George Bealer’s Publications: Logic, Philosophy of Language, and Metaphysics

“An Inconsistency in Direct Reference Theory,” The Journal of Philosophy, vol. 111, 2004, pp. 574-93.

Direct reference theory faces serious prima facie counterexamples which must be explained away (e.g., that it is possible to know a priori that Hesperus = Phosphorus). This is done by means of various forms of pragmatic explanation. But when those explanations that provisionally succeed are generalized to deal with analogous prima facie counterexamples concerning the identity of propositions, a fatal dilemma results. Either identity must be treated as a four-place relation (contradicting what just about everyone, including direct reference theorists, takes to be essential to identity). Or direct reference theorists must incorporate a view that was rejected in pretty much our first lesson about identity—namely, that Hesperus at twilight is not identical to Hesperus at dawn. One way of the other, the direct reference theory is thus inconsistent with basic principles concerning the logic of identity, which nearly everyone, including direct reference theorists, take as starting points.

(with Uwe Mönnich.) “Property Theory,” Handbook of Philosophical Logic, vol. 4, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, 1989, pp. 133-251.

Revised and reprinted in Handbook of Philosophical Logic, vol. 10, Dov Gabbay and Frans Guenthner (eds.), Dordrecht: Kluwer, forthcoming.

Two sorts of property theory are distinguished, those dealing with intensional contexts property abstracts (infinitive and gerundive phrases) and proposition abstracts (‘that’-clauses) and those dealing with predication (or instantiation) relations. The first is deemed to be epistemologically more primary, for “the argument from intensional logic” is perhaps the best argument for the existence of properties. This argument is presented in the course of discussing generality, quantifying-in, learnability, referential semantics, nominalism, conceptualism, realism, type-freedom, the first-order/higher-order controversy, names, indexicals, descriptions, Mates’ puzzle, and the paradox of analysis. Two first-order intensional logics are then formulated. Finally, fixed-point type-free theories of predication are discussed, especially their relation to the question whether properties may be identified with propositional functions.

“In Defense of Universals,” Contemporary Debates in Metaphysics, John Hawthorne, Theodore Sider, and Dean Zimmerman (eds.), Oxford: Basil Blackwell, forthcoming.

“Logical Form,” Noûs, forthcoming.

“Propositions,” Mind, vol. 107, 1998, pp. 1-32.

Recent work in philosophy of language has raised significant problems for the traditional theory of propositions, engendering skepticism about its general workability. The problems fall into two groups. The first has to do with reductionism, specifically, attempts to reduce propositions to extensional entities — ordered sets, sequences, extensional functions, etc. The second group concerns problems of fine-grained content—both traditional puzzles (e.g., ‘Cicero’/‘Tully’ puzzles) and a cluster of new puzzles associated with scientific essentialism. After characterizing the problems, a nonreductionist approach — the algebraic approach –which avoids the problems associated with reductionism is outlined. The paper then describes how, by incorporating a distinction between descriptive and singular predication, the theory may use non-Platonic modes of presentation (e.g., socially constructed modes) to yield the sort of fine-grained distinctions needed to solve the puzzles of fine-grained content.

“Analyticity,” Routledge Encyclopedia of Philosophy, vol. 1, London: Routledge & Kegan Paul, 1998, pp. 234-9.

“Intensional Entities,” Routledge Encyclopedia of Philosophy, vol. 4, London: Routledge & Kegan Paul, 1998, pp. 803-7.

“Universals and Properties,” Contemporary Readings in the Foundations of Metaphysics, Stephen Laurence and Cynthia Macdonald (eds.), Oxford: Basil Blackwell, 1998, 131-147.

This paper summarizes and extends the transmodal argument for the existence of universals (developed in full detail in “Universals”). This argument establishes, not only the existence of universals, but also that they exist necessarily, thereby confirming the ante rem view against the post rem and in re views (and also anti-existentialism against existentialism). Once summarized, the argument is extended to refute the trope theory of properties and is also shown to succeed even if possibilism is assumed. A nonreductionist theory of universals and properties is then outlined, and it is sketched how to reap the benefits of possibilism and Meinongianism in an actualist setting.

