Logic, Thought, and Action 8

Chapter 8 EMPIRICAL VERSUS THEORETICAL EXISTENCE AND TRUTH∗ Michel Ghins Universite´ Catholique de Louvain

Abstract

On the basis of an analysis of everyday experience and practice, criteria of legitimate assertions of existence and truth are offered. A specific thing, like a newspaper, can be asserted to exist if it has some invariant characteristics and is present in actual perception. A statement, like “This newspaper is black and white”, can be accepted as true if it is wellestablished in some empirical domain. Each of these criteria provides a sufficient condition for acceptance of existence and truth, respectively, at the empirical level. Following Hermann Weyl, it is argued that they can be extended to the scientific theoretical level to support a selective and moderate version of scientific realism according to which entities like the electromagnetic and gravitational fields, but not crystalline spheres or some topological manifolds, can legitimately be asserted to exist.

Keywords: Existence, truth, scientific realism, constructive empiricism, underdetermination.

1.

Existence and truth in ordinary experiencce

Everyday experience and our sensory presence to ordinary objects are the starting point of any knowledge. On this, I agree with logical and constructive empiricists (and also with Aristotle and Aquinas). An examination of the use of the terms “existence” and “truth” in the context of everyday experience must reveal the criteria of their legitimate ap-

∗ This paper has been published, followed by Prof. Bas van Fraassen’s comments, in Foundations of Physics (Vol. 30, No. 10, 2000) in a special issue dedicated to Prof. Maria Luisa Dalla Chiara. I would like to thank Kluwer for granting permission to republish this paper in the present volume. I am also grateful to Giovanni Boniolo, Harvey R. Brown, Benito Muller, Mauricio Suarez, ´ Bas van Fraassen for their stimulating comments and suggestions.

D. Vanderveken (ed.), Logic, Thought & Action, 163–174. 2005 Springer. Printed in The Netherlands.

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plications. I am allowed to say that this newspaper in front of me, for example, exists when I am visually acquainted with it. Some empiricists tried to analyse statements like “This newspaper exists” in terms of more elementary statements about “immediate” sense data. I do not intend to discuss this question. Let me just point out that the “myth of the given” has been widely criticized, including within the empiricist tradition, by Quine (1953) and van Fraassen (1980) among others, and I deem these criticisms successful. Why am I entitled to assert the existence of this newspaper? In the first place because I see it, and not because I am making some kind of (justified?) inference from data (or, more accurately, from statements on data). Actual presence in sensory perception is the first condition for the legitimacy of an affirmation of existence. But it is not sufficient on its own. A second condition is the permanence or invariance 1 for some time of some characteristics of the perceived object. These two conditions of presence and invariance constitute jointly the sufficient condition, the criterion 2 , of existence that will be used. An affirmation of existence goes usually beyond actual presence. Its acceptance calls, at least implicitly, for other possible experiences, by myself or other people. When I say that this newspaper exists, I also implicitly say that I will be able, for some (even very short) time, to perceive its shape, its colour, its texture, etc. In other words, I assert the permanence in time of some properties of the object. The Cartesian notion of “punctual” (durationless), vanishing existence seems unintelligible and, moreover, does not seem to find any correlate in ordinary experience. But an affirmation of existence also calls for possible perceptions by other observers, at different spatiotemporal locations. Nobody doubts (except perhaps lunatics and some — very rare — philosophers. . . 3 ) that, in the usual contexts, several people can see the same, unique, object, even if their visions differ, precisely because these perceptions also have constant, invariant, aspects, and because the observed variations show a systematic character. This point is stressed by phenomenologists when they say that the object presents itself through a variety of profiles 1A

connection between objectivity and reality on the one hand, and invariance on the other has been discussed by phenomenologists, espoused by Einstein and Weyl and revived more recently by Michael Friedman (1983, p. 321). 2 I do not propose a definition of existence. In accordance with a philosophical tradition which goes back to Aristotle and includes Aquinas, Kant and Carnap, I think that existence is not a property. Moreover, I want to leave open the possibility of the existence of metasensible entities even if they may be cognitively inaccessible to us. 3 Even Sextus Empiricus, the “sceptic”, did not put the existence of ordinary objects into question, unlike the radical sceptic fabricated by Descartes.

