AN1271 What is Science? Is a first-year course in Philosophy of Mathematics at King's College London. Here is my first-year essay.

1. Introduction
2. Outline of Popper's ideas
3. The Inductivist model
4. How Inductivism applies to Kepler's Discovery
5. How Popper's model applies to Kepler's Discovery
6. Conclusions

1. Introduction

In particular I wish to examine their relevance in the example of Kepler's Discovery of the Laws of Planetary Motion in 1609.
In my view the opposing philosophies, Inductivism vs. Falsificationism are, looking simplistically, mirror images of each other. The former advocates much observation followed by theorising, where a theory is established as truthful if it can be verified; and the latter advocates taking an existing conjecture and subjecting it to tests and information from observations, where it is rejected as false if it can be falsified.

2. Outline of Popper's Ideas

In chapter 1, page 46 of his work, he outlines his opposition to inductivism:

'The belief that science proceeds from observation to theory is still so widely and so firmly held that my denial of it is often met with incredulity. I have been suspected of being insincere - of denying what no one in his senses can doubt.'

He goes on to illustrate the inferiority of inductivism:
'But, in fact, the belief that we can start with pure observations alone, without anything in the nature of a theory is absurd, as may be illustrated by the story of a man who dedicated his life to natural science, wrote down everything he could observe, and bequeathed his priceless collection of observations to the Royal Society to be used as inductive evidence. This story should show us that though beetles may be profitably collected, observations may not.'

This point is further illustrated by Popper in 1965, when he instructs a group of Physics students to "Take pencil and paper, carefully observe, and write down what you have observed" he remarked: 'Clearly, the instruction "observe" is absurd.'

He proposes that since observation is always selective, scientists must always have a guiding hypothesis in order to distinguish relevant data from the irrelevant.

A general example given for this is that of the historical beginning of science. It did not begin per se with a group of philosophers resolving to embark on a mass hunt for scientific observations. In Ancient Greece, people went along with the ideas supplied by mythology (which he would class as conjectures). These were then contradicted by people's everyday experience and the mythology was replaced by more scientific and correct theories. As Popper says in his Preface to Conjectures and Refutations: '…knowledge can grow and Science can progress, just because we can learn from our mistakes.' - p. vii

He continues: '…the way in which knowledge progresses and especially our scientific knowledge, is by unjustified (and unjustifiable) anticipations, by guesses, by tentative solutions to our own problems, by conjectures. The conjectures are controlled by criticism, that is by attempted refutations, which include severely critical tests. They may survive these tests, but can never be positively justified: they can never be established as certainly true, nor even as "probable" (in the sense of probability calculus)'

Popper would argue that we always have preconceptions, which may or may not turn out to be true. For example, a new-born baby has an in-built expectation that it will be fed, but it may in fact starve to death if no one is around to feed it.

3. The Inductivist Model

These guidelines for scientific method are immortalised in Bacon's famous wine-making analogy in Novum Organum, 1620:

"…I pledge mankind in a liquor strained from countless grapes, from grapes ripe and fully seasoned; collected in clusters and gathered, and then squeezed in the press and finally purified and clarified in the vat."

4. How Inductivism applies to Kepler's Discovery

The story of the discovery of Kepler's laws is a story of two parts. It began with Danish astronomer Tycho Brahe. Before the invention of the telescope in 1609, Tycho Brahe made thousands of accurate observations of the positions of the planets in the night sky over time. The quantity and quality of these observations were remarkable, and they were made during the period 1576-1597. At which time Tycho Brahe went to Prague and was made Imperial Mathematician at the appointment of the Holy Roman Emperor. Kepler was taken on as his assistant in 1600. Tycho Brahe then died and Kepler was made Imperial Mathematician. His aim was now to work out Mars's orbit by using Tycho Brahe's data. He suspected the task would take three weeks.