“Toward a New Theory of Content,” Philosophy and Cognitive Sciences: Proceedings of the 16th International Wittgenstein Symposium, Roberto Casati, Barry Smith, and Graham White (eds.), Vienna: Hölder-Pichler-Tempsky, 1994, pp. 179-192.

A new approach to the theory of intentional content is characterized in this paper. After various puzzles and desiderata are set forth, it is shown that an algebraic semantics allows for fine-grained intensional distinctions based on differences in logical form, differences that, e.g., the propositional-function approach cannot capture. It also leads to a new analysis of the theory of predication implicit in Frege’s theory of senses. Taken together, these features create an opening in logical space for non-descriptive, non-metalinguistic intensional contents, which allow us to solve the indicated family of puzzles –including Kripke’s Pierre, negative existentials, Mates’s puzzle, and demonstrative puzzles.

“Property Theory: the Type-free Approach v. the Church Approach,” The Journal of Philosophical Logic, vol. 23, 1994, pp. 139-171.

In a lengthy review article, C. Anthony Anderson criticizes the approach to property theory developed in Quality and Concept (1982). That approach is first-order, type-free, and broadly Russellian. Anderson favors Alonzo Church’s higher-order, type-theoretic, broadly Fregean approach. His worries concern the way in which the theory of intensional entities is developed. It is shown that the worries can be handled within the approach developed in the book but they remain serious obstacles for the Church approach. The discussion focuses on: (1) the fine-grained/coarse-grained distinction, (2) proper names and definite descriptions, (3) the paradox of analysis and Mates’ puzzle, and (4) the logical, semantical, and intentional paradoxes.

“Universals,” The Journal of Philosophy, vol. 90, 1993, pp. 5-32.

Reprinted in Analytical Metaphysics: The Nature of Properties, Michael Tooley (ed.), New York: Garland, 1999, pp. 157-84.

Presented here is an argument for the existence of universals. Like Church’s translation-test argument, the argument turns on considerations from intensional logic. But whereas Church’s argument turns on the fine-grained informational content of intensional sentences, this argument turns on the distinctive logical features of ‘that’-clauses embedded within modal contexts. And unlike Church’s argument, this argument applies against truth-conditions nominalism and also against conceptualism and in re realism (the doctrine that universals are ontologically dependent upon the existence of instances). So if the argument is successful, it serves as a defense of full ante rem realism (the doctrine that universals exist independently of the existence of instances). The argument emphasizes the need for a unified treatment of intensional statements — modal statements as well as statements of assertion and belief. The larger philosophical moral will be that ante rem universals are uniquely suited to carry a certain kind of modal information. Linguistic entities, mind-dependent universals, and instance-dependent universals are incapable of serving that function.

“A Solution to Frege,” Revue Internationale du traitement automatique du language, Special Issue on Semantics After Montague, vol. 31, 1992, pp. 7-38.

Reprinted in Philosophical Perspectives, vol. 7, 1993, pp. 17-61.

This paper provides a new approach to a family of outstanding logical and semantical puzzles, the most famous being Frege’s puzzle. The three main reductionist theories of propositions (the possible-worlds theory, the propositional-function theory, the propositional-complex theory) are shown to be vulnerable to Benacerraf-style problems, difficulties involving modality, and other problems. The nonreductionist algebraic theory avoids these problems and allows us to identify the elusive nondescriptive, non-metalinguistic, necessary propositions responsible for the indicated family of puzzles. The algebraic approach is also used to defend antiexistentialism against existentialist prejudices. The paper closes with a suggestion about how this theory of content might enable us to give purely semantic (as opposed to pragmatic) solutions to the puzzles based on a novel formulation of the principle of compositionality.

