this infinite number of infinities to finite magnitudes - then those whom one is trying to instruct or hoping to persuade will not necessarily possess the insight needed to see clearly into such profound depths'.21 In more diplomatic form, here was a warning on the new calculus every bit as firm as Berkeley's.
At the end of the seventeenth century, in both Catholic and Protestant countries, the relationship between science and religion was marked by a certain ambiguity. Scientific progress aroused considerable interest among the general public, as demonstrated by the birth of a specialist press after the 1660s (in England, The Philosophical Transactions; in France the Journal des savants; and in Germany the Acta Eruditorum). Catholic and Protestant ecclesiastics usually encouraged this curiosity, considering it the best defence against scepticism, atheism, or simple religious indifference, and feeling that the wonders waiting to be discovered could lead only to the Creator. However, there came a moment towards the end of the seventeenth century and the beginning of the next, when the advances in the scientific movement and the honing of new research techniques did not lead quite so obviously towards God. Certain people felt that the prodigious development of the human mind might be sufficient to account for everything.
The problem of infinity: from Hell to Paradise
It is scarcely surprising that towards 1700 Newton's discoveries should renew the debate over the problem of the infinity of space and time. In reality, such discussions had not ceased since the writings of Epicurus and Lucretius in Antiquity. But it took on a new dimension at the time of the Counter-Reformation, with Giordano Bruno's trial and death at the stake in Rome (1600).22 Bruno had been accused of appropriating ideas from ancient pagan and atheist authors for his celebrated work, De l'infinito, universo e mondi (1584). As a result of this, the very idea of infinity threw even the most learned thinkers into a state of terror. One of Blaise Pascal's correspondents wrote to him, 'I tell you that as soon as the idea of infinity enters into a question, however slightly, then the entire problem is rendered inexplicable, for the mind becomes troubled and confused'.23 Pascal himself explained the reason for this fear in a celebrated passage from the Pensees: 'Unable to observe infinity', he wrote, 'men have gone recklessly in search of nature, imagining themselves to be of a similar proportion'. And he added, 'When that is truly understood, I think men will rest, each in the place accorded him by nature'.24 A few years later, the authors of La Logique de Port-Royal, Antoine Arnauld and Pierre Nicole, would be even more precise. They urged their readers 'never to become involved
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