Observation,Character, and A Purely First-Person Point of View

In Values and the Reflective Point of View (2006), Robert Dunn defends a certain expressivist view about evaluative beliefs from which some implications about self-knowledge are explicitly derived. He thus distinguishes between an observational and a deliberative attitude towards oneself, so that the latter involves a purely first-person point of view that gives rise to an especially authoritative, but wholly non-observational, kind of self-knowledge. Even though I sympathize with many aspects of Dunn's approach to evaluative beliefs and also with his stress on the practical significance of self-knowledge, I argue that his proposal seriously misinterprets the role of observation and evidence within the first-person point of view and, derivatively, in the formation of evaluative beliefs.     

Frege,Dedekind, and the Modern Epistemology of Arithmetic

In early analytic philosophy, one of the most central questions concerned the status of arithmetical objects. Frege argued against the popular conception that we arrive at natural numbers with a psychological process of abstraction. Instead, he wanted to show that arithmetical truths can be derived from the truths of logic, thus eliminating all psychological components. Meanwhile, Dedekind and Peano developed axiomatic systems of arithmetic. The differences between the logicist and axiomatic approaches turned out to be philosophical as well as mathematical. In this paper, I will argue that Dedekind’s approach can be seen as a precursor to modern structuralism and as such, it enjoys many advantages over Frege’s logicism. I also show that from a modern perspective, Frege’s criticism of abstraction and psychologism is one-sided and fails against the psychological processes that modern research suggests to be at the heart of numerical cognition. The approach here is twofold. First, through historical analysis, I will try to build a clear image of what Frege’s and Dedekind’s views on arithmetic were. Then, I will consider those views from the perspective of modern philosophy of mathematics, and in particular, the empirical study of arithmetical cognition. I aim to show that there is nothing to suggest that the axiomatic Dedekind approach could not provide a perfectly adequate basis for philosophy of arithmetic.     

中国住房开发投资空间聚集变动及影响因素研究

本文基于中国1998~2014年度各省住房开发投资数据,运用Moran’s I指标测度了各年度住房开发投资的空间聚集指数,测度结果表明中国的住房开发投资呈现出典型的空间聚集特征,且在不同的年份随着社会经济发展形势的变化,空间聚集的程度也发生相应的变动。通过建立多元线性回归模型,对影响中国住房开发投资空间聚集变动的因素进行实证研究,结果表明经济增长率、产业升级、基础设施投资、人口城市化对房地产投资空间聚集水平的变化有着显著的影响。     

Moral Ambivalence,Relativism, and Pluralism

David Wong (2006) has introduced the notion of moral ambivalence in the philosophical debate. In this paper, we focus on the nature of moral ambivalence and on its interpretation. We hold that moral ambivalence is not a phenomenon that provides evidence for relativism, as Wong claims, and as relativism is usually understood. Rather, ambivalence denotes a pluralist attitude, an attitude characterized by the thought that two different, even incompatible, courses of action can both be permissible when considered from a single perspective. We distinguish pluralism from relativism and argue that it is more appropriate to consider Wong’s position as an objectivist pluralism (as pluralism is characterized by Berlin and others). We also highlight the similarity between Wong and Hume’s accounts.     

Informational Semantics and Frege Cases

One of the most important objections to information-based semantic theories is that they are incapable of explaining Frege cases. The worry is that if a concept’s intentional content is a function of its informational content, as such theories propose, then it would appear that coreferring expressions have to be synonymous, and if this is true, it’s difficult to see how an agent could believe that a is F without believing that b is F whenever a and b are identical. I argue that this appearance is deceptive. If we heed the distinction between the analog and digital contents of a signal, it is actually possible to reconstruct something akin to Frege’s sense/reference distinction in purely information-theoretic terms. This allows informational semanticists to treat coreferring expressions as semantically distinct and to solve Frege cases in the same way that Frege did—namely, by appealing to the different contents of coreferring expressions.     

Maxwell’s equations,the Euler index,and Morse theory

We show that the singularities of the Fresnel surface for Maxwell’s equation on an anisotrpic material can be accounted from purely topological considerations. The importance of these singularities is that they explain the phenomenon of conical refraction predicted by Hamilton. We show how to desingularise the Fresnel surface, which will allow us to use Morse theory to find lower bounds for the number of critical wave velocities inside the material under consideration. Finally, we propose a program to generalise the results obtained to the general case of hyperbolic differential operators on differentiable bundles.     

