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Philosophy & Science

Philosophy of Science: The First 2½ Millennia

Will Bouwman asks what really matters when studying matter.

With which of these three propositions do you most agree? A scientific theory must be:

(1) A logically coherent explanation.

(2) Supported by evidence.

(3) Useful.

If you are firmly of the opinion that one of these is the defining feature of science, then in philosophical terms you are either (1) a rationalist, (2) an empiricist, or (3) a pragmatist. Moreover, if you happen to be a scientist, then it is likely that your main interest is (1) Theoretical, (2) Experimental, or (3) Instrumental. More generally, you might just like to (1) Have an idea about how something works, (2) Find out how it works, or (3) Just make it work.

When philosophers of science are doing what they are paid for, one of the key things they consider is what blend of the above elements makes an activity a science. On the face of it, it shouldn’t be all that difficult to work out. There are only three variables; how hard can it be?

Rather than think in terms of abstract ideas, it’s probably easier to copy many philosophers of science and look at examples from history. The story of gravity is a useful example of the development of scientific understanding, because it’s something we all experience, its science involves all of the above points, and it’s still a mystery. There’s a simple story about how ideas about gravity developed up to the twentieth century, according to which it’s a hop, skip and a jump from Aristotle to Galileo to Newton, to Einstein; from an explanation to a demonstration to a useful equation or two.

Aristotle (384-322 BC)

If longevity were any measure, then by far the most successful theory of gravity is Aristotle’s explanation, or rather his two explanations, of it. One of those ideas is based on the behaviour of the Greeks’ four elements, earth, water, air, and fire (Aristotle himself was to add spirit or aether, to make five elements). We all know that stones sink in water; that air bubbles to the surface, and flames leap upwards, because we have seen the evidence. Aristotle explained that it is the nature of the different elements to seek their natural place: earth and water move down, air and fire move up. In other words, there is something about the elements that makes them move the way they do. But does calling it a ‘nature’ make it science?

Aristotle went on to make a rudimentary quantitative claim: that the more of a particular nature an object contains – the more earth or air it is made of, for instance – the faster or slower it will fall. In other words, freefall velocity is proportional to mass. This is an hypothesis that can be measured relatively easily, and would be useful to know, if true. So does that make it science? Aristotle never tested the idea.

What Aristotle actually believed, to be more precise, is that the terrestrial (non-spirit) elements move towards or away from the centre of the universe, and the Earth, being mostly earth, was therefore in the middle. Since it had already reached its destination, Aristotle argued that the Earth wasn’t moving. His evidence for this claim was that when you drop a stone it lands at your feet. If the Earth were moving, it should land as far away from you as the Earth had moved in the time it took to fall. His explanation for why the Sun, Moon, planets and stars move round the Earth is that they are set in a series of concentric spheres that are spinning around an axis that goes through the Pole Star. The spheres are made of aether, the fifth element, which unlike the terrestrial elements moves in circles. This Aristotle explained by claiming that there are only two types of basic motion, linear and circular. All motion can be described as a combination of those two; and since earth, water, air and fire all move in straight lines, there must be an element that moves in circles.

The premises are a bit shaky, but if you accept them, it’s a logically coherent explanation. Aristotle’s model was developed by Ptolemy into a mathematical description that was reasonably successful at predicting the positions of the heavenly bodies. So it was supported by the available evidence too; and if the position of the stars is important to you (say for navigation or for religious observance), it’s a useful model as well.

We now know that practically everything Aristotle said about gravity is wrong, but his explanation taken as a whole made so much sense that for two thousand years it resisted all challenges. In the century after Aristotle, Aristarchus of Samos argued that the Sun rather than the Earth is the centre of the universe; but this idea wasn’t fully revived until Copernicus in the sixteenth century AD. When it did finally triumph, it also undermined Aristotle’s explanation of gravity. If the Earth isn’t at the centre, and is moving, then Aristotle’s explanation for why stones always fall straight down, and indeed, why they fall at all, must be wrong, and a new explanation is needed.

After Copernicus’s death, responsibility for the publication of his book De revolutionibus orbium coelestium (On the Revolutions of the Celestial Spheres, 1543) was given to Andreas Osiander. Osiander added a Preface in which he argued that different explanations can be supported by the same evidence. It doesn’t matter to the calculations whether people choose the explanation they find most plausible or the one they find most useful to work with. As Osiander said, “If they provide a calculus consistent with the observations, that alone is enough.” And although Copernicus’s mathematics wasn’t as developed as Ptolemy’s, bits of it were easier to work with. So some mathematicians and astronomers adopted Copernicus’s model; not necessarily because they believed the Sun-centred explanation, but because it was useful.