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(abschattungen), potentially infinite in number. These profiles are not sense data but different perceptions of the same object. The two conditions of presence and invariance are jointly sufficient for the legitimacy of the assertions of existence about ordinary observable objects. But these conditions do not exhaust the meaning (or, rather, the meanings) of the term “existence”. We often associate to the existence of an object some idea of independence with respect to our desires, our language, our actual perceptions, etc.4 : a real object is something that imposes itself upon us and opposes resistance to our actions. A real thing is something that can hurt us. It is generally accepted that an actually perceived tree (to take over a famous example due to Hans Reichenbach) will continue to exist when nobody looks at it, and existed for some time before. The affirmation of its existence or independent reality rests upon the possibility of perceiving it at arbitrarily chosen times. If the independent existence of perceived objects is admitted, then the existence of perceivable objects must also be accepted. Thus, the acceptance of an assertion of existence implies also the acceptance of counterfactuals like: “If I looked at the tree now, then I would see it”. It seems thus reasonable to admit that any affirmation of existence based on presence and invariance, can legitimately be extended to moments and circumstances that go beyond the actual presence in order to include merely possible presence as well. Assertions about the reality of specific things or objects, even confined to ordinary, sensory experience, reach beyond actual perception to include possible observations, and, to that extent, they run the risk of falsification. Empirical everyday assertions about observable objects are not immune from error. The statement of the independent existence of specific objects carries an anticipating power with respect to possible perceptions (Nelson Goodman (1955) speaks of projectibility). If I say that this newspaper in front of me exists, I also predict that myself, and others, will see it in the (even very short) future. And this also implies that I would see this newspaper if I was located elsewhere, etc. But the newspaper could also disappear (by burning), and this would simply falsify the affirmation of its existence. It must be stressed that the independent reality discussed here pertains to ordinary perceived objects. This does not commit us to the existence an sich or “for God”, or in any other way, of ordinary objects. We do not have any reason, at least on the basis of the foregoing argu-

4 See

for example Putnam (1981).

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mentation, to believe that ordinary objects exist, in themselves (whatever this may mean) in the way they are perceived (remember the 17th century debate about primary and secondary qualities).

2.

Existence and truth in theoretical science

Now, I want to argue, if we accept the existence (or reality) of observable everyday objects, and the truth of some statements about them, there is no reason not to accept that some theoretical entities exist and that some physical laws are true. My whole argumentation rests on a parallelism on certain crucial respects between everyday assertions and scientific assertions. The problem is to apply the criterion of acceptance of existence to some (not all) unobservable theoretical entities, postulated by scientific theories accepted today. Kant, in his Critique of Pure Reason, formulates the following criterion of reality : “that which is connected with perception according to laws” is real (A231; B284)5 . This passage is quoted by Hermann Weyl in his The Philosophy of Mathematics and Natural Science (1963, p. 122). I will limit my discussion to physical, mathematized, theories. But it is in physics, where the most “abstract” and seemingly most remote from experience entities occur, that the issue of realism is considered most controversial6 . Hermann Weyl takes the example of the electric field. We have the following law: ¯ )q F¯ (P ) = E(P The force F¯ , experienced by a charge q at a point P is proportional to the size of the charge. Weyl sees an analogy between the different perceptions of an ordinary object and the different observable manifestations of the electric field. Forces correspond to perceptions7 , and different charges correspond to different positions of the observers. An objective reality can thus be attributed to an electric field8 when it is experienced by means of actual forces (condition of presence) and when a systematic variation of some properties together with the invariance of other properties is ascertained within the sequence of perceptions, namely the 5 Kant

specifies that the laws in question are empirical, thus not apodictic, laws. realist like Ernan McMullin (1984) for example does not want to commit himself to the existence of theoretical entities introduced by mathematical physics, like electrons and fields. 7 For the sake of argument, Weyl takes forces to be observable. 8 Actually, the real object is the electromagnetic field which is covariant under the Lorentz group. Here Weyl restricts himself to one reference frame in which there is no magnetic component. 6A

