In this paper I provide a decompositional analysis of three kinds of plural indefinites in two related languages, European Spanish and Brazilian Portuguese. The three indefinites studied are bare plurals, the unos (Spanish)/uns (Portuguese) type, and the algunos (Spanish)/alguns (Portuguese) type. The paper concentrates on four properties: semantic plurality, positive polarity, partitivity, and event distribution. The logic underlying the analysis is that of compositionality, applied at the subword level: as items become bigger in form (with the addition of morphemes), they (...) also acquire more semantic properties. The paper proposes the “indefinite hierarchy", which establishes a set of components for languages to build their indefinites with, in a particular order. (shrink)

It is a commonplace of set theory to say that there is no set of all well-orderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can (...) talk about the collection of all the sets and many more collections beyond that. A method of articulating this idea is offered through an indefinitely extending hierarchy of set theories. It is argued that this approach provides a natural extension to ordinary set theory and leaves ordinary mathematical practice untouched. (shrink)

Hierarchy of systems organization is used as a framework in advancing methodological guidelines for posing correct questions related to ecological diversity.Diversity if defined in general terms as a property of a set of elements dependent on and determines: by the epistemological perspective. Ontological diversity, because it is indefinite, is regarded as unmeasurable.

The use of tensed language and the metaphor of set ‘formation’ found in informal descriptions of the iterative conception of set are seldom taken at all seriously. Both are eliminated in the nonmodal stage theories that formalise this account. To avoid the paradoxes, such accounts deny the Maximality thesis, the compelling thesis that any sets can form a set. This paper seeks to save the Maximality thesis by taking the tense more seriously than has been customary (although not literally). A (...) modal stage theory, MST, is developed in a bimodal language, governed by a tenselike logic. Such a language permits a very natural axiomatisation of the iterative conception, which upholds the Maximality thesis. It is argued that the modal approach is consonant with mathematical practice and a plausible metaphysics of sets and shown that MST interprets a natural extension of Zermelo set theory less the axiom of Infinity and, when extended with a further axiom concerning the extent of the hierarchy, interprets Zermelo–Fraenkel set theory. (shrink)

The purpose of this article is to assess the prospects for a Scottish neo-logicist foundation for a set theory. We show how to reformulate a key aspect of our set theory as a neo-logicist abstraction principle. That puts the enterprise on the neo-logicist map, and allows us to assess its prospects, both as a mathematical theory in its own right and in terms of the foundational role that has been advertised for set theory. On the positive side, we show that (...) our abstraction based theory can be modified to yield much of ordinary mathematics, indeed everything needed to recapture all branches of mathematics short of set theory itself. However, our conclusions are mostly negative. The theory will fall far short of the power of ordinary Zermelo-Fraenkel set theory. It is consistent that our set theory has models that are relatively small, smaller than the first cardinal with an uncountable index. More important, there is a strong tension between the idea that the iterative hierarchy is somehow ineffable, or indefinitely extensible, and the neo-logicist theme of capturing mathematical theories with abstraction principles. (shrink)

This article uses tagmemic theory as a semiotic framework to analyze symbolic logic. It attends particularly to the issue of context for meaning and the role of personal observer/participants. It focuses on formal languages, which employ no ordinary words and from one point of view have “no meaning.” Attention to the context and the theorists who deploy these languages shows that formal languages have meanings at a higher level, colored by the purposes of the analysts. In fact, there is an (...) indefinitely ascending hierarchy of theories of theories, each of which analyzes and evaluates the theories at a lower level. By analogy with Kurt Gödel’s incompleteness theory, no level of the hierarchy can capture within formalism everything in a sufficiently complex system. The personal analysts always have to make judgments about how a formalized system is analogous to the world outside the system. Arguments in analytic philosophy can be useful in clarification, but neither clarification of terms nor clarification of the structure of arguments can eliminate the need for personal judgment. (shrink)

