The Unity of Knowledge and Understanding in Science

Foreword

The following article summarises one of the main lines of argument from my doctoral thesis. It was published in Craig Dilworth (ed): Idealization IV: Intelligibility in Science, Amsterdam/Atlanta, GA, Rodopi, 1992 (Poznań Studies in the Philosophy of the Sciences and the Humanities 26)

Objectives.

It is my intention in this article to show that modern science can be adequately understood as a process of creation of a certain kind of knowledge: knowledge of those parts of the structure of the world of which our senses leave us in ignorance. Since science has been seen by many as also or primarily providing understanding of the world, it will also be argued that such knowledge, given the nature of its object, will also inescapably provide understanding. In the scientific case, the two are effectively one.

Definitions.

Knowledge.

The argument does not require a general theory of the nature of knowledge. I take it that knowledge can be understood as information in fact reasonably accurate obtained by means in fact reliable and reasonably thought to be so: this  ‘definition’ is intended to leave any substantial philosophical issues aside; the only one relevant to this paper is that of the possibility of knowledge about unobservables, which is discussed below (4.4).

It should, however, be noted that knowledge does not require total or even relative certainty. We may know equally that 2+2=4 and that illiteracy is a major cause of overpopulation, although the degree of certainty involved in the two cases is clearly different. Similarly, although we may be more sure about our knowledge of some things (for example, observable objects) than of that of others (for example, unobservables), this does not imply that either is any more or less knowledge, but only reflects that some knowledge is harder to come by.

Understanding.

Nor is a specific view of understanding required. Scientific understanding has typically been taken to involve one or more of the following: unification of phenomena, demonstration of their causes, revelation of their underlying nature (or  ‘real essence’), demonstration of how they are possible or why they are necessary, their organisation in a hypothetico-deductive system, and the ability to predict their future course. Obviously, these various versions of what understanding is come from widely differing philosophical backgrounds, generally in competition with one another. But it seems reasonable to assume that anything that satisfies all of them can be safely taken to provide understanding. ( ‘Phenomena’ are to be taken as  ‘things that happen that we would like to understand,’ to preserve the lack of commitment to specifics or to any determinate philosophical tradition.)

Grounding and Constituents.

The argument does require a fairly clear grasp of the metaphysical concept of  ‘grounding.’ A dispositional property of a particular thing I say to be  ‘grounded’ in a given collection of entities and a given structure if all that is or can be caused by that thing and is attributable to the dispositional property is or would be also caused by those entities and by the fact that they are related in that structure. The entities and the structure are the  ‘grounding’ of the dispositional property (or  ‘disposition’). footnote 1

For something to have a disposition is for it to be apt to be causally active in a particular way in a given kind of circumstances. Thus, any instance of causation is vacuously the manifestation of dispositional properties: anything that in fact is causally active in some way must be  ‘apt’ to be so and thus have the appropriate disposition. Thus all the causal activity of anything is attributable to its dispositions, and thus I identify the  ‘constituents’ of any complex thing (thing with more than one part, and thus with a structure) in the actual world with the entities that ground the totality of its dispositional properties. By this definition are counted as constituents exactly those entities that are responsible for all of the thing’s actual and possible causal behaviour, which seems a good reason to count them as being  ‘parts’ of the thing.

All that may be caused by a complex thing is caused by its constituents, but not vice versa: removed from the thing of which they are a part, the constituents of a thing may still be causally active. A thing with only one constituent (itself) I call a  ‘simple.’ Since it only has one constituent, there are no relationships between its constituents, and it thus has no structure. At various times, different things have been taken as simple by various people. Protagoras thought the whole world was one simple. Berkeley thought that his mind was a simple. At present, most scientists would opt for the fundamental particles of modern physics. (They may of course turn out to be wrong.)

The grounding structure of reality.

The picture of the world offered to us by science includes a rich account of the constitution of things. For example, people are said to be made of various organs, which are composed of cells, made of organelles, composed of molecules, made of atoms, made of subatomic particles. All arranged in their own particular structures. The whole of reality is presented as having a complex structure, which I will call its  ‘grounding structure,’ in which simpler things are the contituents of complex things, which are themselves the constituents of more complex things: the grounding structure of reality is presented as having various levels.

