The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is (...) reflected in the vagueness of the very term indispensability, which is essential to the Argument. The paper will remind of a recent definition of the concept of indispensability of a mathematical object, reveal its deficiency and propose an improvement of this definition. Following this, we will deal with one of the consequences of the arbitrary employment of the concept of indispensability of a mathematical theory. We will propose a definition of this concept as well, in accordance with the common intuition about it. Eventually, on the basis of these two definitions, the paper will describe the relation between these two concepts, in the attempt to clarify the conceptual apparatus of the EIA. (shrink)

Under free institutions the exercise of human reason leads to a plurality of reasonable, yet irreconcilable doctrines. Rawls's political liberalism is intended as a response to this fundamental feature of modern democratic life. Justifying coercive political power by appeal to any one (or sample) of these doctrines is, Rawls believes, oppressive and illiberal. If we are to achieve unity without oppression, he tells us, we must all affirm a public political conception that is supported by these diverse reasonable doctrines. The (...) first part of this essay argues that the free use of human reason leads to reasonable pluralism over most of what we call the political. Rawls's notion of the political does not avoid the problem of state oppression under conditions of reasonable pluralism. The second part tries to show how justificatory liberalism provides (1) a conception of the political that takes seriously the fact that the free use of human reason leads us to sharply disagree in the domain of the political while (2) articulating a conception of the political according to which the coercive intervention of the state must be justified by public reasons. (shrink)

A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prüfer domains and integral group rings.

Modifying the descriptive and theoretical generalizations of Relativized Minimality, we argue that a significant subset of weak island violations arise when an extracted phrase should scope over some intervener but is unable to. Harmless interveners seem harmless because they can support an alternative reading. This paper focuses on why certain wh-phrases are poor wide scope takers, and offers an algebraic perspective on scope interaction. Each scopal element SE is associated with certain operations (e.g., not with complements). When a wh-phrase (...) scopes over some SE, the operations associated with that SE are performed in its denotation domain. The requisite operations may or may not be available in a domain, however. We present an empirical analysis of a variety of wh-phrases. It is argued that the wh-phrases that escape all weak islands (i.e., can scope over any intervener) are those that range over individuals, the reason being that all Boolean operations are defined for their domain. Collectives, manners, amounts, numbers, etc. all denote in domains with fewer operations and are thus selectively sensitive to scopal interveners—a “semantic relativized minimality effect”. (shrink)

This volume brings together studies in the domain of weak referentiality, the phenomenon that a definite or indefinite noun phrase lacks its usual referential force. Several papers investigate syntactic or semantic properties of indefinite noun phrases, such as modality, number neutrality, narrow scope, incorporation, predication, and case marking, and that in a range of languages (Arabic, Brazilian Portuguese, Catalan, German, Papiamentu, Russian). Other papers deal with weakly referential definite noun phrases in various languages (Basque, Dutch, English, French) involving (...) scrambling, modification, possession, and accessibility. The papers demonstrate a range of empirical methods and theoretical models. This volume will not only be of interest to researchers and students in syntax and semantics, but also in psycholinguistics and language typology. (shrink)

The weak natural law thesis asserts that any instance of law is either a rational standard for conduct or defective. At first glance, the thesis seems compatible with the proposition that the validity of a law within a legal system depends upon its sources rather than its merits. Mark C. Murphy has nonetheless argued that the weak natural law thesis can challenge this core commitment of legal positivism via an appeal to law’s function and defectiveness conditions. My contention (...) in the current paper is that in order to make good on the challenge, the defender of the weak natural law thesis should appeal explicitly to the common good, understood as the principal normative reason in the political domain. In section I I outline the main implications of the weak natural law thesis and clarify a common misunderstanding regarding its explanatory role. Section II then argues for the indispensability of the common good to the natural law jurisprudential thesis on the grounds that it has an essential role to play in a natural law account of law’s defectiveness conditions and the presumptive moral obligatoriness of legal norms. Finally, in section III I examine the compatibility of a strengthened version of the weak natural law thesis with legal positivism in light of the centrality of the common good to the natural law jurisprudential position. (shrink)