In fact it took 6 years. Kepler is upheld as an example to all inductive scientists, because at the end of these years of work, in 1609, he published his Laws in Astronomia Nova and revealed that the orbits of the planets were in fact ellipses.

Here the story fits in quite consistently with Inductivism:

(1) Observations by Tycho Brahe

(2) Inferences by Kepler

5. How Popper's Model applies to Kepler's Discovery

The first thing he points out is the theoretical background to Tycho Brahe and Kepler. It is time to give due thought to when and why the observations were made. Tycho Brahe began the observations in 1576, which is 33 years after Copernicus' groundbreaking discovery of a heliocentric system. Copernicus' work was not immediately accepted, and there was a conflict of ideas between some scientists and the establishment, who did not take kindly to the threatening of a geocentric universe with perfect circular paths. Even by the end of Copernicus' life, his monumental discovery was not accepted because he could not attribute circular paths to the planets in a heliocentric model. This is where the background comes in. Tycho Brahe and Kepler both in some respect already believed in a heliocentric model, and were looking for evidence to prove this and establish the real orbits of the planets.

So, contrary to inductivist method, there was allegedly some theoretical background to Tycho Brahe's observations, and there was a necessary guiding hypothesis of Kepler to discover heliocentric orbits which fitted better than those Copernicus had.

Kepler's first hypothesis was circular orbits. These matched 4 positions of Mars, the circular curve agreed with 10 points to 2 minutes, but the overall deviation was 8 minutes. This led Kepler to reject this hypothesis.

Second he used the idea of circular epicycles, an idea which had also existed previously, because it had always been assumed that heavenly bodies move in circles. (A conjecture.) This too was rejected because it didn't match the data of Tycho Brahe.

Thirdly he tried a curve which was not a circle. It was in fact an ellipse but he didn't realise this, and because of mathematical mistakes he rejected the third hypothesis.

Finally he tried an ellipse, with the sun at one focus. This did fit the data and Kepler went on to establish his law of elliptical orbits for all the planets.

This version of the story (in which there are a series of conjectures which are refuted) fits much more closely with Popper's model, and casts serious doubts on inductivism as an all-encompassing Philosophy of Science.

6. Conclusions

It seems fairly obvious to me that both are present. There were theories about the planets' orbits, then there were many detailed and careful observations, then there was inferring of theories from the data, and finally a theory which was backed up by the data which constituted Kepler's Laws of Planetary Motion.

The only real ideological disagreement between the two sides is which order things happened. In my view neither order has a monopoly on science. I propose that there was some influence of existing theories and conjectures in setting out to obtain the observations, although the observations themselves could arguably be held up as independent of any theory. Next there was an interaction between the observations and hypotheses, and through this interaction a hypothesis was found which matches the observations.

I would argue that Science is not a one-way street from observation to inference and scientific laws. Nor is it such a street in the other direction, from conjectures through critical tests to enduring theory. In my view, Science takes on a more cyclic form. Theories are born and observations are begun, and each complements the other. A theory must answer to any observations that are made, and from observations theories may surface or they may be augmented. A theory may pass through the stages of observation or testing and inspiration or philosophy many times around before it either gains widespread approval or is contradicted and falls.

In such a system, it may be wondered whether the theories are true. As in Popper's model, a scientific theory can never be held up as truth. Although in a cyclic system, a theory might be judged as superior, or comparatively more justified than another, depending on both the amount of observations which support it, and the severity of the tests which it has been subjected to.
It is not the business of science to be absolutely true all the time. In so doing science would not be science. Logic and philosophy can preserve truth through logical deduction, but these are too narrow for science, for it is required to say more and be more far-reaching.

References:

• Bacon, F. (1620) Novum Organum (translation R. L. Ellis and J. Spedding, The Philosophical Works of Francis Bacon, Routledge, 1905.)
• Popper, K. (1963) Conjectures and Refutations
• 'The End of Science?'
  http://www.csicop.org/si/9703/end.html