Outlines of a Formalist Philosophy of Mathematics

Outlines of a Formalist Philosophy of Mathematics

Outlines of a Formalist Philosophy of Mathematics

Outlines of a Formalist Philosophy of Mathematics

Excerpt

In the opening days of September, 1939, just as the Second World War was breaking out, an International Congress for the Unity of Science was hold at Cambridge, Massachusetts. The committee in charge of that congress invited me to submit a paper there. This invitation suggested that I write out, in a more or less systematic form, the philosophical opinions which I had formed in a little more than a decade of study in mathematical logic. I found the task a longer and more difficult one than I had anticipated; nevertheless I persisted in it. The resulting manuscript was, of course, too long for presentation at the congress; but it formed the basis of the paper presented there, and of several other papers, cited below, which have been written since.

The present monograph represents the publication of the manuscript prepared in 1939. It is published here in essentially the same form in which it was originally written down. The only changes are a revision of Example 9 in Chapter V and some footnotes. These changes date from 1942.

In view of the foregoing origin of this monograph, the reader should bear in mind the following points concerning it.

In the first place, this monograph represents the views which I held in 1939; it does not represent accurately the views which I would defend right now. The later papers, already mentioned, overlap with it greatly and supersede some parts of it. However, the more amplified presentation which is possible in this monograph will presumably be an advantage for some readers; furthermore, the statement of what lies back of the opinions expressed in the later papers may help to make them better understood.

A similar caution should be observed in regard to the views of other persons which are quoted or criticized here. This is particularly true in the case of Carnap and other leaders of the . . .

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