We start with an observation about implicit quantifier domain restriction: certain implicit restrictions (e.g., restricting objects by location and time) appear to be more natural and widely available than others (e.g., restricting objects by color, aesthetic, or historical properties). Our aim is to explain why this is. That is, we aim to explain why some implicit domain restriction possibilities are available by default. We argue that, regardless of their other explanatory virtues, extant pragmatic and metasemantic (...) frameworks leave this question unanswered. We then motivate a partially nativist account of domain restriction that involves a minimal view of joint planning around broad shared goals about navigating and influencing our environments augmented with cognitive heuristics that facilitate these. Finally, we sketch how the view can be extended to account for the ways non-default restriction possibilities become available when conversationalists have shared idiosyncratic goals. (shrink)

Section 1 provides a brief summary of the pair-list literature singling out some points that are particularly relevant for the coming discussion. -/- Section 2 shows that the dilemma of quantifi cation versus domain restriction arises only in extensional complement interrogatives. In matrix questions and in intensional complements only universals support pairlist readings, whence the simplest domain restriction treatment suffices. Related data including conjunction, disjunction, and cumulative readings are discussed -/- Section 3 argues that in the (...) case of extensional complements the domain restriction treatment is inadequate for at least two independent reasons. One has to do with the fact that not only upward monotonic quantifi ers support pairlist readings, and the other with the derivation of apparent scope out readings. The reasoning is supplemented with some discussion of the semantic properties of layered quantifi ers.  The above will establish the need for quantifi cation, so the question arises how the objections explicitly enlisted in the literature against quantifi cation can be answered. Section 4 considers the de dicto reading of the quantifi er s restriction, quanti cational variability, and the absence of pairlist readings with whether questions, and argues that they need not militate against the quanti ficational analysis. -/- Section 5 summarizes the emergent proposal -/- Finally, section 6 discusses the signifi cance of the above findings for the behavior of weak islands. (shrink)

Many of those who accept the universalist thesis that mereological composition is unrestricted also maintain that the folk typically restrict their quantifiers in such a way as to exclude strange fusions when they say things that appear to conflict with universalism. Despite its prima facie implausibility, there are powerful arguments for universalism. By contrast, there is remarkably little evidence for the thesis that strange fusions are excluded from the ordinary domain of quantification. Furthermore, this reconciliatory strategy seems hopeless when (...) applied to the more fundamental conflict between universalism and the intuitions that tell against it. (shrink)

Arguments against the Russellian theory of definite descriptions based on cases that involve failures of uniqueness are a recurrent theme in the relevant literature. In this paper, I discuss a number of such arguments, from Strawson (1950), Ramachandran (1993) and Szabo (2005). I argue that the Russellian has resources to account for these data by deploying a variety of mechanisms of quantifier domain restrictions. Finally, I present a case that is more problematic for the Russellian. While the previous (...) cases all involve referential uses of descriptions (or some variations of such uses), the most effective objection to the uniqueness condition draws on genuine attributive uses. (shrink)

In 'The Reference Book' (2012), Hawthorne and Manley observe the following contrast between (1) and (2): -/- (1) In every race John won. (2) In every race, the colt won. -/- The name 'John' in (1) must intuitively refer to the same single individual for each race. However, the description 'the colt' in (2) has a co-varying reading, i.e. a reading where for each race it refers to a different colt. This observation is a prima facie problem for proponents of (...) so-called The-Predicativism which is the view that the name in (1) is really a covert definite description, viz. 'the John'. If the The-Predicativism is correct, (1) and (2) are therefore syntactically equivalent, but this makes it mysterious why only (2) would have a co-varying reading. In a recent paper, Fara (2015) argues that there is a simple and elegant way for proponents of The-Predicativism to explain this contrast. This explanation relies on discerning some subtle syntactic differences between (1) and (2) which in turn are based on assumptions about nominal restrictions a la Stanley and Szabó (2000). In this short paper, I demonstrate that Fara's proposed explanation has a variety of serious shortcomings and hence that the contrast between (1) and (2) remains a significant problem for Predicativism. (shrink)

Scientific realism holds that the terms in our scientific theories refer and that we should believe in their existence. This presupposes a certain understanding of quantification, namely that it is ontologically committing, which I challenge in this paper. I argue that the ontological loading of the quantifiers is smuggled in through restricting the domains of quantification, without which it is clear to see that quantifiers are ontologically neutral. Once we remove domain restrictions, domains of quantification can include non-existent things, (...) as they do in scientific theorizing. Scientific realism would therefore require redefining without presupposing a view of ontologically committing quantification. (shrink)

When do we judge that someone was forced to do what they did? One relatively well-established finding is that subjects tend to judge that agents were not forced to do actions when those actions violate norms. A surprising discovery of Young & Phillips 2011 is that this effect seems to disappear when we frame the relevant ‘force’-claim in the active rather than passive voice ('X forced Y to φ ' vs. 'Y was forced to φ by X'). Young and Phillips (...) found a similar contrast when the scenario itself shifts attention from Y (the forcee) to X (the forcer). We propose that these effects can be (at least partly) explained by way of the role of attention in the setting of quantifier domains which in turn play a role in the evaluation of ‘force’- claims. We argue for this hypothesis by way of an experiment which shows that sequences of active vs. passive ‘force’-claims display the characteristic “stickiness” of quantifier domain expansion, using a paradigm which we argue provides a useful general paradigm for testing quantifier domain hypotheses. Finally, we sketch a semantics for ‘force’ which we argue is suitable for capturing these effects. (shrink)

