Philosophical Logic. (Summaries And Comments).
In "On Higher-Order Logic and Natural Language," Higginbotham puts forward some possible motivations for higher-order logic derived from natural language, and concludes that, at least, these do not adequately motivate it. He discusses questions such as: Should second-order quantification be construed as substitutional? Should the models considered for evaluating logical truth in higher-order logic be confined to standard ones? How are the properties of objects and relations to be interpreted in a higher-order setting? Are plural terms best interpreted as referring to the second-order notions and if so, how? Could plurals as referring to classes as many be helpful? In his commentary, David Bostock replies that motivation could perhaps be found elsewhere, in logical properties such as categoricity, that is, descriptive completeness of second-order logic, which requires an understanding of axioms close to the ways humans actually reason. In addition, Bostock comments that semantic incompleteness is not a feature to hinder something to be logic.
Sainsbury's "Indexicals and Reported Speech" explores the consequences of two hypotheses: that constraints on reporting speech can be treated as guides to meaning, and that two thoughts differ if either is rationally cotenable with the negation of the other. The first thesis is argued to influence semantic theories as well as the roles indexicals have in sentences reporting action or time. The feature partially relaxed is context-dependence; Sainsbury argues for the reducibility thesis in that indexical thought can always be reported by words that are not indexical. The second hypothesis relates to the Fregean modes of presentation but removes it from its role of explicating the Fregean sense. In a commentary, J. E. J. Altham discusses the relation of these two hypotheses and suggests that reducibility may not after all imply the inexistence of indexical thoughts.
Williamson's "Iterated Attitudes" argues that the set of principles satisfied by one intensional operator differs from and may even be inconsistent with the set of principles satisfied by another operator coextensive with the first, arising when an operator is iterated, that is, applied to a sentence in which it itself occurs. Among the cases in point are the KK-thesis (if one knows something, then one knows that one knows it), Stoic wisdom (one believes only what one knows), Godel's second incompleteness theorem, the iteration of metaphysical modalities with an actuality operator, and even the iteration of some synonymous but coextensive operators. Godel's second theorem is included because it involves an iteration of deviant coextensive provability operations that satisfy different principles in Peano arithmetic, relevant to the mechanistic arguments in the philosophy of mind. In a commentary, Dorothy Edgington discusses all these case studies and adds a further example on iterating conditionals.
The interest of these topics notwithstanding, this book is not particularly accessible to other than a specialized readership, and the style and method of authors tend to turn sometimes rather inconsequential issues into impenetrable prose. Admittedly, some issues are hard, but that fact should not be made more authoritative than it is. Occasionally, then, one gets a quick look of where to locate the continuing encouragement for the current predicament in analytic philosophy.--Ahti Pietarinen, University of Helsinki.
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|Publication:||The Review of Metaphysics|
|Article Type:||Book Review|
|Date:||Dec 1, 2000|
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