In this paper, I will not discuss the wider philosophical issues concerning the nature and status of relations in Leibniz’s thought. This will be done another time. I will instead confine myself to reflect upon Leibnizian strategies of rewriting/reducing relational sentences, especially those that include relational predicates that express relations of connection or concurrence rather than of comparison. More precisely, I will deal with Leibniz’s analysis of the sentence “Paris est amator Helenae” as reducible to “Paris amat et eo ipso (...) Helena amatur”. I intend to show, against Massimo Mugnai’s interpretative proposal, that the phrase “et eo ipso” does not perform a reduplicative function here. (shrink)

The article attempts to reconsider the relationship between Leibniz’s and Kant’s philosophy of geometry on the one hand and the nineteenth century debate on the foundation of geometry on the other. The author argues that the examples used by Leibniz and Kant to explain the peculiarity of the geometrical way of thinking are actually special cases of what the Jewish-German mathematician Felix Hausdorff called “transformation principle”, the very same principle that thinkers such as Helmholtz or Poincaré applied in a more (...) general form in their celebrated philosophical writings about geometry. The first two parts of the article try to show that Leibniz’s and Kant’s philosophies of geometry, despite their differences, appear to be preoccupied with the common problem of the impossibility to grasp conceptually the intuitive difference between two figures (such as a figure and its scaled, displaced or mirrored copy). In the third part, it is argued that from the perspective of Hausdorff’s philosophical-geometrical reflections, this very same problem seems to find a more radical application in Helmholtz’s or Poincaré’s thought experiments on the impossibility of distinguishing distorted copies of our universe from the original one. I draw the conclusion that in Hausdorff’s philosophical work, which has received scholarly attention only recently, one can find not only an original attempt to frame these classical arguments from a set-theoretical point of view, but also the possibility of considering the history of philosophy of geometry from an uncommon perspective, where especially the significance of Kant’s infamous appeal to “intuition” can be judged by more appropriate standards. (shrink)

When the original Dutch version of this book was presented in 1971 to the University of Leiden as a thesis for the Doctorate in philosophy, I was prevented by the academic mores of that university from expressing my sincere thanks to three members of the Philosophical Faculty for their support of and interest in my pursuits. I take the liberty of doing so now, two and a half years later. First and foremost I want to thank Professor G. Nuchelmans warmly (...) for his expert guidance of my research. A number of my most im portant sources were brought to my attention by him. During the whole process of composing this book his criticism and encouragement were carried out in a truly academic spirit. He thereby provided working conditions that are a sine qua non for every author who is attempting to approach controversial matters in a scientific manner, conditions which, however, were not easily available at that time. In a later phase I also came into contact with Professors L. M. de Rijk and J. B. Ubbink, with both of whom I had highly stimulating discussions and exchanges of ideas. The present edition contains some entirely new sections, viz. 1-9, IV-29, V-9, V-20, VII-14 (iii), (iv), VII-17 (i), VIII-22, IX-17, IX-19, X-9 and XI-8. Section X-9 was inspired by a remark made by Professor A. (shrink)

The word “as” enables one to make contexts and aspects of things explicit while attributing properties or descriptions to them. For example “John is rational as a mathematician”; “John is irrational as a driver.” This paper examines the idea according to which all propositions containing “as” should be targeted as potential inferences about the subject; as for the examples given—about John. If the inference is valid—the conception in question holds—one can get rid of “as.” I argue against that view by (...) bringing up several contexts in which “as” is not supposed to express an inference. On this basis I come up with a different (non-inferential) typology which does justice, I believe, to ordinary as well as philosophical uses of the little word at stake. (shrink)

Numerical identity is standardly considered to be a relation between things. This means that two things are identical if they are only one thing. It is not only Wittgenstein who finds this claim rather odd. Another possibility is to understand identity as a relation between names which denote the same thing; or as a relation between the senses of those names which are modes of presentation of the same thing. Or identity statements can be considered as expressions of the fact (...) that there is exactly one thing that has certain characteristics. These conceptions are, in fact, closely interlinked. There are some rather straightforward proposals on how to give these approaches a formal pattern in relative harmony with classical logic. What is important to emphasize and keep in mind is the specific character of identity and essential dissimilarities between identity and relations of objects in logic. (shrink)

O princípio de intersubstituição dos idênticos salva veritate, que constitui uma peça de importância central para a teoria leibniziana da demostração, para não falar de suas implicações ontológicas, recebeu a crítica de que encerra uma confusão entre uso e menção. Em contraste com essa crítica, o presente trabalho defende a tese de que o princípio não está suscetível a essa pretensa confusão, utilizando, para tanto, a distinção leibniziana entre “a consideração do modo de conceber” e a “consideração da coisa mesma”. (...) A introdução dessa distinção, porém, vem acompanhada com a necessidade de estabelecer restrições à aplicação do mencionado princípio. (shrink)