The Facts in Logical Space

In this wide-ranging and ambitious work, Jason Turner explores and articulates more axiomatico the Tractarian view that the world is the totality of facts, not of things. The core of the project involves two stages. In the first, the author develops a metaphysical picture that rests on four main assumptions: ultimately facts are all there is; they are the correlates of atomic predications; they are structureless; and they are arranged like points in a quasi-geometric logical space. In the second stage, the author carries out the task of showing how ordinary truths about things and qualities can be reduced to fundamental truths about facts. Turner argues that, subject to caveats, the resulting theory appears to have a number of important virtues, most notably it is able to deliver a one-category ontology, and it enables a reductive analysis of metaphysical modality (more on this soon).The author carries out the first stage of the project by developing a Tractarian geometry, an axiomatic theory formulated in a plural language quantifying only over atomic facts. The nonlogical ideology of the theory includes two geometric primitives (a tetradic parallelism relation and a dyadic similarity relation), as well as a truth predicate. In a model of Tractarian geometry, the domain of facts is partitioned into quality spaces, which serve as proxies for ordinary qualities. Ordinary objects are represented by hypersurfaces, special collections of pairwise similar facts. A central result proven in the book is the Predicational Determination Theorem (102), which states that a Tractarian geometry is able to individuate every fact in terms of the quality space and hypersurfaces the fact belongs to.Equipped with hypersurfaces and quality spaces, which are proxies for ordinary objects and qualities, respectively, Turner turns to the second stage of the project: reducing ordinary truths to factalist truths. Two methods are developed of carrying out such a reduction. One method is syntactic, and consists of paraphrasing ordinary first-order sentences into sentences of the factalist language. For instance, the ordinary sentence “All humans are mortal” will be paraphrased as “Every hypersurface which picks out a true fact in the human quality space, picks out a true fact in the mortal quality space.” The second method is model-theoretic: Tractarian geometric models can be associated one-to-one with object-and-quality models, in such a way that an ordinary sentence is true in a Tractarian geometric model if and only if it is true in the associated object-and-quality model. Turner proves a key result, the Core Equivalence (179), which states that the two reductive strategies are equivalent: an ordinary sentence “p” is true in an object-and-quality model associated with a Tractarian geometry G if and only if the paraphrase of “p” is true in G.The author deploys Tractarian factalism in order to provide truth conditions for ordinary modal statements by identifying collections of facts with possible worlds. I will focus on reductive accounts, since an alleged virtue of factalism is precisely its ability to do away with primitive modality. The reductionist's main task is to explain away necessary connections between distinct atomic facts: there is no possible collection of facts that includes Socrates's being a human but not Socrates's being a mammal. Two strategies are discussed on behalf of the modal reductionist. One strategy appeals to the neoconventionalism developed in Sider 2012, which regards a truth as necessary just in case it appears in a conventionally agreed upon list L of truths. Accordingly, a collection of facts is a possible world just in case it contains all of the facts picked out by the factalist paraphrase of L. The other strategy implements a two-staged reduction of ordinary modal talk to factalist amodal talk. In the first stage, ordinary object-and-quality language is paraphrased into a sparse object-and-quality language, wherein any two atomic sentences are modally independent. In the second stage, the sparse object-and-quality language is paraphrased into factalist language. Since the atomic predications are modally independent, so are the facts they pick out. The factalist can then regard any collection of facts as representing a possible world.If either strategy is viable, the Tractarian factalist will succeed in eliminating primitive modality. But although that claim is unobjectionable, I believe that the truth of factalism is orthogonal to the viability of a reductionist project along the lines of neoconventionalism or the two-stage paraphrase strategy. Let's consider them in turn. The paraphrastic strategy calls firstly for a suitable reduction of ordinary talk to sparse object-and-quality talk. If the task is viable, possible worlds can be identified with collections of atomic sentences in the sparse object-and-quality language. When it comes to eliminating primitive modality, all the action takes place at the first stage of the strategy, where factalism plays no role.Similar considerations apply to neoconventionalism. For once we have our list establishing which truths are the necessary ones, the reductive job is over. Since the list can be written down in an object-and-quality language, once again factalism plays no role in the viability of the reductive project. As in the previous case, even if the Tractarian factalist was able to analyze away modality, that would not be the case thanks to factalism.The book tests Tractarian factalism against another contemporary debate in the metaphysics of modality, namely, the one between necessitism, the thesis that necessarily everything necessarily exists, and its denial, contingentism. Turner argues that