CONTENTS

1    THE PROBLEM

2    A CONJECTURAL SOLUTION

3    TESTING THE CONJECTURE

4     CONCLUSIONS - A THEORY OF THEORY

1   THE PROBLEM

A problem with empiricism as an account of knowledge, and particularly of scientific knowledge, is making sense within it of the role of theory and the process of theorisation. Why do we have this need for theory, and does it contradict the original realist impulse which lay behind empiricism? We seem here to need a distinction between knowledge and understanding. Knowledge is something that we gain by looking at things (experiment); understanding is obtained by thinking about what we see (theorisation). The distinction between the two can be made clearer by examining the situation when we lack one or the other. There are two types of mysteries:  mysteries of knowledge and mysteries of understanding, and in what follows we shall look at each type in turn.

1.1   Mysteries of Knowledge

A classic case of a mystery of knowledge was the geography of the far side of the moon. There was no failure in our conceptual powers here. The problem was that until rockets were developed, we simply were unable to go there and look. The final acquisition of this long-hidden knowledge was exciting, and the far side of the moon had interesting differences from the familiar near side. However no major conceptual revisions were needed to cope with the new knowledge, as would have been the case had, for example, the space probes found that the far side of the moon was the entrance to a wormhole leading to another universe.

Knowledge starts from the phenomenology of our experience. Out of this phenomenology we distinguish a part which appears to be an experience of any objectively distinct reality. We then can make the grand Ontological Hypothesis that this appearance is based on reality. It then follows that we gain knowledge about the objective Other by participating in it, for example, by sending space probes to the moon, or building bigger telescopes to collect photons from more distant objects. Our epistemology has therefore an ontological basis; we use bits of the world as means of gaining knowledge of the world. Within our ontology we develop a concept of epistemic distance, related to, but distinct from spatial (and temporal) distance. The far side of the moon is spatially not much further from us than the near side, but epistemically it is much more distant. It is more distant than, for example, the spatially more distant surface of Mars. The bottom of our own oceans are epistemically more distant from us than the surface of the near side of the moon, and the centre of our own earth is more distant still. The world of micro-organisms is spatially right under our noses (not to mention, inside), and yet it is epistemically distant from the unaided human eye.

Once we have a notion of epistemic distance, it is not a mystery why there are mysteries of knowledge. These mysteries occur when there is a substantial epistemic distance between ourselves and the object of our questioning. To solve these mysteries we have to build bridges across the distance, either by extending ourselves in epistemic space, or make better use of the objects which cross the gap and come close to us.

1.2            Mysteries of Understanding

A classic example of a mystery of understanding is the Problem of Mind. Here we have the most intimate knowledge possible of the phenomenon in question. My epistemological contact with my own mind is extremely close; the relationship may even be identity. We could say that the epistemic distance in this case is zero. In spite of this, we appear to be quite unable to give a coherent account of mind, and its relation to the material world. Some say that this is a mystery of knowledge, that to solve the Problem of Mind it is necessary, and may be even sufficient, to acquire many more facts about the structure and function of the brain. I would argue with those who hold that, whatever facts we lack, a key element to the solution of this problem is the strengthening of our conceptual apparatus to enable us properly to express the facts about the phenomenon of mind.

Another example is provided by the philosophical problems surrounding Time. Again we are dealing with an intimate and immediate feature of our experience. Temporal passage is perhaps the most important and invariant feature of the environment we human beings find ourselves born into. St Augustine’s celebrated perplexity concerning time:

“What then, is time? If no one asks me, I know. If I wish to explain it to one that asks, I know not:”

is an epitome of the conjunction of knowlege and the failure of understanding. Children can accurately use temporal language from earliest infancy, and yet philosophical analysis seems incapable of explaining to us what it is that they, and we, are talking about.

Such deep philosophical problems are notorious for having resisted solution for hundreds of years. It is useful therefore also to present as an example a lesser problem, and one which has been completely solved. As a child, I was given by my father the puzzle of whether the piston in a reciprocating engine running at a constant speed ever stopped. There are two points, at the top and bottom of its cycle, when the piston slows down and changes direction. Intuitions of continuity tell us that there should be an instant when its velocity passes through zero, but can it at this time be said to have stopped.

Later, when I encountered the machinery of differential calculus, I realised that these techniques totally solved the piston puzzle. The solution comes in two parts. The first comes with the notion of an instantaneous velocity. This allows us to make sense of the statement that there is an instant when the velocity is zero, even though at all other times it is non-zero. The second part is the distinction between the various higher order derivatives. This enables us to say that, at the instant at which the piston has a zero velocity, it has a non-zero acceleration.

What this shows is that the old, pre-calculus, notion of “stopped” is too blunt an instrument to solve the piston problem. It does not distinguish between the cases where the velocity is zero for an instant, and where the velocity is zero for some finite lapse of time. In the former case the higher time derivatives of the position, such as the acceleration can be non-zero, which does not accord with the intuitive notion of something having stopped. The development of the differential calculus as a new set of tools for thought transforms a problem from one which seems almost as slippery and intractable as the great problems of philosophy into one which is trivial, in much the same way that the possession of a tin opener transforms the problem of opening a tin can from impossible to easy.

It is important to note that in the solution of this problem, no new knowledge about pistons, or about moving objects, needed to be imported from the outside world. Instead what was required was successive waves of deep thought setting up the differential calculus and then providing it with a rigorous framework. One of the by-products of modern pure mathematics is the systematic production of new tools of thought which are then available for use in expressing things about the world.