Relative to an ordinary context, an utterance of the sentence ‘Everything is in the car’ communicates a proposition about a restricted domain. But how does this work? One possibility is that quantifier expressions like 'everything' are context sensitive and range over different domains in different contexts. Another possibility is that quantifier expressions are not context sensitive, but have a fixed, absolutely general meaning, and ordinary utterances communicate a restricted content via Gricean mechanisms. I argue that, contrary to (...) received opinion, the latter view has both a number of methodological and also intuitive advantages over the former. I then reply to three objections to the latter view: the binding argument (due to Stanley and Szabo), the availability-based attack (due to Recanati), and an argument based on Recanati’s scope principle. (shrink)

The present paper presents experimental evidence confirming that contextually mismatching scalar implicatures can be generated even when quantifiers range over empty domains. In the literature, this possibility has been interpreted as providing further evidence for a grammatical approach to scalar implicatures. The main result presented here is that scalar sentences with empty domains are judged as more infelicitous when associated with a mismatching implicature than variants with the same empty domains but associated with a non-mismatching implicature. We interpret this result (...) as suggesting that the infelicity judgment associated with the first kind of sentence stems from the cumulative effect of the mismatching implicature and the contextual domain emptiness. Compared to previous literature on blind implicatures, our results indicate that the body of knowledge involved in relevance assignments is restricted to ignoring existential determination while still considering the properties attributed to nonexistent entities. They also show that, while not blocking implicature generation, contextual domain emptiness plays a role in speakers’ evaluation of scalar sentences, reflecting the unconscious nature of scalar implicature generation. (shrink)

Metaphysicians frequently appeal to intuition. But when is that appeal useful? I consider that question by focusing on our existential intuitions. In particular, I want to go some way to answering the question of whether, and when, appeal to existential intuitions is useful, by consid-ering the issue in the light of an argument for unrestricted composition. This argument appeals to a difference in the extent to which restricted and unrestricted compositionalists appeal to existential intuitions, and concludes that at the very (...) least, restricted compositionalists are on shak-ier epistemic ground than unrestricted compositionalists. Having outlined this argument for unrestricted composition, I con-sider the nature of the unrestricted existential quantifier in the context of three different metaphysical scenarios about the way the world might be: scenarios that differ with respect to whether the metaphysics of a world completely or uniquely settles the division of that world into ob-jects. I argue that appeal to intuition is not only useful but necessary if we are to determine the intension of ‘exists’ and hence its extension at any given world. But this appeal is not simply an appeal to our brute ex-istential intuitions—our dispositions actually to quantify over a certain domain. Rather, it requires equilibration over a set of worlds in which we consider our ‘quantificational’ dispositions in each world, where, importantly, included in this set of worlds are worlds in which the meta-physics differently settles the division of those worlds into objects. Ul-timately, I argue, our dispositions yield various conditional claims about our concept <existence>. These are conditional claims of the most ab-stract kind: they tell us, for instance, that if there is some natural, unique division of our world into objects, then the unrestricted quantifier ranges over all and only the objects in that domain. But, I will argue, our untu-tored, world-bound dispositions are no guide at all to what actually ex-ists even on the supposition that metaphysics alone does not uniquely or completely settle a natural division of our world into objects. Hence they are no guide to the nature of composition. And to the extent that certain restricted compositionalist views depend on such intuitions, so much the worse for them. Or so I shall argue. (shrink)

Newton frequently characterized his methodology as distinctive and capable of achieving greater evidential support than that of his contemporaries, due to its mathematical character. Newton's pronouncements reflect a striking position regarding the role of mathematics in natural philosophy. We can give an initial characterization of his position by considering two questions central to seventeenth century debates about the applicability of mathematics. First, how are we to understand the distinctive universality and necessity of mathematical reasoning? One common way to preserve the (...) demonstrative character of mathematics was to restrict its domain, as far as possible, to pure abstractions. The subject matter of mathematics is then taken to be abstracted from the changeable natural world, consisting of quantity and magnitude themselves rather than the objects bearing quantifiable properties. Yet restricting the domain in this way leaves it difficult to see how mathematics relates to natural phenomena. How could the book of nature be written in a language of pure abstractions? Second, what is the proper role of mathematical reasoning in natural philosophy? Many followed Aristotle in consigning mathematics to a subordinate role. Mathematics could not fulfill the main aim of natural philosophy, namely to provide demonstrations reflecting the essences of things and nature's causal order. A related concern was also pressing for the mechanical philosophers: a merely mathematical demonstration fails to provide an intelligible mechanical explanation. The very title of Newton's masterpiece, Philosophiae Naturalis Principia Mathematica, would have been extremely perplexing: how could natural philosophy be based on mathematical principles? My aim is to articulate Newton's position regarding the mathematization of nature in response to these two concerns. (shrink)

In judgment aggregation, unlike preference aggregation, not much is known about domain restrictions that guarantee consistent majority outcomes. We introduce several conditions on individual judgments su¢ - cient for consistent majority judgments. Some are based on global orders of propositions or individuals, others on local orders, still others not on orders at all. Some generalize classic social-choice-theoretic domain conditions, others have no counterpart. Our most general condition generalizes Sen’s triplewise value-restriction, itself the most general classic condition. We (...) also prove a new characterization theorem: for a large class of domains, if there exists any aggregation function satisfying some democratic conditions, then majority voting is the unique such function. Taken together, our results provide new support for the robustness of majority rule. (shrink)