Leaving aside the questions of whether or not modern science is broadly reliable and of whether it is to be interpreted from a realist viewpoint, it is clear that actual reality must have a grounding structure: simples must either form more or less enduring complexes or not. If they do not, then the world is a super-Heracleitian chaos in which one could not step into the same river once, due to the lack of leg, river and life; this does not appear to be the case. If they do, then there is a grounding structure, of at least two levels.

The simples postulated by current science (fundamental particles) have exclusively dispositional properties: mass, charge,  ‘spin,’  ‘colour,’ etc. Again, whether or not science is right or wrong about the actual properties of simples, they cannot in fact be anything other than exclusively dispositional:

I take it as a criterion of actuality that that which is actual is at least potentially causally active. Thus, the completely causally inert does not actually exist. Thus, simples have dispositional properties (or they would not be causally active (2.3 above) and so not exist), and have no causally inert properties (which do not exist). Thus, apart from their dispositional properties, they have only such properties as are necessary for the presence of their dispositions. These properties cannot be structural, since a simple, as pointed out above (2.3), has no structure. Thus they do not give rise to the dispositions of the simple as do the structural properties of a complex thing, by determining the situation in which the constituents of the thing find themselves and so how they will act. They must simply be such that things with them also have the dispositional properties. Thus they are such that things with them are apt to act in certain ways under certain conditions. Thus, they are in fact the dispositional properties, and not  ‘other’ at all.

Knowledge of reality.

On the basis of the general view of reality just outlined — that it has a grounding structure of various levels and that its simples have none but dispositional properties — I now propose to offer an outline account of the nature of science and its products in which it is presented as an enterprise aimed at the increase of knowledge about reality. The starting point is the extent of our ignorance in its absence.

Ignorance.

Uncritical use of the senses informs us of the existence and such properties as correspond to their capacities of objects within a limited range of sizes (four or five orders of magnitude on either side of our own) presently or very recently located on or very near the surface of the earth. In addition it lets us know of the existence but very little of the nature of some meteorological and astronomical phenomena.

This leaves most of reality in the realms of ignorance. It does not include most of the spatio-temporal extent of the universe, and even in that part which it does cover does not include most of the grounding structure, either in the direction of the micro-constitution of things or in that of any larger structures of which familiar things might be a part (ecosystems, social systems, solar systems, etc). As a result, it also leaves us ignorant of any of the causal interrelationships of phenomena rooted in the micro- or macro-structure of reality. To which ignorance is to be added that of any such causal structure of phenomena as is simply not obvious.

Some ignorance can be remedied by time, common sense, money and careful observation: thus we can discover the existence of large islands, continents and seas by travelling around them, we can extend our knowledge of past times by digging holes to find their remains, and we can observe astronomical phenomena with simple instruments and subject the results to mathematical analysis. But such methods leave untouched the wide-ranging aspects of ignorance related to the lack of immediate access to the greater part of the grounding structure of reality. The primary aim of scientific research, seen as a search for a certain kind of knowledge, is the overcoming of this kind of ignorance.

I will now argue for the indispensability of metaphysics in this process, and describe how it makes possible the construction of a description of the grounding structure of the world. footnote 2

Metaphysics and research.

Given the nature of the knowledge that is required, and its relationship with the known, the reduction of ignorance by science will involve the creation of a conception of a more or less complex structure of entities, whose properties may not in general be similar to those of familiar objects, parts of which structure can be identified with parts of the previously known world in such a way that the whole can be taken as a more complete conception of the actual world.

Given the size and complexity of the task, this conception cannot be built at a stroke. It must be fabricated gradually, by the construction and refinement of hypotheses concerning the grounding of the dispositions manifest in particular restricted kinds of phenomena, which may eventually be brought together into a unified overall picture. And whenever it is possible these hypotheses must be tested to check that the parts of the world they attempt to describe do in fact behave as they would lead us to expect.

A little less obviously, neither can such a conception of the world begin to be constructed in the absence of a general idea of what it will be like when it is finished (if it is ever to be finished), an idea which will thus be a conception of what reality is generally like: a metaphysics. This is necessary firstly because unless the parts of the scientific world-view under construction are in conformity with one metaphysics, it will not be possible to integrate them into a unified vision of the one world, and secondly because without it scientists would have no idea how to begin theorising.