This thesis comprises three main chapters—each comprising one relatively standalone paper. The unifying theme is fragmentalism about truth, which is the view that the predicate “true” either expresses distinct concepts or expresses distinct properties. -/- In Chapter 1, I provide a formal development of alethic pluralism. Pluralism is the view that there are distinct truth properties associated with distinct domains of subject matter, where a truth property satisfies certain truth-characterizing principles. On behalf of pluralists, I propose an account of logic (...) and semantics that shows how they can answer central conceptual and logical challenges for their view. -/- In Chapter 2, I motivate and develop a modal account of propositions on the basis of an iterative conception of propositions, where the modality is logico-mathematical. The modal account of propositions takes the conception to motivate an inherently potential hierarchy of propositions. I show that the account helps provide satisfying solutions to the intensional paradoxes of Russell-Myhill, Kaplan, and Prior. -/- In Chapter 3, I propose that “true” is polysemous. I suggest that “true” is initially polysemous between correspondence truth and disquotational truth, and further polysemous between the meanings corresponding to the subconcepts of the concept truth generated by the indefinite extensibility of that concept. I show that the proposal provides satisfying solutions to the semantic paradoxes. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Rhetoric 35.4 (2002) 267-296 [Access article in PDF] Allegory and Democratic Public Culture in the Postmodern Era Robert Hariman The man lies on the hotel bed, clad only in his underwear, as he watches the TV screen just beyond his feet. His right hand holds the remote control, which he uses to scan through the cable channels. To his left sits Abraham Lincoln, clothed in long-sleeved white (...) shirt and black pants and reading a book. Lincoln's long, angular frame is just a bit stooped, and his brow is slightly furrowed, as if long accustomed to thinking on the edge of melancholy. Lincoln is mulling over a statement by Walter Benjamin: "Allegories are, in the realm of thoughts, what ruins are in the realm of things" (Benjamin 1977, 178). 1Seated to the man's right is a woman wearing the terry cloth bathrobe provided by the hotel. She leans slightly forward, legs crossed, as she reads the New York Times Magazine cover story about President Clinton. "Listen to this," she says with a bemused smile. "In the clutter around his desk in the Oval Office stands not a single bust of a favorite predecessor, but five: Lincoln, Teddy Roosevelt, Truman and two of F.D.R., plus a statuette of Will Rogers for good measure. If governing is choosing, this collection is a metaphor for this President's trouble with choices, and he himself allows, 'That's the story of my Presidency, that desk'" (Purdum 1996, 36).The man says nothing as he continues to watch the succession of images on the screen: a lizard flicks its tongue in the desert heat; a child in a stroller laughs as she holds a strawberry ice cream cone; a congressman in blue suit, white shirt, and red tie jabs his finger into the air as he talks earnestly; cars plastered with automotive product logos curl around a race track; Fred and Ginger swirl around the dance floor; soldiers wade ashore at Omaha Beach; the Space Shuttle lifts off; Groucho lifts his eyebrows; Regis smiles; mushrooms and peppers simmer in a pan.The succession of images could go on indefinitely. The tableau remains static. The composition is an allegory: a figural presentation that organizes multiple interpretations regarding collective experience. It also contains and comments on other forms of itself: Clinton's desk is an example [End Page 267] of the figural anecdote that has been a staple of American public address. The manifold of televisual images exemplifies the allegorical encoding that operates within postmodern art forms, including fragmentary appropriation, paratactic association, encyclopedic range, and non-linear temporality. The statement by Benjamin illuminates the nature of allegory in a specific genre and historical period, and as it is a general mode of representation, and perhaps as it is a model for all textual interpretation.The composition also evokes a set of dialectical tensions that are characteristic of both allegory in general and fundamental anxieties in the contemporary period. Past and present sit side by side, but incongruously, as if by artifice alone. So it is also with the print and visual media, which are held together by mutual competencies but otherwise in figural isolation that perhaps represents different destinies. Likewise, one might wonder about the peculiar relationship between public affairs and private life: the succession of images on the screen adhere to no hierarchy of values, no principle of loyalty or sacrifice, no basis for discerning obligations or maintaining rights, yet they are replete with the paraphernalia of these concerns, and the arrangement of figures in the room likewise is at once suggestive yet inconclusive. If this tableau contains familiar features of the mass-mediated experience that now saturates American politics, one might wonder: Is the democratic tradition in ruins?Allegories give us dynamic juxtapositions in a static frame. This principle of composition seems particularly suited to periods of cultural change. To the extent that the genre of allegory has a history, it is one of eternal recurrence at periods of loss and fragmentation produced by the expansion of a new, somewhat... (shrink)