the truth of factalism cuts across that debate, and that either view can be successfully modeled within a Tractarian geometry, essentially by reproducing the distinction between constant and variable domain Kripke frames. Nevertheless, I suspect that the contingentist is likely to be unsatisfied with the factalist's construal of his or her preferred thesis, for even though my merely possible sister ultimately does not exist (since she is not a fact), all merely possibly true facts about her do exist. The factalist may rejoin that the problem is an unintended consequence of the official formulation of the theory. For the way in which a Tractarian geometry has been defined is supersubstantivalist: facts are identical with the points they occupy in logical space; and a fact may or may not be true. Factalism, however, can be formulated in alternative ways. On a substantivalist construal, facts are not identical with points in logical space; and a point may or may not be occupied by a fact. On a relationalist construal, there are only facts and no points; and only those facts exist which are true on the supersubstantivalist account. Either approach avoids the profligate ontology of untrue facts that the official supersubstantivalist formulation forced on us, and in particular does not entail the actual existence of any fact involving my merely possible sister. The new formulations, however, come at a price. Substantivalism countenances two basic kinds of entities, facts and points, and thus fails to provide a one-category ontology, supposedly one of the principal virtues of factalism. Relationalism, on the other hand, is too sparse to validate the axioms of Tractarian geometry, and thus to provide a reduction of ordinary object-and-quality language to factalist language. As Turner discusses, we can formulate a relationalist Tractarian geometry by adding a primitive modal operator to the fundamental language, thus reproducing the desired geometric patterns as merely possible, rather than actual. Unfortunately, since the relationalist factalist language is modal, it cannot provide a reductive analysis of metaphysical modality, another supposed virtue of Tractarian factalism.In the end, should we be factalists? The most compelling evidence in favor of factalism, I believe, might be scientific in character. Shamik Dasgupta (2009) has convincingly argued that individual things do not play any role in our best scientific theories, and that we should therefore wield Ockham's razor and embrace ontological nihilism, the view that ultimately nothing exists. How are ontological nihilists going to regiment their scientific theories? Dasgupta's preferred option is Quine's predicate functor logic, wherein quantifiers and individual variables are eliminated, in such a way that a statement like “there is a table” will be paraphrased as “it is tabling.” However, Turner (2011) has cast doubt on the consensus that predicate functor logic is ontologically innocent. Here is where factalism comes to the rescue: the nihilist can regiment her theories in a sentential language, wherein each sentential constant stands for an atomic fact; singular quantification over facts is dispensed with in favor of infinitary truth-functional compounds of atomic sentences; and, crucially, ordinary talk of things and qualities can be paraphrased away by supposing that the atomic sentences define a Tractarian geometry. In the nihilistic factalist language, the geometric constants (tetradic parallelism, similarity) and identity will have to be sentential operators. Is this project viable? Turner considers it and ultimately rejects it, since the axioms of Tractarian geometry require plural quantification over facts, as well as the plural logical constants “is/are among the”—and it is not clear that such ideology is expressible in the nihilistic sentential language (325). But all is not lost, or so it seems to me. The expressions that, according to Turner, the nihilist may be unable to express are of the form “All the Φ are such that . . . p is among the Φ,” or “For all the Φ there are some Ψ such that . . . the Φ are among the Ψ” (where “p” is a sentential constant, and “Φ,” “Ψ” are plural sentential variables). As far as I can see, the nihilistically objectionable ideology in the above sentences is eliminable in terms of infinitary truth-functional compounds and identity statements.1 Whether the resulting nihilistic factalist framework matches the elegance and explanatory power of standard factalism remains to be seen. Be that as it may, if our best scientific theories give us reasons to believe that we do not live in an object-and-quality world, chances are that factalism will play a crucial role in fleshing out the relevant nihilistic metaphysics. Indeed, this might well be the most surprising and interesting virtue of factalism.We live in an age in which natural sciences, and especially theoretical physics, enjoy the privilege of supplying us with radically new perspectives on reality. This book is a significant exception to the status quo. The idea that the world is ultimately a geometry of facts is wildly original, and developing it axiomatically, leaving no stone unturned, is nothing short of outstanding. This book is a must-read for anyone interested in the metaphysics of facts, in fundamentality and grounding, in the metaphysics of modality, in ontology, and in the intersection of logic and metaphysics

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• Individuals

  Open Access•Shamik Dasgupta•Philosophical Studies•2009

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• Writing the Book of the World

  Theodore Sider•Writing the book of the world•2011

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