Galileo (1564-1632)

A popular image of Pisa in the early seventeenth century, is of Galileo Galilei at the top of the Leaning Tower, dropping different sized cannonballs to prove they all fall at the same rate.

As it happens, very few historians think that Galileo actually performed this experiment. Rather, Galileo was puzzled by a paradoxical consequence of Aristotle’s belief that heavy things fall faster than light ones. What would happen if a heavy thing and a light thing were tied together? On the one hand, according to Aristotle’s philosophy, the heavier weight will fall faster; and since the lighter one will be holding the heavier up, the string will be pulled tight, and overall the falling speed should be something between the speed of the two weights separately. On the other hand, since the two weights are joined, they and the string are effectively one thing with a combined weight, so the combined speed should be faster than the individual speeds. Those two outcomes can’t both be right. Although Galileo may or may not have dropped weights from the Tower, he did do, and recorded, a lot of experiments rolling different weights down slopes whose results flatly contradicted Aristotle’s claim that more weight equals more speed.

Then there were the observations Galileo made with his telescope. They didn’t rule out the possibility that the Earth was at the centre, but they did clearly show that the universe was not as Aristotle had described it. Galileo’s discovery of the moons of Jupiter, for instance, demonstrated that not everything revolves around the Earth. You could get round this by positing that there are ethereal spheres centred on Jupiter. But if you keep making up stuff to explain awkward new facts, are you making claims about how the world actually works, or about your explanation?

Newton (1643-1727)

On 28 November 1660 in London, a group of natural philosophers announced the formation of a ‘College for the Promoting of Physico-Mathematical Experimental Learning’. Hearing of the plan, King Charles II gave his approval, and within two years a charter was signed creating the Royal Society of London. The motto of the Royal Society is Nullius in verba, which can be translated as “Don’t take anyone’s word for it.” In 1660, that ‘anyone’ still largely meant Aristotle.

In 1687 the Royal Society published the Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) by one of its fellows, Isaac Newton. In this book Newton described his law of universal gravitation.

The legend of the apple falling on Newton’s head has about as much historical credibility as that of Galileo dropping cannonballs off the Tower of Pisa. Nevertheless, something made Newton realise that the reason stones fall to the ground is the same reason that moons go around planets and planets go round the Sun. In other words, there aren’t two forces at work here, there’s only one, the force of gravity. Physicists like simplicity, and they particularly like unifying forces. Newton demonstrated that instead of it being the nature of earth to move towards the centre and air to move away, every particle in the universe is attracted to every other. And you can forget about ethereal spheres.

Although Newton and others recognised that a lot of evidence was needed to corroborate his law, as time progressed it became clear that it was extremely successful in accounting for the position of the planets, which at the time were known only far as Saturn. Almost a century later, in 1781, William Herschel recognised that a point of light which earlier astronomers had mistaken for a star was a planet, which he called Uranus, after the god of the heavens. However, by 1845 – by which time Uranus had completed most of an orbit – it was clear that it was not behaving as Newton’s law demanded. Yet by then such was the confidence in Newton’s theory that mathematicians in Paris and Cambridge began calculating the mass and position of another body that could account for the anomalies. Using the results of Urbain Le Verrier as his guide, Johann Gottfried Galle identified the planet Neptune, which, like Uranus, had previously been mistaken for a star. So Newton’s idea of a force of gravity explained the motion of the planets, it was supported by a wealth of evidence, and it had been usefully applied in the discovery of a new planet.

But does saying “There is a force” tell us any more than saying “There is a nature”? The ink was barely dry on the first edition of the Principia before people started objecting that Newton had introduced a force without a mechanism: for all the explanatory power of the idea of ‘the force of gravity’, there was (and is) no explanation for how gravity works. Much of the challenge came from followers of René Descartes (1596-1650). Descartes had also been interested in the movement of the planets, but his main concern was to give a explanation of the orbits. This he did by invoking the idea of vortices, according to which space is composed of infinitesimal ‘corpuscles’ that behave like a fluid. These are swept around the Sun a little like water is dragged around a plughole, and they in turn pull the planets along with them. When in 1713 Newton published a second edition of the Principia, he felt compelled to add an essay called ‘The General Scholium’ in which he directly challenged the idea of vortices. Newton pointed out that the orbits of comets are too eccentric to fit the model, and that they cut across planetary vortices with no apparent effect: “And therefore the celestial spaces, through which the globes of the planets and comets move continually in all directions freely and without any sensible diminution of motion, are devoid of any corporeal fluid”.

