Aristotle's Politics is widely recognized as one of the classics of the history of political philosophy, and like every other such masterpiece, it is a work about which there is deep division.

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)

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)

What is the temporal course of gratitude and indebtedness and how do these feelings influence helping in the context of reciprocity? In an online-game tapping real-life behaviour, Study 1 (N = 106) finds that while gratitude towards a benefactor remains elevated after an opportunity to reciprocate, indebtedness declines along with helping. Yet, indebtedness rather than gratitude better predicts real-life helping of a benefactor. Using a vignette-based experiment, Study 2 (N = 217) finds that after reciprocation indebtedness and likelihood of helping (...) a benefactor reset to a baseline level while gratitude endures. Furthermore, the decrease in helping after reciprocation is better explained by indebtedness than by gratitude. Study 3 (N = 217) assessed the unique influences of gratitude and indebtedness on helping by comparing contexts in which gratitude is at a baseline level but indebtedness is elevated (e.g. before a monetary payment for a service received) to contexts in which indebtedness is at a baseline level but gratitude is elevated (e.g. after reciprocation of benefits freely given by a friend). People are more likely to help in the former compared to latter context, and this difference is better explained by indebtedness rather than by gratitude. We discuss the interrelated and understudied relationships between gratitude, indebtedness, and reciprocity. (shrink)

This essay responds to the characterization Ted Miller offers (in his December 2008 essay in Political Theory) of the kind of nonfoundationalism I have referred to as "weak ontology," and that Gianni Vattimo frequently calls "weak thought." Miller argues that such a position embodies, first, a philosophy of history in which strong ontologies (e.g., religion) are assessed categorically as passé, and, second, are associated essentially with violence. I show that while these characterizations may be appropriate for Vattimo's thought, (...) they are not for weak ontology as I understand it. Finally, I suggest that the former might more usefully be categorized as "antifoundationalism" and the latter as "nonfoundationalism.". (shrink)

Hegel, Derrida, and Restricted Economy: The Case of Mechanical Memory STEPHEN HOULGA'FE A GLANCE AT THE TEXTS OF Jacques Derrida and at the texts and lectures of G. W. F. Hegel indicates that Hegel and Derrida are extraordi- narily different thinkers. Hegel is clearly what Derrida would regard as a philosopher of presence, working toward the point "where knowledge no longer needs to go beyond itself, where knowledge finds itself," where con- sciousness is present to itself as it is (...) in itself. 1 Derrida, on the other hand, suggests that everything that is present, here, now, at this moment, bears within it, as constitutive features of itself, the marks or traces of what is irredeemably past, and that, consequently, we can never talk of entities such as ourselves being simply or wholly present to themselves. ~ Derrida claims in Positions that he tries hard to distinguish "diff6rance" from tlegelian "differ- ence," indeed that "diff~rance" might well be defined precisely as "the inter- ruption, the destruction of Hegelian sublation [relive] wherever it operates"; and, to judge at least from the look of his texts, he would seem to have G. W. F. Hegel, Werke in zwamag B~inden, edited by E. Moldenhauer and K. M. Michel, 20 vols. and Index , Ill [Phi~nomenologie des Geistes], 74. For the English translation, see Hegel, Phenomenolog) of Spirit, translated by A. V. Miller, with analysis of the.. (shrink)

Hegel, Derrida, and Restricted Economy: The Case of Mechanical Memory STEPHEN HOULGA'FE A GLANCE AT THE TEXTS OF Jacques Derrida and at the texts and lectures of G. W. F. Hegel indicates that Hegel and Derrida are extraordi- narily different thinkers. Hegel is clearly what Derrida would regard as a philosopher of presence, working toward the point "where knowledge no longer needs to go beyond itself, where knowledge finds itself," where con- sciousness is present to itself as it is (...) in itself. 1 Derrida, on the other hand, suggests that everything that is present, here, now, at this moment, bears within it, as constitutive features of itself, the marks or traces of what is irredeemably past, and that, consequently, we can never talk of entities such as ourselves being simply or wholly present to themselves. ~ Derrida claims in Positions that he tries hard to distinguish "diff6rance" from tlegelian "differ- ence," indeed that "diff~rance" might well be defined precisely as "the inter- ruption, the destruction of Hegelian sublation [relive] wherever it operates"; and, to judge at least from the look of his texts, he would seem to have G. W. F. Hegel, Werke in zwamag B~inden, edited by E. Moldenhauer and K. M. Michel, 20 vols. and Index, Ill [Phi~nomenologie des Geistes], 74. For the English translation, see Hegel, Phenomenolog) of Spirit, translated by A. V. Miller, with analysis of the... (shrink)

