The question whether numbers are objects is a central question in the philosophy of mathematics. Frege made use of a syntactic criterion for objethood: numbers are objects because there are singular terms that stand for them, and not just singular terms in some formal language, but in natural language in particular. In particular, Frege (1884) thought that both noun phrases like the number of planets and simple numerals like eight as in (1) are singular terms referring to numbers as abstract (...) objects. (shrink)

Nominalizations of modal predicates have received little, if any, attention in the semantic or philosophical literature. This paper will argue that nominalizations of modal predicates require recognizing a novel ontological category of modal objects and it will outline a new semantics of modals based on modal objects.

This paper discusses three approaches to the semantics of event nominalizations and adverbial modification: the Davidsonian account, the Kimian account, and the truthmaker account. It argues that a combination of all three accounts is needed for the semantics of the full range of event, trope, and state nominalizations in English.

In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...) of our PIF account of truth-talk, we demonstrate a few advantages it offers over T-deflationist accounts that do not explicitly acknowledge pretense at work in the discourse. In turning to the Liar Paradox, we explain how the quasi-anaphoric functioning that our account attributes to truth-talk provides a diagnosis of the Liar Paradox (and other instances of semantic pathology) as having no content—in the sense of not specifying any of what we call M-conditions. At the same time, however, we vindicate the intuition that we can understand liar sentences, thereby avoiding one standard objection to “meaningless strategy” responses to the Liar Paradox. With this diagnosis in place, we then, by way of treatment, introduce a new predicate, ‘semantically defective’, and show how the explanation we give for its application allows for a consistent, yet revenge-immune, (dis)solution of the Liar Paradox, and semantic pathology generally. (shrink)

This paper argues that NPs with case as head noun stand for situations in their role as truthmakers within a sentential or epistemic case space. The paper develops a unified semantic analysis of case-constructions of the various sorts within a truthmaker-based version of alternative semantics.

Festschrift in Honor of Barry Smith on the occasion of his 65th Birthday. Published as issue 4:4 of the journal Cosmos + Taxis: Studies in Emergent Order and Organization. Includes contributions by Wolfgang Grassl, Nicola Guarino, John T. Kearns, Rudolf Lüthe, Luc Schneider, Peter Simons, Wojciech Żełaniec, and Jan Woleński.

It is a standard assumption in contemporary metaphysics that concrete objects come with a location in space and time. This applies not only to material objects and events, but also modes (such as the roundness of the apple, the softness of the pillow, Socrates' wisdom) and entities that have been called 'disturbances' (e.g. holes, folds, faults, and scratches). Taking the approach of descriptive metaphysics, I will show that modes and disturbances fail to have a bearer-independent spatial location. This allows for (...) a metaphysical explanation of the Chomskyan contrast between 'There is a fly believed to be in the bottle' and the unacceptable 'There is a flaw believed to be in the argument'. A subsidiary point this paper makes is that in their lack of a direct spatial location, modes need to be sharply distinguished from tropes as a category of foundationalist metaphysics that has been at the center of a pursuit of a one-category ontology since Williams (1953). (shrink)

The present paper argues that when thematic roles are restricted to judgments about causal properties of events, it falls short of accounting for cases where thematic roles reflect judgments about dispositional properties of objects. I develop my argument with a case study on a class of verbs that have been called ‘Emission Verbs’ and which are difficult to bring in line with the unaccusativity hypothesis put forward by Perlmutter. Reviewing two diametrically opposed accounts of Emission Verbs in the literature, I (...) show that the thematic-semantic relation between the events described by Emission Verbs and their single arguments cannot be characterized unambiguously in terms of causal properties of events but pertains to dispositional properties residing in the emitter argument. The paper develops a lexical-semantic analysis of Emission Verbs according to which the event described by an Emission Verb is the manifestation of the dispositional property of the emitter argument when appropriate external circumstances obtain. The paper concludes by outlining how the proposed dispositional analysis of Emission Verbs may inform the analysis of the causative alternation. (shrink)

