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2 Suffice it to say that the constant association between two phenomena in the past does not imply that this association will continue in the future. Indeed the thankfully rare supervolcano eruptions provide evidence that the sudden disappearance of human civilization is a real possibility. We assume that the laws of nature are inviolable, but all we know is that they have not changed significantly in the last thirteen billion years. Hume was not the first to think about cause and effect. In the fourth century bc Aristotle classified causes into four types, which are conveniently explained by reference to the example of a pot: 42 Introduction • • • • The material cause of a pot is the clay that it is made of; The formal cause is the description of its shape or form; The efficient cause is the process by which the potter made it; The final cause is the reason for which it was made, for example to hold grain.

These are somewhat analogous to the Aristotelean formal, efficient and final causes respectively. Almost any human action that involves planning can be analyzed in this way. The idea that an event may have multiple causes, all equally valid from different points of view, is a form of pluralism,3 and should not be confused with cultural relativism. The latter is often characterized as the (absurd) statement that all beliefs of all cultural groups are equally valid, period. The abolition of multiple causation has been such a successful strategy in the physical sciences that one needs to have very good grounds for rehabilitating it.

Proftat apud plures Bibliopolas. Anno MDCLXXXVII. Fig. 1 Title Page of Newton’s Principia Royal Society, which had committed itself to the publication of several volumes of an expensively illustrated work on the History of Fishes, and in the end Halley had to provide the resources to support its publication out of his own, not very deep, pocket. Book 1 of Principia lays down the laws of motion and then develops their consequences in far greater depth than anyone had previously attempted. In particular he uses a geometrical version of calculus to determine the orbit of a body under a variety of hypothetical force laws.

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A brief history of mathematics by Fink K.


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