How do we know that we know what we know?

How Science Works’ is now the focus of the national science specifications in English schools. This article is a brief introduction to the philosophy of science from the Greeks to the present day that underpins this notion. From September 2006, the emphasis for teaching science at GCSE is on ‘How Science Works’. This focus will also shape the revisions of the AS and A2 specifications from September 2008. Ideas about how science should be done and why it works have changed over time. In essence, this article is an introduction to the philosophy of science that underpins the notion of ‘how science works’. The author is a physicist not a philosopher. The short bibliography at the end of the article represents the source of most of the ideas presented here. The article itself originated as a presentation to students taking the International Baccalaureate (IB) diploma and formed part of their Theory of Knowledge course. It consists of a brief summary of the contributions of nine philosophers and/or scientists to the debate: Aristotle, Roger Bacon, Francis Bacon, Galileo, Newton, Wittgenstein, Popper, Kuhn and Gödel. The title of this article derives from Copernicus’s assertion that ‘To know that we know what we know, and to know that we do not know what we do not know, that is true knowledge’. The discussion will be less dogmatic than Donald Rumsfeld’s more recent version of Copernicus’s aphorism, ‘. . . as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don’t know we don’t know’. Hence the more tentative title: ‘How do we know that we know what we know?’. My truth is a dream unless my dream is true; George Santayana Ridley in his book On Science [1] suggests that there are many types of truth, which those of science stand beside: the revealed truth of religion; the persuasive truths of the social sciences; the demonstrable truths of mathematics; and the magical truth associated with the humanities. For the latter—poetry, music, the fine arts etc—uniqueness is the key virtue. In contrast, the scientist focuses on the recurrent, and the repeatable. ‘All men by nature desire to know’, Aristotle (c 384–322 BC) Francis Bacon (who we shall look at in a moment) effectively described Aristotle’s method of doing science and finding what was true in the following way. Gather a group of clever people and encourage them to argue. If they are clever enough then the truth must emerge! The Greeks seem to have been the first to propose that Nature is logical. Greek science however, was ‘non-instrumental’—they did not carry out experiments. Any evidence they used came from human observation and their conclusions relied upon 238 P H Y S I C S E D U C A T I O N 42 (3) 0031-9120/07/030238+07$30.00 © 2007 IOP Publishing Ltd How do we know that we know what we know? pure thought/reasoning. They used deduction to establish the truth of the matter. Deduction derives the consequence(s) implicit in premises; e.g., First premise All teachers are mortal Second premise Susan Jones is a teacher Conclusion Susan Jones is mortal Nothing is necessarily assumed about the actual truth or otherwise of the premises—they are assumed to be true for the purposes of argument. There are obvious flaws in this type of reasoning. If you the reader are not a teacher, or like the author of this article, are no longer a teacher, then you might further conclude that you are not mortal, i.e. you must be immortal! The Greek philosopher Zeno came up with other odd conclusions based upon the use of logical deduction, summed up in his so-called paradoxes. Perhaps the most famous concerns a race between Achilles and a tortoise. If Achilles agrees to give the tortoise a head start, then Zeno can prove that Achilles can never win such a race. He argues as follows. In the time it takes Achilles to get to where the tortoise was at the start of the race, the tortoise will have moved forward. Then, in the time it takes for Achilles to cover this extra distance, the tortoise will have again moved on some more, and so on. The argument can be repeated over and over with the necessary conclusion that Achilles can never catch up with the tortoise let alone overtake it and thus win the race. This logical argument offends both our ‘common sense’ and experience when carrying out the experiment by effectively arranging such a race. Although not as fast as Achilles we could substitute for him. But so strong was the Greeks’ attachment to the power of pure reasoning that when logic disagreed with experience, they concluded that their perception of experience must be at fault, because their logic could not be faulted! This position can be summed up as ‘mind over matter’. ‘Cease to be ruled by dogmas and authorities: look at the world’, Roger Bacon (13th century) To avoid the peculiar conclusions of unbridled reasoning alone Roger Bacon’s (not to be confused with his namesake Francis Bacon) succinct command reversed the Greeks’ position of ‘mind over matter’ to become ‘matter over mind’. However he still advocated logical deduction as the correct way to reason on the basis of the evidence derived from the world about you. Thus specific consequences (conclusions) were to be inferred from general observations (premises); e.g., (i) All students from (name your own school or college) work very hard at their studies. (ii) Amongst this crowd of young people at a night club this is a student from said school or college. (iii) Therefore this student works very hard at his or her studies. Francis Bacon (1561–1626) Francis Bacon is noted for two contributions to our theme. First, he was a great publicist for the central role of experiment, though it seems that Francis Bacon himself never indulged in much actual scientific work. He was reiterating more effectively scientists such as Bernardino Telesio who is on record as advocating the carrying out of experiments as early as 1509, and William Gilbert, who in his book de Magnete published in 1600, was the first person to set out in detail the essence of a scientific method based on ‘perform(ing) experiments’ as well as ‘thinking’. It was a course of action he exploited to great effect. Francis Bacon’s influence came to fruition 34 years after his death with the inauguration of the Royal Society in 1660 for the ‘promotion of experimental philosophy’. Secondly, when it came to ‘thinking’ he reversed Roger Bacon’s inferring specific consequences (conclusions) from general observations (premises) and observed that all we can reasonably do is to generalize the particular. This is known as induction. An example of an inductive argument is as follows. (i) The Sun has risen on every day in recorded history. (ii) Tomorrow is another day. (iii) Therefore the Sun will rise tomorrow. In other words the fact that the Sun has risen every day so far, and there are no known counterinstances or exceptions, and we have no reason to suspect it will change the way it behaves, implies that it will always rise on every day in the future. May 2007 P H Y S I C S E D U C A T I O N 239