For example, faced with the isolated fact that ice melts into water, which then boils when it is further heated, we could concoct any number of plausible accounts of the grounding of the properties of ice and water. It could be that ice is composed of millions of tiny fairies all holding hands to keep warm, who let go when they get warmer and finally fly away when it gets too hot. Or ice could be a confluence of various qualitative principles (of coldness, weight, solidity, etc), some of which are attenuated by the increase of that of hotness. Or it could be that God simply sees fit to replace ice with water and water with steam for the good of His children and His own greater glory. Which of these ideas, if any, is to be taken seriously obviously depends on the ideas already held concerning the general nature of the world and the things in it.

If our metaphysical conception of the world is not at some level approximately correct,footnote 3 we will of course take some quite mistaken ideas quite seriously, and quite reasonably discard, for their failure to be in harmony with our general world view, those that are nearer to the truth.footnote 4 Thus, the possibility of of the reasonable and successful practice of science rests on (among other things) the historical fact of a particular metaphysics gaining credence at some particular time, for reasons that will be essentially non-scientific, given that they operate in the pre-history of science. As science makes progress, this gradually provides scientific reasons for acceptance of the metaphysics that made such progress possible.

A scientific theory is thus designed to fill the gap between a metaphysical and an observationalfootnote 5 view of the world:footnote 6 equipped with a general conception of the way things really are, and faced with a knowledge of how they appear, a scientist attempts to answer the question  ‘how could things that fundamentally are like this appear to us like that?’

This question is answered by a description of the grounding structure of the parts of the world involved, in which postulated constituents possible within the framework of the guiding metaphysics are related in such a way that they could be expected to behave in conjunction in the appropriate way.

Obviously, the description given will not be complete and precise in all respects. On the contrary, given the complexity of the world, it will, especially at first, be highly idealised and schematic. Initially at least, only such phenomena as are susceptible to such an idealised treatment will be studied, others being left aside as complex results of many different influences. (Which phenomena fall into which group will depend on the nature of the guiding metaphysics: as Kuhn pointed out, scientists with divergent world-views disagree over what it is most important to explain.footnote 7)

Once articulated, a theory has to be tested. Given that it is an idealised description of the reality of which it treats, it will give precise indications of the behaviour to be expected of things only in situations in which factors ignored by its idealisations are absent — hence the importance of the highly artificial phenomena created in scientific experiments. In this context, the importance of the mathematical expression of theories cannot be overestimated (see below, 4.3).

Since all that a complex thing can do is caused by its constituents, but not vice versa (see above, 2.3), an important part of the experimental effort of scientists is devoted to the isolation of these constituents and of their independent effects. If this appears to be impossible, the credibility of the theory that proposes the existence of the elusive entities is severely undermined. If it can be done, on the other hand, the confirmation of the ontology of the theory provides powerful support for it.

By the development of many theories, within the framework of the guiding metaphysics, controlled by observation and experiment, is articulated a scientific ontology: a specific inventory of the constituents of things. This ontology specifies which of the range of entities possible relative to the metaphysics are actually to be found in reality. It is stratified, its levels being intended to correspond to those of the actual world.footnote 8 As more theories of greater detail are developed, and the existence of the entities they postulate comes to appear more probable, new theories tend to draw on the ontological resources of old ones, since in this way they draw on the already established plausibility of the old ones. Thus, most of the time, the influence of metaphysics on science is mediated by ontology. (Thus also, it is difficult to say where one theory stops and another begins, and to speak of a theory as if it were an independent, well-defined, and closed set of statements (as in common locutions such as  ‘a theory T1’) is to deprive it of most if not all of its scientific status.)footnote 9

There may come a point at which it is not possible to produce a theory within the confines of accepted ontology, or even those of the guiding metaphysics. In this case, ontology or even metaphysics may in the end be modified, in order to permit belief in entites adequate to the construction of an account of the grounding of the properties of things revealed in the recalcitrant phenomena. This change is likely to be difficult, and may even be described as  ‘revolutionary.’

In science as often in history, revolution does not imply the complete rejection of the old order, but only the replacement of the contents of a part of its structure. Only the metaphysical base of the scientific view of the grounding structure of reality is immediately affected, the greater part of it remains at first unchanged.