W. V. Quine’s criterion of ontological commitment is commonly presented as the slogan: “to be is to be the value of a variable”. More specifically, to be is to be in the domain of values of a bound variable attached to a existential quantifier in the body of a theory. If a sentence of our best available theory quantifies over bachelors, so we conclude that, according to it, there are bachelors. Simplicity and the use of logical apparatus for (...) determining this criterion are responsible for many philosophers to adhere to this standpoint within analytical metaphysics. I will argue that despite this strong influence of the Quinean criterion of ontological commitment in many debates, we find at least three interlinked problems in its original formulation: (1) The criterion depends of a clear definition of theory for the determination of the quantifications counting as entailers of ontological commitments. However, Quine does not present such clear concept of what would be a theory and of how to formalize it. Quine develops this notion under just the metaphor of the knowledge fabric, in which we have a group of sentences, which does not suffice for the required account of ontological commitment. (2) There are distinct possibilities of quantifying over given sentences, which leaves room for different ontological commitments associated with the same statement. In that sense, someone could argue that the Quinean solution would be to endorse just the first order predicate logic. Nonetheless, the Quinean should explain why we ought to be restricted to this logic. (3) The previous problems lead to a possible explosion of the Quinean criterion of ontological commitment, making it trivial, because it permits the quantification over any supposed entities and, hence, that anything can exist. Thus, I will discuss Quine’s criterion of ontological commitment in the light of the abovementioned problems, showing that, unless the Quinean presents a more specific definition of theory beyond just a group of sentences, he leads to an explosion of commitments with different entities. I will conclude that, if you understand ‘theory’ as Alonzo Church’s concept of ‘formalized language’, this knot can be undone. However, Church’s concept is much more akin to Carnap’s linguistic framework than to a notion of knowledge fabric “without borders” as the one proposed by Quine. (shrink)

Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance (...) is not an ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

In this paper, I introduce a quantifier-pluralist theory of time, temporal quantifier relativism. Temporal quantifier relativism includes a restricted quantifier for every instantaneous moment of time. Though it flies in the face of orthodoxy, it compares favorably to rival theories of time. To demonstrate this, I first develop the basic syntax and semantics of temporal quantifier relativism. I then compare the theory to its rivals on three issues: the passage of time, the analysis of change, (...) and temporal ontology. (shrink)

(Open Access.) Quantifiers frequently figure in works of fiction. But occurrences of quantificational expressions within fictions seem no more inevitably to be associated with real domains than uses of names within fictions seem inevitably to be associated with existing referents. The paper outlines some philosophical puzzles resulting from this apparent lack of associated domains, puzzles that are broadly analogous to more familiar ones raised by the apparently nonreferential nature of many fictional names. The paper argues, in the light of an (...) important disanalogy between quantifiers and names, that the quantificational puzzles are substantive, in that they cannot be resolved merely by appealing to the possibility of empty domains. It then argues that, despite the cited parallels between occurrences of quantifiers and names within fictions, promising treatments of fictional names do not always straightforwardly generalise to provide accounts of the quantificational phenomena: the quantificational puzzles are therefore not only substantive but also distinctive. The paper provides further testament to the depth and interest of the problems involving content that are generated by fiction, by identifying a very wide range of previously neglected cases, while also helping to situate within a broader context the notoriously hard philosophical challenges posed by fictional names. (shrink)

This paper extends Kripke’s theory of truth to a language with a variably strict conditional operator, of the kind that Stalnaker and others have used to represent ordinary indicative conditionals of English. It then shows how to combine this with a different and independently motivated conditional operator, to get a substantial logic of restricted quantification within naive truth theory.

We use imperatives to refute a naïve analysis of update potentials (force-operators attaching to sentences), arguing for a dynamic analysis of imperative force as restrictable, directed, and embeddable. We propose a dynamic, non-modal analysis of conditional imperatives, as a counterpoint to static, modal analyses. Our analysis retains Kratzer's analysis of if-clauses as restrictors of some operator, but avoids typing it as a generalized quantifier over worlds (against her), instead as a dynamic force operator. Arguments for a restrictor treatment (but (...) against a quantificational treatment) are mustered, and we propose a novel analysis of update on conditional imperatives (and an independently motivated revision of the standard ordering-semantics for root modals that makes use of it). Finally, we argue that imperative force is embeddable under an operation much like dynamic conjunction. (shrink)

Is there a notion of domain specificity which affords genuine insight in the context of the highly modular mind, i.e. a mind which has not only input modules, but also central ‘conceptual’ modules? Our answer to this question is no. The main argument is simple enough: we lay out some constraints that a theoretically useful notion of domain specificity, in the context of the highly modular mind, would need to meet. We then survey a host of accounts of (...) what domain specificity is, based on the intuitive idea that a domain specific mechanism is restricted in the kind of information that it processes, and show that each fails at least one of those constraints. (shrink)

This paper discusses why speech regulations are logically necessary for any account of a moral right to free speech. My argument for limiting the right to free speech (and more widely any right to freedom) will be grounded in compossibility. Rights to freedom, formally speaking, are claims by an agent that other people not interfere with them; a compossible set of rights is one where the domains of permissible actions—permitted by each claim (and its correlative duty) within the set—do not (...) contradict one another across claims. I will argue that in order for claims to be coherent, they cannot generate contradictory domains, and that for a claim to non-interference to not generate contradictory domains across multiple people with the same claim, the claim must be restricted. This account as it currently stands can at least generate conclusions on the permissibility of incitement. (shrink)