A common view is that natural language treats numbers as abstract objects, with expressions like the number of planets, eight, as well as the number eight acting as referential terms referring to numbers. In this paper I will argue that this view about reference to numbers in natural language is fundamentally mistaken. A more thorough look at natural language reveals a very different view of the ontological status of natural numbers. On this view, numbers are not primarily treated abstract objects, (...) but rather 'aspects' of pluralities of ordinary objects, namely number tropes, a view that in fact appears to have been the Aristotelian view of numbers. Natural language moreover provides support for another view of the ontological status of numbers, on which natural numbers do not act as entities, but rather have the status of plural properties, the meaning of numerals when acting like adjectives. This view matches contemporary approaches in the philosophy of mathematics of what Dummett called the Adjectival Strategy, the view on which number terms in arithmetical sentences are not terms referring to numbers, but rather make contributions to generalizations about ordinary (and possible) objects. It is only with complex expressions somewhat at the periphery of language such as the number eight that reference to pure numbers is permitted. (shrink)

This paper presents a systematic semantic study of constructions with the noun 'case'. It argues that 'cases' are situations acting as truthmakers within a sentential or epistemic case space. It develops a truthmaker-based alternative semantics of 'case'-constructions, based on Fine's recent truthmaker semantics.

The complement of intensional transitive verbs, like any nonreferential complement, can be replaced by a ‘special quantifier’ or ‘special pronoun’ such as 'something', 'the same thing', or 'what'. In this paper, I will defend the ‘Nominalization Theory’ of special quantifiers against a range of apparent counterexamples involving intensional transitive verbs.

This paper explores a novel analysis of adjectives in the comparative and the positive based on the notion of a trope, rather than the notion of a degree. Tropes are particularized properties, concrete manifestations of properties in individuals. The point of departure is that a sentence like ‘John is happier than Mary’ is intuitively equivalent to ‘John’s happiness exceeds Mary’s happiness’, a sentence that expresses a simple comparison between two tropes, John’s happiness and Mary’s happiness. The analysis received particular support (...) from various parallels between adjectival constructions and corresponding adjective nominalizations which make reference to tropes. (shrink)

Causation is generally conceived of as a relation that holds between events. Apart from a few cursory remarks, the case of stative causation has been widely neglected. The paper aims at contributing to a more balanced perspective by arguing for a stative variant of causation, on a par with eventive causation. The stative variant is analyzed in terms of Moltmann’s ontological notion of tropes. German causal von-modifiers are taken as a linguistic window into our understanding of causation. The study of (...) von is particularly suited to this endeavor, because von-modifiers are confined to expressing the core notion of “direct causation” :1–48, 2003). The paper develops a compositional semantics of causal von-modifiers that derives their eventive and stative readings from a single lexical entry and allows for coercive adaptions to account for the observed range of interpretive adjustments. Characteristic features of the interpretation such as the inferential behavior of causal von-modifiers and the holistic effect of the stative reading are traced back to independently motivated conceptual assumptions concerning the spatiotemporal grounding of direct causation. The formal analysis is couched in terms of Asher’s type composition logic. (shrink)

This article introduces, studies, and applies a new system of logic which is called ‘HYPE’. In HYPE, formulas are evaluated at states that may exhibit truth value gaps and truth value gluts. Simple and natural semantic rules for negation and the conditional operator are formulated based on an incompatibility relation and a partial fusion operation on states. The semantics is worked out in formal and philosophical detail, and a sound and complete axiomatization is provided both for the propositional and the (...) predicate logic of the system. The propositional logic of HYPE is shown to contain first-degree entailment, to have the Finite Model Property, to be decidable, to have the Disjunction Property, and to extend intuitionistic propositional logic conservatively when intuitionistic negation is defined appropriately by HYPE’s logical connectives. Furthermore, HYPE’s first-order logic is a conservative extension of intuitionistic logic with the Constant Domain Axiom, when intuitionistic negation is again defined appropriately. The system allows for simple model constructions and intuitive Euler-Venn-like diagrams, and its logical structure matches structures well-known from ordinary mathematics, such as from optimization theory, combinatorics, and graph theory. HYPE may also be used as a general logical framework in which different systems of logic can be studied, compared, and combined. In particular, HYPE is found to relate in interesting ways to classical logic and various systems of relevance and paraconsistent logic, many-valued logic, and truthmaker semantics. On the philosophical side, if used as a logic for theories of type-free truth, HYPE is shown to address semantic paradoxes such as the Liar Paradox by extending non-classical fixed-point interpretations of truth by a conditional as well-behaved as that of intuitionistic logic. Finally, HYPE may be used as a background system for modal operators that create hyperintensional contexts, though the details of this application need to be left to follow-up work. (shrink)

