Programme

Routley’s noneism, a view dating from the 1960s, held that there are two kinds of quantifiers, existentially loaded and neutral, with the neutral quantifier’s expansive range including numerous items that have no form of existence whatsoever — past and future things; unactualized possibilia; universals and numbers; the dead and those not yet born; incomplete and/or inconsistent Meinongian objects, …. A common reaction to the view from the mostly Quinean establishment was an “incredulous stare”, but the most interesting and nuanced reaction came from David Lewis (himself the object of such stares) in his 1990 paper ‘Noneism or Allism’. Here Lewis subjected the view to a kind of hermeneutic examination that in the end concluded that we (the right-thinking establishment) should interpret our one quantification as Routley’s neutral quantification (so that Routley emerges as a particularly extravagant allist), rather than as Routley’s existentially loaded quantification. Along the way, Lewis suggests one alternative option: that “when Routley quantifies without quantifying, he is engaging in some sort of simulated quantification” (similar to the way substitutionalists, for example, “simulate quantification over fictional characters by quantifying for real over fictional names”). But Lewis quickly leaves this suggestion behind, pointing out that, if it were true, Routley “would have no reason to present himself as a heretic”. In later work, however, Lewis seemed willing to accept more relaxed versions of the idea of simulation (see especially one of the last papers he ever presented, ‘Quasi-realism is a fictionalism’). In the present paper I discuss the extent to which Lewis’s more relaxed view of simulation might help us to understand a view like Routley’s. 

We can think of universally quantified statements as true in so far as they resist counter-examples. Against such a reasonable idea, fictional entities, whatever they really are, are puzzling counter-examples. Indeed, it seems that

(1) Nothing travels faster than light.

is true, despite the fact that, in Star Wars, the Millenium Falcon is said to go faster than light. We can safely disregard fictional counter-examples to (1) because fictional entities do not exist outside their fiction of origin. Such routine reasoning is in line with classical quantification theory according to which the universal quantifier ranges over all and only real things. However, it appears that the Millenium Falcon can sometimes be used as a bona fide counter-example to a universal statement. E.g.:

(2) Everything exists.

Indeed, fictional entities are typically thought of as nonexistent entities. There is thus a tension; focusing on (1), it is tempting to say that the Millenium Falcon is outside the (real) quantificational domain; but if we look at (2), one should rather include it.

Noneists (from Routley (1966) onward) typically respond by saying that (1) is in fact false, unless implicitly restricted to existing things: contrary to appearances, the universal quantification in (1) and (2) is not interpreted in the same way. On the other hand, the allist strategy (see Lewis (1990)) consists in either arguing that (2) is not a felicitous sentence, or that the Millenium Falcon cannot count as a counter-example to (2). Rehearsing arguments from free logic, I argue that both approaches are wrong, though they both contain interesting insights. I then resolve the tension by providing a simple dynamic free quantification theory. I thus build unrestricted quantification from the bottom up, contrary to the top-down approach of noneists.

The starting point is the original approach of Hilbert & Bernays to definite descriptions as developed in their Grundlagen der Mathematik Volume 1, 1934. In this theory definite descriptions can only be introduced in the language if the corresponding uniqueness condition is satisfied. Furthermore, the formal system is extended by a characteristic theorem. This theory has often been confronted with the argument that provability and language should be kept apart. Some solutions are known, our way out is by putting a version of negative free logic to use. Based on a negative free logic analytic existence assumptions, i.e. those given by conceptual framework, obtain a natural interpretation. Eventually, an adaption of Bell’s argument for obtaining classical logic from intuitionistic logic via extensional saturation is presented in this context.  

The discussion of non-existents is generally assumes that nonexistent objects are of the same sort ('Pegasus', 'the golden mountain'). However, there is actually a greater range of what one may consider nonexistent entities. 'Nonexistent' events may take the form of plans and projects, which have realization conditions, or as (planned) actions, which come with conditions of taking place. Laws and rules may have the status as nonexistents if they are not currently 'in place' or valid. This talk aims to extend our range of intuitions about kinds of non-existents and modes of non-existence and will hopefully shed a new light on the discussion of existence itself 

In this paper, I will argue for the importance of the semantic distinction between existence entailing, nonexistence entailing and existence neutral predicates. I will give a brief outline of the historical roots of this distinction in the works of Descartes and Lotze. I will then side with Lotze and outline a philosophical and formal semantic account on this issue. 

In this talk, I present the linguistic evidence for categorizing natural-language predicates as existence entailing, nonexistence entailing or existence neutral. I then present a formal semantic account with multiple domains that is able to capure the data.

I distinguish between instantial sentences (There are elephants that swim), particular quantification, and predication of existence in natural language. I explore the logical relation between the first two, while the last one is shown independent of either. I continue to consider the incorporation of the three kinds of sentence in Quarc (which is concisely introduced). The formalisation possibilities are richer in Quarc with compound predicates, and I show that it preserves, within a sound and complete system, the logical relations specified earlier. I also extend the analysis to quantified instantial sentences (There are five elephants that swim) and modal ones. A conclusion of this work is that quantification and instantial sentences provide no guide to ontology. 

In this talk, I use notions of predication and quantification in a modal setting to show (a) how to define what it is for an individual to exist, (b) how to define what it is for a property (or relation) to exist, (c) how to define identity conditions for properties and relations understood as hyperintensional entites, (d) how to prove the necessity of identity for individuals and relations, (e) how to derive the free-logic definition τ↓ (τ exists) ≡df  ∃β(β=τ) as a theorem (where either τ is an individual term and β an individual variable, or τ is an n-ary relation term (n≥0) and β is an n-ary relation variable), (f) how to understand the simplest (i.e., fixed domain) quantified modal logic, and (g) how to derive, not just stipulate, a theory of truth.