For example, the replacement of the classical mechanistic view of reality by that of quantum mechanics was metaphysically far-reaching, but its initial impact on every science except physics, and on most of that, was more or less nil. Its impact since then has of course been immeasurable, as its precepts have been taken up into the further elaboration of old theories and the creation of new ones. But it would be a mistake to overemphasise the propensity of scientists simply to throw successful ideas into the bin.footnote 10

Precision and mathematics.

There have always existed general views of reality and more or less detailed accounts of how the world is constructed expressed in the terms of these views. The peculiarity of the scientific version, aside from its fortunate provision with a viable metaphysics, lies predominantly in the link between the mathematical expression of its accounts of the structure of things (probably linked historically to the quantitative nature of the primary qualities of mechanistic metaphysics) and their subjection to the control of quantitative observation (probably historically linked to the success of quantitative astronomy).

The entities described by a theory are generally described mathematically, in such a way that from their being in the mathematically described structure proposed by the theory a mathematical description is derivable of the behaviour under some given circumstances of the objects whose constituents they are said to be. Thus the theory is in principle rather vulnerable to the adverse effects of observable fact on its plausibility: it is usually possible, with imagination, to produce a variety of entertaining stories of how something qualitatively much like what actually happens could be brought about by some structure of postulated entities. Much more difficult is the creation of a mathematically articulated theory quantitatively adequate to observed realities.

The mathematical form of theories determines the nature of the problem confronting scientists attempting to construct one, which is highly structured and has precise constraints on its solution. Given a quantitative description of a phenomenon or of some phenomena, and an ontology of mathematically characterised entities presumed to be involved in them, there is a severely limited range of mathematically adequate solutions to the problem of how one is produced by the other, any one of which may not be easy to find.footnote 11

The contingency of ignorance.

By their integration in a mathematically described structure yielding numerical expectations of observation, the nature of the entities whose existence is entertained by scientific theories is laid completely open to observational scrutiny. No properties of these entities are postulated that do not affect the possible observable behaviour of the systems of which they are parts, since such postulation would serve no purpose in the solution of the problem addressed by a theory, which is the mathematical linking of the observable with the metaphysical. (It is not only in science that we disapprove of wild speculation without possibility of confirmation or rebuttal.) And due to its mathematical articulation, the precise description of their properties is reflected in the detail of the observable behaviour expected of reality under some conditions. Thus, if the conditions can be sufficiently controlled, we can obtain evidence for or against the accuracy of our theories, although as with any issue of empirical fact total logical certainty will be unattainable, and even though reasonable certainty may be quite difficult to obtain given the multiplicity of factors that generally have to be manipulated.

The restriction of scientific descriptions to the field of what may have an observable effect does not exclude any part of the actual nature of things from its possible scope: the properties of the simple things that science aspires to describe are all dispositional (section 3, above), and thus all such as to be completely manifested in their effects, the further effects of which cannot be excluded in principle from reaching any level of the grounding structure of the world, including the observable levels. Thus, our knowledge of the constituents and of the grounding structure of reality is restricted only by our ingenuity in the construction of theories and of experiments to test them, by our location in a particular place and time, and by the resources available given the economic situation. Ignorance is contingent, and may be reduced by science. Thus we can adopt the realist position that science provides knowledge of the unobservable. footnote 12

How scientific knowledge is also understanding.

That science also provides understanding has not been explicit in the foregoing argument, but it should be clear that the production as described of knowledge of the grounding structure of the world is inseparable from increase of understanding of the world, on any of the views of understanding mentioned at the outset of this article.

First, by showing how a wide range of phenomena and objects are all brought about by or composed of a relatively small selection of kinds of entities, a unification is achieved, and a consequent reduction in the number of independent phenomena and kinds of thing that must be accepted as being in the world.

Second, since the entities in unobservable levels of the grounding structure of the world of whose existence science informs us are causally responsible for phenomena involving the things whose constituents they are, science provides information concerning the causes of events and of the behaviour corresponding to the various properties of things.

Third, by providing another, and in some contexts more useful way of describing objects and events, in terms of their composition as described by our theories, it reveals their  ‘underlying nature’ or  ‘real essence,’ if we wish to express ourselves in such terms.

Fourth, by incorporating phenomena and objects into an integrated account in terms of a scientific ontology understood as providing an inventory of the constituents of all actually possible things, scientific theory shows how objects constructed out of the elements of that ontology and their actions are possible, and by excluding those possibilities not realisable with the resources of that ontology shows how under some circumstances what actually happens is the only possibility and is thus necessary. (Always assuming that there are not more things in heaven and earth than we realise whose existence would be relevant to the case in question.)