Lacker (1981) and Lacker & Akin (1988) developed a mathematical model of follicular maturation and ovulation; this model of only four parameters accounts for a large number of results obtained over the past decade or more on the control of follicular growth and ovulation in mammals. It establishes a single law of maturation for each follicle which describes the interactions between growing follicles. The function put forward is sufficient to explain the constancy of the number of ovulations or large follicles (...) in a female as well as the variability of this number among strains or species and for either induced or spontaneous ovulators. According to the model, the number of ovulations or large follicles lies between two limits that are themselves simple functions of two parameters of the model. Moreover, Lacker's model exhibits interesting characteristics in agreement with results obtained by physiologists: in particular, it predicts that the number of ovulating or large follicles is independent of:1. the total number of maturing follicles, 2. the process of recruitment of newly maturing follicles towards the terminal maturation (Poisson or other), 3. the form of the LH or FSH secretion curves as functions of the systemic level of oestradiol. The model further predicts that 4. selection and dominance of follicles result from the feedback between the ovary and the hypophysis through the interactions between follicles; these interactions are expressed by the maturation function of the model. 5. recovery from atresia is possible for a follicle: from decreasing, the rate of secretion of oestradiol may increase. 6. the revised model suggests a renewal of follicles during the sexual cycle, as waves of follicular growth. Lacker's model is a model of strict dominance; it maintains a hierarchy of the follicles as soon as they start their final maturation to the ovulations as that is observed in bird or reptile ovary. Such a strict hierarchy is possible but it is probably not a general situation in all mammals. We therefore modified the maturing function of the follicle in order to make it compatible with the observations of physiologists: follicles always interact as in the initial model but they individually become old, the hierarchy of follicles can be modified with time and the largest follicles do not indefinitely grow as in the initial model. (shrink)

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in (...) particular the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

The article concerns the situation of the judicial application of the law where the entity applying the law refers in a decision-making process to moral principles. The decision should be based on the directives of interpretation, which indicate the need for such a determination of the meaning of the applicable norms so that it remains in harmony with commonly accepted moral rules of the society. The equity has one more purpose; namely, it allows for the process of decision-making—and not just (...) for the process of unifying the decisions—since the mere rule does not specify the algorithm of undertaking them. This rule thus assumes that it will be further specified by phronesis judge who in a given situation will determine—for the purposes of a particular decision—a hierarchy between the criteria of substantive justice “embedded” in this rule. The reference to equity stands for the concretization of an unspecified general rule. We deal here with an indefinite general rule, the application of which is facilitated by a reference to rightness. (shrink)

The article concerns the situation of the judicial application of the law where the entity applying the law refers in a decision-making process to moral principles. The decision should be based on the directives of interpretation, which indicate the need for such a determination of the meaning of the applicable norms so that it remains in harmony with commonly accepted moral rules of the society. The equity has one more purpose; namely, it allows for the process of decision-making—and not just (...) for the process of unifying the decisions—since the mere rule does not specify the algorithm of undertaking them. This rule thus assumes that it will be further specified by phronesis judge who in a given situation will determine—for the purposes of a particular decision—a hierarchy between the criteria of substantive justice “embedded” in this rule. The reference to equity stands for the concretization of an unspecified general rule. We deal here with an indefinite general rule, the application of which is facilitated by a reference to rightness. (shrink)

These two meticulous volumes reissue in a Library Edition a standard work from the catalogue of the Cambridge University Press. Edited without revision from the author’s own edition of Volume I in 1921 and Dr Broad’s posthumous edition of Volume II in 1927, they offer a determined paradigm of the a priori building of an absolute metaphysic which dominated the modern English university scene up to World War I. Elsewhere Dr Broad has remarked that Professor McTaggart’s system probably did not (...) make a single convert—though it viewed the Hegelian Absolute as a universe of spiritual substances whose totality had no positive ground for a God—but that he exerted considerable influence on his pupils by the honesty, clarity and subtlety of his a priori deductions. It is instructive to compare McTaggart’s high-minded totality of selves and their perceptions with the contemporary plurality of atomic facts and logical truth-functions, with which the more radical Russell challenged the reigning Idealism. And it is a wry turn of history that Russell’s logical atomism should have been promptly condemned under its own logical protocol for trying to say the unsayable by Wittgenstein’s Tractatus. If their new logic claims an insight into the totality of languages, rather than into a more empirical hierarchy of languages which might permit indefinite meta-statements and avoid the antinomy of the class of all classes which is not a member of itself, then its linguistic absolutism is as evident and as unsatisfactory as any Idealist metaphysic. (shrink)

