Constructive Logic and the Sorites Paradox

Author(s):  
Seiki Akama ◽  
Kazumi Nakamatsu ◽  
Jair Minoro Abe
Author(s):  
Kit Fine

The book is about the problem of vagueness. It begins by discussing some of the existing views on vagueness and then explains why they have not been thought to be satisfactory. It then outlines a new account of vagueness, based on the general idea that vagueness is a global rather than a local phenomenon. In other words, the vagueness of an expression or object is not an intrinsic feature of the object or an expression but a matter of how it relates to other objects and expression. The development of this idea leads to a new semantics and logic for vagueness. The semantics and logic are then applied to a number of issues, including the sorites paradox, the transparency or luminosity of mental states, and personal identity. It is shown that the view allows one to hew to a much more intuitive position on these various issues.


1994 ◽  
Vol 54 (2) ◽  
pp. 483
Author(s):  
Roy A. Sorensen ◽  
Linda Claire Burns

Author(s):  
KHROMUSHIN V.A. ◽  
◽  
VOLKOV A.V. ◽  
KHADARTSEV A.A. ◽  
◽  
...  

The article presents the relevance of the problem, defines the research purpose: to compare the average life expectancy of the population in the areas of the Tula region with different contents of heavy metals in the class of causes of death “Respiratory diseases ”. The authors used the data of the regional mortality register, the results of analyzes of the content of heavy metals (copper, lead, zinc, nickel) in the soil by atomic absorption spectroscopy, and the calculation of the average life expectancy by the algebraic model of constructive logic. The results indicate a decrease in average life expectancy due to the presence of heavy metals in the soil, but the average life expectancy in both contaminated and non-contaminated areas is gradually increasing.


Author(s):  
Crispin Wright

This anthology includes fourteen of Crispin Wrights’s highly influential essays on the phenomenon of vagueness in natural language, collectively representing almost half a century of cutting-edge systematic research. Key issues addressed include whether or under what assumptions vague expressions’ apparent tolerance of marginal changes in things to which they apply indicates that they are governed by inconsistent semantic rules, the varieties of Sorites paradox and the roots of the plausibility of their respective major premises, what it is for something to be a borderline case of a vague expression, whether vagueness should be viewed as fundamentally a semantic or an epistemic phenomenon, whether there is ‘higher-order’ vagueness, and what should be the appropriate logic for vague statements. The essays reprinted here jointly document the development of a distinctively original treatment of the philosophy and logic of vagueness, broadly analogous to the intuitionistic philosophy and logic for pure mathematics. Richard Kimberly Heck contributes an extended introductory essay, providing both an insightful critical overview of the development of the distinctive elements of Wright’s thought about vagueness, and indeed an invaluable advanced introduction to the topic.


2018 ◽  
Vol 24 (1) ◽  
pp. 90-106
Author(s):  
ERIK PALMGREN

AbstractIn this article we examine the natural interpretation of a ramified type hierarchy into Martin-Löf type theory with an infinite sequence of universes. It is shown that under this predicative interpretation some useful special cases of Russell’s reducibility axiom are valid, namely functional reducibility. This is sufficient to make the type hierarchy usable for development of constructive mathematical analysis in the style of Bishop. We present a ramified type theory suitable for this purpose. One may regard the results of this article as an alternative solution to the problem of the proliferation of levels of real numbers in Russell’s theory, which avoids impredicativity, but instead imposes constructive logic. The intuitionistic ramified type theory introduced here also suggests that there is a natural associated notion of predicative elementary topos.


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