory choice in logic happens by abduction. Abduction cannot serve as a neutral arbiter in many foundational disputes in logic. For we must identify the relevant data in order to use abduction. Which data one deems relevant depends on what I call one's conception of logic. One's conception of logic is, however, not independent of one's views regarding many of the foundational disputes that one may hope to solve by abductivism.

The Laws of Thought and the Laws of Truth as Two Sides of One Coin

“…Definition 2 (Fusion) The fusion of a set of states T = {t 1 , t 2 , t 3 , ...}, written t 1 t 2 t 3 ... or T , is the least upper bound of T with respect to [8,646]. 6 4 See my [10] for more details on what I mean by an account of what consequence is, and how it interacts with technical work in logic. 5 I do not foresee any particular problems with the extension of my results to first-order logic.…”

“…This formulation differs from Fine's in the quantification over further states u. In the presence of Downward-Closure, the two formulations are equivalent 10. Stipulating these constraints for atomic sentences suffices (given the semantic clauses) to enforce them for the whole language.…”

Logical anti‐exceptionalism meets the “logic‐as‐models” approach

“…Now, that is precisely where troubles begin. We shall not deal with difficulties in explaining what are the facts of logic (that was already done in Hjortland, 2019; Hlobil, 2020); rather, we shall concentrate on the most basic assumption that there are such facts. The trouble seems to be that although we have a fairly clear picture of what validity means inside a logical system, the same is not true of facts about validity; explaining what the logical facts are like without using the resources of some particular logical theorising is not an easy task.…”

Should the Non‐Classical Logician be Embarrassed?*

“…10), (Williamson, 2017), and (Hjortland, 2017) for several refinements of the idea. An argument against the view that rational theory choice in logic happens by abduction can be found in (Hlobil, 2020).…”