This article discusses a relation between the formal science of logical semantics and some monotheistic, polytheistic and Trinitarian Christian notions. This relation appears in the use of the existential quantifier and of logical-modal notions when some monotheistic and polytheistic concepts and, principally, the concept of Trinity Dogma are analyzed. Thus, some presupposed modal notions will appear in some monotheistic propositions, such as the notion of “logically necessary”. From this, it will be shown how the term “God” is a (...) polysemic term and is often treated as both subject and predicate. This will make it clear that there is no plausible intellectual justification for believing that the term “God” can only be used as a name and never as a predicate, and vice versa. After that analysis, I will show that the conjunction of the “Trinity Dogma” with some type of “monotheistic position” would necessarily imply some class of absurdity and/or semantic “oddity”. (shrink)

There is a significant difference between the words `is' and `exists' that has either been overlooked or under-appreciated by many philosophers. This difference comes in sentences that express existential quantification using `is', `exists', or their cognates, such as, "There are cookies in the jar," or, "There exists a strange species of fish that nobody has studied yet." Phrases such as `there are' and `there exists' are existential quantifier expressions, since they're used to express existential quantification. The (...) orthodox view of these expressions is that they are, in the words of David K. Lewis, "entirely synonymous and interchangeable". This dissertation presents and argues for an anti-orthodox view of meaning of `there is' and `there exists'. The root of the difference in meaning between the two expressions is that `there is' turns out to be context-sensitive, on the model of demonstratives like `this' or `that', while `there exists' is invariant in its meaning. These views are motivated through the introduction of a notion called `ontological robustness', which helps us evaluate the level of ontological commitment in our assertions. The anti-orthodox view is defended over orthodoxy through holistic arguments that compare the virtues of each theory, including such metrics as how they fare in accounting for our stubborn desire to talk about and quantify over nonexistent objects. (shrink)

Human civilisation faces a range of existential risks, including nuclear war, runaway climate change and superintelligent artificial intelligence run amok. As we show here with calculations for the New Zealand setting, large numbers of currently living and, especially, future people are potentially threatened by existential risks. A just process for resource allocation demands that we consider future generations but also account for solidarity with the present. Here we consider the various ethical and policy issues involved and make a (...) case for further engagement with the New Zealand public to determine societal values towards future lives and their protection. (shrink)

Formal semantic analyses often take words to be minimal building blocks for the purposes of compositionality. But various recent theories of morphology and syntax have converged on the view that there is no demarcation line corresponding to the word level. The same conclusion has emerged from the compositional semantics of superlatives. In the spirit of extending compositionality below the word level, this paper explores how a small set of particles (Japanese KA and MO, Chinese DOU, and Hungarian VALA/VAGY, MIND, and (...) IS) form quantifier words and serve as connectives, additive and scalar particles, question markers, and existential verbs. The main question is whether the meanings of these particles across the varied environments are highly regular, or they are lexicalized with a variety of different meanings that bear a family resemblance. This paper does not reach definitive conclusions, but it raises analytical possibilities using Boolean semantics and the semantics of alternatives. It also draws attention to systematic similarities and some differences between MO and DOU that have not been studied in the literature. (shrink)

The aim of the paper is to bring clarity regarding the doctrine of quantifier variance (due to Eli Hirsch), and two prominent arguments against this doctrine, the collapse argument and the Eklund-Hawthorne argument. Different versions of the doctrine of quantifier variance are distinguished, and it is shown that the effectiveness of the arguments against it depends on what version of the doctrine is at issue. The metaontological significance of the different versions of the doctrine are also assessed. Roughly, (...) quantifier variance concerns there being different possible existential quantifier meanings, and often the doctrine involves a claim to the effect there is no unique “best” quantifier meaning. Much of the discussion in the paper concerns what it is to be an existential quantifier meaning in the sense at issue. (shrink)

I here argue that Ted Sider's indeterminacy argument against vagueness in quantifiers fails. Sider claims that vagueness entails precisifications, but holds that precisifications of quantifiers cannot be coherently described: they will either deliver the wrong logical form to quantified sentences, or involve a presupposition that contradicts the claim that the quantifier is vague. Assuming (as does Sider) that the “connectedness” of objects can be precisely defined, I present a counter-example to Sider's contention, consisting of a partial, implicit definition of (...) the existential quantifier that in effect sets a given degree of connectedness among the putative parts of an object as a condition upon there being something (in the sense in question) with those parts. I then argue that such an implicit definition, taken together with an “auxiliary logic” (e.g., introduction and elimination rules), proves to function as a precisification in just the same way as paradigmatic precisifications of, e.g., “red”. I also argue that with a quantifier that is stipulated as maximally tolerant as to what mereological sums there are, precisifications can be given in the form of truth-conditions of quantified sentences, rather than by implicit definition. (shrink)

