More on Putnam’s models: a reply to Belloti

In an earlier paper, I claimed that one version of Putnam's model-theoretic argument against realism turned on a subtle, but philosophically significant, mathematical mistake. Recently, Luca Bellotti has criticized my argument for this claim. This paper responds to Bellotti's criticisms.     

How are base‐rates used,when they are used: a comparison of additive and Bayesian models of base‐rate use

Previous research has uncovered many conditions that encourage base‐rate use. The present research investigates how base‐rates are used when conditions are manipulated to encourage their use in the lawyer/engineer paradigm. To examine the functional form of the response to base‐rate, a factorial design was employed in which both base‐rate and the individuating information were varied within‐subject. We compared the performance of several models of base‐rate use, including a model that allows base‐rate and individuating information to be combined in a strictly additive fashion, and a model which presumes that respondents use Bayes' Rule in forming their judgments. Results from 1493 respondents showed that the additive model is a stronger predictor of base‐rate use than any other model considered, suggesting that the base‐rate and individuating information are processed independently in the lawyer/engineer paradigm. A possible mechanism for this finding is discussed. Copyright © 1999 John Wiley & Sons, Ltd.     

Age and probabilistic reasoning: Biases in conjunctive,disjunctive and Bayesian judgements in early and late adulthood

Probabilistic reasoning plays an essential part in many aspects of our daily routine and it has been argued that as we grow older, the need to make judgements under uncertainty becomes increasingly important. Two studies were conducted to establish whether the propensity to commit probabilistic reasoning errors increased with age. Young (aged 16–24), middle aged (25–54), and older persons (55 years and above) were included. Study 1 revealed systematic biases and errors across a range of judgement tasks. However, no evidence of any age effect in Bayesian inference, the incidence of the conjunction fallacy, or in the number of disjunction errors was found. The results obtained in Study 1 were replicated in Study 2, where the potential mediating role of working memory processes and intellectual capacity were explicitly assessed. While some aspects of probabilistic reasoning performance were correlated with measures of intelligence and working memory functioning among young adults, this was much less evident in older persons. The present findings are discussed in relation to the evolution of the dualistic heuristic–analytical system over the adult lifespan. Copyright © 2005 John Wiley & Sons, Ltd.     

Vagueness-Adaptive Logic: A Pragmatical Approach to Sorites Paradoxes

Kripke-completeness of every classical modal logic with Sahlqvist formulas is one of the basic general results on completeness of classical modal logics. This paper shows a Sahlqvist theorem for modal logic over the relevant logic Bin terms of Routley-Meyer semantics. It is shown that usual Sahlqvist theorem for classical modal logics can be obtained as a special case of our theorem.     

Rule Separation and Embedding Theorems for Logics Without Weakening

A full separation theorem for the derivable rules of intuitionistic linear logic without bounds, 0 and exponentials is proved. Several structural consequences of this theorem for subreducts of (commutative) residuated lattices are obtained. The theorem is then extended to the logic LR ⁺ and its proof is extended to obtain the finite embeddability property for the class of square increasing residuated lattices.     

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.