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Switch to: References
Citations of:
Higher-order logic reconsidered
In Stewart Shapiro (ed.), Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press. pp. 781--810 (2005)
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After analysing the issue of normativity in different subjects in order to see how it is vindicated, the case of logic is considered. Subsequently we turn to explore two different epistemologies for logic to see the sort of defence of the normativity of logic they let; if any. The analysis concentrates on the case of classical logic. |
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Forthcoming in Philosophical Compass. I explain why plural quantifiers and predicates have been thought to be philosophically significant. |
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Competent speakers of natural languages can borrow reference from one another. You can arrange for your utterances of ‘Kirksville’ to refer to the same thing as my utterances of ‘Kirksville’. We can then talk about the same thing when we discuss Kirksville. In cases like this, you borrow “ aboutness ” from me by borrowing reference. Now suppose I wish to initiate a line of reasoning applicable to any prime number. I might signal my intention by saying, “Let p be (...) |
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After analysing the issue of normativity in different subjects in order to see how it is vindicated, the case of logic is considered. Subsequently we turn to explore two different epistemologies for logic to see the sort of defence of the normativity of logic they let; if any. The analysis concentrates on the case of classical logic. |
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Set theory deals with the most fundamental existence questions in mathematics—questions which affect other areas of mathematics, from the real numbers to structures of all kinds, but which are posed as dealing with the existence of sets. Especially noteworthy are principles establishing the existence of some infinite sets, the so-called “arbitrary sets.” This paper is devoted to an analysis of the motivating goal of studying arbitrary sets, usually referred to under the labels of quasi-combinatorialism or combinatorial maximality. After explaining what (...) |
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L’Ipotesi del Continuo, formulata da Cantor nel 1878, è una delle congetture più note della teoria degli insiemi. Il Problema del Continuo, che ad essa è collegato, fu collocato da Hilbert, nel 1900, fra i principali problemi insoluti della matematica. A seguito della dimostrazione di indipendenza dell’Ipotesi del Continuo dagli assiomi della teoria degli insiemi, lo status attuale del problema è controverso. In anni più recenti, la ricerca di una soluzione del Problema del Continuo è stata anche una delle ragioni (...) |
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