Having dismissed Descartes’ explanation of how gravitational attraction works, Newton included a passage known by a phrase that occurs in it: hypotheses non fingo – ‘I make no hypotheses’. He writes: “But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I make no hypotheses. For whatever is not deduced from the phenomena, is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.” To Newton, an explanation of how something works isn’t essential to science; as long as the mathematical model gives us the power to map, predict, and manipulate our environment, the job of physics is done. As the passage concludes: “And to us it is enough, that gravity does really exist, and act according to the laws which we have explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.” The explanation of why it works isn’t that important to science. As Osiander had said, what matters is, can you use the theory?

Newton could just as easily have called the force of gravity the ‘nature’ of gravity. The real difference between Aristotle’s ‘nature’ and Newton’s ‘force’ is not so much in the explanation: it is in the quality and therefore usefulness of the mathematics, and the abundance of evidence for it. However, if being right were a criterion for science, then we’d have to throw Newton out along with Aristotle.

Einstein (1879-1955)

Uranus was not the only planet that appeared to be breaking Newton’s laws of motion. In fact Le Verrier, instrumental in the discovery of Neptune, had been working on anomalies in Mercury’s orbit since 1840. However, when his predictions were tested by observations of the transit of Mercury across the face of the Sun in 1843, they didn’t match. But with the success of Neptune behind him, Le Verrier returned to the problem, once again calculating the mass and position of another planet near Mercury that could explain Mercury’s erratic behaviour. So confident was he that he even gave this planet a name – Vulcan. Astronomers began looking for Vulcan. Some claimed to have found it: Edmond Modeste Lescarbault was even awarded the Legion D’Honneur for doing so. But on closer inspection all the claims proved unfounded. There is no Planet Vulcan. The Newtonian explanation was not supported by the evidence. Something else was causing the discrepancy.

There is also another story, concerning how Einstein discovered relativity. In 1865 the Royal Society published James Clerk Maxwell’s A Dynamical Theory of the Electromagnetic Field. Maxwell’s elegant equations described electromagnetism as a wave that travels through space at the speed of light. But waves, as a rule, require a medium; after all, a wave on the ocean isn’t a wave if there’s no ocean. Against the advice of Newton, Maxwell was prepared to offer an explanation: that “light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.” The hypothetical substance through which light waves propagated – the explanation of the observed behaviour – became known as the ‘luminiferous aether’. Unlike the swirling corpuscular medium proposed by Descartes, this was believed to be static, and something that the Earth and all other celestial bodies were moving through: more like a fog than a whirlpool.

Given that light’s speed through the aether was supposed to be constant, and that the Earth was supposed to be moving through the aether, the speed of light measured here on Earth should vary according to whether it is moving in the same direction as the Earth or perpendicular to it. In 1887 two American physicists, Albert Michelson and Edward Morley, devised a sensitive experiment to compare the time taken for light to travel two equal paths at right angles to each other. From this they expected to be able to prove the existence of the aether and calculate the speed and direction of the Earth’s movement through it. To their surprise, they found there was no difference in the time taken for the light to travel the two paths. Either the Earth was stationary – and by this time everyone knew from astronomy that it was not – or else the speed of light for an observer on Earth is the same regardless of the Earth’s motion. How could this be?

For a while, physicists scratched their heads and produced explanations for how the luminiferous aether could produce such baffling results. Then, in 1905 Albert Einstein put forward his special theory of relativity. He jettisoned the luminiferous aether in favour of empty space, and created a mathematical description that accurately accounts for the evidence: that the speed of light is the same for all observers, regardless of their own velocity, because time passes more slowly for the observer the faster they are travelling.

However, Einstein took a different view of space when he published his general theory of relativity in 1915. General relativity explains gravity by imagining that rather than being simply a vacuum, space is a medium which is warped by the presence of mass. Space is like a stretched rubber sheet – if you put an iron ball on it, it will make a dip in the sheet, and any smaller balls nearby will tend to roll down into the dip. Einstein offers no hypothesis for how mass warps spacetime, any more than Newton offered one about how gravity works. ‘Warped spacetime’ is an explanation of gravity without an explanation. But again that doesn’t matter in order for the theory to be useful. And as the evidence soon showed, the equations Einstein deduced are more accurate (for predicting planetary motion, say) than Newton’s laws.

Twentieth Century Philosophy of Science

In 1919 the British physicist Arthur Eddington led an expedition to the island of Principe off the West coast of Africa to photograph a total eclipse of the Sun. The aim was to test general relativity by measuring how much the light from stars was bent by the Sun’s gravity (if space is warped by mass then light will noticeably bend around large enough masses). The deflection was twice what Newtonian gravity could account for and much closer to Einstein’s predictions. They made headlines around the world and turned Einstein into the byword for scientific genius that he remains to this day.

