Formulating my comments I have had difficulties of three kinds. First, I am not at all sure that I have understood Davidson correctly at every point. Secondly, not being aware of how far I may take for granted that Davidson and I share what may be called the same background ...
The epistemic function of observation of the figure in a Euclidean geometrical proof is discussed. It has been thought that by a complete axiomatization and formalization of a proof the inspection of the figure as a piece of evidence is entirely eliminated. This is shown to be a mistake. What actually happens is that the inspection of a figure in the ordinary sense is replaced by an observation of symbolic expressions and their formal relations.
The objective of this paper is to show the unity of leibniz's philosophical system. the connection between his inesse-principle and the idea that our world is the best of all possible worlds is this: the individual 'concept' of alexander may be defined as containing his whole biography, but the existence of an 'individual' falling under this concept can be deduced a priori only on the basis of the principle of sufficient reason, the application of which takes into account not only (...) god's intellect but also his goodness. (shrink)
SummaryThe key terms in Kant's argument for the synthetic apriority of mathematics are analyzed. The result is a somewhat “idealized” interpretation of these terms, which, however, is appropriate in respect of Kant's main argument. Taking this interpretation as a framework, a model for giving evidence for numerical statements is presented, which is in good agreement with Kant's argument, and according to which numerical statements are indeed synthetic and also, in a sense, a priori. Thus they formally render counter‐instances to Hume's (...) thesis that no general synthetic statements can be a priori. Nevertheless they do not play the part given to them in Kant's metaphysics, since they turn out not to be “genuinely” general, so that no Copernican revolution is required to explain their epistemic nature. (shrink)