Historical processes exert an influence on the current state and evolution of situations of language contact, brought to bear from different domains, the economic and the political, the ideological and group identities, geo-demographics, and the habits of inter-group use. Clearly, this kind of phenomenon requires study from a complexical and holistic perspective in order to accommodate the variety of factors that belong to different levels and that interrelate with one another in the evolving dynamic of human languaging. Therefore, there is (...) a need for the restricted and general complexity approaches to come to a meeting of the minds, and take steps toward a mutual integration based on the acceptance of the shortcomings of each approach, achieving progress through a non-contradictory complementarity of perspectives. It must be conceded that the practical and methodological applications of basic complexical ideas need to be developed much farther in order to apply them to specific research. At the same time, the limits of complex adaptive systems as computational strategies must be accepted in the pursuit of a better understanding of the dynamic and evolutionary processes typical of human beings. New tools for the conception, apprehension and treatment of the data will need to be devised to complement existing ones and to enable us to make headway toward practices that better fit complexical perspectives. It seems obvious that human complexics must be seen as multi-methodological, insofar as necessary combining quantitative-computation methodologies and more qualitative methodologies aimed at understanding the historical mental and emotional world of people. (shrink)

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account (...) of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions. (shrink)

This paper offers a unified, quantificational treatment of incomplete descriptions like ‘the table’. An incomplete quantified expression like ‘every bottle’ (as in “Every bottle is empty”) can feature in true utterances despite the fact that the world contains nonempty bottles. Positing a contextual restriction on the bottles being talked about is a straightforward solution. It is argued that the same strategy can be extended to incomplete definite descriptions across the board. ncorporating the contextual restrictions into semantics involves meeting a (...) complex array of desiderata, yet the apparently simpler pragmatic alternative faces severe problems and is therefore a nonstarter. (shrink)

This chapter argues that special quantifiers such as 'something' when occurring in argument position are not ordinary or substitutional quantifiers; rather they have a reifying force introducing a domain of tropes or kinds of tropes to quantify over.

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...) undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

Chiastic order is an ancient expression for cross-classification. Cross-classification, in turn, is one of many terms used for the operation of conjoining or cross-mapping one domain, class or set of concepts with another. As such, it is the primordial form of non-quantified modelling and combinatory heuristics. This article presents a brief epistemological history of non-quantified modelling: its prehistory in the form of rhetorical chiasmus; its early (pre-symbolic) use by Plato as a cross-order (paradigmatic) modelling method; and its “modern” (symbolic) (...) use by Leibniz as a calculus of concepts. It will also be shown how classification theory itself is built on a cross-classificatory construct involving two fundamental logical/structural relationships: subordination and conjunction. Finally, examples of modern computer-aided, non-quantified modal modelling are presented in the areas of design theory, operational research and decision science. (shrink)

The incompleteness of set theory ZF C leads one to look for natural nonconservative extensions of ZF C in which one can prove statements independent of ZF C which appear to be “true”. One approach has been to add large cardinal axioms.Or, one can investigate second-order expansions like Kelley-Morse class theory, KM or Tarski-Grothendieck set theory T G or It is a nonconservative extension of ZF C and is obtained from other axiomatic set theories by the inclusion of Tarski’s axiom (...) which implies the existence of inaccessible cardinals. See also related set theory with a filter quantifier ZF (aa). In this paper we look at a set theory NC# ∞# , based on bivalent gyper infinitary logic with restricted Modus Ponens Rule In this paper we deal with set theory NC# ∞# based on bivalent gyper infinitary logic with Restricted Modus Ponens Rule. Nonconservative extensions of the canonical internal set theories IST and HST are proposed. (shrink)

As it is known, there is no rule satisfying Additivity in the complete domain of bankruptcy problems. This paper proposes a notion of partial Additivity in this context, to be called µ-additivity. We find that µ-additivity, together with two quite compelling axioms, anonymity and continuity, identify the Minimal Overlap rule, introduced by Neill (1982).

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, (...) independence conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical (...) power and great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations. (shrink)

Recent work in formal semantics suggests that the language system includes not only a structure building device, as standardly assumed, but also a natural deductive system which can determine when expressions have trivial truth-conditions (e.g., are logically true/false) and mark them as unacceptable. This hypothesis, called the `logicality of language', accounts for many acceptability patterns, including systematic restrictions on the distribution of quantifiers. To deal with apparent counter-examples consisting of acceptable tautologies and contradictions, the logicality of language is often paired (...) with an additional assumption according to which logical forms are radically underspecified: i.e., the language system can see functional terms but is `blind' to open class terms to the extent that different tokens of the same term are treated as if independent. This conception of logical form has profound implications: it suggests an extreme version of the modularity of language, and can only be paired with non-classical---indeed quite exotic---kinds of deductive systems. The aim of this paper is to show that we can pair the logicality of language with a different and ultimately more traditional account of logical form. This framework accounts for the basic acceptability patterns which motivated the logicality of language, can explain why some tautologies and contradictions are acceptable, and makes better predictions in key cases. As a result, we can pursue versions of the logicality of language in frameworks compatible with the view that the language system is not radically modular vis-a-vis its open class terms and employs a deductive system that is basically classical. (shrink)