Forgotten Truth is primarily a presentation of the traditional esoteric view that reality consists of a hierarchy of Being. Within the hierarchy there are an indefinite number of worlds, but they can be classified into four levels: the terrestrial, psychic, and celestial planes, and the Infinite. The corresponding levels within the human microcosm are body, mind, soul, and spirit. “From the multiple heavens of Judaism to the storied structure of the Hindu temple and the angelologies of innumerable (...) traditions, the view was reached convergently and independently, as if by innate tropism, by virtually all known societies…” (18). The important exception is our current society, whose fundamental flaw is its inclination to reduce all reality to the terrestrial plane alone. Modernity is “captive of an outlook presumed to be scientific but in fact scientistic” (17); it goes beyond the actual findings of science to deny that other approaches to knowledge are valid and other truths true” (16). (shrink)

Across languages, we find indefinites that trigger modal inferences. This article contributes to a semantic typology of these items by contrasting Spanish algún with indefinites like German irgendein or Italian uno qualsiasi. While irgendein-type indefinites trigger a Free Choice effect (Kratzer and Shimoyama 2002; Chierchia 2006), algún simply signals that at least two individuals in its domain are possibilities. Additionally, algún, but not irgendein, can convey that the speaker does not know how many individuals satisfy the existential claim in the (...) world of evaluation. We contend that the two types of indefinites impose different constraints on their domain of quantification: irgendein and its kin are domain wideners (Kratzer and Shimoyama 2002), whereas algún is an ‘anti-singleton’ indefinite (its domain cannot be restricted to a singleton). This, together with the fact that algún does not require uniqueness, allows us to derive the contrast between irgendein and algún by using the pragmatic reasoning presented by Kratzer and Shimoyama. (shrink)

The paper proposes a novel solution to the problem of scope posed by natural language indefinites that captures both the difference in scopal freedom between indefinites and bona fide quantifiers and the syntactic sensitivity that the scope of indefinites does nevertheless exhibit. Following the main insight of choice functional approaches, we connect the special scopal properties of indefinites to the fact that their semantics can be stated in terms of choosing a suitable witness. This is in contrast to bona fide (...) quantifiers, the semantics of which crucially involves relations between sets of entities. We provide empirical arguments that this insight should not be captured by adding choice/Skolem functions to classical first-order logic, but in a semantics that follows Independence-Friendly Logic, in which scopal relations involving existentials are part of the recursive definition of truth and satisfaction. These scopal relations are resolved automatically as part of the interpretation of existentials. Additional support for this approach is provided by dependent indefinites, a cross-linguistically common class of special indefinites that can be straightforwardly analyzed in our semantic framework. (shrink)

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of (...) this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch. (shrink)

This paper investigates the truth conditions of sentences containing indefinite noun phrases, focusing on occurrences in attitude reports, and, in particular, a puzzle case due to Walter Edelberg. It is argued that indefinites semantically contribute the (thought-)object they denote, in a manner analogous to attributive definite descriptions. While there is an existential reading of attitude reports containing indefinites, it is argued that the existential quantifier is contributed by the de re interpretation of the indefinite (as the de re (...) reading adds existential quantification to the interpretation of definites on Kaplan’s analysis). (shrink)

Cognitive Science, Volume 46, Issue 5, May 2022.

In recent years, many people writing on set theory have invoked the notion of an indefinitely extensible concept. The notion, it is usually claimed, plays an important role in solving the paradoxes of absolute infinity. It is not clear, however, how the notion should be formulated in a coherent way, since it appears to run into a number of problems concerning, for example, unrestricted quantification. In fact, the notion makes perfectly good sense if one endorses a dialetheic solution to the (...) paradoxes. It then morphs from a supposed solution to the paradoxes into a diagnosis of their structure. In this paper I show how. (shrink)

In this paper I argue against grounding being necessarily well-founded, and provide some reasons to think it's actually not well-founded.

