Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. Synthese Library, vol 373. Springer (2015)
This volume covers a wide range of topics that fall under the 'philosophy of quantifiers', a philosophy that spans across multiple areas such as logic, metaphysics, epistemology, and even the history of philosophy. It discusses the import of quantifier variance in the model theory of mathematics. It advances an argument for the uniqueness of quantifier meaning in terms of Evert Beth’s notion of implicit definition, and clarifies the oldest explicit formulation of quantifier variance: the one proposed by Rudolf Carnap.
The volume further examines what it means that a quantifier can have multiple meanings, and addresses how existential vagueness can induce vagueness in our modal notions. Finally, the book explores the role played by quantifiers with respect to various kinds of semantic paradoxes, the logicality issue, ontological commitment, and the behavior of quantifiers in intensional contexts.
Selected articles & book chapters
Structural Indeterminacy. Philosophy and Phenomenological Research (2019), DOI 10.1111/phpr.12588
Abstract. The threat of ontological deflationism (the view that disagreement about what there is can be non-substantive) is averted by appealing to realism about fundamental structure—or so tells us Ted Sider. In this paper, the notion of structural indeterminacy is introduced as a particular case of metaphysical indeterminacy; then it is argued that structural indeterminacy is not only compatible with a metaphysics of fundamental structure, but it can even safeguard it from a crucial objection; finally, it is shown that, if there are instances of structural indeterminacy, a hitherto unacknowledged variety of ontological deflationism will arise. Unless structure is shown to be determinate, ontological deflationism remains a live option. Furthermore, I will consider whether structural indeterminacy could be challenged by adopting a naturalistic epistemology of structure; the question is answered in the negative on the basis of a formal result concerning theory choice. Finally, I submit a new way of articulating the epistemology of structure, which hinges on the very possibility of structural indeterminacy.
Ideology in a Desert Landscape. Philosophical Issues, Vol. 27, No. 1 (2017), pp. 383-406.
Abstract. On one influential view, fundamentality can be understood in terms of the notion of a joint-carving term. Ted Sider has recently argued that (i) some first order quantifier is joint-carving, and (ii) modal notions are not joint-carving. I will defend a logical result due to Arnold Koslow which implies that (i) and (ii) are incompatible. I will therefore consider an alternative understanding of Sider’s metaphysics to the effect that (i) some first order quantifier is joint-carving, and (iii) intensional notions are not joint-carving. Another result due to Koslow entails that (i) and (iii) are also incompatible. I will argue that this second result is inconclusive. Nevertheless, (iii) is incompatible with another tenet of Sider’s metaphysics, namely that (iv) ‘being joint-carving’ is itself joint-carving. In order to resolve the tension, I will tentatively argue that condition (iv) should be renounced.
Quantum Metaphysical Indeterminacy and Worldly Incompleteness. Synthese (2017), DOI 10.1007/s11229-017-1581-y
Abstract. An influential theory has it that metaphysical indeterminacy occurs just when reality can be made completely precise in multiple ways. That characterization is formulated by employing the modal apparatus of ersatz possible worlds. As quantum physics taught us, reality cannot be made completely precise. I meet the challenge by providing an alternative theory which preserves the use of ersatz worlds but rejects the precisificational view of metaphysical indeterminacy. The upshot of the proposed theory is that it is metaphysically indeterminate whether p just in case it is neither true nor false that p, and no terms in ‘p’ are semantically defective. In other words, metaphysical indeterminacy arises when the world cannot be adequately described by a complete set of sentences defined in a semantically nondefective language. Moreover, the present theory provides a reductive analysis of metaphysical indeterminacy, unlike its influential predecessor. Finally, I argue that any adequate logic of a language with an indeterminate subject matter is neither compositional nor bivalent.
Vague Existence. In Bennett, K. and Zimmerman, D. (eds.) Oxford Studies in Metaphysics, vol. 10, Oxford University Press (2017), pp. 201-33.
Runner-up in the 2012 Oxford Studies in Metaphysics Younger Scholars Prize competition
Abstract. Ted Sider has famously argued that existence, in the unrestricted sense of ontology, cannot be vague, as long as vagueness is modeled by means of precisifications. The first section exposes some controversial assumptions underlying Ted Sider's alleged reductio of vague existence. In particular, although it has been shown that existence cannot be definitely vague, it has not been shown that existence cannot be vaguely vague. The upshot will be that, although existence cannot be vague simpliciter, it can be super-vague, i.e. higher-order vague, for all orders. The second section develops and defends a novel framework, dubbed negative supervaluationary semantics, which makes room for the possibility of super-vague existence.
Necessarily Maybe. Quantifiers, Modality and Vagueness. In Torza, A. (ed.) Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. Synthese Library, vol. 373. Springer (2015), pp. 367-387.
Abstract. Languages involving modalities and languages involving vagueness have each been thoroughly studied. On the other hand, virtually nothing has been said about the interaction of modality and vagueness. This paper aims to start filling that gap. Section 1 is a discussion of various possible sources of vague modality. Section 2 puts forward a model theory for a quantified language with operators for modality and vagueness. The model theory is followed by a discussion of the resulting logic. In Section 3, the framework will permit us to address a puzzle raised by Elizabeth Barnes and Robert Williams.