At the time a young Karl Popper (1902-1994) was attending the University of Vienna. He was impressed by the fact that general relativity made such definite predictions. It was a bold strategy, because if the evidence didn’t support it, the theory would be shown to be wrong. Popper decided that this was a defining feature of science: a theory could only count as scientific if it could in principle be shown to be wrong. It has to be falsifiable. According to this view, Aristotle’s claim that freefall speed is proportional to mass is scientific, because a simple experiment can determine whether it is true or not. And Galileo had shown it isn’t true. But according to Popper it’s still a scientific claim, because being true isn’t a defining feature of a scientific theory.

Even as Popper was developing his theory of falsifiability, scientists were already pointing out that actually, that’s not how scientists work. Ludwik Fleck, a biologist, introduced the idea of a ‘thought collective’ – a group of scientists who share some common theory and working practices, their scientific method, and who collaborate to develop that research structure to its fullest potential. Michael Polanyi, a professor of chemistry, made a similar point. Science, in his experience, was not a single objective method that could simply be prescribed and followed; rather scientists put into practice the philosophy and methods they have been taught by other scientists. Essentially, once they have been initiated into a thought collective, they contribute to that collective. The physicist Max Planck, like Einstein, never fully accepted the interpretations of quantum mechanics given by younger scientists; but he observed that “a new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.” So a prominent biologist, chemist, and physicist were all saying that in their professional experience, science did not work as philosophers such as Popper thought it should, and there isn’t one scientific method, there are many. And in 1962 Thomas Kuhn (1922-1996) published The Structure of Scientific Revolutions, which made everyone pay attention to the growing conviction that science is not the pristine singular enterprise philosophers had been trying to describe.

The structure of scientific progress referred to in Kuhn’s title has three parts. There is a ‘pre-science’ period, when some feature of the world has no scientific explanation. People speculate and offer suggestions until one comes along in which a sufficient number of scientists see enough potential to commit time and resources to researching it. Rather than try to destroy the idea, as Popper recommended, if experiments designed in terms of this explanation produce results that match the theory, scientists collaborate to enhance the growing paradigm (the paradigm is the overarching type of explanation being used). If the paradigm is any good this can be a very productive period because it gives the scientists a conceptual framework to explore that will raise questions that wouldn’t occur outside the paradigm. Such puzzle solving within a paradigm is what Kuhn called ‘normal science’. However, no matter how good a given paradigm is, we can never know for sure that some new discovery will not undermine it. It happened to Aristotle’s paradigm of nature; it happened to Newton’s; and no scientist can guarantee it won’t happen to our current models, either. If, or more likely when it happens, at first there can be some tinkering to protect the old paradigm, as Kuhn argued from studying the history of science. But as the anomalies build up and eventually plunge the extant paradigm into crisis, a new paradigm will be required which can account for everything the old paradigm could explain plus the stuff it couldn’t – just as general relativity explains behaviour that Newtonian gravity can’t.

Paul Feyerabend (1924-1994) was one of four people personally thanked by Kuhn in the Preface to The Structure of Scientific Revolutions. Feyerabend had turned down an offer to be Popper’s research assistant. Having started his academic career as a physicist he was well qualified to make that judgement. As the history of gravity shows, explanation, demonstration, and usefulness have all played a critical role in science; and Feyerabend was concerned that any reductive scientific method, such as Popper was advocating, would have ruled out some part of that history. No one likes being told what to think or do, and scientists are no exception. Rather, Feyerabend thought that the only prescription for science that could accommodate every stumble and leap is methodological anarchy, or as Feyerabend put it, anything goes. He took the view that by far the most important criterion is that a theory should be useful – it didn’t matter to who, or what for. Feyerabend gave this insight: “Having listened to one of my anarchistic sermons, Professor Wigner exclaimed: ‘But surely, you do not read all the manuscripts which people send you, you must throw most of them into the wastepaper basket.’ I most certainly do. ‘Anything goes’ does not mean that I shall read every single paper that has been written – God forbid! – it means that I make my selection in a highly individual and idiosyncratic way, partly because I can’t be bothered to read what doesn’t interest me – and my interests change from week to week and day to day – partly because I am convinced that humanity and even science will profit from everyone doing their own thing” (Against Method, 1975). Whatever anyone thinks should or shouldn’t qualify as science, the fact is that science is done by people. Some of those people are rationalists, some are empiricists, and some are pragmatists; and no matter what rules are imposed, people break them.

Will Bouwman is the author of Einstein on the Train and Other Stories: How to Make Sense of the Big Bang, Quantum Mechanics and Relativity.