I argue that we can and should extend Tarski's model-theoretic criterion of logicality to cover indefinite expressions like Hilbert's ɛ operator, Russell's indefinite description operator η, and abstraction operators like 'the number of'. I draw on this extension to discuss the logical status of both abstraction operators and abstraction principles.

A number of authors have noted that the key steps in Fitch’s argument are not intuitionistically valid, and some have proposed this as a reason for an anti-realist to accept intuitionistic logic (e.g. Williamson 1982, 1988). This line of reasoning rests upon two assumptions. The first is that the premises of Fitch’s argument make sense from an anti-realist point of view – and in particular, that an anti-realist can and should maintain the principle that all truths are knowable. The second (...) is that we have some independent reason for thinking that classical logic is not appropriate in this area. This paper explores these two assumptions in the context of Michael Dummett’s version of anti-realism, with particular reference to the argument from indefinite extensibility developed at various points in Dummett’s writings (e.g. Dummett 1991 Ch. 24). -/- Dummett argues that certain concepts, the indefinitely extensible concepts, are such that we cannot form a clear and determinate conception of all the objects that fall under them. The most familiar examples of indefinitely extensible concepts are mathematical. Dummett discusses the concepts ordinal number, real number, and natural number, which are indefinitely extensible because any conception that one might form of their complete extension can be extended to a more inclusive conception (as, for example, in Cantor’s proof of the non-denumerability of the set of real numbers). This paper argues that the concept of a truth is indefinitely extensible. This gives a Dummettian anti-realist an independent motivation for rejecting the classical understanding of the quantifiers in this area. At the same time, however, it places in doubt the admissibility of the knowability principle, which seems to involve quantification over the “totality” of truths. As Dummett is at pains to point out (1991: 316), some sentences that purport to quantify over the extension of an indefinitely extensible concept plainly have a truth-value (we can truly say, for example, that every ordinal number has a successor, even though when we say that we are not quantifying over the set of all ordinals). But is the knowability principle one of these sentences? (shrink)

In spite of feminist recognition that hierarchical organizations are an important location of male dominance, most feminists writing about organizations assume that organizational structure is gender neutral. This article argues that organizational structure is not gender neutral; on the contrary, assumptions about gender underlie the documents and contracts used to construct organizations and to provide the commonsense ground for theorizing about them. Their gendered nature is partly masked through obscuring the embodied nature of work.jobs and hierarchies, common concepts in organizational (...) thinking, assume a disembodies and universal worker. This worker is actually a man; men's bodies, sexuality, and relationships to procreation and paid work are subsumed in the image of the worker. Images of men's bodies and masculinity pervade organizational processes, marginalizing women and contributing to the maintenance of gender segregation in organizations. The positing of gender-neutral and disembodied organizational structures and work relations is part of the larger strategy of control in industrial capitalist societies, which, at least partly, are built upon a deeply embedded substructure of gender difference. (shrink)

In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic (...) is to be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences. (shrink)

Across languages, we find indefinites that overtly mark a speaker’s lack of knowledge: they signal that the speaker is unable to give any further information about who or what satisfies her existential claim (Becker, 1999; Haspelmath, 1997). From now on, we will refer to the marking of the speaker’s lack of knowledge as an epistemic effect and to the indefinites that induce epistemic effects as epistemic indefinites.

Dummett's account of the semantic paradoxes in terms of his theory of indefinitely extensible concepts is compared with Bürge's account in terms of indexicality. Dummett's appeal to intuitionistic logic does not block the paradoxes but Bürge's attempt to avoid the Strengthened Liar is unconvincing. It is argued that in order to avoid the Strengthened Liar and other semantic paradoxes involving nonindexical expressions (constants), one must postulate that when we reflect on the paradoxes there are slight shifts in the meaning (not (...) just reference) we ascribe to metalinguistic expressions (in particular 'say', and derivatively 'true' and 'false'). Consideration of metaphor and gradual linguistic change suggests that such semantic shifts are consistent with language-learning and communication. On this account there is no threat to classical logic, bivalence or the fundamental principles governing 'true' and 'false'. (shrink)