In many languages, the same particles that form quantifier words also serve as connectives, additive and scalar particles, question markers, roots of existential verbs, and so on. Do these have a unified semantics, or do they merely bear a family resemblance? Are they aided by silent operators in their varied roles―if yes, what operators? I dub the particles “quantifier particles” and refer to them generically with capitalized versions of the Japanese morphemes. I argue that both MO and (...) KA can be assigned a stable semantics across their various roles. The specific analysis I offer is motivated by the fact that MO and KA often combine with just one argument; I propose that this is their characteristic behavior. Their role is to impose semantic requirements that are satisfied when the immediately larger context is interpreted as the meet/join of their host’s semantic contribution with something else. They do not perform meet/join themselves. The obligatory vs. optional appearance of the particles depends on whether the meet/join interpretations arise by default in the given constellation. I explicate the proposal using the toolkit of basic Inquisitive Semantics. (shrink)

It is a received view of the post-Fregean predicate logic that a universal statement has no existential import and thus does not entail its particular (existential) counterpart. This paper takes issue with the view by discussing the trespasser case, which has widely been employed for supporting the view. The trespasser case in fact involves a shift of context. Properly understood, the case provides no support for the received view but rather suggests that we rethink the ‘quantity view’ of (...) the existential import of quantifiers. (shrink)

In many languages, the same particles build quantifier words and serve as connectives, additive and scalar particles, question markers, existential verbs, and so on. Do the roles of each particle form a natural class with a stable semantics? Are the particles aided by additional elements, overt or covert, in fulfilling their varied roles? I propose a unified analysis, according to which the particles impose partial ordering requirements (glb and lub) on the interpretations of their hosts and the immediate (...) larger contexts, but do not embody algebraic operations themselves. (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)

We re-examine the problem of existential import by using classical predicate logic. Our problem is: How to distribute the existential import among the quantified propositions in order for all the relations of the logical square to be valid? After defining existential import and scrutinizing the available solutions, we distinguish between three possible cases: explicit import, implicit non-import, explicit negative import and formalize the propositions accordingly. Then, we examine the 16 combinations between the 8 propositions having the first (...) two kinds of import, the third one being trivial and rule out the squares where at least one relation does not hold. This leads to the following results: (1) three squares are valid when the domain is non-empty; (2) one of them is valid even in the empty domain: the square can thus be saved in arbitrary domains and (3) the aforementioned eight propositions give rise to a cube, which contains two more (non-classical) valid squares and several hexagons. A classical solution to the problem of existential import is thus possible, without resorting to deviant systems and merely relying upon the symbolism of First-order Logic (FOL). Aristotle’s system appears then as a fragment of a broader system which can be developed by using FOL. (shrink)

‘Quantified pure existentials’ are sentences (e.g., ‘Some things do not exist’) which meet these conditions: (i) the verb EXIST is contained in, and is, apart from quantificational BE, the only full (as against auxiliary) verb in the sentence; (ii) no (other) logical predicate features in the sentence; (iii) no name or other sub-sentential referring expression features in the sentence; (iv) the sentence contains a quantifier that is not an occurrence of EXIST. Colin McGinn and Rod Girle have alleged that (...) standard first-order logic cannot adequately deal with some such existentials. The article defends the view that it can. (shrink)

In this article, logical concepts are defined using the internal syntactic and semantic structure of language. For a first-order language, it has been shown that its logical constants are connectives and a certain type of quantifiers for which the universal and existential quantifiers form a functionally complete set of quantifiers. Neither equality nor cardinal quantifiers belong to the logical constants of a first-order language.

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)

"The main aim of the paper is to compare two types of abstractionistic accounts of fictional objects, and to analyze their consequences for interpretation of existential quantification. According to a proponent of general abstractionistic theory, fictional objects have abstract nature in a way similar to contracts, marriages, and the likes. This view is an alternative to strongly realistic accounts of fictional objects, defended by Terence Parsons or David Lewis. Within abstractionistic theories, as in all philosophical areas, one can find (...) divergences of opinions. The main differences between two of them – Peter van Inwagen's and Edward Zalta's – are connected with the interpretation of existential quantification. According to van Inwagen, “being” is the same as “existence” and its sense is captured by the existential quantifier. Edward Zalta's theory is much closer to the Meinongian Theory of Objects. He argues for the need of distinguishing between “being” and “existence” and for invoking nonexistent objects. Because of that he suggests an alternative interpretation of quantification. Admittedly, there is one abstractionistic source for both theories, but their ontological consequences are different - van Inwagen is a staunch opponent of nonexistent objects, and Zalta describes his own theory as "Meinongian".". (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)