“On the Identification of Properties and Propositional Functions,” Linguistics and Philosophy, vol. 12, 1989, pp. 1-14.

Arguments are given against the thesis that properties and propositional functions are identical. The first shows that the familiar extensional treatment of propositional functions — that, for all x, if f(x) = g(x), then f = g — must be abandoned. Second, given the usual assumptions of propositional-function semantics, various propositional functions (e.g., constant functions) are shown not to be properties. Third, novel examples are given to show that, if properties were identified with propositional functions, crucial fine-grained intensional distinctions would be lost.

“Fine-Grained Type-Free Intensionality,” Properties, Types and Meaning, Genarro Chierchia, Barbara H. Partee, Raymond Turner (eds.), Dordrecht: Kluwer, 1989, pp. 177-230.

Commonplace syntactic constructions seem to generate ontological commitments to numerous metaphysical categories (events, states of affairs, properties, pluralities, etc.). But to be seriously justified, such ontologies must satisfy a higher standard — they must be essential to an acceptable comprehensive theory. Fine-grained type-free intensional entities are so justified, for they constitute the minimal framework needed for a comprehensive theory that is not epistemically self-defeating. In the course of defending this thesis, the paper provides a general characterization of intensionality, a catalogue of six types of type-freedom, a survey of various degrees of fine-grainedness, etc.

“Completeness in the Theory of Properties, Relations, and Propositions,” The Journal of Symbolic Logic, vol. 48, 1983, pp. 415-26.

Higher-order theories of properties, relations, and propositions (PRPs) are known to be essentially incomplete relative to their standard notions of validity. It turns out that the first-order theory of PRPs that results when first-order logic is supplemented with a generalized intensional abstraction operation is complete. The construction involves the development of an intensional algebraic semantic method that does not appeal to possible worlds, but rather takes PRPs as primitive entities. This allows for a satisfactory treatment of both the modalities and the propositional attitudes, and it suggests a general strategy for developing a comprehensive treatment of intensional logic.

“Remarks on Classical Analysis,” The Journal of Philosophy, vol. 80, 1983, pp. 711-12.

“Foundations Without Sets,” American Philosophical Quarterly, vol. 18, 1981, pp. 347-54.

The dominant school of logic, semantics, and the foundation of mathematics construct its theories within the framework of set theory. There are three strategies by means of which a member of this school might attempt to justify his ontology of sets. One strategy is to show that sets are already included in the naturalistic part of our everyday ontology. If they are, then one may assume that whatever justifies the everyday ontology justifies the ontology of sets. Another strategy is to show that set theory is already part of logic. In this case, the ontology of sets would be justified in the sam way logic is justified. The third strategy is to show that set theory plays some unique role in theoretical work. If it does, then its ontology would be justified pragmatically. In this paper it is shown that none of these strategies is successful. One properly constructs foundations, not within set theory. bit within an intensional logic that takes properties, relations, propositions as basic.

“Theories of PRP,” The Journal of Philosophy, vol. 76, 1979, pp. 634-48.

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula.

“Predication and Matter,” Synthese, vol. 31, 1975, pp. 493-508.

Reprinted in Mass Terms, F. Jeffrey Pelletier (ed.), Dordrecht: D. Reidel, 1979.

First, given criteria for identifying universals and particulars, it is shown that stuffs appear to qualify as neither. Second, the standard solutions to the logico-linguistic problem of mass terms are examined and evidence is presented in favor of the view that mass terms are straightforward singular terms and, relatedly, that stuffs indeed belong to a metaphysical category distinct from the categories of universal and particular. Finally, a new theory of the copula is offered: ‘The cue is cold’, ‘The cube is ice’, and ‘Ice is water’ all have the form ‘A is B’. On the basis of the logical behavior of stuff-names with respect to this univocal copula, definitions are suggested for ‘X is a stuff’, ‘X composes Y’, ‘X is a material object’, and even ‘Matter’. Hence an expanded form of logicism.