I argue that indefinite descriptions are referring terms. This is not the ambiguity thesis: that sometimes they are referring terms and sometimes something else, such as quantifiers . No. On my view they are always referring terms; and never quantifiers. I defend this thesis by modifying the standard conception of what a referring term is: a modification that needs to be made anyway, irrespective of the treatment of indefinites. I derive this approach from my speech-act theoretic semantics . The (...) basic thought is that referring terms have as their meanings speech-acts of a certain kind called proto-referring acts. These are acts in which speakers advertise or present intentions to denote, where denotation is a word-world relation, and advertising an intention is acting as if one has intentions, where it is open whether one has them or not, or whether the referring term used denotes or not. I show how this works for proper names. The meaning of a proper name is the speech-act proto-referring act type defined by a certain referential tree. This gives us the basis for an account of proper name meaning irrespective of denotation: a uniform treatment of full and empty names. Applied to indefinites, we can capture cases where speakers perform proto-acts—in which they advertise an intention to denote something—where they intend to denote, but others where they do not, but they still perform the proto-act: advertising an intention to denote. Two cases are ‘Fred saw a hippo’ and ‘Jane did not see a hippo’. In both cases U performs the same proto-act, represent it as Rpro, but possesses the advertised intention in the first case, but not in the second. In the first case, Rpro gains referential content—its descriptive content is expanded to include seen by Fred, whereas in its second token use it has no content augmentation or sentential determination of reference. In the second case ‘a hippo’ is an empty referring term, just as ‘Pegasus’ is empty in ‘Fred did not see Pegasus; he does not exist’. But in both sentences ‘a hippo’ functions in the same basic way: in both cases the basic proto-referring act Rpro is performed. Using this approach, I show how definite descriptions can be construed as indefinites with added meaning. (shrink)

The principle of sufficient reason threatens modal collapse. Some have suggested that by appealing to the indefinite extensibility of contingent truth, the threat is neutralized. This paper argues that this is not so. If the indefinite extensibility of contingent truth is developed in an analogous fashion to the most promising models of the indefinite extensibility of the concept set, plausible principles permit the derivation of modal collapse.

The paper proves a conjecture of Solomon Feferman concerning the indefiniteness of the continuum hypothesis relative to a semi-intuitionistic set theory.

The view that mathematical objects are indefinite in nature is presented and defended, hi the first section, Field's argument for fictionalism, given in response to Benacerraf's problem of identification, is closely examined, and it is contended that platonists can solve the problem equally well if they take the view that mathematical objects are indefinite. In the second section, two general arguments against the intelligibility of objectual indefiniteness are shown erroneous, hi the final section, the view is compared to (...) mathematical structuralism, and it is shown that a version of structuralism should be understood as embracing the same view. (shrink)

Working on the assumption that ideas are embedded in socio-technical arrangements which actualize them, this essay sheds light on the way the Open Method of Co-ordination (OMC) achieves the Lisbon strategic goal: to become the most competitive and dynamic knowledge-based economy in the world . Rather than framing the issue in utilitarian terms, it focuses attention on quantified indicators, comparable statistics and common targets resulting from the increasing practice of intergovernmental benchmarking, in order to tackle the following questions: how does (...) the OMC go about co-ordinating Member States through the benchmarking of national policies? And to what extent does this managerial device impact the path of European construction? Beyond the ideological and discursive construction of the competitive imperative, this technology of government transforms it into an indefinite discipline (Foucault) which constantly urges decision-makers to hit the top of the charts. This contribution thus argues that the practice of intergovernmental benchmarking is far from being neutral in purpose and effect. On the contrary, it lays the foundation for building a competitive Europe which unites Member States through competition. (shrink)

Large scale experiments at CERN’s Large Hadron Collider rely heavily on computer simulations, a fact that has recently caught philosophers’ attention. CSs obviously require appropriate modeling, and it is a common assumption among philosophers that the relevant models can be ordered into hierarchical structures. Focusing on LHC’s ATLAS experiment, we will establish three central results here: with some distinct modifications, individual components of ATLAS’ overall simulation infrastructure can be ordered into hierarchical structures. Hence, to a good degree of approximation, hierarchical (...) accounts remain valid at least as descriptive accounts of initial modeling steps. In order to perform the epistemic function Winsberg Model-based reasoning in scientific discovery. Kluwer Academic/plenum Publishers, New York, pp 255–269, 1999) assigns to models in simulation—generate knowledge through a sequence of skillful but non-deductive transformations—ATLAS’ simulation models have to be considered part of a network rather than a hierarchy, in turn making the associated simulation modeling messy rather than motley. Deriving knowledge-claims from this ‘mess’ requires two sources of justification: holistic validation :253–262, 2010; in Carrier M, Nordmann A Science in the context of application. Springer, Berlin, pp 115–130, 2011), and model coherence. As it turns out, the degree of model coherence sets HEP apart from other messy, simulation-intensive disciplines such as climate science, and the reasons for this are to be sought in the historical, empirical and theoretical foundations of the respective discipline. (shrink)