Introduction. In Torza, A. (ed.) Quantifiers, Quantifiers, and Quantifiers. Themes in Logic, Metaphysics, and Language. Synthese Library, vol. 373. Springer (2015), pp. 1-15.
Abstract. This introductory chapter provides a summary of the contributions to the volume, as well as some critical remarks.
Speaking of Essence. The Philosophical Quarterly, Vol. 65, No. 261 (2015), pp. 211-31.
Abstract. Classical modalism about essence is the view that essence can be analyzed in modal terms. Despite Kit Fine's influential critique, no general refutation of classical modalism has yet been provided. In the first part of the paper I provide such a refutation by showing that the notion of essence cannot be analyzed in terms of any sentential operator definable in the language of standard quantified modal logic. As a reaction to Fine's critique, some have defended sophisticated modalism, which attempts to analyze essence in an enriched modal language quantifying over both possible and impossible worlds. In the second part of the paper I argue that sophisticated modalism falls prey to variations on Fine's counterexamples to classical modalism. I conclude that the most promising approaches to understanding the notion of essence consist in taking essence either as primitive or as analyzable via a combination of modal and non-modal notions.
What Trans-World Causation Could and Could not Be. Metaphysica, Vol. 15, No. 1 (2014), pp. 187-208.
Abstract. Eduardo García-Ramírez has recently offered a reductio of the counterfactual analysis of causation. The argument purportedly shows that, given a natural generalization of Lewis’ semantics for counterfactuals, statements expressing the existence of causal dependence across worlds turn out to be satisfiable. The aim of the present paper is twofold. In the first part, I show that the purported reductio is flawed, as it relies on an overly strong construal of the semantics for counterfactuals. The second part of the paper is devoted to a new proof of the possibility of trans-world causation. Nevertheless, the new proof does not amount to a reductio of Lewis’ account of causation per se, but rather of the conjunction of several substantive theses (the counterfactual analysis of causation, modal plenitude, the existence of mereological sums and the best theory account of natural laws).
How to Lewis a Kripke-Hintikka. Synthese, Vol. 190, No. 4 (2013), pp. 743-779.
Abstract. It has been argued that a combination of game-theoretic semantics and independence-friendly (IF) languages can provide a novel approach to the conceptual foundations of mathematics and the sciences. Here, I introduce and motivate an IF first-order modal language endowed with a game-theoretic semantics of perfect information. The resulting interpretive independence-friendly logic (IIF) allows to formulate some basic model-theoretic notions that are inexpressible in the ordinary quantified modal logic. Moreover, I argue that some key concepts of Kripke’s new theory of reference are adequately modeled within IIF. Finally, I compare the logic IIF to David Lewis’ counterpart theory, drawing some morals concerning the interrelation between metaphysical and semantic issue in possible-world semantics.
'Identity' without Identity. Mind, Vol. 121, No. 481 (2012), pp. 67-95.
Abstract. I introduce and defend the semantic notion of counterfactual identity, distinguishing it from the metaphysical notion of transworld identity. After showing that Lewis's counterpart theory misconstrues counterfactual identity facts, I outline and motivate a ‘Leibnizian counterpart theory’ where the notion of counterfactual identity is adequately modelled. Finally, I show that counterfactual identity can be characterized without relying on some implausible features of Lewis's theory of conditionals.
A Characterization of Haecceitism. Analytic Philosophy, Vol. 52, No. 4 (2011), pp. 262–266.
Abstract. Anti-haecceitism is the thesis that things cannot differ from actuality in a purely non-qualitatively fashion. Anti-haecceitism being a modal notion, we would expect it to be explicable in terms of possible worlds. Bradford Skow has denied that, arguing that alternative conceptions of possible worlds prompt non-equivalent characterizations of anti-haecceitism. Therefore, the haecceitism debate should take place in the modal language, rather than in the language of possible worlds. The aim of this paper is to provide a metaphysically neutral possible-world characterization of anti-haecceitism, i.e. one compatible with alternative understandings of the nature of possible worlds.
Models for Counterparts. Axiomathes, Vol. 21, No. 4 (2011), pp. 553–579.
Abstract. Lewis proposed to test the validity of a modal thesis by checking whether its possible-world translation is a theorem of counterpart theory. However, that criterion fails to validate many standard modal laws, thus raising doubts about the logical adequacy of the Lewisian framework. The present paper considers systems of counterpart theory of increasing strength and shows how each can be motivated by exhibiting a suitable intended model. In particular, perfect counterpart theory validates all the desired modal laws and therefore provides a way out of the logical objection. Finally, a weakening of perfect counterpart theory is put forward as a response to some metaphysical objections.
Turner, Jason. The Facts in Logical Space: A Tractarian Ontology. Oxford University Press, 2016. Philosophical Review, vol. 127, No. 2 (2018), pp. 273-277. [REVIEW]
Iacona, Andrea. Logical Form: Between Logic and Natural Language. Springer, 2018, pp. vi + 133. Argumenta 7 (2018), pp. 197-201. [REVIEW]
Photographs by Alessandro Torza. All rights reserved.