A central question for ontology is the question of whether numbers really exist. But it seems easy to answer this question in the affirmative. The truth of a sentence like ‘Seven students came to the party’ can be established simply by looking around at the party and counting students. A trivial paraphrase of is ‘The number of students who came to the party is seven’. But appears to entail the existence of a number, and so it seems that we must (...) conclude that numbers exist. This is sometimes called the puzzle of how we can get something from nothing. Most extant attempts to solve the puzzle take it for granted that is ontologically innocent, and focus their attention either on or on the transition from to. We argue that both attempts go wrong at the first step: the assumption that is ontologically innocent is undermined by a highly attractive and independently well-motivated degree-based account of number word constructions. Thus the degree-based account provides a straightforward linguistic resolution of the puzzle of how we can get something from nothing. But the paper also has a second aim. The semantics we present treats ‘seven’ as a referring expression that refers to a degree of a certain sort. But what are degrees? We consider various anti-platonist proposals that seek to account for degrees in terms of relations between concrete entities, and argue that they are incompatible with the Universal Density of Measurement hypothesis of Fox and Hackl. While the UDM cannot yet claim to be the consensus view among degree-based semanticists, our aim is to use it to illustrate how views about the nature of degrees can be evaluated by considering the properties degrees must have if they are to play the explanatory roles they are called upon to play in linguistics. In the present state of development of degree-based semantics there are difficult open questions about what these properties are. These questions need to be addressed if we are to develop a clear picture of what natural language semantics has to contribute to ontology and metaphysics. (shrink)

We present in this paper a novel ontological theory of events whose central tenet is the Aristotelian distinction between the object that changes and the actual subject of change, which is what we call an individual quality. While in the Kimian tradition events are individuated by a triple ⟨ o, P, t ⟩, where o is an object, P a property, and t an interval of time, for us the simplest events are qualitative changes, individuated by a triple ⟨ o, (...) q, t ⟩, where q is an individual quality inhering in o or in one of its parts. Detaching the individuation of events from the property they exemplify results in a fine-grained theory that keeps metaphysics and semantics clearly separate, and lies between the multiplicative and the unitarian approaches. We discuss then the way language refers to events, observing that, in most cases, event descriptions refer to complex, cognitively relevant clusters of co-occurring qualitative changes, which exhibit a synchronic structure depending on the way they are described. Contra Bennett, who famously argued that the semantics of event names ultimately depends on “local context and unprincipled intuitions”, we show how the lexicon provides systematic principles for individuating such clusters and classifying them into kinds. Finally, we address some open challenges in the semantics of locative and manner modifiers. (shrink)

Truth-makers are the dark matter of metaphysics. On the one hand, truth-makers seem obvious and necessary: if there are truths then there must be something that makes these truths true. On the other hand, it’s proven difficult to say exactly what these truth-makers are. Even defenders disagree about what sort of entity truth-makers are or whether all truths have truth-makers. Skeptics have questioned whether truth-makers are actually so obvious and necessary, or even whether they exist at all. Here I offer (...) an account of this unhappy state of affairs and a modest proposal. First, I argue that not only are there no good arguments for truth-makers but it’s unlikely that there ever will be. Second I point to how much can be done without resorting to truth-makers in the first place: they are not as essential as often assumed. Finally, I conclude that we needn’t jettison the concept of truth-makers entirely. Understood in a modest and pragmatic spirit we can hold on to truth-makers while recognizing their inherent limitations. (shrink)

A survey of the similarities and differences between BFO and DOLCE, and of the mutual interactions between Nicola Guarino and Barry Smith.