In his contribution, Mark Alfano lays out a new (to virtue theory) naturalistic way of determining what the virtues are, what it would take for them to be realized, and what it would take for them to be at least possible. This method is derived in large part from David Lewis’s development of Frank Ramsey’s method of implicit definition. The basic idea is to define a set of terms not individually but in tandem. This is accomplished by assembling all and (...) only the common sense platitudes that involve them (e.g., typically, people want to be virtuous), conjoining those platitudes, and replacing the terms in question by existentially quantified variables. If the resulting sentence is satisfied, then whatever satisfies are the virtues. If it isn’t satisfied, there are a couple of options. First, one could just admit defeat by saying that people can’t be virtuous. More plausibly, one could weaken the conjunction by dropping a small number of the platitudes from it (and potentially adding some others). Alfano suggests that the most attractive way to do this is by dropping the platitudes that deal with cross-situational consistency and replacing them with platitudes that involve social construction: basically, people are virtuous (when they are) at least in part because other people signal their expectations of virtuous conduct, which induces virtuous conduct, which in turn induces further signals of expected virtuous conduct, and so on. (shrink)

The meaning of definite descriptions (like ‘the King of France’, ‘the girl’, etc.) has been a central topic in philosophy and linguistics for the past century. Indefinites (‘Something is on the floor’, ‘A child sat down’, etc.) have been relatively neglected in philosophy, under the Russellian assumption that they can be unproblematically treated as existential quantifiers. However, an important tradition, drawing from Stoic logic, has pointed to patterns which suggest that indefinites cannot be treated simply as existential quantifiers. (...) The standard dynamic semantic treatment of those phenomena, however, has well-known problems with negation and disjunction. -/- In this paper I develop a new approach to (in)definites. On my theory, truth-conditions are classical. But in addition to truth-conditions, meanings comprise a second dimension of what I call bounds. It is at the level of bounds, not truth-conditions, that I locate the characteristically dynamic coordination between indefinites and definites. The resulting system thus has a classical logic. This approach avoids dynamic semantics’ logical problems, and, more generally, yields a new perspective on the relation between truth-conditional and dynamic effects in natural language. (shrink)

Popper's well-known demarcation criterion has often been understood to distinguish statements of empirical science according to their logical form. Implicit in this interpretation of Popper's philosophy is the belief that when the universe of discourse of the empirical scientist is infinite, empirical universal sentences are falsifiable but not verifiable, whereas the converse holds for existential sentences. A remarkable elaboration of this belief is to be found in Watkins's early work on the statements he calls “all-and-some,” such as: “For every (...) metal there is a melting point.” All-and-some statements are both universally and existentially quantified in that order. Watkins argued that AS should be regarded as both nonfalsifiable and nonverifiable, for they partake in the logical fate of both universal and existential statements. This claim is subject to the proviso that the bound variables are “uncircumscribed” ; i.e., that the universe of discourse is infinite. (shrink)

I use the Corcoran–Smiley interpretation of Aristotle's syllogistic as my starting point for an examination of the syllogistic from the vantage point of modern proof theory. I aim to show that fresh logical insights are afforded by a proof-theoretically more systematic account of all four figures. First I regiment the syllogisms in the Gentzen–Prawitz system of natural deduction, using the universal and existential quantifiers of standard first-order logic, and the usual formalizations of Aristotle's sentence-forms. I explain how the syllogistic (...) is a fragment of my system of Core Logic. Then I introduce my main innovation: the use of binary quantifiers, governed by introduction and elimination rules. The syllogisms in all four figures are re-proved in the binary system, and are thereby revealed as all on a par with each other. I conclude with some comments and results about grammatical generativity, ecthesis, perfect validity, skeletal validity and Aristotle's chain principle. (shrink)

Clare Batty has recently argued that the content of human olfactory experience is 'a very weak kind of abstract, or existentially quantified content', and so that 'there is no way things smell'. Her arguments are based on two claims. Firstly, that there is no intuitive distinction between olfactory hallucination and olfactory illusion. Secondly, that olfaction 'does not present smell at particular locations', and 'seems disengaged from any particular object'. The present article shows both of these claims to be false. It (...) shows that naïve subjects find it quite natural to draw a distinction between olfactory hallucination and olfactory illusion. And it argues that the phenomenology of normal olfactory experience is of particular objects as having smells. Two confusions are responsible for Batty thinking otherwise: (1) Batty's examples are cases of extreme pungency, and she mistakes a peculiarity of intense perceptions for a property of olfaction more generally; (2) Batty focuses on very short time slices and so confuses limitations on the information carried by a single sniff for a limitation on the logical form of all olfactory content. (shrink)

