Abstract
Fragmentalism is the view that reality is not a metaphysically unified place, but fragmented in a certain sense, and constituted by incompatible facts across such fragments. It was introduced by Kit Fine in a discussion of tense realist theories of time (Modality and tense: philosophical papers. Oxford University Press, Oxford, pp 261–320, 2005). Here I discuss the conceptual foundations of fragmentalism, identify several open questions in Fine’s characterization of the view, and propose an understanding of fragmentalism that addresses these open questions.
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Notes
The statements of the principles in the informal idiom are Fine’s exact formulations; their translations into the official idiom are mine.
One might have thought that fragmentalism is simply the view that denies that if \({\Re }\) A and \({\Re }\) B, then \({\Re }\)(A, B), so that our overall conception of reality would take this form: \({\Re }\)(A, B, …), \({\Re }\)(A, ¬B, …), … We do not then need a separate notion of coherence. This is not Fine’s view, in fact, in a footnote, he suggests the opposite direction of reduction, that ‘given a primitive relation of coherence, one might take a fact to belong to reality when it is self-coherent’ (2005: 281 fn. 13).
When Fine first introduces fragmentalism, he writes that ‘reality will divide up into a number of different but possibly overlapping fragments’ (2005: 281). The mentioned possibility of overlap is however being allowed by Fine in relativistic cases only, which are ignored here.
Think of Quine’s (1960: 171) views that events are spatiotemporal regions; Lewis’ (1986) view that events are properties of spatiotemporal regions; Kim’s (1993) view that events are compounds <x, F, t> of an object x, property F, and time t; or Chisholm’s (1976: 126) view that events are states of affairs that are concretized at a place and time. For a tense realist critique of irreducible reference to events, see Prior (1968).
The semantics is intimately related to the ‘discussive logic’ of Jaśkowski (1948/1969)—with the important difference that Jaśkowski’s logic is paraconsistent, whereas the semantics below isn't. For interestingly related logics, see Rescher and Brandom (1980), Priest (2008) and, in particular, Restall (1997). For an interesting philosophical discussion of fragmentation, see Lewis (1982).
By M \({ \Vdash }\) Σ we mean that M \({ \Vdash }\) B for all B \(\in\) Σ.
To see why co-obtainment is associative, note that if we have A∘(B∘C) this means, by the truth in a model clause for co-obtainment that there is a point w where both A and B∘C are true, but by the v-clause for co-obtainment the latter is only true at w if both B and C are true at w. This means that all three, A, B and C are true at w, which means that A∘B must be true at w together with C, and hence that (A∘B)∘C is true in the model.
Consider a model where we have a point w 1 at which atomic sentences p and q are true but r isn't, and a point w 2 at which q and r are true but p isn't. In such a model, p∘q and q∘r are true, but p∘r isn't.
Consider a model where we have w 1 at which p is true and w 2 at which q is true. Here p and q are true, but p∘q isn't true, given that there is no point at which p and q are both true.
Consider a model where we have w 1 at which p is true and w 2 at which ¬p is true. At w 2 , ¬p∘¬p is true, and hence that this co-obtainment is true simpliciter in the model. But ¬p is not true in the model, given that p is true at w 1 . So this is a case where we have ¬p∘¬p but not ¬p.
If p∘A is true, then there is a point w at which p and A are true, but by the truth-in-a-model clause for atomic sentences, this suffices for p to be true in the model.
Indeed, given that negation is classical, we also have the principle of explosion (or ex falso quodlibet) A&¬A ⊨ B.
Thanks to an anonymous referee for pointing this out.
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Acknowledgments
Many thanks to Katherine Hawley and Aaron Cotnoir, to an anonymous referee of this journal, and to Bruno Jacinto and Sander Werkhoven for many helpful suggestions.
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Lipman, M.A. On Fine’s fragmentalism. Philos Stud 172, 3119–3133 (2015). https://doi.org/10.1007/s11098-015-0460-y
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DOI: https://doi.org/10.1007/s11098-015-0460-y