Pupils’ attitudes towards mathematics: a comparative study of Norwegian and English secondary students

Comparing English and Norwegian pupils’ attitude towards mathematics, in this article I develop a deeper understanding of the factors that may shape and influence ‘pupil attitude towards mathematics’, and argue for it as a socio-cultural construct embedded in and shaped by students’ environment and context in which they learn mathematics. The theoretical framework leans on work by Zan and Di Martino (The Montana Mathematics Enthusiast, Monograph 3, pp. 157–168, 2007) to elicit Norwegian and English pupils’ attitude of mathematics as they experience it in their respective environments. Whilst there were differences which could be seen to be accounted for by differently ‘figured’ environments, there are also many similarities. It was interesting to see that, albeit based on a small statistical sample, in both countries students had a positive attitude towards mathematics in year 7/8, which dropped in year 9, and increased again in years 10/11. This result could be explained and compared with other larger scale studies (e.g. Hodgen et al. in Proceedings of the British Society for Research into Learning Mathematics. 29(3), 2009). The analysis of pupils’ qualitative comments (and classroom observations) suggested seven factors that appeared to influence pupil attitude most, and these had ‘superficial’ commonalities, but the perceptions that appeared to underpin these mentions were different, and could be linked to the environments of learning mathematics in their respective classrooms. In summary, it is claimed that it is not enough to identify the factors that may shape and influence pupil attitude, but more importantly, to study how these are ‘lived’ by pupils, what meanings are made in classrooms and in different contexts, and how the factors interrelate and can be understood.     

Naturalising Austin

In this paper I will try to defend a quasi-naturalistic interpretation of J.L. Austin’s work. I will rely on P. Kitcher’s 1992 paper “The Naturalists Return” to compile four general criteria by which a philosopher can be called a naturalist. Then I will turn to Austin’s work and examine whether he meets these criteria. I will try to claim that versions of such naturalistic elements can be found in his work.     

Consistency statements and iterations of computable functions in IΣ1 and PRA

In this paper we will state and prove some comparative theorems concerning PRA and IΣ₁. We shall provide a characterization of IΣ₁ in terms of PRA and iterations of a class of functions. In particular, we prove that for this class of functions the difference between IΣ₁ and PRA is exactly that, where PRA is closed under iterations of these functions, IΣ₁ is moreover provably closed under iteration. We will formulate a sufficient condition for a model of PRA to be a model of IΣ₁. This condition is used to give a model-theoretic proof of Parsons’ theorem, that is, IΣ₁ is Π₂-conservative over PRA. We shall also give a purely syntactical proof of Parsons’ theorem. Finally, we show that IΣ₁ proves the consistency of PRA on a definable IΣ₁-cut. This implies that proofs in IΣ₁ can have non-elementary speed up over proofs in PRA.     

Robert Patterson: American ‘revolutionary’ mathematician

You will not see Robert Patterson’s name mentioned in many mathematics books. While his mathematical works survive, his name is more likely to appear in American history books dealing with the Colonial period, given his associations with the most influential men of that time. In this article, we will examine his mathematical work, as well as his contributions to a newly-formed nation. Most of what we know about Robert Patterson’s ancestors and life is due to his grandson, William Ewing DuBois, who wrote a family history in 1847. For other information, I have drawn upon diaries and a great many letters. All spelling and syntax are copied exactly as they appear.     

Some properties for the intersection of Moran sets with their translates

Motivated by Mandelbrot’s idea of referring to lacunarity of Cantor sets in terms of departure from translation invariance, Nekka and Li studied the properties of these translation sets and showed how they can be used for the classification purpose. In this paper, we pursue this study on a class of Moran sets with their rational translates. We also get the fractal structure of intersection I(x, y) of a class of Moran sets with their rational translates, and the formula of the box-counting dimension. We find that the Hausdorff measures of these sets form a discrete spectrum whose non-zero values come only from shifting vector with the expansion in fraction of (x, y). Concretely, when (x, y) has a finite expansion in fraction, a very brief calculation formula of the measure is given.     

The New Riddle of Induction and the New Riddle of Deduction

Many believe that Goodman’s new riddle of induction proves the impossibility of a purely syntactical theory of confirmation. After discussing and rejecting Jackson’s solution to Goodman’s paradox, I formulate the “new riddle of deduction,” in analogy to the new riddle of induction. Since it is generally agreed that deductive validity can be defined syntactically, the new riddle of induction equally does not show that inductive validity cannot be defined syntactically. I further rely on the analogy between induction and deduction in order to explain why some predicates, such as “grue,” are unprojectible.     

Maxwell's equations when the charge conservation is not satisfied

Maxwell's equations are overdetermined when the charge conservation equation is not verified. In order to overcome this problem, different methods have been introduced. We notice that they fit into a framework in which a new formulation which we introduce also fits. These formulations can be classified according to the type of the resulting PDE-system as hyperbolic-elliptic, hyperbolic-parabolic and purely hyperbolic. We show that the resolution of Maxwell's equation through the potentials is always equivalent to the purely hyperbolic formulation and that the hyperbolic-parabolic and hyperbolic-elliptic formulations converge to the purely hyperbolic formulation when introducing a parameter which goes to 0.     

On Crane’s Psychologistic Account of Intentionality

The intuition that we can think about non-existent objects seems to be in tension with philosophical concerns about the relationality of intentionality. Tim Crane’s psychologism removes this tension by proposing a psychologistic account of intentionality according to which intentionality is a purely non-relational notion. I argue that his account has counterintuitive consequences regarding our thoughts about existing objects, and as such is insufficiently plausible to convince us to reject the relationality of intentionality.     