Data involving epistemic modals suggest that some classically valid argument forms, such as _reductio_, are invalid in natural language reasoning as they lead to modal collapses. We adduce further data showing that the classical argument forms governing the existential quantifier are similarly defective, as they lead to a _de re–de dicto_ collapse. We observe a similar problem for disjunction. But if the classical argument forms for negation, disjunction and existential quantification are invalid, what are the correct forms (...) that govern the use of these items? Our diagnosis is that epistemic modals interfere with hypothetical reasoning. We present a modal first-order logic and model theory that characterizes hypothetical reasoning with epistemic modals in a principled manner. One upshot is a sound and complete natural deduction system for reasoning with epistemic modals in first-order logic. (shrink)

Existentialist accounts maintain that visual phenomenal content takes the logical form of an existentially quantified sentence. These accounts do not make phenomenal content specific enough. Singularist accounts posit a singular content in which the seen object is a constituent. These accounts make phenomenal content too specific. My account gets the specificity of visual phenomenal content just right. My account begins with John Searle's suggestion that visual experience represents an object as seen, moves this relation outside the scope of the (...) class='Hi'>existential quantifier and then replaces it with the relation of objects being ‘present as accessible’, as described by Alva Noë. (shrink)

Combinatory logic (Curry and Feys 1958) is a “variable-free” alternative to the lambda calculus. The two have the same expressive power but build their expressions differently. “Variable-free” semantics is, more precisely, “free of variable binding”: it has no operation like abstraction that turns a free variable into a bound one; it uses combinators—operations on functions—instead. For the general linguistic motivation of this approach, see the works of Steedman, Szabolcsi, and Jacobson, among others. The standard view in linguistics is that reflexive (...) and personal pronouns are free variables that get bound by an antecedent through some coindexing mechanism. In variable free semantics the same task is performed by some combinator that identifies two arguments of the function it operates on (a duplicator). This combinator may be built into the lexical semantics of the pronoun, into that of the antecedent, or it may be a free-floating operation applicable to predicates or larger chunks of texts, i.e. a typeshifter. This note is concerned with the case of cross-sentential anaphora. It adopts Hepple’s and Jacobson’s interpretation of pronouns as identity maps and asks how this can be extended to the cross-sentential case, assuming the dynamic semantic view of anaphora. It first outlines the possibility of interpreting indefinites that antecede non-ccommanded pronouns as existential quantifiers enriched with a duplicator. Then it argues that it is preferable to use the duplicator as a type-shifter that applies “on the fly”. The proposal has consequences for two central ingredients of the classical dynamic semantic treatment: it does away with abstraction over assignments and with treating indefinites as inherently existentially quantified. However, cross-sentential anaphora remains a matter of binding, and the idea of propositions as context change potentials is retained. (shrink)

In a previous work we introduced the algorithm \SQEMA\ for computing first-order equivalents and proving canonicity of modal formulae, and thus established a very general correspondence and canonical completeness result. \SQEMA\ is based on transformation rules, the most important of which employs a modal version of a result by Ackermann that enables elimination of an existentially quantified predicate variable in a formula, provided a certain negative polarity condition on that variable is satisfied. In this paper we develop several extensions of (...) \SQEMA\ where that syntactic condition is replaced by a semantic one, viz. downward monotonicity. For the first, and most general, extension \SSQEMA\ we prove correctness for a large class of modal formulae containing an extension of the Sahlqvist formulae, defined by replacing polarity with monotonicity. By employing a special modal version of Lyndon's monotonicity theorem and imposing additional requirements on the Ackermann rule we obtain restricted versions of \SSQEMA\ which guarantee canonicity, too. (shrink)

The problem concerns quantifiers that seem to hover between universal and existential readings. I argue that they are neither, but a different quantifier that has features of each. NOTE the published paper has a mistake. I have corrected this in the version on this site. A correction note will appear in Analysis.

