What Intentionality Is Like

Intentionality is a mark of the mental, as Brentano (1874) noted. Any representation or conception of anything has the feature of intentionality, which informally put, is the feature of being about something that may or may not exist. Visual artworks are about something, whether something literal or abstract. The artwork is a mentalized physical object. Aesthetic experience of the artwork illustrates the nature of intentionality as we focus attention on the phenomenology of the sensory exemplar. This focus of attention on the exemplar in aesthetic experience simultaneously exhibits what the intentional object is like and what our conception of it is like. The exemplar is Janus-faced, looking in one direction outward toward the objects conceived and in the other direction inward toward our conceiving of them. It shows us what intentionality is like and how we know it.     

Intentionality as a Conceptually Primitive Relation

If conceptual analysis is possible for finite thinkers, then there must ultimately be a distinction between complex and primitive or irreducible and unanalyzable concepts, by which complex concepts are analyzed as relations among primitive concepts. This investigation considers the advantages of categorizing intentionality as a primitive rather than analyzable concept, in both a historical Brentanian context and in terms of contemporary philosophy of mind. Arguments in support of intentionality as a primitive relation are evaluated relative to objections, especially a recent criticism by Jerry A. Fodor. Against this background, the relation between qualia and intentionality in the understanding of consciousness is explored.     

Physical Intentionality,Extrinsicness, and the Direction of Causation

The Physical Intentionality Thesis claims that dispositions share the marks of psychological intentionality; therefore, intentionality is not exclusively a mental phenomenon. Beyond the standard five marks, Alexander Bird introduces two additional marks of intentionality that he argues dispositions do not satisfy: first, thoughts are extrinsic; second, the direction of causation is that objects cause thoughts, not vice versa. In response, this paper identifies two relevant conceptions of extrinsicness, arguing that dispositions show deep parallels to thoughts on both conceptions. Then, it shows that Bird’s discussion of direction of causation overlooks complexities of dispositionality and intentionality that problematize apparent differences between thoughts and dispositions. The paper ends with a discussion of why we find these parallels between thoughts and dispositions.     

Is There a Conceptual Connection Between Intentionality and Consciousness?

It is argued that Searle’s argument for the thesis that there is a conceptual connection between intentionality and consciousness suffers from serious ambiguities. Searle’s argument is reconstructed as consisting of three premises that contain the notions of aspectual shape and irreducible subjectivity. Having identified two different readings of ‘aspectual shape’ and ‘irreducibly subjective,’ I conclude that each version of Searle’s argument incorporates at least one false premise. This paper is a descendant of a paper presented at the Wittgenstein Symposium at Kirchberg am Wechsel in August 2004. I would like to thank the reviewer of this journal for his/her helpful comments on a previous draft.     

Partitions and pairwise sums and products

A seven cell partition of N is constructed with the property that no infinite set has all of its pairwise sums and products in any one cell. A related Ramsey Theory question is shown to have different answers for two and three cell partitions.     

Affine-inscribed and affine-circumscribed polygons and polytopes

Five theorems on polygons and polytopes inscribed in (or circumscribed about) a convex compact set in the plane or space are proved by topological methods. In particular, it is proved that for every interior point O of a convex compact set in ℝ³, there exists a two-dimensional section through O circumscribed about an affine image of a regular octagon. It is also proved that every compact convex set in ℝ³ (except the cases listed below) is circumscribed about an affine image of a cube-octahedron (the convex hull of the midpoints of the edges of a cube). Possible exceptions are provided by the bodies containing a parallelogram P and contained in a cylinder with directrix P. Bibliography: 29 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 231, 1995, pp. 286–298. Translated by B. M. Bekker.     

Linear birth and death models and associated Laguerre and Meixner polynomials

We study birth and death processes with linear rates λ_n = n + α + c + 1, μ_{n + 1} = n + c, n 0 and μ₀ is either zero or c. The spectral measures of both processes are found using generating functions and the integral transforms of Laplace and Stieltjes. The corresponding orthogonal polynomials generalize Laguerre polynomials and the choice μ₀ = c generates the associated Laguerre polynomials of Askey and Wimp. We investigate the orthogonal polynomials in both cases and give alternate proofs of some of the results of Askey and Wimp on the associated Laguerre polynomials. We also identify the spectra of the associated Charlier and Meixner polynomials as zeros of certain transcendental equations.     

Distributive and Multiplication Modules and Rings

We study rings in which every ideal is a finitely generated multiplication right ideal.     

Beliefs and beyond: affect and the teaching and learning of mathematics

The importance of beliefs for the teaching and learning of mathematics is widely recognized among mathematics educators. In this special issue, we explicitly address what we call “beliefs and beyond” to indicate the larger field surrounding beliefs in mathematics education. This is done to broaden the discussion to related concepts (which may not originate in mathematics education) and to consider the interconnectedness of concepts. In particular, we present some new developments at the conceptual level, address different approaches to investigate beliefs, highlight the role of student beliefs in problem-solving activities, and discuss teacher beliefs and their significance for professional development. One specific intention is to consider expertise from colleagues in the fields of educational research and psychology, side by side with perspectives provided by researchers from mathematics education.     

Ritz and harmonic Ritz values and the convergence of FOM and GMRES

The Ritz and harmonic Ritz values are approximate eigenvalues, which can be computed cheaply within the FOM and GMRES Krylov subspace iterative methods for solving non‐symmetric linear systems. They are also the zeros of the residual polynomials of FOM and GMRES, respectively. In this paper we show that the Walker–Zhou interpretation of GMRES enables us to formulate the relation between the harmonic Ritz values and GMRES in the same way as the relation between the Ritz values and FOM. We present an upper bound for the norm of the difference between the matrices from which the Ritz and harmonic Ritz values are computed. The differences between the Ritz and harmonic Ritz values enable us to describe the breakdown of FOM and stagnation of GMRES. Copyright © 1999 John Wiley & Sons, Ltd.     

C_(pk)写控制图的研究与应用

控制图与过程能力指数Cp(Cpk)都是用来进行质量分析与处理的重要工具。文 [1]谈及控制图的两类错误 (其概率分别为α、β) ,文 [2 ]讨论了Cpk与α的关系 ,但涉及Cpk与控制图检出力 (1- β)关系的文章却不多。本文以 X控制图为例 ,讨论了α、β、1- β、与Cpk的关系 ,得出了联合应用它们会对工序状态有较好的了解 ,对其适当的调整有助於提高产品质量     

Monotone and cash-invariant convex functions and hulls

This paper provides some useful results for convex risk measures. In fact, we consider convex functions on a locally convex vector space E which are monotone with respect to the preference relation implied by some convex cone and invariant with respect to some numeraire (‘cash’). As a main result, for any function f, we find the greatest closed convex monotone and cash-invariant function majorized by f. We then apply our results to some well-known risk measures and problems arising in connection with insurance regulation.     

Navier and Stokes meet Poincare and Dulac

This paper surveys various precise (long-time) asymptotic results for the solutions of the Navier-Stokes equations with potential forces in bounded domains. It turns out that the asymptotic expansion leads surprisingly to a kind of Poincare-Dulac normal form of the Navier-Stokes equations. We will also discuss some related results and a few open issues.     

Shellability and homology of q-complexes and q-matroids

Journal of Algebraic Combinatorics - We consider a q-analogue of abstract simplicial complexes, called q-complexes, and discuss the notion of shellability for such complexes. It is shown that...