A dynamic programming model for effect of worker’s type on wage arrears

We analyze how wage arrears are affected by the worker’s type (in this paper, the worker’s type means the worker’s attitude to wage arrears). Wage arrears cause workers’ negative emotion which may lead to serious social problem and the government may intervene. In this paper, we model the process of wage arrears as a Markov decision process in which the firm is the decision maker. We develop an optimal solution approach under the assumption that the worker’s negative emotion threshold (The worker’s negative emotion increases monotonically with increasing back pay. Once the cumulative back pay exceeds a particular value, the worker will take legal actions and the government will intervene. We define the particular value as the worker’s negative emotion threshold.) is normally distributed and provide insights into how wage arrears vary with the worker’s type and the government intervention. We propose the optimal government intervention which stops wage arrears and does not disturb the normal order of the market economy. We show that the intervention depends on the worker’s type and the results imply that the government intervention should be adjusted dynamically according to different regions, industrial sectors and time periods.     

Bilateral truncated Jacobi’s identity

Recently, Andrews and Merca considered the truncated version of Euler’s pentagonal number theorem and obtained a non-negative result on the coefficients of this truncated series. Guo and Zeng showed the coefficients of two truncated Gauss’ identities are non-negative and they conjectured that truncated Jacobi’s identity also has non-negative coefficients. Mao provided a proof of this conjecture by using an algebraic method. In this paper, we consider bilateral truncated Jacobi’s identity and show that when the upper and lower bounds of the summation satisfy some certain restrictions, then this bilateral truncated identity has non-negative coefficients. As a corollary, we show the conjecture of Guo and Zeng holds. Our proof is purely combinatorial and mainly based on a bijection for Jacobi’s identity.     

Are Bare Particulars Constituents?

In this article I examine an as yet unexplored aspect of J.P. Moreland’s defense of so-called bare particularism — the ontological theory according to which ordinary concrete particulars (e.g., Socrates) contain bare particulars as individuating constituents and property ‘hubs.’ I begin with the observation that if there is a constituency relation obtaining between Socrates and his bare particular, it must be an internal relation, in which case the natures of the relata will necessitate the relation. I then distinguish various ways in which a bare particular might be thought to have a nature and show that on none of these is it possible for a bare particular to be a constituent of a complex particular. Thus, Moreland’s attempt to resurrect bare particulars as ontologically indispensable entities is not wholly without difficulties.     

Topological duality and lattice expansions,I: A topological construction of canonical extensions

The two main objectives of this paper are (a) to prove purely topological duality theorems for semilattices and bounded lattices, and (b) to show that the topological duality from (a) provides a construction of canonical extensions of bounded lattices. In previously known dualities for semilattices and bounded lattices, the dual spaces are compact 0-dimensional spaces with additional algebraic structure. For example, semilattices are dual to 0-dimensional compact semilattices. Here we establish dual categories in which the spaces are characterized purely in topological terms, with no additional algebraic structure. Thus the results can be seen as generalizing Stone’s duality for distributive lattices rather than Priestley’s. The paper is the first of two parts. The main objective of the sequel is to establish a characterization of lattice expansions, i.e., lattices with additional operations, in the topological setting built in this paper.     

Rawls’s Rejection of Preinstitutional Desert

For many, the idea that people should be rewarded in proportion to what they deserve is the very essence of distributive justice. However, while the notion of moral desert is otherwise widely accepted, Rawls rejects it entirely in his A Theory of Justice. Many authors have argued that Rawls’s claims about desert have serious and unappealing consequences for his conception of justice as fairness, and also that they deny the possibility of autonomous choice to the very agents whose decisions are supposed to underlie Rawls’s approach to justice. In this paper, I analyze the arguments of those who believe that Rawls can be interpreted in a way that doesn’t in fact deny either desert or the possibility of autonomous action. I conclude by allowing for the interpretation that Rawls does not necessarily deny autonomous action, but I contend that he nevertheless finds the idea of preinstitutional desert entirely off the mark.     

Impacts of risk attitude and outside option on compensation contracts under different information structures

We consider an agency problem where a firm (she) hires a manager (he) who has related managerial expertise to implement a new project. The manager’s managerial expertise is his private information and characterized as an uncertain variable. The revenue brought about by the project in the future is also assumed to be uncertain. In light of these challenges, this paper investigates the impacts of the manager’s risk attitude and the type-and-effort dependent outside option on the optimal compensation contracts under different information structures. Through developing the manager’s decision criterion based on his risk attitude instead of the expected-utility-maximization criterion, we find that, if the manager is conservative and the outside option’s revenue uncertainty is sufficiently high, the optimal commission rate will be distorted upwards under asymmetric managerial expertise information compared with that under symmetric managerial expertise information. Our analysis also confirms that the existence of a type-and-effort dependent outside option distorts up the compensation structure tailored at a fixed outside option. We further show that, comparing with the setting of a fixed outside option when the manager is aggressive, the presence of a type-and-effort dependent outside option results in a surprising phenomenon that the manager’s private information makes no distortion of the firm’s profit.