Much debate in contemporary metaphysics of time has centred on whether or not tense is essential to the understanding of a temporal reality. The rival positions in this debate are associated with two very different pictures of the relationship between time and existence. Those who argue for the dispensability of tense see the phenomenon of tense as an epistemological accretion which infects our perception of the world but is in no way essential to a complete description of reality. With respect (...) to existence, things past and future are supposed to be on an equal footing with things present. Thus the Quinean ‘time slice’ ontology, which sees the world as a four-dimensional entity in space-time, repudiates any ontological significance to the differences between past, present and future. For the Quinean, what differences we see between past, present and future existents pertain to our limited mode of access to reality. In a perception which grasped the world as it really is tense differences would have no place. In this respect the Quinean position resembles Spinoza's claim in the Ethics that in so far as the mind conceives a thing under the dictates of reason it is affected equally, whether the idea be of a thing future, past or present. (shrink)

Donkey sentences have existential and universal readings, but they are not often perceived as ambiguous. We extend the pragmatic theory of nonmaximality in plural definites by Križ (2016) to explain how context disambiguates donkey sentences. We propose that the denotations of such sentences produce truth-value gaps — in certain scenarios the sentences are neither true nor false — and demonstrate that Križ’s pragmatic theory fills these gaps to generate the standard judgments of the literature. Building on Muskens’s (1996) Compositional (...) Discourse Representation Theory and on ideas from supervaluation semantics, the semantic analysis defines a general schema for quantification that delivers the required truth-value gaps. Given the independently motivated pragmatic theory of Križ 2016, we argue that mixed readings of donkey sentences require neither plural information states, contra Brasoveanu 2008, 2010, nor error states, contra Champollion 2016, nor singular donkey pronouns with plural referents, contra Krifka 1996, Yoon 1996. We also show that the pragmatic account improves over alternatives like Kanazawa 1994 that attribute the readings of donkey sentences to the monotonicity properties of the embedding quantifier. (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)

Semantic externalism in the style of McDowell and Evans faces a puzzle formulated by Pryor: to explain that a sentence such as 'Jack exists' is only a posteriori knowable, despite being logically entailed by the seemingly logical truth 'Jack is self-identical', and hence being itself a logical truth and therefore a priori knowable. Free logics can dissolve the puzzle. Moreover, Pryor has argued that the existentially hedged 'If Jack exists, then Jack is self-identical', when properly formalised, is a logical truth (...) in a system of neutral free logic and therefore a priori knowable, while it does not entail that Jack exists. The latter holds also for negative free logic. In response, Yeakel has argued that on any system of neutral free logic existence hedges will either entail some unwanted existence claims or they will not entail some wanted existence claims. The dilemma also holds for any non-positive free logic. It will be shown that the extension of one of the systems of neutral free logic with a truth operator escapes Yeakel's dilemma, whereas no other non-positive free logic when extended with the truth operator does the same (or it breaks quantifier exchangeability). (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

We argue that the extant evidence for Stoic logic provides all the elements required for a variable-free theory of multiple generality, including a number of remarkably modern features that straddle logic and semantics, such as the understanding of one- and two-place predicates as functions, the canonical formulation of universals as quantified conditionals, a straightforward relation between elements of propositional and first-order logic, and the roles of anaphora and rigid order in the regimented sentences that express multiply general propositions. We consider (...) and reinterpret some ancient texts that have been neglected in the context of Stoic universal and existential propositions and offer new explanations of some puzzling features in Stoic logic. Our results confirm that Stoic logic surpasses Aristotle’s with regard to multiple generality, and are a reminder that focusing on multiple generality through the lens of Frege-inspired variable-binding quantifier theory may hamper our understanding and appreciation of pre-Fregean theories of multiple generality. (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)

Excellence in sport performance is normally taken to be a matter of superior performance of physical movements or quantitative outcomes of movements. This paper considers whether a wider conception can be afforded by certain kinds of nature based sport. The interplay between technical skill and aesthetic experience in nature based sports is explored, and the extent to which it contributes to a distinction between different sport-based approaches to natural environments. The potential for aesthetic appreciation of environmental engagement is found to (...) be strongly dependent on whether or not environmental engagement is exploited for the end of producing a quantifiable result or enhancing technical skill. It is also argued that an existential rather than spectatorial attitude to aesthetic experience is offered by specifically nature oriented sport. Aesthetic experience achieved in this way is therefore neither passive nor detached, but extends Berleant's concept of participatory environmental aesthetics and underpins both an alternate (wide) conception of excellence in sport activity and a richer experience of aesthetic engagement than more objectivised standpoints. (shrink)

This paper is about an underappreciated aspect of generics: their non-specificity. Many uses of generics, utterances like ‘Seagulls swoop down to steal food’, express non-specific generalisations which do not specify their quantificational force or flavour. I consider whether this non-specificity arises as a by-product of context-sensitivity or semantic incompleteness but argue instead that generics semantically express non-specific generalisations by default as a result of quantifying existentially over more specific ones.

