## Facts in Logical Space: A Tractarian Ontology

JASON TURNER Oxford: Oxford University Press, 2016; 362 pp.; $85.00 (hardcover)

Appearances to the contrary, the world consists ultimately of facts, not of things. Familiar objects and properties of experience are mere abstractions from this single ontological category. So says Factualism. Jason Turner's defence of a version of this t hesis is precise, exhaustive, and persuasive. Those working on facts will find much of interest, as will those working at the intersection of formal logic and metaphysics. In Chapter 1, Turner introduces and motivates his version of Factualism (roughly): fundamental reality consists of facts arranged in logical space (11). An obvious challenge for theories such as Factualism that claim there are ultimately neither objects nor properties is reconciling this with the pervasive appearances of objects and properties in ordinary life. Turner holds that facts provide the grounds for ordinary appearances, such as 'Harry is bald' or 'Harry met Sally,' but notes that this leads to fur ther challenges: the appearance 'Harry met Sally' and the appearance 'Harry is bald' both intuitively involve Harry , but Harry is no fact. Explaining exactly how facts ground, or give rise to, such patterned appearances of objects and properties is a principal part of Turner's project (23, 48). Turner's explanation relies on facts standing in external relations to other facts in 'logical space' (14, 61). Stated simply, we label facts via linguistic practices, and our labelling is sensitive to the structure of logical space. Moreover, while external relations among facts are not themselves facts, they are also not part of the Factualist ontology; rather, they are ideological commitments (22). Turner spends the next two chapters filling in the details of this explanation. In Chapter 2, Turner adds formal precision to the preceding by providing an axiomatization of external relations among facts, treating facts as points that may be connected to other points. From collections of connected points, sub-spaces of logical space are defined, e.g., Quality Spaces corresponding to appearances of properties or relations (80), and Hypersurfaces corresponding to appearances of objects (94). Turner's axiomatization is intended to provide a foundation on which to tell grounding stories. Note, Turner includes an appendix to this chapter (109) devoted to relevant formal proofs. Each subsequent chapter is similarly accompanied by a proof appendix. In Chapter 3, Turner examines several grounding stories that relate the preceding axiomatization to a language of appearances, i.e., relating facts to appearances. One approach is holistic, matching complete descriptions of appearances with complete descriptions of facts. The other two are piecemeal, matching individual appearances with individual facts. Turner proves a representation theorem holding between his axiomatization of facts and structures of objects and relations (137), and ultimately shows the holistic and piecemeal stories align (178). Factualism fits naturally with combinatorial accounts of modality (19), and Chapter 4 is largely concerned with overcoming two standard objections to Factualism with Combinatorialism. Namely, the result: (i) entails Necessitism, i.e., for all x necessarily x exists, and (ii) is susceptible to the colour- exclusion problem, e.g., facts provide no way to account for the impossibility of something being both red and green all over. Concerning (i), Turner attempts to mitigate worries associated with Necessitism (223). Concerning (ii), Turner advocates either adopting Sarah Moss's solution to the colour -exclusion 1 problem or accepting primitive entailments among facts. Chapter 5 examines how names for appearances are labelled without reliance on functions, which are not facts. In effect, Turner shows how Factualism can make sense of whatever story semanticists provide for how words attach to facts (288). In Chapter 6, Turner canvasses alternative versions of Factualism thus far defended, and explores how the resources of Factualism might supplement grounding stories for metaphysical views