The revival of civilizational analysis is closely linked to a broader cultural turn in the human sciences. Comparative civilizational approaches accept the primacy of culture, but at the same time, they strive to avoid the cultural determinism familiar from twentieth-century sociology, especially from the Parsonian version of functionalism. To situate this twofold strategy within contemporary cultural sociology, it seems useful to link up with the distinction between a strong and a weak program for the sociological analysis of culture, proposed (...) by Jeffrey Alexander and Philip Smith. The strong program, also described as cultural sociology, stresses the constitutive role of culture in all domains and across the field of social life; the weak program, more precisely the sociology of culture, treats culture as a variable factor among others, and in some important respects subordinate to others. From this point of view, civilizational analysis is, first and foremost, a particularly ambitious version of the strong program: its emphasis on different cultural articulations of the world, as well as on the large-scale and long-term social-historical formations crystallizing around such articulations, adds new dimensions to the autonomy of culture. It also reinforces the hermeneutical stance of cultural sociology and cautions against the acceptance of mainstream explanatory models. On the other hand, the civilizational perspective highlights the variety of interconnections between culture and other components of the social world, and thus takes into account some of the themes favoured by the weak program. (shrink)

The article deals with Habermas's intersubjective approach to critical social theory, focusing on his intersubjective accounts of truth, justice and democratic legitimacy. Distinguishing between stronger and weaker versions of an intersubjective account, it draws attention to Habermas's recent move from a strong intersubjective, constructivist, interpretation of truth to a weaker, non-constructivist, one. It then looks at his refusal to make a similar move in the case of justice, arguing that it is not well-founded, even from the point of view of (...) Habermas's overall concerns. It contends, in particular, that a strong intersubjective conception is not necessary in order to maintain the close link between normative validity and argumentation that plays an important role in Habermas's project of a critical social theory and concludes that the advantages of abandoning a strong intersubjective position outweigh the disadvantages. Consequently, it recommends extension of the weaker, non-constructivist, account that Habermas now proposes in the case of truth to justice as well. In the final section, it considers the implications of this recommendation for Habermas's conception of normative validity in the domain of law and politics. (shrink)

The term functional domain is often used to describe the region containing the cis acting sequences that regulate a gene locus. “Strong” domain models propose that the domain is a spatially isolated entity consisting of a region of extended accessible chromatin bordered by insulators that have evolved to act as functional boundaries. However, the observation that independently regulated loci can overlap partially or completely raises questions about functional requirements for physically isolated domain structures. An alternative model, (...) the “weak” domain model, proposes that domain structure is determined by the distribution of binding sites for positively acting factors, without a requirement for functional boundaries. The domain would effectively be the region that contains these factor-binding sites. Specificity of promoter-enhancer interactions would play a major role in maintaining the functional autonomy of adjacent genes. Sequences that interfere with these interactions (frequently characterised as insulators) would be selected against if they occurred within the domain but not at the edges, or in the interdomain regions. As a result, insulators would often be found near the borders of domains without necessarily being selected to act as boundaries. BioEssays 22:657–665, 2000. © 2000 John Wiley & Sons, Inc. (shrink)

Approaches to anaphora generally seek to explain the potential for a DP to covary with a pronoun in terms of a combination of factors, such as the inherent semantics of the antecedent DP, its scope properties, and its structural position. A case in point is Reinhart’s classic condition on bound anaphora, paraphrasable as A DP can antecede a pronoun pro only if the DP c-commands pro at S-structure, supplemented with some extra machinery to allow indefinites to covary with pronouns beyond (...) their c-command domains. In the present paper, I explore a different take. I propose that anaphora is governed not by DPs and their properties; it is governed by predicates and their properties. To use a metaphor from dynamic semantics: discourse referents can only be ‘activated’ by predicates, never by DPs. This conceptually simple assumption is shown to have far-reaching consequences. For one, it yields a new take on weak crossover, arguably worthy of consideration. Moreover, it leads to a further general “restatement of the anaphora question”, in Reinhart’s words. (shrink)

We investigate risk attitudes when the underlying domain of payoffs is finite and the payoffs are, in general, not numerical. In such cases, the traditional notions of absolute risk attitudes, that are designed for convex domains of numerical payoffs, are not applicable. We introduce comparative notions of weak and strong risk attitudes that remain applicable. We examine how they are characterized within the rank-dependent utility model, thus including expected utility as a special case. In particular, we characterize strong (...) comparative risk aversion under rank-dependent utility. This is our main result. From this and other findings, we draw two novel conclusions. First, under expected utility, weak and strong comparative risk aversion are characterized by the same condition over finite domains. By contrast, such is not the case under non-expected utility. Second, under expected utility, weak comparative risk aversion is characterized by the same condition when the utility functions have finite range and when they have convex range. By contrast, such is not the case under non-expected utility. Thus, considering comparative risk aversion over finite domains leads to a better understanding of the divide between expected and non-expected utility, more generally, the structural properties of the main models of decision-making under risk. (shrink)

We consider domains with a natural property called top-circularity. We show that if such a domain satisfies either the maximal conflict property or the weak conflict property, then it is dictatorial. We obtain the result in Sato :331–342, 2010) as a corollary. Furthermore, it follows from our results that the union of a single-peaked domain and a single-dipped domain is dictatorial.

