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.

Introduction; Alessandro Torza.- Part 1. Logical Constants.- Which Quantifiers are Logical? A Combined Semantical and Inferential Criterion; Solomon Feferman.- Implicit Definitions, Second-Order Quantifiers, and the Robustness of the Logical Operators; Arnold Koslow.- Quantifiers are Logical Constants, but Only Ambiguously; Sun-Joo Shin.- Part 2. Semantics of Natural Language.- Conjunctive, Disjunctive, Negative Objects and Generalized Quantification; Ken Akiba.- Quantifiers and Referential Use; Mario Gómez-Torrente.- Quantification and Logical Form; Andrea Iacona.- Quantification with Intentional and with Intensional Verbs; Frederike Moltmann.- Part III The Carnap-Quine Legacy.- Life on the Range: Quine's Thesis and Semantic Indeterminacy; G. Aldo Antonelli.- Chalmers, Quantifier Variance and Mathematicians' Freedom; Sharon Berry.- "There Is an 'Is' in There Is": Meinongian Quantification and Existence; Francesco Berto.- Qualifying Quantifying-in; Bjørn Jespersen.- Carnap, Quine, Quantification and Ontology; Gregory Lavers.- Quantifier Variance, Intensionality and Metaphysical Merit; David Liebesman.- Part 4. Metaphysics and Ontology.- Making Quantified Truths True; Axel Arturo Barcel¿ Aspeitia.- Absolute Generality and Semantic Pessimism; J.P. Studd.- Necessarily Maybe. Quantifiers, Modality and Vagueness: Alessandro Torza.- What's in a (Mental) Picture; Alberto Voltolini.- Part 5. Logical Systems.- Cross-World Identity, Temporal Quantifiers and the Question of Tensed Contents; Tero Tulenheimo.- What's So Bad about Second-Order Logic?; Jason Turner.- ¿ and ¿; Elia Zardini.