Since last year, major initiatives have been undertaken by the chair of theoretical philosophy at the University of Tübingen in order to enhance the reception of analytic metaphysics in the European landscape. Here we review the 2013 summer workshop, intended to be the first of an annual series, on “Existence, Truth and Fundamentality”, the invited speakers being Graham Priest (Melbourne), Stephan Leuenberger (Glasgow), Dan López de Sa (Barcelona), Francesco Berto (Aberdeen), Friederike Moltmann (Paris – Pantheon Sorbonne) and Jason Turner (Leeds). (...) The workshop’s scope is fairly large, focusing on three different aspects of contemporary research in metaphysics. However, the underlying idea of organizers Thomas Sattig and Alessandro Torza consisted in exploring their interconnections and even new areas which possibly share the same problem spectrum. Also, they thought of bringing together both young and senior protagonists of the contemporary debate. In this sense, the main thread followed by the speakers consisted in enquiring the ideas of fundamentality, dependence and grounding with respect to ontology (Berto, López de Sa, Turner) and the truthmaking debate (Priest, Moltmann, Leuenberger), thus pretty much in line with some latest tendencies in metaphysics, such as, prima inter paria, the works of Kit Fine. When we say that something is more fundamental than something else, we move into a non-conventional (for the standards of 20 th century philosophy) metodological framework, hardly focusing on the question about what there is, and rather tackling the issue of how fundamentally there is what there is, or how the existence of something is required as a ground for the existence of other things. Here is how Jonathan Schaffer explains the methodological transition in his influential “On What Grounds What” (2009): -/- Among the many assumptions Quine and Carnap share is that metaphysical questions are existence questions, such as whether numbers exist. They only disagree on the further issue of whether such questions are meaningful (at least as the metaphysician might pose them). But why think that metaphysical questions are existence question of this sort? Return to Aristotle’s Metaphysics. There are virtually no existence question posed. The whole discussion is about substances (fundamental units of being). At one point Aristotle pauses to ask if numbers exist, and his answer is a brief and dismissive yes. [. . . ] For Aristotle, the question about numbers is whether they are transcendent substances or grounded in concreta. The question is not whether numbers exist, but how. (Schaffer, 2009, p. 347) -/- The conference opened with Graham Priest’s intriguing and peculiar review of Buddhist cornerstone “The Fundamental Verses of the Middle Way” (Mūlamadhyakamakārikā) by Nāgārjuna (ca. 150-ca. 250 AD), seen as a unrecognized forerunner of multi-valued semantics and dialetheism. Priest shows that Nagarjuna’s thought indeed has valuable analytic grip (contrary to the traditional mystical dismiss of his works altogether) and is even in accord to some formal schemas rejecting both the laws of excluded middle and non-contradiction. Dan López de Sa was interested in the topic of grounding, raising concerns about how to explain the kind of “reality” exemplified by what is not fundamental, but rather derivative on something else. He proposes a conceptual and non-primitive analysis of grounding as linked to fundamentality and derivation, and argues that the view can be advocated along with the acceptance that at least something is not fundamental. Subsequently, he illustrates an impressive range of applications linked to contemporary debates in meta-ontology, truthmaking and philosophy of time. Stephan Leuenberger discussed a semantics for “total logic”, a variant of first order logic which is claimed to have several applications with respect to the issue of excluding negative existentials from the scope of theories accounting for a given ’totality’ of facts. For example, materialism is the claim that everything there is can be traced back to physical facts or to truth implied by those facts. What about the claim that “There are no angels”? According to Leuenberger, ordinary logic falls prey of modal arguments (if it is possible that there are angels, by modus tollens, that it is not metaphysically necessary that everything there is is physical). So, there is space for the introduction of a new operator, the totality operator, claiming of what enters its scope that “that’s the whole truth”. Consequently, total logic’s semantics tackles David Chalmers’ well-known conceivability-based argument in favour of zombie’s (subjects producing behaviour but experiencing no qualia) possible existence. Friederike Moltmann presented a massive array of natural language-based examples on the role played by case-constructions, such as “it is the case that Caesar crossed the Rubicon”, “the case of the stolen statue”, “the case in which it might rain”, and so forth. She suggests that we should take surface phenomena of our language very seriously with regard to the determination of ontological categories and truth-makers. Cases are provided by many natural languages with their own existence predicates (“to occur” and “to present itself ”), and these do not apply to other kind of entities, such as objects and events. Trying to derive a substantive thesis on their nature, she claims that they are filtered entities, a structure taking into account some features of the corresponding objects and events and preserving their relational pattern. Jason Turner discussed meta-ontological concerns against the claim that ontological debates are defective. Analysed the structure of a metaphysical theory and identified two different forms of defectiveness that can occur in ontological questions, the defection from without and the defection from within, the author provided an original solution in order to avoid such difficulties. He argued thus in favor of a logical constancy, a translation principle thanks to it would be possible reconceive an ontological defection. Lastly, Francesco Berto’s talk closed the workshop with a sagacious discussion of meinongian quantification. He substains that Meinongians and Quineans experience no conceptual equivocation. Even if the former claims that “There are things that do not exist”, something that the latter contrasts with the interpretation of existential quantifiers as all-including, they still rely upon the same concept of “existence” and they understand each other when they are outside the ontology room, so that it cannot be that they lack competence. Subsequently, Berto deals with the objection that Meinongians commit analytic falsehood in separating the meaning of “to be” from that of “exists”. The Quinean has no independent evidence for analytic equivalence aside from her emphatic stress on the “is” in “there is”. Meinongians, however, can retort to linguistic considerations and claim that existence predicates display fairly different functions. -/- As for what regards our internal division of the “philosophical labor”, Fabio Ceravolo reviewed Moltmann and Berto’s talks; whereas Mattia Cozzi took care of Priest’s and Leuenberger’s, and Mattia Sorgon of those given by López de Sa and Turner. Conclusively, we would like to thank Thomas Sattig and Alessandro Torza for all of their organizational efforts and the kind welcome they reserved to us. We hope we will have further opportunities to collaborate with Tübingen in supporting similarly innovative and valiant european initiatives. (shrink)

