Joshua D. K. Brown

Are properties perfectly natural (or not) relative to worlds, or are they perfectly natural (or not) tout court? That is, could there be a property P that is instanti-ated at worlds w1 and w2, and is perfectly natural at w1 but not at w2? Here, we offer an original argument for the non-world-relativity of perfect naturalness. Along the way, we reply to a prima facie compelling argument for the contin-gency of perfect naturalness, based upon the connection between natural prop-erties and laws of nature.

It is widely assumed in philosophy that there is a tight connection between semantics and metaphysics. Semantic theories about the meanings of natural language terms and phrases are taken to provide evidence for and against various metaphysical theses about the nature of non-linguistic parts of the world. Call this view the widespread thesis. I argue that the widespread thesis is mistaken: semantic theories do not generally have robust metaphysical consequences. I contend that the best arguments for the widespread thesis turn on an interpretation of semantic theories according to which they are metaphysically illuminating: the metaphysical structure of the world is directly mirrored in the structure of the theory. Terms and existential quantification in the theory signal the existence of entities in the world, predicates signal the existence of properties, and the structures of set theoretic objects invoked by the theory directly correspond to structural features of the world. Such an interpretation is not the only one available, however, and it is a substantive philosophical (and linguistic) issue which interpretation is correct. Accordingly, I develop and defend an alternative interpretation of semantic theories according to which the structural features of these theories and of their theorems reflect biological and computational constraints on the architecture of the language faculty and historical contingencies in its evolutionary development. Supposedly metaphysically committing features of the theory—including the appearance of quantification and (ostensibly) referring terms—may thus be arepresentational artifacts of these constraints, rather than representational features that reflect metaphysical reality. To determine the metaphysical consequences of a semantic theory then, we must determine which of its features represent language-independent characteristics of the world and which are arepresentational consequences of the structure of the language faculty. To do this, however, we must have some prior idea what the language-independent world is like—that is, we must engage in prior metaphysical theorizing that is not beholden to the semantic theory itself.

Intuitively, vagueness involves some sort of indeterminacy: if Plato is a borderline case of baldness, then there is no fact of the matter about whether or not he’s bald—he’s neither bald nor not bald. The leading formal treatments of such indeterminacy—three valued logic, supervaluationism, etc.—either fail to validate the classical theorems, or require that various classically valid inference rules be restricted. Here we show how a fully classical, yet indeterminist account of vagueness can be given within natural semantics, an alternative semantics for classical proof theory. The key features of the account are: there is a single notion of truth—definite truth—and a single notion of validity; sentences can be true, false, or undetermined; all classical theorems and all classical inference rule are valid; the sorites argument is unsound; ‘definitely’ is treated as a meta-language predicate; higher-order vagueness is handled via semantic ascent.

Quine, taking the molecular constitution of matter as a paradigmatic example, offers an account of the relation between theory confirmation and ontology. Elsewhere, he deploys a similar ontological methodology to argue for the existence of mathematical objects. Penelope Maddy considers the atomic/molecular theory in more historical detail. She argues that the actual ontological practices of science display a positivistic demand for “direct observation,” and that fulfillment of this demand allows us to distinguish molecules and other physical objects from mathematical abstracta. However, the confirmation of the atomic/molecular theory and the development of scientists’ ontological attitudes towards atoms was more complicated and subtle than even Maddy supposes. The present paper argues that the history of the theory in fact supports neither Quine’s and Maddy’s accounts of scientific ontology. There was no general demand from scientists to “see” atoms before they were reckoned to be real; but neither did the indispensable appearance of atoms in the best theory of chemical combination suffice to convince scientists of their reality

This paper introduces a framework for thinking about ontological questions—in particular, the Special Composition Question—and shows how the framework might help support something like an account of restricted composition. The framework takes the form of an account of natural objects, in analogy with David Lewis’s account of natural properties. Objects, like properties, come in various metaphysical grades, from the fundamental, fully objective, perfectly natural objects to the nomologically otiose, maximally gerrymandered, perfectly non-natural objects. The perfectly natural objects, I argue, are the mereological simples, and (roughly) a collection composes an object of degree-n naturalness if and only if its members are arranged F-wise, for some property F that appears in the degree-n natural laws. Arbitrary composites turn out to be perfectly non-natural objects and are metaphysical bystanders. Ordinary composite objects fall in between. Some—e.g., atoms—are very (though not perfectly) natural; others—e.g., tables—are highly non-natural.