This report outlines the findings from a Delphi study designed to establish consensus on the definitions of cognitive style and learning style amongst an international style researcher community. The study yields long-needed definitions for each construct that reflect high levels of agreement. In a field that has been criticised for a bewildering array of definitions and a proliferation of terms and concepts, this study represents an important step to address confusion in the meaning of the two terms. New researchers interested (...) in styles are encouraged to draw on these definitions when developing new research agendas aimed at deepening our understanding of style as a core construct in educational psychology. (shrink)

The thesis that scientists give greater weight to novel predictions than to explanations of known facts is tested against historical cases in physical science. Several theories were accepted after successful novel predictions but there is little evidence that extra credit was given for novelty. Other theories were rejected despite, or accepted without, making successful novel predictions. No examples were found of theories that were accepted primarily because of successful novel predictions and would not have been accepted if those facts had (...) been previously known. (shrink)

This essay traces the interlinked origins of two concepts found in Charles Darwin's writings: "unconscious selection," and sexual selection as applied to humanity's anatomical race distinctions. Unconscious selection constituted a significant elaboration of Darwin's artificial selection analogy. As originally conceived in his theoretical notebooks, that analogy had focused exclusively on what Darwin later would call "methodical selection," the calculated production of desired changes in domestic breeds. By contrast, unconscious selection produced its results unintentionally and at a much slower pace. Inspiration (...) for this concept likely came from Darwin's early reading of works on both animal breeding and physical ethnology. Texts in these fields described the slow and unplanned divergence of anatomical types, whether animal or human, under the guidance of contrasting ideals of physical perfection. These readings, it is argued, also led Darwin to his theory of sexual selection as applied to race, a theme he discussed mainly in his book The Descent of Man. There Darwin described how the racial version of sexual selection operated on the same principle as unconscious selection. He thereby effectively reunited these kindred concepts. (shrink)

We investigate the provability or nonprovability of certain ordinary mathematical theorems within certain weak subsystems of second order arithmetic. Specifically, we consider the Cauchy/Peano existence theorem for solutions of ordinary differential equations, in the context of the formal system RCA 0 whose principal axioms are ▵ 0 1 comprehension and Σ 0 1 induction. Our main result is that, over RCA 0 , the Cauchy/Peano Theorem is provably equivalent to weak Konig's lemma, i.e. the statement that every infinite {0, 1}-tree (...) has a path. We also show that, over RCA 0 , the Ascoli lemma is provably equivalent to arithmetical comprehension, as is Osgood's theorem on the existence of maximum solutions. At the end of the paper we digress to relate our results to degrees of unsolvability and to computable analysis. (shrink)

A mass problem is a set of Turing oracles. If P and Q are mass problems, we say that P is weakly reducible to Q if every member of Q Turing computes a member of P. We say that P is strongly reducible to Q if every member of Q Turing computes a member of P via a fixed Turing functional. The weak degrees and strong degrees are the equivalence classes of mass problems under weak and strong reducibility, respectively. We (...) focus on the countable distributive lattices P w and P s of weak and strong degrees of mass problems given by nonempty Π 1 0 subsets of 2 ω . Using an abstract Gödel/Rosser incompleteness property, we characterize the Π 1 0 subsets of 2 ω whose associated mass problems are of top degree in P w and P s , respectively. Let R be the set of Turing oracles which are random in the sense of Martin-Löf, and let r be the weak degree of R. We show that r is a natural intermediate degree within P w . Namely, we characterize r as the unique largest weak degree of a Π 1 0 subset of 2 ω of positive measure. Within P w we show that r is meet irreducible, does not join to 1, and is incomparable with all weak degrees of nonempty thin perfect Π 1 0 subsets of 2 ω . In addition, we present other natural examples of intermediate degrees in P w . We relate these examples to reverse mathematics, computational complexity, and Gentzen-style proof theory. (shrink)

Let ω be the set of natural numbers. For functions f, g: ω → ω, we say f is dominated by g if f < g for all but finitely many n ∈ ω. We consider the standard “fair coin” probability measure on the space 2ω of in-finite sequences of 0's and 1's. A Turing oracle B is said to be almost everywhere dominating if, for measure 1 many X ∈ 2ω, each function which is Turing computable from X is (...) dominated by some function which is Turing computable from B. Dobrinen and Simpson have shown that the almost everywhere domination property and some of its variant properties are closely related to the reverse mathematics of measure theory. In this paper we exposit some recent results of Kjos-Hanssen, Kjos-Hanssen/Miller/Solomon, and others concerning LR-reducibility and almost everywhere domination. We also prove the following new result: If B is almost everywhere dominating, then B is superhigh, i. e., 0″ is truth-table computable from B ′, the Turing jump of B. (shrink)

An examination of verbal hallucinations and thought insertion as examples of "alienated self-consciousness.".

