Rene Descartes

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There seems little to justify  Wallis's claim, which was probably made partly through partiotism but also through his just desires to give  Harriot more credit for his work.  Harriot's work on equations, however, may indeed have influenced Descartes who always claimed, clearly falsely, that nothing in his work was influenced by the work of others.

Descartes' Meditations on First Philosophy, was published in 1641, designed for the philosopher and for the theologian. It consists of six meditations, Of the Things that we may doubt, Of the Nature of the Human Mind, Of God: that He exists, Of Truth and Error, Of the Essence of Material Things, Of the Existence of Material Things and of the Real Distinction between the Mind and the Body of Man. However many scientists were opposed to Descartes' ideas including  Arnauld,  Hobbes and  Gassendi.

The most comprehensive of Descartes' works, Principia Philosophiae was published in Amsterdam in 1644. In four parts, The Principles of Human Knowledge, The Principles of Material Things, Of the Visible World and The Earth, it attempts to put the whole universe on a mathematical foundation reducing the study to one of mechanics.

This is an important point of view and was to point the way forward. Descartes did not believe in action at a distance. Therefore, given this, there could be no vacuum around the Earth otherwise there was way that forces could be transferred. In many ways Descartes's theory, where forces work through contact, is more satisfactory than the mysterious effect of gravity acting at a distance.

However Descartes' mechanics leaves much to be desired. He assumes that the universe is filled with matter which, due to some initial motion, has settled down into a system of vortices which carry the sun, the stars, the planets and comets in their paths. Despite the problems with the vortex theory it was championed in France for nearly one hundred years even after  Newton showed it was impossible as a  dynamical system. As Brewster, one of  Newton's 19th century biographers, puts it:-

Thus entrenched as the Cartesian system was ... it was not to be wondered at that the pure and sublime doctrines of the Principia were distrustfully received ... The uninstructed mind could not readily admit the idea that the great masses of the planets were suspended in empty space, and retained their orbits by an invisible influence...

Pleasing as Descartes's theory was even the supporters of his natural philosophy, such as the Cambridge metaphysical theologian  Henry More, found objections. Certainly  More admired Descartes, writing:-

I should look upon Des-Cartes as a man most truly inspired in the knowledge of Nature, than any that have professed themselves so these sixteen hundred years...

However between 1648 and 1649 they exchanged a number of letters in which More made some telling objections, Descartes however in his replies making no concessions to  More's points.  More went on to ask:-

Why are not your vortices in the form of columns or cylinders rather than  ellipses, since any point of the axis of a vortex is as it were a centre from which the celestial matter recedes with, as far as I can see, a wholly constant impetus? ... Who causes all the planets not to revolve in one plane (the plane of the  ecliptic)? ... And the Moon itself, neither in the plane of the Earth's equator nor in a plane parallel to this?

In 1644, the year his Meditations were published, Descartes visited France. He returned again in 1647, when he met  Pascal and argued with him that a vacuum could not exist, and then again in 1648.

In 1649 Queen Christina of Sweden persuaded Descartes to go to Stockholm. However the Queen wanted to draw  tangents at 5 a.m. and Descartes broke the habit of his lifetime of getting up at 11 o'clock. After only a few months in the cold northern climate, walking to the palace for 5 o'clock every morning, he died of pneumonia.

J J O'Connor and E F Robertson

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