This chapter focuses on the issue of methodological usefulness of a strong versus weak adaptationist position in attempting to gain significant insight and to make scientifically important advances and discoveries in human cognition. Strong adaptationism holds that complex design is best explained by task-specific adaptations to particular ancestral environments; whereas weak adaptationism claims that we should not assume that complex design is the result of such narrowly determined task- or niche-specific evolutionary pressures in the absence of substantial corroborating (...) evidence. It argues that in cases of certain domain-specific cognitive competencies strong adaptationism has proven useful but not necessary to recent progress in the field. In other cases, a weak adaptationist strategy has been arguably most productive in advancing scientific understanding, without precluding that the structures uncovered by other means are actually adaptations. (shrink)

The paper proposes a novel analysis of quantificational subordination, e.g. Harvey courts a woman at every convention. {She is very pretty. vs. She always comes to the banquet with him.} (Karttunen 1976), in particular of the fact that the indefinite in the initial sentence can have wide or narrow scope, but the first discourse as a whole allows only for the wide scope reading, while the second discourse allows for both readings. The cross-sentential interaction between scope and anaphora is captured (...) in terms of structured anaphora to quantifier domains, formalized in a new dynamic system couched in classical type logic; given the underlying type logic, Montague-style compositionality at sub-clausal level follows automatically. Modal subordination (Roberts 1987) is analyzed in a parallel way, thereby capturing the parallels between the individual and modal domains argued for in Stone (1999). Several other phenomena are analyzed in terms of structured anaphora: exceptional wide scope, weak / strong donkey readings, anaphoric / uniqueness-implying definite descriptions and interactions between same / different and quantifier scope. (shrink)

Motivated by the problem of finding finite versions of classical incompleteness theorems, we present some conjectures that go beyond NP ≠ coNP. These conjectures formally connect computational complexity with the difficulty of proving some sentences, which means that high computational complexity of a problem associated with a sentence implies that the sentence is not provable in a weak theory, or requires a long proof. Another reason for putting forward these conjectures is that some results in proof complexity seem to (...) be special cases of such general statements and we want to formalize and fully understand these statements. Roughly speaking, we are trying to connect syntactic complexity, by which we mean the complexity of sentences and strengths of the theories in which they are provable, with the semantic concept of complexity of the computational problems represented by these sentences. -/- We have introduced the most fundamental conjectures in our earlier works. Our aim in this article is to present them in a more systematic way, along with several new conjectures, and prove new connections between them and some other statements studied before. (shrink)

This paper considers two of the most prominent kinds of evidence that have been used to argue that certain embedded questions receive weakly exhaustive interpretations. The first kind is exemplified by judgments of consistency for declarative sentences that attribute knowledge of a wh-question and ignorance of the negation of that question to the same person, and the second concerns asymmetries between the role of positive and negative information in validating question-embedding surprise ascriptions, and similar judgments for other attitudes. I argue (...) that neither type suffices to show weak exhaustivity. The first can be analyzed in terms of strong exhaustivity in combination with domain restriction effects, while the second can be analyzed in terms of a mention-some interpretation. These kinds of evidence have served as the empirical basis for many claims about weakly exhaustive readings, so the observation that they are unreliable calls into questions a large body of established work on the semantics of question embedding. (shrink)

The ability to understand the mental states of others has sometimes been attributed to a domain‐specific mechanism which privileges the processing of these states over similar but nonmental representations. If correct, then others’ beliefs should be processed more efficiently than similar information contained within nonmental states. We tested this by examining whether adults would be faster to process others’ false beliefs than equivalent “false” photos. Additionally, we tested whether they would be faster to process others’ true beliefs about something (...) than their own (matched) personal knowledge about the same event. Across four experiments, we found a small but reliable effect in favor of the first prediction, but no evidence for the second. Results are consistent with accounts positing specialized processes for (false) mental states. The size of the effect does, however, suggest that alternative explanations such as practice effects cannot be ruled out. (shrink)

A modern assessment of the classical Boltzmann-Schuetz argument for large-scale entropy fluctuations as the origin of our observable cosmological domain is given.The emphasis is put on the central implication of this picture which flatly contradicts the weak anthropic principle as an epistemological statement about the universe. Therefore, to associate this picture with the anthropic principle as it is usually done is unwarranted. In particular, Feynman's criticism of theanthropic principle based on the entropy-fluctuation picture is a product of this (...) semantic confusion. (shrink)