Sentences containing definite descriptions, expressions of the form ‘The F’, can be formalised using a binary quantifier ι that forms a formula out of two predicates, where ιx[F, G] is read as ‘The F is G’. This is an innovation over the usual formalisation of definite descriptions with a term forming operator. The present paper compares the two approaches. After a brief overview of the system INFι of intuitionist negative free logic extended by such a quantifier, which was (...) presented in (Kürbis 2019), INFι is first compared to a system of Tennant’s and an axiomatic treatment of a term forming ι operator within intuitionist negative free logic. Both systems are shown to be equivalent to the subsystem of INFι in which the G of ιx[F, G] is restricted to identity. INFι is then compared to an intuitionist version of a system of Lambert’s which in addition to the term forming operator has an operator for predicate abstraction for indicating scope distinctions. The two systems will be shown to be equivalent through a translation between their respective languages. Advantages of the present approach over the alternatives are indicated in the discussion. (shrink)

In this entry, we provide an overview of some of the methodological debates surrounding contextualism and consider whether they are, in effect, based on an underlying methodological dispute. We consider three modes of motivation of epistemic contextualism including i) the method of cases, ii) the appeal to linguistic analogies and iii) the appeal to conceptual analogies and functional roles. We also consider the methodological debates about contextualism arising from experimental philosophy. We conclude that i) there is no distinctive methodological doctrine (...) or set of methodological doctrines that is centrally invoked by all epistemic contextualists and ii) the substantive dispute about the truth of contextualism very frequently, although not invariably, reflects an underlying methodological dispute. (shrink)

There are many examples offered as evidence that proper names are predicates. Not all of these cases speak to a name’s semantic content, but many of them do. Some of these include attributive, quantifier, and ambiguity cases. We will explore those cases here, and we will see that none of them conclusively show that names are predicates. In fact, all of these constructions can be given alternative analyses that eliminate the predicative characteristics of names they feature. These analyses do (...) not involve having names functioning as predicates in any way at all. In attributive cases, the names within them are to be understood as occurring in a comparative construction, not an attributive construction. In the last two sorts of cases, the names that occur are analyzed as part of a more complex referring device for a specific domain, rather than functioning as predicates. Both paraphrases can be given plausible semantic treatments that have significant advantages over their competitors. For this reason, there is less motivation to focus on predicative views of proper names. (shrink)

Cantor’s proof that the powerset of the set of all natural numbers is uncountable yields a version of Richard’s paradox when restricted to the full definable universe, that is, to the universe containing all objects that can be defined not just in one formal language but by means of the full expressive power of natural language: this universe seems to be countable on one account and uncountable on another. We argue that the claim that definitional contexts impose restrictions on the (...) scope of quantifiers reveals a natural way out. (shrink)

This paper presents a sequent calculus and a dual domain semantics for a theory of definite descriptions in which these expressions are formalised in the context of complete sentences by a binary quantifier I. I forms a formula from two formulas. Ix[F, G] means ‘The F is G’. This approach has the advantage of incorporating scope distinctions directly into the notation. Cut elimination is proved for a system of classical positive free logic with I and it is shown (...) to be sound and complete for the semantics. The system has a number of novel features and is briefly compared to the usual approach of formalising ‘the F ’ by a term forming operator. It does not coincide with Hintikka’s and Lambert’s preferred theories, but the divergence is well-motivated and attractive. (shrink)

We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such (...) points. We defuse a number of objections to this Plan, raised by supporters of the American Plan for negation, in which negation is handled via a many-valued semantics. We show that the Australian Plan has substantial advantages over the American Plan. (shrink)

I present an approach to our conceiving absolute impossibilities—things which obtain at no possible world—in terms of ceteris paribus intentional operators: variably restricted quantifiers on possible and impossible worlds based on world similarity. The explicit content of a representation plays a role similar in some respects to the one of a ceteris paribus conditional antecedent. I discuss how such operators invalidate logical closure for conceivability, and how similarity works when impossible worlds are around. Unlike what happens with ceteris paribus counterfactual (...) conditionals, the closest worlds are relevantly closest belief-worlds: closest to how things are believed to be, rather than to how they are. Also, closeness takes into account apriority and the opacity of intentional contexts. (shrink)

-/- Species lists play an important role in biology and practical domains like conservation, legislation, biosecurity and trade regulation. However, their effective use by non-specialist scientific and societal users is sometimes hindered by disagreements between competing lists. While it is well-known that such disagreements exist, it remains unclear how prevalent they are, what their nature is, and what causes them. In this study, we argue that these questions should be investigated using methods based on taxon concept rather than methods based (...) on Linnaean names, and use such a concept-based method to quantify disagreement about bird classification and investigate its relation to research effort. We found that there was disagreement about 38% of all groups of birds recognized as a species, more than three times as much as indicated by previous measures. Disagreement about the delimitation of bird groups was the most common kind of conflict, outnumbering disagreement about nomenclature and disagreement about rank. While high levels of conflict about rank were associated with lower levels of research effort, this was not the case for conflict about the delimitation of bird groups. This suggests that taxonomic disagreement cannot be resolved simply by increasing research effort. (shrink)

