We study the strength of RRT32, Rainbow Ramsey Theorem for colorings of triples, and prove that RCA0 + RRT32 implies neither WKL0 nor RRT42 source. To this end, we establish some recursion theoretic properties of cohesive sets and rainbows for colorings of pairs. We show that every sequence admits a cohesive set of non-PA Turing degree; and that every ∅′-recursive sequence admits a low3 cohesive set.
The notion of techné in Husserl’s phenomenology is related to his treatment of the three layers of the “teaching of craft” and the two layers of the science of “life-world.” The superior layer of both is of philosophical significance. Aristotle’s statement in ethics and metaphysics: techné is man-made, but can transit to spontaneity, and then to natural becoming, which manifests physis as the ultimate aim of his philosophical system, enlightens us to notice the following aspects in Husserl’s phenomenology. 1. Pure (...) or formal ethics is of a high-level téchne in the philosophical sense. 2. The concept of life-world leads to transcendental phenomenology. 3. What Ideas II implies – as a technique the method of phenomenology tends to let the pure I and spiritual I as matters appear themselves by the natural attitude – could conduct us to understand the artistic aspect of Husserl’s philosophical theory. (shrink)
The ideas of fixed points (Kripke in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 53–81, 1975; Martin and Woodruff in Recent essays on truth and the liar paradox. Clarendon Press, London, pp 47–51, 1984) and revision sequences (Gupta and Belnap in The revision theory of truth. MIT, London, 1993; Gupta in The Blackwell guide to philosophical logic. Blackwell, London, pp 90–114, 2001) have been exploited to provide solutions to the semantic paradox and have achieved admirable (...) success. This happy situation naturally encourages one to look for other philosophical areas of their further applications where paradoxical results seem to follow from intuitively acceptable principles. In this paper, I propose to extend the use of these ideas to give two new treatments of abstract objects. Sections 1 and 2 below check several abstractionist theories and their main defects. Section 3 shows how the two ideas can be applied to generate consistent theories of abstract objects without any ad hoc restriction on any principle. (shrink)
In this paper, we will prove that the plus cupping degrees generate a definable ideal on c.e. degrees different from other ones known so far, thus answering a question asked by Li and Yang (Proceedings of the 7th and the 8th Asian Logic Conferences. World Scientific Press, Singapore, 2003).
Although pioneering studies using statistical methods in geographical data analysis were published in the 1930s, it was only in the 1960s that their increasing use in human geography led to a claim that a ‘quantitative revolution’ had taken place. The widespread use of quantitative methods from then on was associated with changes in both disciplinary philosophy and substantive focus. The first decades of the ‘revolution’ saw quantitative analyses focused on the search for spatial order of a geometric form within an, (...) often implicit, logical positivist framework. In the first of three reviews of the use of quantitative methods in human geography, this progress report uncovers their origin with regard to the underlying philosophy, the focus on spatial order, and the nature of the methods deployed. Subsequent reports will outline the changes in all three that occurred in later decades and will chart the contemporary situation. (shrink)
The debate between the dynamical and the statistical interpretations of natural selection is centred on the question of whether all explanations that employ the concepts of natural selection and drift are reducible to causal explanations. The proponents of the statistical interpretation answer negatively, but insist on the fact that selection/drift arguments are explanatory. However, they remain unclear on where the explanatory power comes from. The proponents of the dynamical interpretation answer positively and try to reduce selection/drift arguments to some of (...) the most prominent accounts of causal explanation. In turn, they face the criticism raised by statisticalists that current accounts of causation have to be violated in some of their core conditions or otherwise used in a very loose manner in order to account for selection/drift explanations. We propose a reconciliation of both interpretations by conveying evolutionary explanations within the unificationist model of scientific explanation. Therefore, we argue that the explanatory power in natural selection arguments is a result of successful unification of individual- and population-level facts. A short case study based on research on sympatric speciation will be presented as an example of how population- and individual-level facts are unified to explain the morphological mosaic of bill shape in island scrub jays. (shrink)
