Fitts' Theorem and Movement Time Dissociation for Amplitude and Width Manipulations: Replying to Hoffmann

The commentary by Errol Hoffmann in this issue asserts that previous work by our group provides the spurious conclusion that amplitude and width manipulations to a movement environment elicit dissociable relations between movement time (MT) and P. M. Fitts' (1954) index of difficulty (ID). Hoffmann concludes that any such dissociation is the result of actions evoked entirely as ballistic. In this reply, we demonstrate that Hoffmann's commentary is a clear misrepresentation of the study goals and conclusions stated by our group. Additionally, we provide kinematic evidence that actions involving online trajectory amendments are associated with dissociable MT–ID relations for amplitude versus width manipulations. Finally, we contend that the kinematic analyses of movement trajectories, and Hoffmann's failure to acknowledge its importance, is an important step in further understanding speed–accuracy relations in human movement.     

The road to two theorems of logic

Work on how to axiomatize the subtheories of a first-order theory in which only a proper subset of their extra-logical vocabulary is being used led to a theorem on recursive axiomatizability and to an interpolation theorem for first-order logic. There were some fortuitous events and several logicians played a helpful role.     

PANTHEISM RECONSTRUCTED: ECOTHEOLOGY AS A SUCCESSOR TO THE JUDEO‐CHRISTIAN,ENLIGHTENMENT, AND POSTMODERNIST PARADIGMS

The Judeo‐Christian, Enlightenment, and postmodernist paradigms have become intellectually and ethically exhausted. They are obviously failing to provide a conceptual framework conducive to eliminating some of humanity's worst scourges, including war and environmental destruction. This raises the issue of a successor, which necessitates a reexamination of first principles, starting with our concept of God. Pantheism, which is differentiated from panentheism, denies the existence of a transcendent, supernatural creator and instead asserts that God and the universe are one and the same. Understood via intuition, modern cosmology, and other natural sciences, it offers an alternative worldview that posits the divine and sacred nature of the universe/creation. By asserting the fallacy of the creator/creation dichotomy and any attempts to anthropomorphize or personalize God, pantheism precludes hubris stemming from erroneous notions of divine favoritism. The links between Judeo‐Christianity and the Enlightenment are traced and a case made that the latter has resulted in the equally erroneous and hubristic notion of human ascendancy to a Godlike status, with the concept of progress providing a secular version of the Christian belief in salvation. By reestablishing the natural sciences’metanarrative, even as it asserts the divinity of the material universe, pantheism simultaneously demotes postmodernism and reconciles science with religion. Pantheism provides a theological foundation for deep ecology and also stakes out a viable third position in relation to the ongoing dispute between advocates of intelligent design and the scientific establishment.     

Hilbert's epsilon as an operator of indefinite committed choice

Hilbert and Bernays avoided overspecification of Hilbert's ε-operator. They axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. After briefly reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the ε simplifies proof search and is natural in the sense that it mirrors some cases of referential interpretation of indefinite articles in natural language.     

一种可融入额外信息的机器学习诊断法

研究将PNN和曼哈顿距离、贝叶斯定理相结合,提出了一种相对简洁的可融入额外信息的认知诊断法MB-PNN,通过模拟和实证研究考察了MB-PNN的有效性和适宜性,得到以下结论:(1)M-PNN的判准率高于PNN,表明将PNN中的ED修改为MD是适宜的;(2)MB-PNN的判准率较M-PNN和PNN高,表明基于多种信息的判别较基于单一信息的判别更为精准;(3)MB-PNN保留了PNN原有的非参数优势,基本不受知识状态分布和样本容量影响;(4)MB-PNN最能区分不同类型的学生,在认知诊断评估实践中更为适宜。     

Analogy Between the Theorem of Pythagoras and the Relations of Uncertainty of Heisenberg

In this work I propose an analogy between Pythagoras's theorem and the logical-formal structure of Werner Heisenberg's “relations of uncertainty.” The reasons that they have pushed to me to place this analogy have been determined from the following ascertainment: Often, when in exact sciences a problem of measurement precision arises, it has been resolved with the resource of the elevation to the square. To me it seems also that the aporie deriving from the uncertainty principle can find one solution with the resource to this stratagem. In fact, if the first classic example of the argument is the solution of the incommensurability between catheti and the hypotenuse of the triangle rectangle, one of the last cases is that which is represented from Heisenberg's principle of uncertainty.     

时间信息在情景模型建构中的作用

考察时间信息在情景模型建构中的作用 ,探讨被试能否把一系列相关的事实整合进基于时间组织的情景模型中。实验一、二考察明确的空间信息条件下 ,被试能否把绝对和相对的时间信息整合到情景模型中 ;实验三考察无明确的空间信息条件下 ,被试能否把绝对的时间信息整合到情景模型中。运用扇效应研究的提取干扰技术评定是否出现了整合。 3个实验结果一致表明 ,当几个相关的事实发生在相同的时间段时 ,都发现被试建构了基于时间的情景模型的证据。实验三结果同时也表明 ,无明确的空间信息的条件下 ,阅读材料中时间信息本身足以使被试建构基于时间组织的情景模型。     

A Map of Common Knowledge Logics

In order to capture the concept of common knowledge, various extensions of multi-modal epistemic logics, such as fixed-point ones and infinitary ones, have been proposed. Although we have now a good list of such proposed extensions, the relationships among them are still unclear. The purpose of this paper is to draw a map showing the relationships among them. In the propositional case, these extensions turn out to be all Kripke complete and can be comparable in a meaningful manner. F. Wolter showed that the predicate extension of the Halpern-Moses fixed-point type common knowledge logic is Kripke incomplete. However, if we go further to an infinitary extension, Kripke completeness would be recovered. Thus there is some gap in the predicate case. In drawing the map, we focus on what is happening around the gap in the predicate case. The map enables us to better understand the common knowledge logics as a whole.     

A new formulation of the Principle of Indifference

The idea of a probabilistic logic of inductive inference based on some form of the principle of indifference has always retained a powerful appeal. However, up to now all modifications of the principle failed. In this paper, a new formulation of such a principle is provided that avoids generating paradoxes and inconsistencies. Because of these results, the thesis that probabilities cannot be logical quantities, determined in an objective way through some form of the principle of indifference, is no longer supportable. Later, the paper investigates some implications of the new principle of indifference. To conclude, a re-examination of the foundations of the so-called objective Bayesian inference is called for.