This paper examines Charles Darwin’s idea that language-use and humanity’s unique cognitive abilities reinforced each other’s evolutionary emergence—an idea Darwin sketched in his early notebooks, set forth in his Descent of man , and qualified in Descent’s second edition. Darwin understood this coevolution process in essentially Lockean terms, based on John Locke’s hints about the way language shapes thinking itself. Ironically, the linguist Friedrich Max Müller attacked Darwin’s human descent theory by invoking a similar thesis, the German romantic notion of (...) an identity between language and thought. Although Darwin avoided outright contradiction, when he came to defend himself against Müller’s attacks, he undercut some of his own argumentation in favor of the coevolution idea. That is, he found it difficult to counter Müller’s argument while also making a case for coevolution. Darwin’s efforts in this area were further complicated by British and American writers who held a naturalistic view of speech origins yet still taught that language had been invented by fully evolved homo sapiens, thus denying coevolution. (shrink)

We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i∈A and f:A→A. A subset X⊆A is said to be inductive if i∈X and ∀a ∈X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be (...) an inductive system such that f is one-to-one and i∉the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…}=the set of natural numbers and S:N→N is given by S=n+1 for all n∈N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL0 over RCA0⁎ source. From this and similar equivalences we draw some foundational/philosophical consequences. (shrink)

This paper examines the way Charles Darwin applied his domestic breeding analogy to the practical workings of species evolution: that application, it is argued, centered on Darwin's distinction between methodical and unconscious selection. Methodical selection, which entailed pairing particular individuals for mating purposes, represented conditions of strict geographic isolation, obviously useful for species multiplication (speciation). By contrast, unconscious selection represented an open landmass with a large breeding population. Yet Darwin held that this latter scenario, which often would include multiple ecological (...) subdistricts and thus partial isolation, was better suited for speciation than were isolated conditions. At the same time, many passages in Darwin's writings that apparently portrayed phyletic evolution exclusively (these including references to unconscious selection), actually applied to speciation as well, for phyletic change in a single district could constitute a local manifestation of a larger common-descent pattern. This generic use of "phyletic" change was reflected in Darwin's deployment of the unconscious selection analogy in his published writings as well as in his dispute with Moritz Wagner over the necessity of geographic isolation for speciation. We can thus understand Darwin's otherwise puzzling declaration in The Origin of Species that unconscious selection was 'more important' than the methodical approach. (shrink)

Higher order unification is a way of combining information (or equivalently, solving equations) expressed as terms of a typed higher order logic. A suitably restricted form of the notion has been used as a simple and perspicuous basis for the resolution of the meaning of elliptical expressions and for the interpretation of some non-compositional types of comparative construction also involving ellipsis. This paper explores another area of application for this concept in the interpretation of sentences containing intonationally marked focus, or (...) various semantic constructs which are sensitive to focus.Similarities and differences between this approach, and theories using alternative semantics, structured meanings, or flexible categorial grammars, are described. The paper argues that the higher order unification approach offers descriptive advantages over these alternatives, as well as the practical advantage of being capable of fairly direct computational implementation. (shrink)

Let CKDT be the assertion that for every countably infinite bipartite graph G, there exist a vertex covering C of G and a matching M in G such that C consists of exactly one vertex from each edge in M. (This is a theorem of Podewski and Steffens [12].) Let ATR0 be the subsystem of second-order arithmetic with arithmetical transfinite recursion and restricted induction. Let RCA0 be the subsystem of second-order arithmetic with recursive comprehension and restricted induction. We show that (...) CKDT is provable in ART0. Combining this with a result of Aharoni, Magidor, and Shore [2], we see that CKDT is logically equivalent to the axioms of ATR0, the equivalence being provable in RCA0. (shrink)

By , we denote the system of second-order arithmetic based on recursive comprehension axioms and Σ10 induction. is defined to be plus weak König's lemma: every infinite tree of sequences of 0's and 1's has an infinite path. In this paper, we first show that for any countable model M of , there exists a countable model M′ of whose first-order part is the same as that of M, and whose second-order part consists of the M-recursive sets and sets not (...) in the second-order part of M. By combining this fact with a certain forcing argument over universal trees, we obtain the following result : if proves X!Y with arithmetical, so does . We also discuss several improvements of this results. (shrink)

In this paper, we introduce a system of nonstandard second-order arithmetic $\mathsf{ns}$-$\mathsf{WWKL_0}$ which consists of $\mathsf{ns}$-$\mathsf{BASIC}$ plus Loeb measure property. Then we show that $\mathsf{ns}$-$\mathsf{WWKL_0}$ is a conservative extension of $\mathsf{WWKL_0}$ and we do Reverse Mathematics for this system.

