On the Logic of Factual Equivalence

Abstract

Abstract. Say that two sentences are factually equivalent when they describe the same facts or situations, understood as worldly items, i.e. as bits of reality rather than as representations of reality. The notion of factual equivalence is certainly of central interest to philosophical semantics, but it plays a role in a much wider range of philosophical areas. What is the logic of factual equivalence? This paper attempts to give a partial answer to this question, by providing an answer the following, more specific question: Given a standard propositional language with negation, conjunction and disjunction as primitive operators, which sentences of the language should be taken to be factually equivalent by virtue of their logical form? The system for factual equivalence advocated in this paper is a proper fragment of the first-degree system for the logic of analytic equivalence put forward in the late seventies by R. B. Angell. I provide the system with two semantics, both formulated in terms of the notion of a situation's being fittingly described by a linguistic item. In the final part of the paper I argue, contra a view I defended in my " Grounding and Truth-Functions" (2010), that the logic for factual equivalence I advocate here should be preferred to Angell's logic if one wishes to follow the general conception of the relationships between factual equivalence and the notion of grounding put forward in the 2010 paper.

To Be F Is To Be G

“…The replacement of Idempotence with its negation (at least in complex types) is perhaps the most distinctive hallmark of the particular kind of “fine‐grained” theory we are developing. It distinguishes it, for example, from Jeremy Goodman's theory of aboutness (mentioned in note 40), and from the theories of “worldly factual equivalence” developed by Correia (, ), all of which endorse Idempotence . I admit that this feature is quite surprising: especially given that we are endorsing Involution , you might have expected other especially “trifling” equivalences in propositional logic to correspond to true identifications.…”

Real Definitions

“…Factual Identity is an account I propose in Correia , while both Factual Representational Grounding and Factual Comparative Joint‐Carvingness are new. Factual Identity can be formulated in Fine's truth‐maker framework (just replace ‘fittingly describe’ by ‘are exactly verified by’), but none of the other accounts can: as I previously stressed, the idea that different statements can be verified more or less perspicuously by a state makes no sense.…”

“…Fine () proposes this very account for R. B. Angell's notion of analytic equivalence, assuming certain specific conditions on contents. The conditions on contents that I impose in Correia are weaker.…”

“…The fitting description framework does not require that all statements have non‐empty contents (the requirement is not in place in Correia ), but it is reasonable to assume that the statements which play the role of definiens or definiendum in real definitions do have non‐empty contents.…”

Grounding, Essence, and Identity

“…Our take on generalized identity builds on—yet in certain key respects deviates from—frameworks put forward by Correia (; ), Rayo (), and Dorr (). Space limitations preclude a full development and comparison, so we concentrate only on those elements of the resulting theory most relevant for later purposes.…”