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A Semantic Framework for the Impure Logic of Ground
Ist Teil von
Journal of philosophical logic, 2024-04, Vol.53 (2), p.463-491
Ort / Verlag
Dordrecht: Springer Netherlands
Erscheinungsjahr
2024
Link zum Volltext
Quelle
SpringerLink
Beschreibungen/Notizen
There is a curious bifurcation in the literature on ground and its logic. On the one hand, there has been a great deal of work that presumes that logical complexity invariably yields grounding. So, for instance, it is widely presumed that any fact stated by a true conjunction is grounded in those stated by its conjuncts, that any fact stated by a true disjunction is grounded in that stated by any of its true disjuncts, and that any fact stated by a true double negation is grounded in that stated by the doubly-negated formula. This commitment is encapsulated in the system GG axiomatized and semantically characterized by [deRosset and Fine,
2023
] (following [Fine,
2012
]). On the other hand, there has been a great deal of important formal work on “flatter” theories of ground, yielding logics very different from GG [Correia,
2010
] [Fine,
2016
,
2017b
]. For instance, these theories identify the fact stated by a self-conjunction
(
ϕ
∧
ϕ
)
with that stated by its conjunct
ϕ
. Since, in these systems, no fact grounds itself, the “flatter” theories are inconsistent with the principles of GG. This bifurcation raises the question of whether there is a single notion of ground suited to fulfill the philosophical ambitions of grounding enthusiasts. There is, at present, no unified semantic framework employing a single conception of ground for simultaneously characterizing both GG and the “flatter” approaches. This paper fills this gap by specifying such a framework and demonstrating its adequacy.