The epistemological version of structural realism, proposed by Cao Tianyu, has great influence in the philosophy of science. Syntheses has published a special volume discussing the topic. Cao criticizes anti-realism, as well as the epistemic and ontic versions of structural realism. From the concepts of structure, ontology, and construction, he analyzes the objectivity of scientific theories as having five aspects: construction, historicity, holism, revision, and revolution. This paper systematically analyzes and comments on Cao's structural realism. The author agrees with his (...) criticism of the under-determination thesis, is neutral to his argument against ontological discontinuity, and questions his universal language argument. (shrink)
This paper argues that the structural obscurity in Kant’s Critique of the Power of Judgment reflects his tacit employment of three correlated but distinct notions: necessity considered as the universal validity of the judgment of taste; necessity considered as a feature of the judgment itself; and necessity considered as a feature of the mental free harmony that obtains in judging certain forms with taste. These distinctions have not been sufficiently recognized by commentators so far. Clarification of these three notions can (...) shed new light on the structure of the first part of Kant’s third Critique as well as on debates over the plausibility of his claims regarding taste. (shrink)
Dialetheism is the view that there are true contradictions. Classical dialetheism holds further the view that the law of excluded middle is indeed a logical law. Most famous dialetheists, such as G. Priest and J. Beall, are classical dialetheists; they take classical dialetheism to be the only plausible solution to the semantic paradoxes. The main contention of the paper is, however, that their views should be rejected. Based on inspecting Priest’s and Beall’s dialetheist theories from a special perspective, this paper (...) contends that classical dialetheism has no natural and plausible way to assign truth values to various truth-ineliminable sentences, i.e., sentences whose truth-conditions essentially involve the property of being true . Several examples of such truth-ineliminable sentences are given in the paper, and two classical dialetheist strategies for assigning them truth values are inspected. This paper argues that none of these strategies is successful. (shrink)
Gideon Rosen proposes a view called "modal fictionalism" which Rosen thinks has all the benefits of modal realism without its ontological costs. Whereas modal realists have a paraphrase r(0) of a modal claim "0", modal fictionalists claim that the correct translation of "0" is rather the result of prefixing "according to the hypothesis of a plurality of worlds" to r(0). Rosen takes the prefix to be primitive and defines other modal notions in terms of it. Bob Hale, however, thinks the (...) fictionalist's project suffers from a "simple" dilemma. The purpose of this paper is to show that Rosen is right in taking the prefix as primitive and Hale is wrong in thinking fictionalism as being threatened by the dilemma. (shrink)
Since the publication of The Structure of Scientific Revolution , relativism, resulting from the concepts of paradigm and paradigm shift, becomes one of the central problems in the philosophy of science. The author of this dissertation agrees with Thomas Kuhn in his criticism of the Logical Positivism, but denies that relativism arrives as a direct consequence. In this dissertation, the author tries to tackle the problem by analyzing some underlying basic concepts, e.g. paradigm, language and rationality. Firstly, he points out (...) that a hard-core model of paradigm, as understood by I. Lakatos, is not totally appropriate for an all-rounded understanding of a paradigm. Rather, among the elements certain "family resemblance" comes to the surface, they are therefore regarded as belonging to the same paradigm. A paradigm is not a hindrance to but an exemplar for our learning. And a paradigm shift needs not result in a total switch over, it could be a revolution with inheritance. Secondly, the incommesurability of languages does not mean the breakdown of communication between different linguistic communities. True bilinguals can achieve cross-paradigm understanding. In addition, due to the creative activities within a language, the problem of untranslatability could be solved. Finally, rationality, rather than assuming a hierarchical structure, could be taken as a reticulated model. As a result, various disagreements at the axiological level could be rationally resolved. ;The author also tackles in passing some issues concerning language and rationality in the Chinese tradition of science, and compares this tradition with that of the western. (shrink)