Fifth, by virtue of the integration of the quantitative description of phenomena into a mathematical structure based in a mathematically described ontology, they can be seen, albeit in an idealised sense, as incorporated into a hypothetico-deductive system: a perfect knowledge of the detail of the grounding of some phenomenon and a great deal of mathematical talent would permit a rigorous (deductive) mathematical derivation of its precise course, or of the respective probabilities of its various possible courses if the entities involved act non-deterministically. It would be a mistake to overemphasise the deductive logical features of scientific reasoning and of the theories it produces: for example, as is well known, there is no known way of rigorously deducing the precise motions of as few as three objects under the influence of a single force as simple as Newtonian gravity. In this case, as in general, the procedure is to make idealising assumptions and compensate for the inaccuracy produced by the later incorporation of correction factors into the calculation.

Finally, since knowledge of some of the detail of the structure of things may enable us to work out how they will behave in novel situations, it provides for the possibility of prediction of some of the future course of events. Again, this aspect of scientific knowledge/understanding should not be overemphasised: as I have just pointed out, scientific derivations of the course of events from theoretical principles depend on a blend of idealisation and correction, and which factors of the real world situation initially glossed over in the idealisation are in fact important enough to require account to be taken of them and corrections to be made may well not be apparent until after the event. In addition, it is in the nature of some theories to be unable to predict: for example, the global mathematical description appropriate for open systems far from thermodynamic equilibrium is such as to lead to the dependence of the precise course of events that is to be expected on the arising of random fluctuations in the system.footnote 13 Nonetheless, theories of systems of this kind (such as some chemical systems, ecosystems, and possibly social systems) perform the same function as any other in the mathematical unification of observable reality with what we have reason to believe, and may in fact know, is its ontological basis.

The nature of knowledge/understanding.

At the outset of this article I avoided making specific commitments concerning the nature of knowledge and that of understanding. But in the course of the argument some commitment has clearly been made concerning both.

Knowledge, at least that part of it not accessible to animals, appears as the product of no small effort, in the form of a highly organised system whose extent and complexity requires that its production be cooperative, and such that any one part of it requires for its production, grasp and value an extensive web of surrounding knowledge and understanding.

Thus, it does not appear likely to me that there can be given any generally applicable account of the nature of knowledge of the form  ‘A knows that P if ...,’ since the precise nature of the relationships between any item or part of knowledge with that implied for the understanding that must surround it will depend on the nature of the parts of reality of which it treats (given that  ‘knowledge’ implies success), and the course of events that has led to that knowledge, which are both imprevisible.

With regard to understanding, on the other hand, it seems to me that the account I have given of reality and of the nature of scientific views of the world and of parts of it itself constitutes an outline account of the nature of scientific understanding, since as I have shown it incorporates and places in relation with one another other standard views of such understanding. Since the description given was nothing more or less than an account of the nature of scientific knowledge, the conclusion is to be drawn that in the context of science, and taken as a whole, knowledge and understanding are one.

References

Dilworth, C (1989):  ‘Idealization and the Abstractive-Theoretical Model of Scientific Explanation’ in Brzeziński et al. (eds): Idealization I: General Problems, Poznań Studies in the Philosophy of the Sciences and the Humanities 16

Harré, H.R. (1970): The Principles of Scientific Thinking, London, Macmillan

Kuhn, T.S. (1962): The Structure of Scientific Revolutions, 2nd edn. Chicago, University of Chicago Press, 1970

Mackie, J.L: (1977):  ‘Dispositions, Grounds and Causes’ in Synthese 34 pp361-370

Newton-Smith, W. (1981):  ‘In Defence of Truth’ in V.J. Jensen and H.R. Harre (eds): The Philosophy of Evolution, London, Blackwell

Prigogine, I. (1977):  ‘The Evolution of Complexity and the Laws of Nature’ in E. Laszlo and J. Biermann (eds): Goals in a Global Community, London, Pergamon Press

Tiles, J.E. (1985):  ‘A  ‘rationalist’ approach to dispositional properties’ in Theoria 51

Tiles, M.E. (1984): Bachelard: Science and Objectivity, Cambridge, Cambridge University Press

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