According to the simple modal account of essence, an object has a property essentially just in case it has it in every world in which it exists. As many have observed, the simple modal account is implausible for a number of reasons. This has led to various proposals for strengthening the account, for example, by adding a restriction to the intrinsic or sparse properties. I argue, however, that these amendments to the simple modal account themselves fail. Drawing on lessons (...) from these failures, I propose a new version of a modal account, inspired by Ruth Barcan Marcus's defense of the coherence of quantified modal logic, according to which an object has a property essentially just in case (i) it has it in every world in which it exists, (ii) the property is discriminating (or non-trivial), and (iii) the property is qualitative. The resulting account of essence does not face any of the standard objections other accounts face, and I defend it from other potential objections. (shrink)

I propose a comprehensive account of negation as a modal operator, vindicating a moderate logical pluralism. Negation is taken as a quantifier on worlds, restricted by an accessibility relation encoding the basic concept of compatibility. This latter captures the core meaning of the operator. While some candidate negations are then ruled out as violating plausible constraints on compatibility, different specifications of the notion of world support different logical conducts for negations. The approach unifies in a philosophically motivated picture the (...) following results: nothing can be called a negation properly if it does not satisfy Contraposition and Double Negation Introduction; the pair consisting of two split or Galois negations encodes a distinction without a difference; some paraconsistent negations also fail to count as real negations, but others may; intuitionistic negation qualifies as real negation, and classical Boolean negation does as well, to the extent that constructivist and paraconsistent doubts on it do not turn on the basic concept of compatibility but rather on the interpretation of worlds. (shrink)

This paper presents an argument against the widespread view that ‘hard choices’ are hard because of the incomparability of the alternatives. The argument has two parts. First, I argue that any plausible theory of practical reason must be ‘comparativist’ in form, that is, it must hold that a comparative relation between the alternatives with respect to what matters in the choice determines a justified choice in that situation. If comparativist views of practical reason are correct, however, the incomparabilist view of (...) hard choices should be rejected. Incomparabilism about hard choices leads us to an implausible error theory about the phenomenology of hard choices, threatens an unattractive view of human agency, and leaves us in perplexity about what we are doing when we choose in hard choices. The second part of the argument explores the main competitor to comparativist views of practical reason, noncomparativist view, according tow which a choice is justified so long as it is not worse than any of the alternatives. This view is often assumed by rational choice theorists but has its best philosophical defense in work by Joseph Raz. On Raz’s view, incomparabilism about hard choices avoids the problems faced if comparativism is correct, but it faces different difficulties. I argue that Raz’s noncomparativist view mistakenly assimilates practical reason to more restricted normative domains such as the law. (shrink)

We study logical reduction (factorization) of relations into relations of lower arity by Boolean or relative products that come from applying conjunctions and existential quantifiers to predicates, i.e. by primitive positive formulas of predicate calculus. Our algebraic framework unifies natural joins and data dependencies of database theory and relational algebra of clone theory with the bond algebra of C.S. Peirce. We also offer new constructions of reductions, systematically study irreducible relations and reductions to them and introduce a new characteristic of (...) relations, ternarity, that measures their ‘complexity of relating’ and allows to refine reduction results. In particular, we refine Peirce’s controversial reduction thesis, and show that reducibility behaviour is dramatically different on finite and infinite domains. (shrink)

