priori mathematics, according to Galileo, does not entirely obviate the need for observation (only the most extreme of rationalists, Spinoza and Leibniz, were to argue the expendability, at least in principle, of all empirical knowledge, claiming that all could be a priori deduced from first principles6); but mathematics does allow us to deduce unobservable properties and thus to penetrate into the structure of nature.
Of course, this meant that not all of the processes conceived of as motions by Aristotle were Galilean motions. Only motions susceptible to mathematical translation came under the purview of science; the rest were expelled from the possibility of physical explanation. Even more than this, Galileo, and those who followed him, defined physical nature itself in terms of mathematics. It was Galileo who first drew the distinction between primary and secondary qualities. If all aspects of physical reality are mathematically expressible, and if not all aspects of our experience are susceptible to mathematical treatment, the implication is that not all aspects of our experience are physically real. Our minds contribute to what we seem to see out there in the world. Our experience is not transparent; there is a gauzy veil of subjectivity hung between us and the objective physical world of mathematical bodies, compounded out of mathematically arranged mathematical constituents, mathematically moving through mathematical space over the course of mathematical time. All those aspects of our experience that can be rendered in mathematical language are ‘primary’ and correlated with what is out there; the rest are ‘secondary’ qualities, features of our subjective experience, caused by the interaction between the primary qualities out there and our own sensory organs. This distinction was widely accepted, not only by rationalists like Galileo and Descartes, but empiricists like John Locke. The portions of res cogitans lurking in our cerebral hemispheres provide a sanctuary for the otherwise inexplicable flotsam and jetsam of perception.
Scientific rationalism, then, as it emerged to challenge the old system, placed its hopes not in logic but in mathematics. Whereas the old system’s working hypothesis had been that all physical processes are striving toward an end they seek to accomplish, the working hypothesis of the new rationalists was that all physical processes have a quantitative structure, and it is this abstract structure that distils the laws of nature that provide their explanation. As the über-rationalist Spinoza was to express it:
Thus the prejudice developed into superstitions, and took deep root in the human mind; and for this reason everyone strove most zealously to understand and explain the final causes of things; but in their endeavour to show that nature does nothing in vain, i.e. nothing which is useless to man, they only seem to have demonstrated that nature, the gods, and men are all mad together…Such a doctrine might well have sufficed to conceal the truth from the human race for all eternity if mathematics had not furnished another standard of verity in considering solely the essence and properties of figures without regard to their final causes.7
But what of the new empiricism? How was it in opposition to the old system? Aristotle may not himself have thought much of mathematics, but he was himself an empiricist, who took observation, most especially of biological organisms, very seriously; it was his mathematical-maniacal teacher, Plato, who dismissed sense-data (and many of those in the Copernicus–Kepler–Galileo camp were neo-Platonists). But Aristotle and the grand cathedral of thought that was erected around him advocated a passive form of observation. Nature, working always with its own ends in view, the very ends which provide the explanation in terms of final causes, was not to be interfered with. Teleology trumped technology. The very windingness of the roads of Europe’s medieval cities testifies to the old system’s hands-off approach toward nature. These roads were laid out on paths the rain took as it rolled down inclines. To transpose our own pathways over nature’s choices was a violation of the fundamental assumption of the old system. One must respectfully observe the motions of nature, since their course had been plotted by their implicit end states, and it is in the hands-off observation that the explanation emerges.
The new empiricism, in seeking its non-teleological form of explanation, took an aggressively interventionist attitude toward observation. In doing so it not only asserted its rejection of Aristotelianism, of the teleology that dictated passive observation; its new active observation, in the form of experimentalism, claimed to present a new science, a scientia operativa, that could supplant the old.
The empiricist Bacon, just like the rationalist Galileo, believed that the experience we are presented with does not reflect nature as it is: ‘For the mind of man is far from the nature of a clear and equal glass, wherein the beams of things should reflect according to their true incidence; nay, it is rather like an enchanted glass, full of superstition and imposture, if it be not delivered and reduced. For this purpose, let us consider the false appearances that are imposed upon us by the general nature of the mind…’
Bacon’s solution to how to circumvent these false appearances, which he called the ‘idols of the cave’, lay in his empirical activism. We are not to stand passively by as submissive observers of what nature might offer of itself, but assert ourselves in the gathering of facts through experiment. This assertion is what transforms sense-data, subject to illusion, into facts. The keen but passive gazing that makes sense under the assumptions of teleology made no sense to Francis Bacon.
The Lord Chancellor’s metaphors are telling. Nature should be looked on as an uncooperative witness in a courtroom, who must be interrogated and even tortured in order that the information be extracted. Nature should be treated as a slave who must be ‘constrained’ and ‘moulded’ and compelled to serve man. We must ‘shake her to her foundations’. In short, we force the sense-data to yield up the factual data that nature is actively keeping from us by asserting our own active power over nature in controlled experiments.8 (Although sometimes these experiments end in nature asserting its power over us: the legend is that Francis Bacon died after contracting pneumonia while undertaking some experiments in the dead of winter on the preservation of meat by freezing.)
Thus for both the new rationalists and the new empiricists there was a veil of subjectivity separating the observer from the observed. In this way the two orientations, no matter how distinct their intellectual temperaments, shared a central attitude that went beyond their mere opposition to the old system and explains why they were, even if rivals, also potential allies. Both insisted, against the old system, on more assertiveness. Mathematics, as opposed to inert logic, inserted a generative power into physical description. Experiments, as opposed to passive observation, allow us to wrest the physical facts from illusory experience.
The old system had seen nature as eminently readable by us. The form of explanation spread throughout the cosmos was one which was familiar and natural to us; after all, it was an essentially human form of explanation, taking the sort of explication that applies to human actions and generalising it. The old system saw us as of the universe. There was no reason to suspect our experience, and Aristotle was an unguarded empiricist, an observer who never seemed to worry about what his own mind might be contributing to perception. But not so the post-teleology Baconian empiricist, no more than the post-teleology Galilean rationalist. For both, the experience we have of the world has to be subjected to special treatment in order for reliable information to be extracted.
OF ENDS AND MEANS
The activist empiricism of Bacon was correlated with a practical stance
toward scientific knowledge, which blazed forth into utopian zeal:
I humbly pray…that knowledge being now discharged of that venom which the serpent infused into it, and which makes the mind of man to swell, we may not be wise above measure and sobriety, but cultivate truth in charity…Lastly, I would address one general admonition to all; that they consider what are the true ends of knowledge, and that they seek it not either for pleasure of the mind, or for contention, or for superiority to others, or for profit, or fame, or power, or any of these inferior things; but for the benefit and use of life; and that they perfect and govern it in charity. For it was from the lust of power that the angels fell, from lust of knowledge that man fell; but