ABSTRACT: In antiquity we encounter a distinction of two types of hypothetical syllogisms. One type are the ‘mixed hypothetical syllogisms’. The other type is the one to which the present paper is devoted. These arguments went by the name of ‘wholly hypothetical syllogisms’. They were thought to make up a self-contained system of valid arguments. Their paradigm case consists of two conditionals as premisses, and a third as conclusion. Their presentation, either schematically or by example, varies in different authors. For (...) instance, we find ‘If (it is) A, (it is) B; if (it is) B, (it is) C; therefore, if (it is) A, (it is) C’. The main contentious point about these arguments is what the ancients thought their logical form was. Are A, B, C schematic letters for terms or propositions? Is ‘is’, where it occurs, predicative, existential, or veridical? That is, should ‘A esti’ be translated as ‘it is an A’, ‘A exists’, ‘As exist’ or ‘It is true/the case that A’? If A, B, C are term letters, and ‘is’ is predicative, are the conditionals quantified propositions or do they contain designators? If one cannot answer these questions, one can hardly claim to know what sort of arguments the wholly hypothetical syllogisms were. In fact, all the above-mentioned possibilities have been taken to describe them correctly. In this paper I argue that it would be mistaken to assume that in antiquity there was one prevalent understanding of the logical form of these arguments - even if the ancients thought they were all talking about the same kind of argument. Rather, there was a complex development in their understanding, starting from a term-logical conception and leading to a propositional-logical one. I trace this development from Aristotle to Philoponus and set out the deductive system on which the logic of the wholly hypothetical syllogisms was grounded. (shrink)

Noun phrases with overt determiners, such as <i>some apples</i> or <i>a quantity of milk</i>, differ from bare noun phrases like <i>apples</i> or <i>milk</i> in their contribution to aspectual composition. While this has been attributed to syntactic or algebraic properties of these noun phrases, such accounts have explanatory shortcomings. We suggest instead that the relevant property that distinguishes between the two classes of noun phrases derives from two modes of existential quantification, one of which holds the values of a variable (...) fixed throughout a quantificational context while the other allows them to vary. Inspired by Dynamic Plural Logic and Dependence Logic, we propose Plural Predicate Logic as an extension of Predicate Logic to formalize this difference. We suggest that temporal <i>for</i>-adverbials are sensitive to aspect because of the way they manipulate quantificational contexts, and that analogous manipulations occur with spatial <i>for</i>-adverbials, habituals, and the quantifier <i>all</i>. (shrink)

The first part of this article (Sections 1–5) focuses on the classical notions of scope and binding and their formal foundations. It argues that once their semantic core is properly understood, it can be implemented in various different ways: with or without movement, with or without variables. The second part (Sections 6–12) takes up the empirical issues that have redrawn the map in the past two decades. It turns out that scope is not a primitive. Existential scope and distributive (...) scope have to be distinguished, leaving few if any run-of-the-mill quantifiers. Scope behavior is also not uniform. At least three classes of expressions emerge: indefinites, distributive universals, and counters. Likewise, the bound variable interpretation of pronouns is joined by co-variation with situations. As a result, the classical notions of scope and binding are likely to end up as building blocks in the varied mechanisms at work in “scope phenomena” and “binding phenomena”, and not as self-contained analyses of those phenomena. (shrink)

Like Bennett's account of ‘even’, my analysis incorporates the following plausible and widespread intuitions. (a) The word ‘even’ does not make a truth-functional difference; it makes a difference only in conventional implicature. In particular, ‘even’ functions neither as a universal quantifier, nor a most or many quantifier. The only quantified statement that ‘Even A is F’ implies is the existential claim ‘There is an x (namely, A) that is F’, but this implication is nothing more than what (...) the Equivalence Thesis already demands. (b) ‘Even’ is epistemic in character, implying some type of unexpectedness, surprise, or unlikelihood. Moreover, despite Kay's arguments to the contrary, this implication is part of the meaning of ‘even’. (c) ‘Even’ is a scalar term, since unexpectedness comes in degrees. And, finally, (d) the felicity of an ‘even’-sentence S requires that S* be sufficiently surprising in comparison to its true neighbors. However,pace Bennett, being more surprising than just one true neighbor will not suffice. At the same time, being more surprising than all true neighbors is unnecessary. Suffice it that S* is more surprising than most true neighbors. (shrink)