Safety theorists prefer a strong version of safety over a weak version, in order to account for our intuition that we do not know lottery propositions. I argue that weak safety has advantages that can outweigh our intuitions in lottery cases. First, I argue that for the nonepistemic domain, we should adopt weak safety to account for experts’ claims about cyber security. Second, I argue that a unified account of safety is preferable. Hence, we should adopt (...) weak safety for the epistemic domain as well. My argument can also be put as follows. It is more plausible to suppose that our intuitions about lottery cases are misguided than to suppose either that experts’ judgments about cyber security are misguided or that there are different versions of safety. (shrink)

The goal of the present study was to investigate whether children’s cognitive strengths can compensate the accompanied weaknesses related to their specific learning difficulties. A Bayesian multigroup mediation SEM analysis in 281 fourth-grade children identified a cognitive compensatory mechanism in children with mathematical learning difficulties : Children with weak number sense, but strong rapid naming performed slightly better on mathematics compared to peers with weak rapid naming. In contrast, a compensatory mechanism was not identified for children with a (...) comorbid mathematical and reading difficulty. One explanation for the latter finding could relate to the lack of ability to compensate, because of the difficulties these children experience in both academic domains. These findings lead to a new direction in research on learning difficulties in mathematics and/or reading by suggesting that children with a learning disability each have a unique profile of interrelated cognitive strengths and weaknesses. Children might compensate with these strengths for their weaknesses, which could lead to learning gains in the affected domain. (shrink)

In this paper, we present a theory of interaction between definiteness and quantifier structure, where the definite determiner (D) performs the function of contextually restricting the domain of quantificational determiners (Qs). Our motivating data come from Greek and Basque, where D appears to compose with the Q itself. Similar compositions are found in Hungarian and Bulgarian. Following earlier work (Giannakidou 2004, Etxeberria 2005, Etxeberria and Giannakidou 2009) we define a domain restricting function DDR, in which D modifies the (...) Q and supplies the contextual variable C to intersect with Q’s domain. DDR can also modify the NP in which case it works like an intersective modfier— and we suggest that this is the case in St’át’imcets Salish (drawing on data from Matthewson’s work). The result of DDR will be restricting the domain of Q by C, a weakly familiar property (in the sense of Roberts 2003, 2010), i.e. it is entailed in the common ground of the context. As a result of intersecting with this property, the Q that undergoes DDR becomes presuppositional, and we hypothesize that all presuppositional Qs (each-like Qs) have an underlying derivation of the domain restriction via D that we see in Greek and Basque overtly. Our analysis provides support for the program that domain restriction is grammatically represented, but we propose an important refinement: domain restriction can affect the Q itself (in agreement with von Fintel 1998, Martí 2003, Giannakidou 2004; pace Stanley 2002), and in fact quite systematically. We also show that the Q that is affected by DDR is a strong one, and explain the inability of weak Qs to undergo DDR as following from their status as adjectival. (shrink)

The logic CD is an intermediate logic which exactly corresponds to the Kripke models with constant domains. It is known that the logic CD has a Gentzen-type formulation called LD and rules are replaced by the corresponding intuitionistic rules) and that the cut-elimination theorem does not hold for LD. In this paper we present a modification of LD and prove the cut-elimination theorem for it. Moreover we prove a “weak” version of cut-elimination theorem for LD, saying that all “cuts” (...) except some special forms can be eliminated from a proof in LD. From these cut-elimination theorems we obtain some corollaries on syntactical properties of CD: fragments collapsing into intuitionistic logic. Harrop disjunction and existence properties, and a fact on the number of logical symbols in the axiom of CD. (shrink)

This paper deals with the study of the existence of weak positive solutions for sublinear Kirchhoff elliptic systems with zero Dirichlet boundary condition in bounded domainΩ⊂ℝNby using the subsuper solutions method.