NPs with intensional relative clauses such as 'the book John needs to write' pose a significant challenge for semantic theory. Such NPs act like referential terms, yet they do not stand for a particular actual object. This paper will develop a semantic analysis of such NPs on the basis of the notion of a variable object. The analysis avoids a range of difficulties that a more standard analysis based on the notion of an individual concept would face. Most importantly, unlike (...) the latter, the proposed analysis can be carried over NPs such as 'the number of people that fit into the bus', which describe tropes (particularized properties). (shrink)

What semantics should we attribute to mass expressions like "wisdom" and "love", which are derived from gradable expressions? We first examine how these expressions are used, then how they are interpreted in their various uses. We then propose a model to account for these data, in which derived mass nouns denote instances of properties.

Words have meaning. Sentences also have meaning, but their meaning is different in kind from any collection of the meanings of the words they contain. I discuss two puzzles related to this difference. The first is how the meanings of the parts of a sentence combine to give rise to a unified sentential meaning, as opposed to a mere collection of disparate meanings (UP1). The second is why the formal ontology of linguistic meaning changes when grammatical structure is built up (...) (UP2). For example, the meaning of a sentence is a proposition evaluable for truth and falsity. In contrast, a collection of the meanings of its parts does not constitute a proposition and is not evaluable for truth. These two puzzles are closely related, since change in formal ontology is the clearest sign of the unity of meaning. The most popular strategy for answering them is taking the meanings of the parts as abstractions from primitive sentence meanings. However, I argue that, given plausible psychological constraints, sentence meanings cannot be taken as explanatory primitives. Drawing on recent work in Generative Grammar and its philosophy, I suggest that the key to both unity questions is to distinguish strictly between lexical and grammatical meaning. The latter is irreducible and determines how lexical content is used in referential acts. I argue that these referential properties determine a formal ontology, which explains why and how formal ontology changes when grammatical structure is built up (UP2). As for UP1, I suggest that, strictly speaking, lexical meanings never combine. Instead, whenever grammar specifies a formal ontology for the lexical meanings entering a grammatical derivation, further lexical (or phrasal) meanings can only specify aspects of this recursive grammatical process. In this way, contemporary grammatical theory can be used to address old philosophical problems. (shrink)