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forces in the present case (condition of invariance). For example, the direction of the force remains constant whereas its strength varies in a systematic way in function of the electric charge. The mathematical expression above gives a precise formulation of this variation. ¯ occurs in other laws too (optical, among others). The electric field E, This reinforces the credibility of its existence, in the same manner that a larger variety of perceptions (shape, colour, texture, smell, etc.) of a newspaper gives more weight to the assertion of its existence. After having defined a criterion of existence we must now give a criterion of truth. Any statement about ordinary observable objects can be accepted as true on the basis of simple experiences. The truth of the statement “This newspaper is black and white” is grounded on actual, effective perceptions. I say: effective perceptions, in the plural. Even at the level which is closest to sensory experience, truth rests on several perceptions, even if these perceptions are relatively few in number, belonging to a given domain (visual, tactile, acoustic, etc.) We already have here a sort of “induction”9 . I do not mean here an inference or an inductive argument (which is a set of statements). It is a kind of fact (call it a metafact, if you wish) that human beings make assertions on the basis of their perceptions and that the latter are put forward as grounds for the truth of their assertions. Moreover, as we saw above, what holds for existence also holds for truth: both reach beyond the strict framework of actual perceptions. Assertions can then go beyond the individual sphere and enter the domain of intersubjectivity. The affirmation “This newspaper is black and white” includes an invitation, as it were, to verify it yourself. This assertion implies, at least implicitly, a series of counterfactuals like: if you came closer, you would continue seeing a newspaper, etc. The criterion of truth that comes out from these (admittedly too brief) considerations is this: a statement “inductively” well-established in a certain domain of perceptions can be accepted -if only provisionally- as true. Acceptance of the truth of a statement does not commit oneself to the belief in its absolute or unrevisable truth. It does not commit oneself to the belief in the corresponding actualisation of an independent fact, existing somehow “in itself”, either. According to this criterion, we can also accept as true numerous physical statements (commonly referred to as “laws”), although their connection with experience is less direct (we briefly discuss the question of

9I

will use the term “induction”, with quotation marks, to mean the, somewhat mysterious, connection between statements and observations which would require further analysis (“Induction” is not abduction in Peirce’s sense.)

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underdetermination below). The mathematical laws of classical mechanics of pointlike masses, for example, are “inductively” well established in an empirical domain limited by what David Speiser (1990) called negligibility relations 10 . They circumscribe the domain of truth of the famous three Newton’s laws11 : m¯ v = k¯ F¯ = m¯ a F¯A = −F¯R The domain of truth of these laws is bounded by the following negligibility relations: vc
pdq  h/2π Gm/c2  R These relations12 restrict the truth of Newton’s laws to velocities which are small with respect to the velocity of light, to actions which are large relatively to Planck’s constant and to weak gravitational fields (if the force is given by Newton’s law of gravitation). They must be considered as an integral part of classical mechanics because we know that outside this domain we must use special relativity, general relativity or quantum mechanics. These relations permit also to endow the notion of approximate truth with a precise meaning. A physical law is not approximately true when it is a more or less faithful image of some “reality”, but when measurement results in a certain domain do not deviate from the predictions more than some antecedently specified value. Even within this limited empirical domain, classical mechanics (including the three negligibility relations) is still able to predict new facts, in empirical fields that have not been investigated yet, and, consequently, this theory runs the risk of being falsified. If that happens, new negligibility relations will be introduced. This provides an answer to Popper’s objection according to which limiting a theory to a given domain would be tantamount to protect it against any adverse evidence, any possible falsification, which would be the very negation of the scientific enterprise. 10 Krajewski

(1977, p. 11) speaks of limit conditions. But this expression can lead to a confusion with boundary conditions. 11 These laws hold for point mechanics only: for rigid bodies, fluids and elastic bodies respectively, other sets of laws must be used. 12 v is the velocity of a moving body, c the velocity of light, p the linear momentum, q the position, h Planck’s constant, G the gravitational constant, M the mass of the source, R the distance from the source.