Another thing these examples of mysteries of the understanding show is the emergence of some sort of partition into two types:

• those which can be addressed and solved within the framework of theoretical science;
  
  
• those which lie in the province of philosophical analysis.

Notice that I was careful not to characterise the second type as “those which can be solved by philosophical analysis”. Problems which find themselves in the second type are usually the ones which are persistently intractable. If a problem is solved, then the solution typically manifests itself as a new branch of theoretical science, and so the problem shifts into the first type. An example of one moving the other way is provided by quantum mechanics. Quantum mechanics is a highly successful theoretical solution to a broad range of challenges to our understanding presented by experimental advances into the atomic and sub-atomic realms. Its interpretation however raised problems which eluded resolution from within theoretical physics and which have taken their place alongside the other great mysteries of philosophy.

It is however far from clear that there is a separate method called “philosophical analysis” which is actually capable of solving problems. Compared with science, philosophy seems to be a singularly unsuccessful mental activity, toying with problems, often making them more obscure, but never actually solving any of them. In this essay we shall focus on the way scientific theory can address and solve a subset of the mysteries of understanding (as well as generating new ones all of its own). The broader questions of the role of philosophical analysis in the development of understanding, and of the boundary between philosophy and science, are addressed in a companion essay.

1.3       The Importance of Theory

Cultural relativists delight in telling us about different types of science: Western science, Chinese science, Islamic science and so on. They assert that each of these is valid within its own cultural context. In fact Western science is qualitatively different than all the other knowledge traditions, and qualitatively more successful. The word “science” should be used, unqualified, to denote this entirely different and entirely new endeavour. To attach the label “Western” to it is to focus on one of its least interesting attributes, a historical accident of little relevance to its true nature. Science is above all the true heritage of all of humankind.

The qualitative difference, and the qualitative improvement, which gives science this status is the continuing dialogue set up between systematic experiment and mathematised theorisation. Experiment challenges theory with new results, and theory challenges experiment to test new conjectures. Experiment stops theory becoming mere imaginative speculation, and theory stops experiment becoming an undirected collection of facts. Traditional Chinese science for example, had a vast body of empirical knowledge and elaborate theoretical constructs, but the two were not brought into this dialogue where the one continually challenged the other.

Historically, the beginnings of this synthesis can be seen in the combined work of Tycho and Kepler. The latter became the first theoretician when he let the eight minutes of arc discrepancy between his theoretical predictions of the motion of Mars and Tycho’s accurate observations be the occasion for utterly rejecting his current theory and starting out on a quest for an accurate one. The synthesis was perfected with the advent of Newton’s mechanics, where a fully-developed mathematical theory was confronted successfully with a wide range of experimental facts. This has remained the paradigm for the sciences to this date. The subsequent search for a theoretical basis of chemistry found that this basis was physics, albeit a form strikingly different from Newton’s. Biology was transformed from being a collection of facts into a science with a theoretical backbone by Darwin. In doing so, he did not merely explain biological facts, but also deepened our understanding of the meaning of the word “biological”.

1.4       The Problem of Theory

Science owes its success to the way it links the pursuits of knowledge and of understanding. It is less clear why this should be so. As indicated above, the fact that there are of knowledge is easily explained. To gain knowledge of some part of the world, our physical being has to interact physically with it, in such a way that part of our brain becomes correlated with the state it is in. To understand how this correlation becomes knowledge requires a solution of the Problem of Mind, but this is not required to explain failures of knowledge. These are due to the absence of the necessary interactions. Light reflected from the far side of the Moon simply does not reach the surface of the Earth, and so until we go somewhere else and catch some of that light, we can not see that part of the lunar surface.

What, though, is missing when we have a failure of understanding? To put the question in a positive form: what does understanding add to the knowledge of the world we gain by interacting with the world? A third formulation of the question is: what role does theory play in the empirical sciences? The fact that something else has to be put in by our thinking appears to compromise the realist account of science which is the initial ontological motivation for an empiricist epistemology. The development of this line of thought can be crudely sketched out as follows.

• Realist Ontology – what there is out there in the world is independent of what human minds think or believe about it.
  
  
• Empiricist Epistemology – knowledge about the world should therefore be gained by pure observation of the things in the world.
  
  
• Positivist Philosophy of Science – scientific discourse should be carried out entirely with observational terms, without superimposing theoretical considerations on it.
  
  
• Observation – theoretical terms can not be eliminated from scientific discourse.
  
  
• Conclusion – because science is irredemably “theory laden”, a realist account of its ontology can not be sustained. Scientific statements can not be seen as true or false only by virtue of the nature of the external world. Their truth-value has to be relativised to the theoretical framework in terms of which they are expressed.

From this logical relativism, it is only a short step back to the cultural relativism repudiated above, in the assertion of the uniqueness of Western science.

The problem addressed in this essay is then:

How might one develop a realist account of understanding?

Such an account would see understanding as a necessary complement to knowledge, but not one which compromises the objective reference of what is known and understood. The development of my conjectural solution is carried out in the context of what I call “Fregean Ontology” (see the essay of the same name). In outline the idea is that there are objective features of the world which have to be teased out my thinking about our experience of the world before we can express our knowledge in the form of fully articulated understanding.

Click here to go to Section 2