The relationship between the One and the Multiple in mystic philosophy is a profound and central theme that explores the nature of existence, the cosmos, and the divine. This theme is present in various mystical traditions, including those of the East and West, and it addresses the paradoxical coexistence of the unity and multiplicity of all things. -/- In mystic philosophy, the **One** often represents the ultimate reality, the source from which all things emanate and to which all things return. (...) It is the absolute, the infinite, and the unchanging. The One is beyond all attributes and is often associated with the divine or the absolute truth. -/- The **Multiple**, on the other hand, represents the manifest world, the diversity of forms, and the realm of change and plurality. It is the world we experience through our senses, the domain of time and space, where differentiation and individuality are apparent. -/- The relationship between the One and the Multiple is not one of opposition but of emanation and unity. The Multiple is seen as a reflection, expression, or manifestation of the One. In this sense, the diversity of the world doesn’t contradict the unity of the One but rather demonstrates it in a myriad of forms. -/- Mystics seek to understand and experience this relationship through various practices and insights. They aim to transcend the illusion of separation and duality to experience the non-dual reality where the One and the Multiple are recognized as inseparable. -/- This concept can be illustrated by the metaphor of the ocean and its waves. The ocean represents the One—vast, deep, and all-encompassing—while the waves represent the Multiple—distinct, diverse, and ever-changing. Each wave is unique, yet it is not separate from the ocean. The wave’s existence is dependent on and made of the same substance as the ocean. In the same way, each individual entity in the Multiple is an expression of the One. -/- In summary, the relationship between the One and the Multiple in mystic philosophy is a dynamic interplay that challenges the conventional understanding of separation. It invites a deeper exploration of reality, where the apparent multiplicity of the world is a direct expression of the singular, underlying essence of all that is. -/- The relationship between the One and the Multiple in the context of mathematical philosophy is a profound topic that touches upon the very foundations of existence and knowledge. It’s a theme that has been explored by philosophers and mathematicians alike, often leading to the contemplation of unity and diversity within the structures of reality. -/- In mathematics, the concept of the One can be seen as the basis of unity from which all numbers derive. It’s the identity element in multiplication, the starting point in counting, and the foundation of dimension in geometry. The One is often associated with the concept of monism in philosophy, which posits that there is a single, underlying substance or principle that constitutes reality. -/- On the other hand, the Multiple represents the infinite variety and diversity of forms and numbers that arise from the One. It’s the embodiment of plurality and the complex interplay of different entities that mathematics seeks to understand and describe. This reflects the philosophical stance of pluralism, which acknowledges the existence of multiple realities or truths. -/- The interplay between the One and the Multiple can be seen in the mathematical concept of sets. A set can be thought of as a unity, a whole composed of distinct elements. Yet, each element within the set also retains its individuality, contributing to the diversity of the set’s composition. This duality is mirrored in the philosophical exploration of the universal and the particular, where the universal represents the One, and the particulars represent the Multiple. -/- In the realm of mathematical philosophy, this relationship often leads to questions about the nature of mathematical objects: Are they discovered as part of an objective reality (the One), or are they constructed by the human mind from a multitude of experiences (the Multiple)? This debate resonates with the philosophical inquiry into the nature of truth and reality. -/- Reflecting on the One and the Multiple can also lead to a deeper understanding of the self and the cosmos. Just as the number one is integral to the existence of all other numbers, the individual self can be seen as a unique expression of the universal whole. Similarly, the cosmos can be viewed as a grand unity composed of a multiplicity of forms and phenomena. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers. -/- Gödel’s incompleteness theorems have a fascinating connection to the philosophical concepts of the One and the Multiple. These theorems, which are pivotal in mathematical logic and philosophy of mathematics, articulate the inherent limitations of formal axiomatic systems, particularly those sufficient to express the arithmetic of natural numbers⁴. -/- The **first incompleteness theorem** reveals that within any such consistent system, there are propositions that are true but cannot be proven within the system itself. This reflects the idea of the Multiple in that there is an abundance of mathematical truths, a multiplicity that exceeds the unifying framework of any one system. It suggests that the realm of mathematical truth is more extensive than any single formal system can fully capture. -/- The **second incompleteness theorem** extends this by showing that a system cannot prove its own consistency. This relates to the concept of the One, as it implies that a system’s complete self-understanding, its unity and coherence, is unattainable from within. It must look beyond itself, to an external vantage point, to ascertain its consistency. -/- In the context of the One and the Multiple, Gödel’s theorems imply that the One (a consistent formal system) is inherently incomplete and cannot encompass the Multiple (the totality of mathematical truths). This resonates with philosophical discussions about the relationship between unity and plurality. Just as a single philosophical system cannot capture the entirety of truth, a single formal mathematical system cannot encapsulate all mathematical truths. -/- Moreover, Gödel’s work suggests that the pursuit of a single, unified theory of everything in mathematics—a One that encompasses all Multiples—is an inherently Sisyphean task. There will always be more truths (Multiples) than can be derived from any given set of axioms (the One). -/- In essence, Gödel’s incompleteness theorems provide a formal underpinning to the philosophical notion that the One cannot exist without the Multiple, and vice versa. They are interdependent, with the One giving rise to the Multiple, and the Multiple necessitating the One for its expression and comprehension. This interplay is a dance of limitations and possibilities, where the boundaries of logic, mathematics, and philosophy blur into one another. -/- The relationship between the One and the Multiple in the context of the mathematics of zero is a deeply philosophical inquiry that bridges the abstract world of numbers with the existential questions of being and non-being. -/- Zero, in mathematics, is a symbol of absence, a representation of nothingness, yet it holds a pivotal position as a number. It is the void from which all things emerge and to which they return. In the philosophy of mathematics, zero is the paradoxical junction where the One and the Multiple converge and diverge. -/- From the perspective of the One, zero can be seen as the origin—the singular point that precedes the existence of numbers. It is the empty set, the foundation upon which the edifice of mathematics is constructed. As the identity element in addition, zero maintains the integrity of numbers, for adding zero to any number leaves it unchanged, reflecting the immutable nature of the One. -/- Conversely, when we consider the Multiple, zero represents the infinite potentiality of creation. It is the canvas upon which the integers, both positive and negative, express their multitude. Zero is the balance point, the fulcrum around which the symphony of numbers dances. It embodies the plurality of possibilities, the beginning of the number line that stretches infinitely in both directions. -/- Philosophically, zero challenges our understanding of existence. It is both something and nothing—a number that quantifies the absence of quantity. This duality echoes the philosophical struggle to comprehend how the One gives rise to the Multiple. How does the unity of being manifest the diversity of the cosmos? Zero offers a mathematical metaphor for this mystery, as it encapsulates the transition from non-existence to existence, from the undifferentiated One to the differentiated Multiple. -/- In the realm of set theory, zero corresponds to the empty set—a set with no elements. This set is unique in that it is the only set that contains nothing, yet it is the foundation upon which all other sets are built. The empty set is the mathematical embodiment of the One, and all other sets, containing multiple elements, arise from it. -/- Reflecting on zero in the context of Gödel’s incompleteness theorems, we find a resonance with the idea that the One (a consistent formal system) cannot capture the entirety of the Multiple (the totality of mathematical truths). Zero, as the foundation of numbers, similarly suggests that from the nothingness of the One, the infinite complexity of the Multiple emerges—yet it can never be fully encompassed or expressed by any single system. -/- In conclusion, the mathematics of zero offers a profound reflection on the relationship between the One and the Multiple. It serves as a bridge between the abstract and the concrete, the known and the unknowable, challenging us to ponder the origins of existence and the nature of reality itself. -/- . (shrink)