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

Philosophers often suggest that their theories of free will are supported by our phenomenology. Just as their theories conflict, their descriptions of the phenomenology of free will often conflict as well. We suggest that this should motivate an effort to study the phenomenology of free will in a more systematic way that goes beyond merely the introspective reports of the philosophers themselves. After presenting three disputes about the phenomenology of free will, we survey the (limited) psychological research on the experiences (...) relevant to the philosophical debates and then describe some pilot studies of our own with the aim of encouraging further research. The data seem to support compatibilist descriptions of the phenomenology more than libertarian descriptions. We conclude that the burden is on libertarians to find empirical support for their more demanding metaphysical theories with their more controversial phenomenological claims. (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)

In recent years, several remarkable results have shown that certain theorems of finite combinatorics are unprovable in certain logical systems. These developments have been instrumental in stimulating research in both areas, with the interface between logic and combinatorics being especially important because of its relation to crucial issues in the foundations of mathematics which were raised by the work of Kurt Godel. Because of the diversity of the lines of research that have begun to shed light on these issues, there (...) was a need for a comprehensive overview which would tie the lines together. This volume fills that need by presenting a balanced mixture of high quality expository and research articles that were presented at the August 1985 AMS-IMS-SIAM Joint Summer Research Conference, held at Humboldt State University in Arcata, California.With an introductory survey to put the works into an appropriate context, the collection consists of papers dealing with various aspects of 'unprovable theorems and fast-growing functions'. Among the topics addressed are: ordinal notations, the dynamical systems approach to Ramsey theory, Hindman's finite sums theorem and related ultrafilters, well quasiordering theory, uncountable combinatorics, nonstandard models of set theory, and a length-of-proof analysis of Godel's incompleteness theorem. Many of the articles bring the reader to the frontiers of research in this area, and most assume familiarity with combinatorics and/or mathematical logic only at the senior undergraduate or first-year graduate level. (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)

A selective history of the benzene problem is presented, starting with August Kekulé's proposal of a hexagonal structure in 1865 and his hypothesis of 1872 that the carbon–carbon bonds oscillate between single and double. Only those theories are included that were accepted or at least discussed by a significant number of chemists. Special attention is given to predictions, their empirical tests, and the effect of the outcomes of those tests on the reception of the theories. At the end of the (...) period covered by this article, chemists generally accepted the valence bond theory proposed by Linus Pauling; some of them considered this a more sophisticated version of Kekulé's oscillation hypothesis. The sequel describes the replacement of the valence bond theory by the molecular orbital theory in the period ending around 1980. (shrink)

In the first part of the 19th century, geologists explained volcanoes, earthquakes and mountain-formation on the assumption that the earth has a large molten core underneath a very thin solid crust. This assumption was attacked on astronomical grounds by William Hopkins, who argued that the crust must be at least 800 miles thick, and on physical grounds by William Thomson, who showed that the earth as a whole behaves like a solid with high rigidity. Other participants in the debate insisted (...) that there is evidence for a fluid or plastic layer not far below the crust. It was also suggested that the interior of the earth is a supercritical fluid. By the end of the century many geologists had incorporated the doctrine of a completely solid earth into their theories. Acceptance of a relatively small liquid core, indicated by seismological research, was delayed for another two decades. (shrink)

In the second chapter of The descent of man , Charles Darwin interrupted his discussion of the evolutionary origins of language to describe ten ways in which the formation of languages and of biological species were ‘curiously’ similar. I argue that these comparisons served mainly as analogies in which linguistic processes stood for aspects of biological evolution. Darwin used these analogies to recapitulate themes from On the origin of species , including common descent, genealogical classification, the struggle for existence, and (...) natural selection, among others. Skeptical of this interpretation, Gregory Radick sees the naturalistic account of language formation in the Descent comparisons as reinforcing Darwin’s idea that languages and the races of mankind have both undergone progressive development. Yet the details of Darwin’s language–species comparisons, as well as the polemical context in which they appear, show that they were not aimed at so limited a function. Rather, they addressed issues related to species transmutation in general. (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)

Summary In The Origin of Species, Charles Darwin famously accounted for the lack of fossil evidence in support of species evolution on the grounds that the fossil record is naturally incomplete. This essay examines a similar argument that Darwin applied to his analogy between natural and artificial selection: the scarcity of data about the historical backgrounds of domestic breeds was the natural by-product of an extremely gradual change process. The point was to enhance the ability of the artificial selection analogy (...) to suggest that nature's species had undergone a similar transformation. Darwin did not depend on this negative inference alone, however, for in his writings he included whatever information he could find about the actual histories of particular breeds. A comparison with Darwin's treatment of the fossil record suggests the reasonableness of this combined use of opposite kinds of evidence to establish a single point. The comparison also suggests the unique qualities of negative inference as applied to the breeding analogy. (shrink)

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)