We look at recent accounts of the indefinite extensibility of the concept set and compare them with a certain linguistic model of indefinite extensibility. We suggest that the linguistic model has much to recommend over alternative accounts of indefinite extensibility, and we defend it against three prima facie objections.

Indefinite probability statements can be analysed in terms of statements which attribute probability to propositions. Therefore, there is no need to find a special place in probability theory for them; once we have an adequate account of statements that straightforwardly attribute probability to propositions, we will automatically have an adequate account of indefinite probability statements.

Applied Evolutionary Epistemology is a scientific-philosophical theory that defines evolution as the set of phenomena whereby units evolve at levels of ontological hierarchies by mechanisms and processes. This theory also provides a methodology to study evolution, namely, studying evolution involves identifying the units that evolve, the levels at which they evolve, and the mechanisms and processes whereby they evolve. Identifying units and levels of evolution in turn requires the development of ontological hierarchy theories, and examining mechanisms and processes necessitates (...) theorizing about causality. Together, hierarchy and causality theories explain how biorealities form and diversify with time. This paper analyzes how Applied EE redefines both hierarchy and causality theories in the light of the recent explosion of network approaches to causal reasoning associated with studies on reticulate and macroevolution. Causality theories have often been framed from within a rigid, ladder-like hierarchy theory where the rungs of the ladder represent the different levels, and the elements on the rungs represent the evolving units. Causality then is either defined reductionistically as an upward movement along the strands of a singular hierarchy, or holistically as a downward movement along that same hierarchy. Upward causation theories thereby analyze causal processes in time, i.e. over the course of natural history or phylogenetically, as Darwin and the founders of the Modern Synthesis intended. Downward causation theories analyze causal processes in space, ontogenetically or ecologically, as the current eco-evo-devo schools are evidencing. This work demonstrates how macroevolution and reticulate evolution theories add to the complexity by examining reticulate causal processes in space–time, and the interactional hierarchies that such studies bring forth introduce a new form of causation that is here called reticulate causation. Reticulate causation occurs between units and levels belonging to different as well as to the same ontological hierarchies. This article concludes that beyond recognizing the existence of multiple units, levels, and mechanisms or processes of evolution, also the existence of multiple kinds of evolutionary causation as well as the existence of multiple evolutionary hierarchies needs to be acknowledged. This furthermore implies that evolution is a pluralistic process divisible into different kinds. (shrink)

A trenchant defense of hierarchy in different spheres of our lives, from the personal to the political All complex and large-scale societies are organized along certain hierarchies, but the concept of hierarchy has become almost taboo in the modern world. Just Hierarchy contends that this stigma is a mistake. In fact, as Daniel Bell and Wang Pei show, it is neither possible nor advisable to do away with social hierarchies. Drawing their arguments from Chinese thought and culture (...) as well as other philosophies and traditions, Bell and Wang ask which forms of hierarchy are justified and how these can serve morally desirable goals. They look at ways of promoting just forms of hierarchy while minimizing the influence of unjust ones, such as those based on race, sex, or caste. Which hierarchical relations are morally justified and why? Bell and Wang argue that it depends on the nature of the social relation and context. Different hierarchical principles ought to govern different kinds of social relations: what justifies hierarchy among intimates is different from what justifies hierarchy among citizens, countries, humans and animals, and humans and intelligent machines. Morally justified hierarchies can and should govern different spheres of our social lives, though these will be very different from the unjust hierarchies that have governed us in the past. A vigorous, systematic defense of hierarchy in the modern world, Just Hierarchy examines how hierarchical social relations can have a useful purpose, not only in personal domains but also in larger political realms. (shrink)