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We must acknowledge that logical positivists were essentially right when they claimed that it is extremely unlikely that a well-established theory in a certain domain would be falsified in that same domain. It is totally pointless to indefinitely repeat Galileo’s experiments on inclined planes (except perhaps for students in physics. . . ), in the same way that it would be a waste of time to keep looking for hours at a newspaper to make sure it is still really there. On the other hand, well-established statements and theories remain conjectural, in the sense that they could be abandoned some day, in the face of other, different, experiences. Previous experience does not warrant, with necessity, that future experience will be similar to it. It is quite possible that bodies suddenly begin to move in a quite surprising way according to new “laws”, although we all consider this extremely unlikely.

3.

Illustrative applications of the criteria

I would like now to illustrate the specific, selective and moderate, version of scientific realism I advocate with two particular examples, the gravitational field and the crystalline spheres of ancient astronomy. Are we entitled to accept that the sun is surrounded by a real gravitational field13 g, the Schwarzschild solution of Einstein’s field equations? The metric g represents, according to the general theory of relativity, both the gravitational and the inertial field. The metric determines the geodesics, which are at the same time the straightest (along which parallely transported tangent vectors stay parallel) and the extremal — longest 14 - paths. These paths are not only the trajectories of free (submitted to the sole gravitational field) particles, but are also the extremal paths marked by the behaviour of metrical devices (clocks): the affine and the metrical structures coincide. The distinction between geodesics and other paths is an objective feature, i.e. invariant under the wide group of continuous transformations15 . Physically, this means that any observer, whatever its state of motion, who explores a sufficiently large region of spacetime will detect the presence of the gravitational field. Although the affine connection can be cancelled out locally by means of an adequate (and non-linear) transformation of the coordinates, there is no way to annihilate a non-

13 One

often refers to g as the field. But the field is actually represented by the affine connection Γ and g is the gravitational potential. The components of the affine connection are expressed in terms of derivatives of the components of the metric. 14 They correspond to a maximal proper time. 15 It is possible to give a “coordinate-free” formulation of the metric g. See for example Friedman (1983).

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uniform gravitational field in any finite region of spacetime16 . Particles, and generally bodies, moving along paths which are not geodesics will experience some deformations (just as water in Newton’s rotating bucket) or will manifest other phenomena which may be called “inertial manifestations” (We want to avoid the expression “inertial effects” which would seem to imply some sort of causality. Only functional, mathematical correlations are at stake here). We can then apply the criterion of existence to the field g. It is indeed connected with observable manifestations in agreement with “inductively” well-established mathematical laws, like the law for geodesics17 . A spacetime can then be considered to exist to the exact extent that we can accept the existence of the metrical field in some region (notice that this argument doesn’t warrant the belief in the existence of a continuum of points). Let us now examine an objection that can be directed against our realistic conception of the metrical-gravitational field. This objection relies on the possibility of formulating equivalent descriptions of the same observations. If another (“non-normal”, according to Reichenbach’s terminology) definition of congruence18 is used, we can account for the same inertial phenomena by using another metrical structure. In that case, however, the inertial and metrical structures do not coincide anymore. The trajectories of free particles are no longer geodesics and extremal paths are no longer the straightest lines. Everybody, including constructive empiricists like van Fraassen, will prefer the “model” corresponding to the normal definition of congruence, since it is simpler and more integrated. The antirealist will nonetheless refrain from attributing a reality to the simplest model which was chosen for purely practical reasons. What could the realist reply to this powerful objection? Notice first that equivalent descriptions can also be provided at the level of everyday experience. Let us suppose, to take over one of van Fraassen’s examples (1980, p. 19), that we observe the following phenomena: cheese disappears, scratches are heard in the wall, hair is found on the floor, etc. From these phenomena, the existence of a mouse is established. Since mice are observable entities, the assertion of the existence of a mouse on the basis of experience, according to van Fraassen, is legitimate: at the level of phenomena, empirical adequacy is tantamount to truth. With a little luck, one could observe the mouse “directly”, but this would only enlarge the amount of empirical evidence in favour of the existence of

16 For

more details on this see Ghins and Budden (2001). can be found in standard textbooks, like Sklar (1974). See also Ghins (1990). 18 This would involve an, at least partial, change, in the empirical meaning of the word “congruence”, but I leave this (already widely discussed) issue aside here. 17 Details

