A successivity in a linear order is a pair of elements with no other elements between them. A recursive linear order with recursive successivities U is recursively categorical if every recursive linear order with recursive successivities isomorphic to U is in fact recursively isomorphic to U . We characterize those recursive linear orders with recursive successivities that are recursively categorical as precisely those with order type k 1 + g 1 + k 2 + g 2 +…+ g n -1 (...) + k n where each k n is a finite order type, non-empty for i ϵ{2,…, n -1} and each g i is an order type from among {ω,ω * ,ω+ω * }∪{ k ·η: k. (shrink)

A linear order is -decidable if its universe is and the relations defined by formulas are uniformly computable. This means that there is a computable procedure which, when applied to a formula and a sequence of elements of the linear order, will determine whether or not is true in the structure. A linear order is decidable if the relations defined by all formulas are uniformly computable. These definitions suggest two questions. Are there, for each , -decidable linear orders that are (...) not -decidable? Are there linear orders that are -decidable for all but not decidable? The former was answered in the positive by Moses in 1993. Here we answer the latter, also positively. (shrink)

This article attempts a philosophical defense of an autonomy-based approach to multicultural education. I contend that multicultural education is necessary in order for students to be able to develop personal autonomy. This, in turn, can empower students to effectively formulate their own version of the good life. The development of autonomy need not, as many critics claim, promote atomistic individualism. Rather, contemporary liberal autonomy strives for a balance between the individual and the community. In defending multicultural education, my argument relies (...) on Joseph Raz's notion of autonomy and Will Kymlicka's concept of a context of choice. I conclude that through multicultural education, students can expand their contexts of choice and consequently develop individual autonomy, an essential ingredient of the good life. (shrink)

We prove a number of structural theorems about the honest polynomial m-degrees contingent on the assumption P = NP . In particular, we show that if P = NP , then the topped finite initial segments of Hm are exactly the topped finite distributive lattices, the topped initial segments of Hm are exactly the direct limits of ascending sequences of finite distributive lattices, and all recursively presentable distributive lattices are initial segments of Hm ∩ RE. Additionally, assuming ¦∑¦ = 1, (...) we show that the theory of the hpm-degrees is undecidable. We also show that index sets cannot be minimal. Lastly, we examine an alternative definition of honest m-reduction under which recursive minimal sets can be constructed. (shrink)

Three classes of decidable discrete linear orders with varying degrees of effectiveness are investigated. We consider how a classical order type may lie in relation to these three classes, and we characterize by their order types elements of these classes that have effective nontrivial self-embeddings.

This essay examines the educational opportunities of people in poverty who receive social welfare assistance. The dominant political theory underlying social policy (including education policy) in the United States has evolved from 1960s and 1970s welfare liberalism into 1980s and 1990s style neo-conservatism—a theory that embraces principles of the market and individual liberty as paramount social values. Against this backdrop, I review two recent books that provide compelling evidence for this turn and I call for increased understanding of the relationship (...) between social welfare policies and higher education opportunities for those in poverty. (shrink)

(2004). Toward a Critical Deliberative Strategy for Addressing Ideology in Educational Policy Processes. Educational Studies: Vol. 36, No. 3, pp. null.

The block relation B(x,y) in a linear order is satisfied by elements that are finitely far apart; a block is an equivalence class under this relation. We show that every computable linear order with dense condensation-type (i.e., a dense collection of blocks) but no infinite, strongly η-like interval (i.e., with all blocks of size less than some fixed, finite k ) has a computable copy with the nonblock relation ¬ B(x,y) computably enumerable. This implies that every computable linear order has (...) a computable copy with a computable nontrivial self-embedding and that the long-standing conjecture characterizing those computable linear orders every computable copy of which has a computable nontrivial self-embedding (as precisely those that contain an infinite, strongly η-like interval) holds for all linear orders with dense condensation-type. (shrink)

The project we highlight in this article stems from our philosophical work on moral disagreements that appear to be—and sometimes are—intractable. Deliberative democratic theorists tout the merits of dialogue as an effective way to bridge differences of values and opinion, ideally resulting in agreement, or perhaps more often resulting in greater mutual understanding. Could dialogue mitigate disagreements about a controversial education policy such as affirmative action? Could it foster greater understanding? We conceived of a project that would simultaneously fulfill two (...) goals that we had as philosophers, education researchers, and aspiring public intellectuals. First, it would allow us to use philosophy in research, grounding our mixed methods research in a philosophically informed framework. The tools and analytic techniques that are particular to philosophers felt uniquely suited for an empirical study concerning political theory. Second, we aimed to use philosophy in the community. We were able to put our own expertise in philosophy and race-conscious education policy to good use by purposefully creating opportunities for diverse community members in our larger metropolitan area to engage in dialogue and deliberation with each other over the issue of affirmative action. (shrink)

: The purposes of this critical analysis are to clarify why high stakes testing reforms have become so prevalent in the United States and to explain the connection between current federal and state emphases on standardized testing reforms and educational opportunities. The article outlines the policy context for high stakes examinations, as well as the ideas of testing and accountability as major tenets of current education reform and policy. In partial explanation of the widespread acceptance and use of standardized tests (...) in the United States, we argue that there is a pervasive testing culture, in addition to other contributing factors such as administrative utility, profit motives, and political ideology. Finally, we offer a critique of high stakes testing reforms in light of concerns about equality of educational opportunity. (shrink)