The prototypes of definiteness and indefiniteness in English are the definite article the and the indefinite article a/an, and singular noun phrases (NPs)1 determined by them. That being the case it is not to be predicted that the concepts, whatever their content, will extend satisfactorily to other determiners or NP types. However it has become standard to extend these notions. Of the two categories definites have received rather more attention, and more than one researcher has characterized the category of (...) definite NPs by enumerating NP types. Westerståhl (1985), who is concerned only with determiners in the paper cited, gives a very short list: demonstrative NPs, possessive NPs, and definite descriptions. Prince (1992) lists proper names and personal pronouns, as well as NPs with the, a demonstrative, or a possessive NP as determiner. She notes, in addition, that “certain quantifiers (e.g. all, every) have been argued to be definite” (Prince 1992: 299). This list, with the quantifiers added, agrees with that given by Birner & Ward (1998, 114). Ariel (1988, 1990) adds null anaphoric NPs. (shrink)

One of the big questions about indefinites is why they can escape scope islands. In the recent approach of Brasoveanu and Farkas :1–55, 2011) scopal relations with syntactically dominating quantifiers are hard wired into the semantic definition of the existential quantifier, which immediately explains why the semantic scope of indefinites may exceed their syntactic scope. In this paper, I argue for the revival of an alternative approach which places the explanatory burden on the idea that indefinites are essentially referential expressions, (...) similar to definites, and not plain existential quantifiers. I propose one fully explicit variant of such theories and argue that it comes with a number of conceptual and empirical advantages over competing theories. (shrink)

This essay clarifies quantifier variance and uses it to provide a theory of indefinite extensibility that I call the variance theory of indefinite extensibility. The indefinite extensibility response to the set-theoretic paradoxes sees each argument for paradox as a demonstration that we have come to a different and more expansive understanding of ‘all sets’. But indefinite extensibility is philosophically puzzling: extant accounts are either metasemantically suspect in requiring mysterious mechanisms of domain expansion, or metaphysically suspect in (...) requiring nonstandard assumptions about mathematical objects. Happily, the view of quantifier meanings that underwrites quantifier variance can be used to provide an account of indefinite extensibility that is both metasemantically and metaphysically satisfying. Section 1 introduces the puzzle of indefinite extensibility; section 2 develops and clarifies the metasemantics of quantifier variance; section 3 solves section 1's puzzle of indefinite extensibility by applying section 2's account of quantifier meanings; and section 4 compares the theory developed in section 3 to several other theories in the literature. (shrink)

The gap between a definite and an indefinite is reduced in the case of specific indefinites, in the sense that they both have determined reference. This fact is reflected in most accounts, particularly so in the analysis of Schwarzschild where specific indefinites are argued to quantify over singleton sets. If definites and specific indefinites share the singleton domain property, how are we to separate the two? The Privacy Principle, which is cued to the information state of discourse participants, is (...) argued to apply to definites as well as indefinites, making it even harder to draw the line between definites and specific indefinites. We look at issues surrounding the distinction between definiteness and specificity through the lens of two empirical phenomena, bare nominals and specificity markers. Bare nominals in languages with determiners, for example, English, and bare nominals in languages without determiners, for example, Hindi, highlight different aspects of the problem. English bare plurals are known to have indefinite readings but not specific indefinite readings. Hindi bare nominals are thought to have definite and indefinite readings but can be shown not to have specific indefinite readings. The second empirical phenomenon we consider are specificity markers like certain. In many languages, they require a determiner in the singular but not in the plural, raising questions about their syntactic status as determiners or modifiers. They also do not occur in certain constructions, for example, imperatives. Probing such restrictions provides a window into their semantic profile. This paper thus presents some puzzles that center around the creation of singleton sets and its relation to the Privacy Principle. (shrink)

This essay endeavors to define the concept of indefinite extensibility in the setting of category theory. I argue that the generative property of indefinite extensibility for set-theoretic truths in category theory is identifiable with the Grothendieck Universe Axiom and the elementary embeddings in Vopenka's principle. The interaction between the interpretational and objective modalities of indefinite extensibility is defined via the epistemic interpretation of two-dimensional semantics. The semantics can be defined intensionally or hyperintensionally. By characterizing the modal profile (...) of $\Omega$-logical validity, and thus the generic invariance of mathematical truth, modal coalgebras are further capable of capturing the notion of definiteness for set-theoretic truths, in order to yield a non-circular definition of indefinite extensibility. (shrink)