The paper is Part III of the large research, dedicated to both the revision of the system of basic logical categories and the generalization of modern predicate logic to functional logic. We determinate and contrapose modern Fregean logistics and proposed by the author ultra-Fregean logistics, next we describe values and arguments of functions, arguments of relations, relations themselves, sets (classes), and subsets (subclasses) as derivative categories (concepts) of ultrafregean logistics. Logistics is a part of metalogic, independent of semantics. Fregean logictics (...) is a metalogical theory, based on the quadruple <particular (individual), predicate, equality, sequence>; it generates predicate logic. Ultrafregean logictics is based on the quadruple <particular, function, representation, sequence>, where the notion of a function is a generalization of the notion of a predicate and the notion of representation is a generalization of the notion of equality; this logictics generates functional logic. For the completely correct denotation of the functional values, we need the Churchian symbolics with parenthesis. Predicates are usually identified with relations. A relation is the derived and even definable category of ultra-Fregean logictics. Namely, relations are representations by functions (of one of their arguments). We show that Frege could really establish this definition and the notion (category) of representation but, unfortunately, rejected this course of thought. Next, we show that every n-ary relation can be resolved for some of its arguments via some (n-1)-ary function. A set, or class, is a derived and not definable category of ultra-Fregean logistics. The universal way to introduce the sets is Frege’s abstraction principle. We formulate this principle for functional logic and show that the notion of a set is quantified, so there is the dual existential notion of a nonempty subset, involved by the same abstraction principle. (shrink)

The problem of algorithmic structuring of proofs in the sequent calculi LK and LKB ( LK where blocks of quantifiers can be introduced in one step) is investigated, where a distinction is made between linear proofs and proofs in tree form. In this framework, structuring coincides with the introduction of cuts into a proof. The algorithmic solvability of this problem can be reduced to the question of k-l-compressibility: "Given a proof of length k , and l ≤ k : Is (...) there is a proof of length ≤ l ?" When restricted to proofs with universal or existential cuts, this problem is shown to be (1) undecidable for linear or tree-like LK-proofs (corresponds to the undecidability of second order unification), (2) undecidable for linear LKB-proofs (corresponds to the undecidability of semi-unification), and (3) decidable for tree-like LKB -proofs (corresponds to a decidable subprob- lem of semi-unification). (shrink)

This paper is the twin of (Duží and Jespersen, in submission), which provides a logical rule for transparent quantification into hyperprop- ositional contexts de dicto, as in: Mary believes that the Evening Star is a planet; therefore, there is a concept c such that Mary be- lieves that what c conceptualizes is a planet. Here we provide two logical rules for transparent quantification into hyperpropositional contexts de re. (As a by-product, we also offer rules for possible- world propositional contexts.) One (...) rule validates this inference: Mary believes of the Evening Star that it is a planet; therefore, there is an x such that Mary believes of x that it is a planet. The other rule validates this inference: the Evening Star is such that it is believed by Mary to be a planet; therefore, there is an x such that x is believed by Mary to be a planet. Issues unique to the de re variant include partiality and existential presupposition, sub- stitutivity of co-referential (as opposed to co-denoting or synony- mous) terms, anaphora, and active vs. passive voice. The validity of quantifying-in presupposes an extensional logic of hyperinten- sions preserving transparency and compositionality in hyperinten- sional contexts. This requires raising the bar for what qualifies as co-denotation or equivalence in extensional contexts. Our logic is Tichý’s Transparent Intensional Logic. The syntax of TIL is the typed lambda calculus; its highly expressive semantics is based on a procedural redefinition of, inter alia, functional abstraction and application. The two non-standard features we need are a hyper- intension (called Trivialization) that presents other hyperintensions and a four-place substitution function (called Sub) defined over hy- perintensions. (shrink)

Russell is often taken as a forerunner of the Quinean position that “to be is to be the value of a bound variable”, whereupon the ontological commitment of a theory is given by what it quantifies over. Among other reasons, Russell was among the first to suggest that all existence statements should be analyzed by means of existential quantification. That there was more to Russell’s metaphysics than what existential quantifications come out as true is obvious in the earlier (...) period where Russell still made a distinction between existence and being/subsistence. But even the later Russell, including that of the Logical Atomism lectures period, would not have understood ontological questions to be first and foremost questions of quantification. He would take fundamentality to be important too, which explains in part his assertions to the effect the the values of individual variables have a reality not attributable to values of higher-order variables, even ineliminable higher-order variables. (shrink)