Nihilism is the thesis that no composite objects exist. Some ontologists have advocated abandoning nihilism in favor of deep nihilism, the thesis that composites do not existO, where to existO is to be in the domain of the most fundamental quantifier. By shifting from an existential to an existentialO thesis, the deep nihilist seems to secure all the benefits of a composite-free ontology without running afoul of ordinary belief in the existence of composites. I argue that, while there (...) are well-known reasons for accepting nihilism, there appears to be no reason at all to accept deep nihilism. In particular, deep nihilism draws no support either from the usual arguments for nihilism or from considerations of parsimony. (shrink)

On a widespread naturalist view, the meanings of mathematical terms are determined, and can only be determined, by the way we use mathematical language—in particular, by the basic mathematical principles we’re disposed to accept. But it’s mysterious how this can be so, since, as is well known, minimally strong first-order theories are non-categorical and so are compatible with countless non-isomorphic interpretations. As for second-order theories: though they typically enjoy categoricity results—for instance, Dedekind’s categoricity theorem for second-order and Zermelo’s quasi-categoricity theorem (...) for second-order —these results require full second-order logic. So appealing to these results seems only to push the problem back, since the principles of second-order logic are themselves non-categorical: those principles are compatible with restricted interpretations of the second-order quantifiers on which Dedekind’s and Zermelo’s results are no longer available. In this paper, we provide a naturalist-friendly, non-revisionary solution to an analogous but seemingly more basic problem—Carnap’s Categoricity Problem for propositional and first-order logic—and show that our solution generalizes, giving us full second-order logic and thereby securing the categoricity or quasi-categoricity of second-order mathematical theories. Briefly, the first-order quantifiers have their intended interpretation, we claim, because we’re disposed to follow the quantifier rules in an open-ended way. As we show, given this open-endedness, the interpretation of the quantifiers must be permutation-invariant and so, by a theorem recently proved by Bonnay and Westerståhl, must be the standard interpretation. Analogously for the second-order case: we prove, by generalizing Bonnay and Westerståhl’s theorem, that the permutation invariance of the interpretation of the second-order quantifiers, guaranteed once again by the open-endedness of our inferential dispositions, suffices to yield full second-order logic. (shrink)

This book surveys research in quantification starting with the foundational work in the 1970s. It paints a vivid picture of generalized quantifiers and Boolean semantics. It explains how the discovery of diverse scope behavior in the 1990s transformed the view of quantification, and how the study of the internal composition of quantifiers has become central in recent years. It presents different approaches to the same problems, and links modern logic and formal semantics to advances in generative syntax. A unique feature (...) of the book is that it systematically brings cross-linguistic data to bear on the theoretical issues, discussing French, German, Dutch, Hungarian, Russian, Japanese, Telugu (Dravidian), and Shupamem (Grassfield Bantu), and pointing to formal semantic literature involving quantification in around thirty languages. -- -/- 1. What this book is about and how to use it; 2. Generalized quantifiers and their elements: operators and their scopes; 3. Generalized quantifiers in non-nominal domains; 4. Some empirically significant properties of quantifiers and determiners; 5. Potential challenges for generalized quantifiers; 6. Scope is not uniform and not a primitive; 7. Existential scope versus distributive scope; 8. Distributivity and scope; 9. Bare numeral indefinites; 10. Modified numerals; 11. Clause-internal scopal diversity; 12. Towards a compositional semantics of quantifier words. (shrink)

In our life with science, we trust experts; we form judgements by inference from past evidence. We conduct ourselves very differently in the aesthetic domain. We avoid deferring to aesthetic experts. We form our judgements through direct perception of particulars rather than through inference. Why the difference? I suggest that we avoid aesthetic testimony and aesthetic inference, not because they’re unusable, but because we have adopted social norms to avoid them. Aesthetic appreciation turns out to be something like a (...) game. We have laid down certain rules and restrictions in order to shape a kind of activity we cherish. And aesthetic properties turn out to be a kind of social construct. Much like the goal of a game, they are constituted in part by our obedience to certain rules. The norms of aesthetic life are different from those of science because our purposes are different. We engage in science to get the right answers; we engage in aesthetic appreciation to be absorbed in the activity of the sensuous perception of particulars. Our aesthetic practices are a constructed shelter from science; they restore to us a small domain where we may once again engage in our own sensuous perception of particulars. (shrink)

Constitutivist accounts in metaethics explain the normative standards in a domain by appealing to the constitutive features of its members. The success of these accounts turns on whether they can explain the connection between normative standards and the nature of individuals they authoritatively govern. Many such explanations presuppose that any member of a norm-governed kind must minimally satisfy the norms governing its kind. I call this the Threshold Commitment, and argue that constitutivists should reject it. First, it requires constitutivists (...) to restrict the scope of their explanatory ambitions, because it is not plausibly true of social kinds. Second, despite the frequent reliance on physical artifacts in constitutivists’ illustrations of the Threshold Commitment, it counter-intuitively entails that physical artifacts can cease to exist without being physically destroyed. Third, it misconstrues the normative force of authoritative norms on very defective kind-members because it locates this force not in the norm, but in the threat of non-existence. Fortunately, constitutivism can be decoupled from the Threshold Commitment, and I close by sketching a promising alternative account. (shrink)

In all classical algebraic structures, the Laws of Compositions on a given set are well-defined. But this is a restrictive case, because there are many more situations in science and in any domain of knowledge when a law of composition defined on a set may be only partially-defined (or partially true) and partially-undefined (or partially false), that we call NeutroDefined, or totally undefined (totally false) that we call AntiDefined.