The knowledge extraction from data with noise or outliers is a complex problem in the data mining area. Normally, it is not easy to eliminate those problematic instances. To obtain information from this type of data, robust classifiers are the best option to use. One of them is the application of bagging scheme on weak single classifiers. The Credal C4.5 model is a new classification tree procedure based on the classical C4.5 algorithm and imprecise probabilities. It represents a type (...) of the so-calledcredal trees. It has been proven that CC4.5 is more robust to noise than C4.5 method and even than other previous credal tree models. In this paper, the performance of the CC4.5 model in bagging schemes on noisy domains is shown. An experimental study on data sets with added noise is carried out in order to compare results where bagging schemes are applied on credal trees and C4.5 procedure. As a benchmark point, the known Random Forest classification method is also used. It will be shown that the bagging ensemble using pruned credal trees outperforms the successful bagging C4.5 and RF when data sets with medium-to-high noise level are classified. (shrink)

Named entity recognition (NER) is a very relevant task for text information retrieval in natural language processing (NLP) problems. Most recent state-of-the-art NER methods require humans to annotate and provide useful data for model training. However, using human power to identify, circumscribe and label entities manually can be very expensive in terms of time, money, and effort. This paper investigates the use of prompt-based language models (OpenAI’s GPT-3) and weak supervision in the legal domain. We apply both strategies (...) as alternative approaches to the traditional human-based annotation method, relying on computer power instead human effort for labeling, and subsequently compare model performance between computer and human-generated data. We also introduce combinations of all three mentioned methods (prompt-based, weak supervision, and human annotation), aiming to find ways to maintain high model efficiency and low annotation costs. We showed that, despite human labeling still maintaining better overall performance results, the alternative strategies and their combinations presented themselves as valid options, displaying positive results and similar model scores at lower costs. Final results demonstrate preservation of human-trained models scores averaging 74.0% for GPT-3, 95.6% for weak supervision, 90.7% for GPT + weak supervision combination, and 83.9% for GPT + 30% human-labeling combination. (shrink)

In this paper I investigate the properties of social welfare functions defined on domains where the preferences of one agent remain fixed. Such a domain is a degenerate case of those investigated, and proved Arrow consistent, by Sakai and Shimoji :435–445, 2006). Thus, they admit functions from them to a social preference that satisfy Arrow’s conditions of Weak Pareto, Independence of Irrelevant Alternatives, and Non-dictatorship. However, I prove that according to any function that satisfies these conditions on such (...) a domain, for any triple of alternatives, if the agent with the fixed preferences does not determine the social preference on any pair of them, then some other agent determines the social preference on the entire triple. (shrink)

In this paper, we discuss the weakness of current action languages for sensing actions with respect to modeling domains with multi-valued fluents. To address this problem, we propose a language with sensing actions and multi-valued fluents, called AMK, provide a transition function based semantics for the language, and demonstrate its use through several examples from the literature. We then define the entailment relationship between action theories and queries in AMK, denoted by ⊧AMK, and discuss some properties about AMK.

Lee and Schwarz propose grounded procedures of separation as a domain-general mechanism underlying cleansing effects. One strong test of domain generality is to investigate the ontogenetic origins of a process. Here, we argue that the developmental evidence provides weak support for a domain-general grounded procedures account. Instead, it is likely that distinct separation procedures develop uniquely for different content domains.

The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is (...) a weakened version of the well-known constant domains principle D . Namely, the formula D states that any individual has ancestors in earlier worlds, and D * states that any individual has $${\neg\neg}$$ -ancestors (i.e., ancestors up to $${\neg\neg}$$ -equality) in earlier worlds. In particular, the logic ( Q - H + D *& K & J ) is the Kripke sheaf completion of ( Q - H + E & K & J ), where E is a version of Markov’s principle (cf. [ 12 ]). On the other hand, we show that the logic ( Q - H + D *& J ) is incomplete w.r.t. Kripke sheaves. (shrink)

In 2002 Coecke and Martin (Research Report PRG-RR-02-07, Oxford University Computing Laboratory, 2002) created a model for the finite classical and quantum states in physics. This model is based on a type of ordered set which is standard in the study of information systems. It allows the information content of its elements to be compared and measured. Their work is extended to a model for the infinite classical states. These are the states which result when an observable is applied to (...) a quantum system. When this extended order is restricted to a finite number of coordinates, the model of Coecke and Martin is obtained. The infinite model retains many desirable aspects of the finite model, such as pure states as maximal elements and expected behavior of thermodynamic entropy. But it looses some of the important domain theoretic aspects, such as having a least element and exactness. Shannon entropy is no longer defined over the entire model and both it and thermodynamic entropy cease to be a measurements in the sense of Martin. (shrink)

This article investigates the relationship among the weak Pareto principle, the strong Pareto principle, and positive responsiveness in the context of voting. First, it is shown that under a mild domain condition, if an anonymous and neutral collective choice rule (CCR) is complete and transitive, then the weak Pareto principle and the strong Pareto principle are equivalent. Next, it is shown that under another mild domain condition, if a neutral CCR is transitive, then the strong Pareto (...) principle and positive responsiveness are equivalent. By applying these results, we obtain a new characterization of the method of majority decision. (shrink)