The Evolution of Principia Mathematica; Bertrand Russell's Manuscripts and Notes for the Second Edition

This paper deals with Popper's little-known work on deductive logic, published between 1947 and 1949. According to his theory of deductive inference, the meaning of logical signs is determined by certain rules derived from ‘inferential definitions’ of those signs. Although strong arguments have been presented against Popper's claims (e.g. by Curry, Kleene, Lejewski and McKinsey), his theory can be reconstructed when it is viewed primarily as an attempt to demarcate logical from non-logical constants rather than as a semantic foundation for logic. A criterion of logicality is obtained which is based on conjunction, implication and universal quantification as fundamental logical operations.     

The ontological foundation of Russell's theory of modality

Prominent thinkers such as Kripke and Rescher hold that Russell has no modal logic, even that Russell was indisposed toward modal logic. In Part I, I show that Russell had a modal logic which he repeatedly described and that Russell repeatedly endorsed Leibniz's multiplicity of possible worlds. In Part II, I describe Russell's theory as having three ontological levels. In Part III, I describe six Parmenidean theories of being Russell held, including: literal in 1903; universal in 1912; timeless in 1914; transcendental in 1918–1948. The transcendental theory underlies the primary level of Russell's modal logic. In Part IV, I examine Rescher's view that Russell and modal logic did not mix.The United States Naval Academy Research Council kindly provided a summer 1988 research grant for work on this essay. This essay was presented at the Bertrand Russell Society Meeting during the December 1988 Eastern Division Meeting of the American Philosophical Association in Washington, D.C.     

A theory of relative judgment

This paper is concerned with the scaling method of “ratio estimation.” The simple theory that equates reported ratio judgments to ratios of psychological magnitudes is first considered, then two close relatives of this theory are formulated, each of which places weaker constraints on the structure of the data. Structural conditions are stated that express the relations that must hold among observed ratio judgments for each of the models. The models proposed are “cumulative” in the sense that the second is a weakened version of the first, and the third a weakened version of the second. A special feature of the models is that they may be tested entirely in terms of observables, avoiding the necessity of scale construction prior to testing. Tests were carried out on data from 9 published studies. The strongest model, typically used in scale construction using ratio estimation data, was generally inadequate, showing large systematic errors. However, the weakest version generally passed the tests of internal consistency, and the model equation provided a basis for constructing ratio scales utilizing bias parameters.     

Transformation theory of size judgment.

Perception of size is assessed by having observers adjust a comparison target at a fixed distance to match the size of a standard located at different distances. Results depend on instructions, target orientation, and available stimulus cues. A mathematical theory assumes that the brain performs an inverse transformation on the proximal information impinging on the retina to recover the original distal size of the target. Results depend on the target visual angle, and the effective target distance and orientation applied in performing the inverse transformation. Effective values are linked to instructions, target location, and stimulus cues. Two models are developed and successfully fit to empirical data. One emphasizes the distance parameter; the second, the orientation parameter.     

Psychophysical judgment: Wundt's theory revisited

Summary Wundt's psychological interpretation of Weber's and Fechner's laws rests on two main postulates. First, the magnitude of sensory excitation is proportional to the intensity of the stimulus that produces it. Second, in apperception, sensory comparisons and judgments are made according to psychological relationships: Two sensations are just-noticeably different when they fall in a constant psychological ratio. Wundt's theory implies a hierarchical organization, in which sensory-perceptual processes are embedded within higher-level, apperceptive processes. Such an organization is compatible with recent psychophysical research on loudness and with a model that goes toward resolving some controversies in loudness scaling, notably the seeming incompatibility of Stevens's sone scale and Garner's lambda scale.     

On Russell's vulnerability to Russell's paradox

Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ‘the most important event’ in ‘the most important year in my intellectual life’. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory.     

The context principle and Wittgenstein's criticism of Russell's theory of types

In this paper, I try to uncover the role played by Wittgenstein's context principle in his criticism of Russell's theory of types. There is evidence in Wittgenstein's writings that a syntactical version of the context principle in connection with the theory of symbolism functions as a good reason for his dispensing with the theory of types.I would like to thank Michael Wrigley (UNICAMP) and Gottfried Gabriel (Universität Konstanz) as well as an anonymous journal referee for their valuable comments on a previous version of this paper.     

解释水平视角下的道德判断

道德判断对社会合作有重要意义。近20年来涌现出大量对道德判断的研究。经典的社会直觉模型和双加工模型已经不足以解释所有的研究发现。近年来,解释水平理论为道德判断的研究提供了一个新的视角。通过文献梳理发现,基于解释水平理论的道德判断研究可以分为两难的道德判断研究和一般的道德判断研究。两难的道德判断研究已经有了较为一致的结论,但是一般的道德判断研究还存在争议。解释水平影响道德判断的深层原因可能是通过关注点影响道德判断的标准。未来的研究可以着眼于跨文化研究和深层机制的剖析,为解释水平视角下的道德判断研究提供更多的实验证据,加深人们对道德判断的理解。     

Analyst judgment: The efficient market hypothesis versus a psychological theory of human judgment

This paper considers the psychological processes used by financial analysts in making earnings forecasts by pitting two models against each other: the efficient market hypothesis, an economic model which asserts that the stock market virtually instantaneously and perfectly assimilates all available investment information; and personal construct theory, a psychological model of human judgment which emphasizes the fact that human decision making is based on formal and informal models of the phenomenon under consideration. Path models derived from personal construct theory fit data for 1963 gathered by Cragg and Malkiel and data for 1979–1983 gathered for this study. The efficient market hypothesis was not supported in any test on either data set.     

Two studies of Piaget's theory of moral judgment

The relationship between conservation skills and subjective responsibility (SR) in moral judgment was examined in two studies. The Kohlberg ontogenetic priority hypothesis stating that conversation is a necessary but not sufficient condition of SR was pitted against the common structural basis hypothesis advanced by Damon. Piaget's notion of heteronomy as a combination of preoperational thought and unilateral respect was studied by using the behavioural independence tasks by Subbotsky as indicators of unilateral respect. A teaching experiment using Galperin's and Obukhova's method to induce conservation indicated significant transfer from conservation to SR. SR was found to be more susceptible to regression over a 3–month period than conservation. Conservers were less likely to regress on SR than nonconservers. Unilateral respect was related to objective responsibility but not to conservation. Taken together the data fail to support Kohlberg's ontogenetic priority hypothesis and only partially support the Piaget and Damon model of a common underlying structure. It is concluded that SR judgments largely reflect individual judgmental strategies and the effect of conservation on SR is intepreted in terms of increasing cross-situational consistency in the use of these strategies.