The different occurrences of a word in a sentence cannot be identified with the one word type, nor with its many tokens. What then are occurrences of a word? How can one type occur more than once in another type? Is the conception of ‘structural universals’ that leads to these questions incoherent, as Lewis maintained? I argue against the answer Wetzel suggested, which identifies sentences with functions from numbers to expressions, and propose instead that occurrences of one type in another (...) are subtypes with different relative positions in the whole. Types have subtypes as well as tokens. Occurrences in non-symmetrical types like sequences are individuated by their relative positions in the type. Occurrences in a symmetrical whole have different positions but stand in the same relations to the other components. They are numerically different subtypes that do not differ from each other qualitatively. (shrink)

El artículo trata sobre la negación estoica y su crítica a la fórmula aristotélica según los testimonios de Apuleyo, Alejandro de Afrodisias y Boecio. La crítica se divide en tres aspectos: (i) sistematicidad (ya que una misma regla no se aplica a todo tipo de proposición); (ii) universalidad (ya que todo par contradictorio no divide la verdad y la falsedad sin excepción alguna); y (iii) rigurosidad (ya que el sujeto de la proposición puede no existir o no ser lo que (...) creemos que es). Se concluye que el fondo de la crítica no se relaciona con que una fórmula es inconsistente o hace imposible la lógica y sus operaciones, sino que tiene relación con cuál fórmula es más ambigua y menos preferible. (shrink)

By an incomplete sentence we shall understand a declarative sentence that can be used, without variation in its meaning, to make different statements in different contexts. Although the point deserves supporting argument, which we will not provide, sentences whose grammatical subjects are indexical expressions or demonstratives are obvious, plausible examples of incomplete sentences. Uttered in one context the sentence ‘He is ill’ may be used to make one statement, for example, that George is ill, while in another context the very (...) same sentence may be used to make a quite different statement, for example, that Paul is ill. (shrink)

This paper proposes a reading of the history of equivalence in mathematics. The paper has two main parts. The first part focuses on a relatively short historical period when the notion of equivalence is about to be decontextualized, but yet, has no commonly agreed-upon name. The method for this part is rather straightforward: following the clues left by the others for the ‘first’ modern use of equivalence. The second part focuses on a relatively long historical period when equivalence is experienced (...) in context. The method for this part is to strip the ideas from their set-theoretic formulations and methodically examine the variations in the ways equivalence appears in some prominent historical texts. The paper reveals several critical differences in the conceptions of equivalence at different points in history that are at variance with the standard account of the mathematical notion of equivalence encompassing the concepts of equivalence relation and equivalence class. (shrink)

Personal reflections on the philosophical career of Henry Johnstone, B.S. Haverford College, 1942, and Ph.D. Harvard, 1950, professor at Williams College 1948-1952 and Pennsylvania State University, 1952 - 2000. Founder and editor of Philosophy and Rhetoric, Johnstone wrote eight books, including two logic texts, three monographs, and over 150 articles or reviews. The focus is on his efforts to resolve problems stemming from the conflict between the logical empiricism Johnstone embraced in his dissertation, and the arguments of his absolute idealist (...) colleagues at Williams, efforts he pursued in Philosophy and Argument (1959), and Validity and Rhetoric in Philosophical Argument (1978). (shrink)