Nathaniel Gan

Fictionalists about a kind of disputed entity aim to give a face-value interpretation of our discourse about those entities without affirming their existence. The fictionalist’s commitment to non-realism leaves open three options regarding their ontological position: they may deny the existence of the disputed entities (anti-realism), remain agnostic regarding their existence (agnosticism), or deny that there are ontological facts of the matter (ontological anti-realism). This paper outlines a method of adjudicating between these options and argues that fictionalists may be expected to hold preferences between them. The typical arguments and motivations for fictionalism lead naturally to a practice-based metaontological framework under which our practices regarding a kind of disputed entity might inform our ontological beliefs about those entities. When that framework is applied to fictionalism, it is found that the usual motivations for fictionalism lead naturally, though not decisively, to ontological anti-realism. And, where there are reasons against ontological anti-realism, fictionalism leans more toward anti-realism than agnosticism.

According to the Quine-Putnam indispensability argument (QPIA), we should be realists about mathematics because mathematics is indispensable to science. QPIA’s reasoning can be understood in two ways. Under the confirmational analysis, QPIA argues that mathematics is confirmed as part of our best scientific theories. Under the pragmatic analysis, QPIA argues that our scientific practices implicitly assume the truth of mathematics. The usual reasons given in favour of the pragmatic analysis are that it affords advantages to proponents of QPIA by avoiding some dependencies of the confirmational analysis. This paper argues that these reasons are indecisive, because the pragmatic analysis introduces some dependencies of its own. Nevertheless, the paper also argues, there are other reasons to prefer the pragmatic analysis. QPIA is an instance of a wider class of realist arguments—indispensability arguments—and the pragmatic analysis yields a preferable overall understanding of indispensability arguments than does the confirmational analysis.

Call the epistemological grounds on which we rationally should determine our ontological (or alethiological) commitments regarding an entity its arbiter of existence (or arbiter of truth). It is commonly thought that arbiters of existence and truth can be provided by our practices. This paper argues that such views have several implications: (1) the relation of arbiters to our metaphysical commitments consists in indispensability, (2) realist views about a kind of entity should take the kinds of practices providing that entity’s arbiters to align with respect to their metaphysical dependencies, (3) if realists take a kind of practice to provide grounds on which to affirm the existence of a kind of entity, they should turn to those same grounds when seeking to provide an epistemology of the relevant domain.

This paper examines ten possible topological interpretations of connection and for each interpretation, identifies sufficient conditions under which a significant class of topological spaces provides models of General Extensional Mereotopology with Closure Conditions (GEMTC) in which some key mereotopological ideas align with their topological analogues. In particular, there is an interpretation under which the non-empty sets of any symmetric topology are a model of GEMTC with alignment between the mereotopological and topological definitions of (self-)connection, open and closed entities, interior, exterior, closure, and boundary.

Fictionalism about a kind of disputed object is often motivated by the fact that the view interprets discourse about those objects literally without an ontological commitment to them. This paper argues that this motivation is inadequate because some viable alternatives to fictionalism have similar attractions. Meinongianism—the view that there are true statements about non-existent objects—is one such view. Meinongianism bears significant similarity to fictionalism, so intuitive doubts about its viability are difficult to sustain for fictionalists. Moreover, Meinongianism avoids some of fictionalism’s weaknesses, thus it is even preferable to fictionalism in some respects.

There are two ways of approaching an ontological debate: ontological realism recommends that metaphysicians seek to discover deep ontological facts of the matter, while ontological anti-realism denies that there are such facts; both views sometimes run into difficulties. This paper suggests an approach to ontology that begins with conceptual analysis and takes the results of that analysis as a guide for which metaontological view to hold. It is argued that in some cases, the functions for which we employ a part of our conceptual scheme might give us reasons to posit ontological facts regarding certain objects. The proposed approach recommends ontological realism about an object just in case our conceptual scheme gives us reason to. This yields a mixed overall metaontological view that adopts ontological realism to some issues and ontological anti-realism to others, and that avoids the difficulties that typically arise for the two views.

This paper examines several intended topological features of the Region Connection Calculus (RCC) and argues that they are either underdetermined by the formal theory or given by the complement axiom. Conditions are identified under which the axioms of RCC are satisfied in topological models under various set restrictions. The results generalise previous results in the literature to non-strict topological models and across possible interpretations of connection. It is shown that the intended interpretation of connection and the alignment of self-connection with topological connection are underdetermined by the axioms of RCC, which suggests that additional axioms are necessary to secure these features. It is also argued that the complement axiom gives RCC models much of their topological structure. In particular, the incompatibility of RCC with interiors is argued to be given by the complement axiom.

In ontological debates, realists typically argue for their view via one of two approaches. The _Quinean approach_ employs naturalistic arguments that say our scientific practices give us reason to affirm the existence of a kind of entity. The _Fregean approach_ employs linguistic arguments that say we should affirm the existence of a kind of entity because our discourse contains reference to those entities. These two approaches are often seen as distinct, with _indispensability arguments_ typically associated with the former, but not the latter, approach. This paper argues for a connection between the two approaches on the grounds that the typical arguments of the Fregean approach can be reformulated as indispensability arguments. This connection is significant in at least two ways. First, it implies that indispensability arguments provide a common framework within which to compare the Quinean and Fregean approaches, which allows for a more precise delineation of the two approaches. Second, it implies the possibility of analogical relations that allow proponents and opponents of each approach to draw upon the ideas that have been developed regarding the other.