We examine the concept of almost everywhere domination from the viewpoint of mass problems. Let AED and MLR be the sets of reals which are almost everywhere dominating and Martin-Löf random, respectively. Let b1, b2, and b3 be the degrees of unsolvability of the mass problems associated with AED, MLR × AED, and MLR ∩ AED, respectively. Let [MATHEMATICAL SCRIPT CAPITAL P]w be the lattice of degrees of unsolvability of mass problems associated with nonempty Π01 subsets of 2ω. Let 1 (...) and 0 be the top and bottom elements of [MATHEMATICAL SCRIPT CAPITAL P]w. We show that inf, inf, and inf belong to [MATHEMATICAL SCRIPT CAPITAL P]w and 0 < inf < inf < inf < 1. Under the natural embedding of the recursively enumerable Turing degrees into [MATHEMATICAL SCRIPT CAPITAL P]w, we show that inf and inf but not inf are comparable with some recursively enumerable Turing degrees other than 0 and 0′. In order to make this paper more self-contained, we exposit the proofs of some recent theorems due to Hirschfeldt, Miller, Nies, and Stephan. (shrink)

The evidence-based medicine movement advocates basing all medical decisions on certain types of quantitative research data and has stimulated protracted controversy and debate since its inception. Evidence-based medicine presupposes an inaccurate and deficient view of medical knowledge. Michael Polanyi’s theory of tacit knowledge both explains this deficiency and suggests remedies for it. Polanyi shows how all explicit human knowledge depends on a wealth of tacit knowledge which accrues from experience and is essential for problem solving. Edmund Pellegrino’s classic treatment of (...) clinical judgment is examined, and a Polanyian critique of this position demonstrates that tacit knowledge is necessary for understanding how clinical judgment and medical decisions involve persons. An adequate medical epistemology requires much more qualitative research relevant to the clinical encounter and medical decision making than is currently being done. This research is necessary for preventing an uncritical application of evidence-based medicine by health care managers that erodes good clinical practice. Polanyi’s epistemology shows the need for this work and provides the structural core for building an adequate and robust medical epistemology that moves beyond evidence-based medicine. (shrink)

Stephen Salkever shows that reading Aristotle is a starting point for discussing contemporary political problems in new ways that avoid the opposition between liberal individualism and republican communitarianism, between the politics of rights and the politics of virtues. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in (...) durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Stephen Salkever shows that reading Aristotle is a starting point for discussing contemporary political problems in new ways that avoid the opposition between liberal individualism and republican communitarianism, between the politics of rights and the politics of virtues. Originally published in 1990. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in (...) durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

Most clinicians take for granted a simple, reductionist understanding of medical knowledge that is at odds with how they actually practice medicine; routine medical decisions incorporate more complicated kinds of information than most standard accounts of medical reasoning suggest. A better understanding of the structure and function of knowledge in medicine can lead to practical improvements in clinical medicine. This understanding requires some familiarity with epistemology, the study of knowledge and its structure, in medicine. Michael Polanyi's theory of tacit knowing (...) is advanced as the basis for developing a more accurate understanding of medical knowledge. Tacit knowing, which explores the taken-for-granted background knowledge that underlies all human knowing, is explained in detail with a focus on its relevance for clinical medicine. The implications of recognizing tacit knowing in medicine and medical decisions are discussed. These include the ability to explain the importance of the clinical encounter in medical practice, mechanisms for analysing patient and doctor as persons, and the need for humility given the uncertainty that the tacit dimension injects into all medical decisions. This more robust medical epistemology allows clinicians to better articulate the nature and importance of patient-centred care, to avoid pitfalls inherent in reductionist approaches to medical knowledge, and to think more clearly about the relationships between medicine and health care at the individual and population levels. (shrink)

Historically, the scientific method has been said to require proposing a theory, making a prediction of something not already known, testing the prediction, and giving up the theory (or substantially changing it) if it fails the test. A theory that leads to several successful predictions is more likely to be accepted than one that only explains what is already known but not understood. This process is widely treated as the conventional method of achieving scientific progress, and was used throughout the (...) twentieth century as the standard route to discovery and experimentation. But does science really work this way? In Making 20th Century Science, Stephen G. Brush discusses this question, as it relates to the development of science throughout the last century. Answering this question requires both a philosophically and historically scientific approach, and Brush blends the two in order to take a close look at how scientific methodology has developed. Several cases from the history of modern physical and biological science are examined, including Mendeleev's Periodic Law, Kekule's structure for benzene, the light-quantum hypothesis, quantum mechanics, chromosome theory, and natural selection. In general it is found that theories are accepted for a combination of successful predictions and better explanations of old facts. Making 20th Century Science is a large-scale historical look at the implementation of the scientific method, and how scientific theories come to be accepted. (shrink)

A well known fact is that every Lebesgue measurable set is regular, i.e., it includes an F$_{\sigma}$ set of the same measure. We analyze this fact from a metamathematical or foundational standpoint. We study a family of Muchnik degrees corresponding to measure-theoretic regularity at all levels of the effective Borel hierarchy. We prove some new results concerning Nies's notion of LR-reducibility. We build some $\omega$-models of RCA$_0$which are relevant for the reverse mathematics of measure-theoretic regularity.