A Fortiori Logic: Innovations, History and Assessments is a wide-ranging and in-depth study of a fortiori reasoning, comprising a great many new theoretical insights into such argument, a history of its use and discussion from antiquity to the present day, and critical analyses of the main attempts at its elucidation. Its purpose is nothing less than to lay the foundations for a new branch of logic and greatly develop it; and thus to once and for all dispel the many fallacious (...) ideas circulating regarding the nature of a fortiori reasoning. -/- The work is divided into three parts. The first part, Formalities, presents the author’s largely original theory of a fortiori argument, in all its forms and varieties. Its four (or eight) principal moods are analyzed in great detail and formally validated, and secondary moods are derived from them. A crescendo argument is distinguished from purely a fortiori argument, and similarly analyzed and validated. These argument forms are clearly distinguished from the pro rata and analogical forms of argument. Moreover, we examine the wide range of a fortiori argument; the possibilities of quantifying it; the formal interrelationships of its various moods; and their relationships to syllogistic and analogical reasoning. Although a fortiori argument is shown to be deductive, inductive forms of it are acknowledged and explained. Although a fortiori argument is essentially ontical in character, more specifically logical-epistemic and ethical-legal variants of it are acknowledged. -/- The second part of the work, Ancient and Medieval History, looks into use and discussion of a fortiori argument in Greece and Rome, in the Talmud, among post-Talmudic rabbis, and in Christian, Moslem, Chinese and Indian sources. Aristotle’s approach to a fortiori argument is described and evaluated. There is a thorough analysis of the Mishnaic qal vachomer argument, and a reassessment of the dayo principle relating to it, as well as of the Gemara’s later take on these topics. The valuable contribution, much later, by Moshe Chaim Luzzatto is duly acknowledged. Lists are drawn up of the use of a fortiori argument in the Jewish Bible, the Mishna, the works of Plato and Aristotle, the Christian Bible and the Koran; and the specific moods used are identified. Moreover, there is a pilot study of the use of a fortiori argument in the Gemara, with reference to Rodkinson’s partial edition of the Babylonian Talmud, setting detailed methodological guidelines for a fuller study. There is also a novel, detailed study of logic in general in the Torah. -/- The third part of the present work, Modern and Contemporary Authors, describes and evaluates the work of numerous (some thirty) recent contributors to a fortiori logic, as well as the articles on the subject in certain lexicons. Here, we discover that whereas a few authors in the last century or so made some significant contributions to the field, most of them shot woefully off-target in various ways. The work of each author, whether famous or unknown, is examined in detail in a dedicated chapter, or at least in a section; and his ideas on the subject are carefully weighed. The variety of theories that have been proposed is impressive, and stands witness to the complexity and elusiveness of the subject, and to the crying need for the present critical and integrative study. But whatever the intrinsic value of each work, it must be realized that even errors and lacunae are interesting because they teach us how not to proceed. -/- This book also contains, in a final appendix, some valuable contributions to general logic, including new analyses of symbolization and axiomatization, existential import, the tetralemma, the Liar paradox and the Russell paradox. (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)

This chapter provides an overview of how existential phenomenology has influenced qualitative research methods across a range of disciplines across the social, health, educational, and psychological sciences. It focuses specifically on how the concepts of “existential structures,” or “existentials”—such as selfhood, temporality, spatiality, affectivity, and embodiment—have been used in qualitative research. After providing a brief introduction to what qualitative research is and why philosophers should be interested in it, the chapter provides clear, straightforward examples of how qualitative researchers (...) have used existentials to analyze qualitative data and design qualitative studies. The chapter is intended to introduce philosophers to existential approaches to phenomenological qualitative research, with the aim of facilitating interdisciplinary dialogue and collaboration. (shrink)

The growth of self-tracking and personal surveillance has given rise to the Quantified Self movement. Members of this movement seek to enhance their personal well-being, productivity, and self-actualization through the tracking and gamification of personal data. The technologies that make this possible can also track and gamify aspects of our interpersonal, romantic relationships. Several authors have begun to challenge the ethical and normative implications of this development. In this article, we build upon this work to provide a detailed ethical analysis (...) of the Quantified Relationship. We identify eight core objections to the QR and subject them to critical scrutiny. We argue that although critics raise legitimate concerns, there are ways in which tracking technologies can be used to support and facilitate good relationships. We thus adopt a stance of cautious openness toward this technology and advocate the development of a research agenda for the positive use of QR technologies. (shrink)

Quantifier variance is a well-known view in contemporary metaontology, but it remains very widely misunderstood by critics. Here we briefly and clearly explain the metasemantics of quantifier variance and distinguish between modest and strong forms of variance (Section I), explain some key applications (Section II), clear up some misunderstandings and address objections (Section III), and point the way toward future directions of quantifier-variance-related research (Section IV).

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)