Excerpt: Countless worlds made from nothing by use of symbols – so might a satirist summarize some of Cassirer’s major themes. These themes – the multiplicity of worlds, the speciousness of ‘the given’, the creative power of the understanding, the variety and formative function of symbols – are also integral to my own thinking. Sometimes, though, I forget that they have been so eloquently set forth by Cassirer, 1 partly perhaps because his emphasis on myth, his concern with the comparative study of cultures, and his talk of the human spirit have been mistakenly associated with current trends toward mystical obscurantism, anti-intellectual intuition ism, or anti-scientific humanism. Acutally these attitudes are as alien to Cassirer as to my own skeptical, analytic, constructionalist orientation. My aim in what follows is less to defend certain theses that Cassirer and I share than to take a hard look at some crucial questions they raise. In just what sense are there many worlds? What distinguishes genuine from spurious worlds? What are worlds made of? How are they made, and what role do symbols play in the making? And how is worldmaking related to knowing? These questions must be faced even if full and final answers are far off.

Excerpt: Readers often find in my work-to their delight or disgust-many quips and cracks, puns and paradoxes, alliterations and allegories, metaphors and metonymies, synecdoches and other sins. If there are as many routes of reference as I think, perhaps some of these devices are not mere decoration or unsuccessful attempts to keep the reader awake but part and parcel of the philosophy presented and the worlds made. While I do not know what is meant by saying that the world is simple or complex, I have some idea what is meant by saying that among the many worlds there are, if there are any, some are simple and some complex, some ingenuous and some ingenious, and even by saying that some are prosaic and some poetic.

A view of the sources of mathematical knowledge is sketched which emphasizes the close connections between mathematical and empirical knowledge. A platonistic interpretation of mathematical discourse is adopted throughout. Two skeptical views are discussed and rejected. One of these, due to Maturana, is supposed to be based on biological considerations. The other, due to Dummett, is derived from a Wittgensteinian position in the philosophy of language. The paper ends with an elaboration of Gödel’s analogy between the mathematician and the physicist.