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a mouse and would not bring in any evidence of a different sort. I am not claiming here that the existence of the mouse explains the presence of some observations and that this explanatory role gives support to the assertion of existence19 . On the contrary, the observations, and the more numerous and various they are the better, give support to the assertion of the existence of the mouse, irrespective of the (perhaps disputable) explanatory value of the fact of its existence per se. But we could give the following equivalent description as well. Instead of saying that there exists only one mouse, we can posit the existence of different entities which we may call mouse1 , mouse2 , mouse3 , etc. Mouse1 eats cheese, mouse2 scratches the door, mouse3 looses hair, etc. Someone may point out that you may see the mouse eat cheese and loose hair at the same time. But then you may say that mouse4 performs both tasks. This seems highly artificial and Ockham would find this unacceptable, but it is logically and empirically admissible. In fact, we are not obliged to suppose that the same mouse perdures in time and performs these various actions. We can formulate an empirically equivalent description that resorts to a plurality of mice. If the constructive empiricist accepts that the (unique) mouse exists and that empirical propositions about this mouse are true, it seems that he or she has no reason to deny that a unique entity, the gravitational field, is at the same time responsible for both metrical and inertial phenomena, instead of assuming that there is an affine connection, associated to inertial phenomena, and a metric, associated to metrical devices. Moreover, a spacetime geodesic is surprisingly easy to visualize: just let a pen drop on the floor, it will follow an inertial and extremal path in spacetime. Admittedly, we can, as we saw, restrict the existence of a tree to the times when it is actually perceived. (We can also go further and posit the existence of a plurality of entities : tree1 , tree2 , tree3 , etc.). But if the existence of the same tree during some time is conceded, even when it is not actually perceived, then it seems that we have no reason to deny that the gravitational and metric field is real. The assertion of the existence of this field is supported, in an immediate and natural way, by its observable manifestations at arbitrarily chosen spacetime locations and the truth of this assertion implies the truth of counterfactuals like: if I put a (free) particle at this or this place, it would follow this or this path. As far as crystalline — transparent and hard — spheres of ancient astronomy are concerned, we must first notice that, although not visi19 For a critique of the vindication of scientific realism by means of the ‘no-miracle argument’, i.e. inference to the best explanation of the success of science, see Ghins (2002).

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ble, they were not unobservable in principle since a possible cosmonaut would hit on them (if they existed). But their hardness was not represented by a mathematical parameter connected to specific observations by means of invariant well-established mathematical laws. Crystalline spheres, even at the time of Ptolemy20 , failed to comply with our criterion of existence. It could be perhaps retorted that, according to our criterion, the circles and epicycles of Ptolemaic astronomy could be legitimately asserted to be real. But the parameters characterizing those circles (radius and angular velocity) were not connected to observations in a clear-cut and well-established manner (Gardner 1983, p. 207-210). On the other hand, the geometrical trajectory — resulting from various possible combinations of circles the existence of which is indefensible (underdetermination is present here) — actually followed by a planet can be asserted to exist. The geometrical trajectory empirically marked by a planet has a different status from a purely geometrical figure, since it is not like a circle drawn on a blackboard. The latter exists spatially “all of a piece”, so to speak, whereas the former is successively and temporally actualised by the planet and could be said perhaps to exist “all of a piece” in spacetime. It can be objected further that Ptolemaic astronomy is false anyway and has been replaced by Keplerian, Newtonian and finally (up to this date) by Einsteinian astronomy. To this I reply with the well-known approximation arguments. Suppose I say that this soccer ball, as I perceive it, is round. Somebody could challenge that contention by pointing out that the soccer ball is not exactly spherical but is closer to an ellipsoid, or that its surface is slightly irregular. Would this falsify my previous assertion ? In a sense, yes, if the ball is not exactly round. But, on the other hand the truth of the assertion “This ball is round” is acceptable in most circumstances. I am ready to concede that truth is relative to some precision requests that are usually left vague in ordinary contexts21 .

4.

Conclusion

Let me conclude with a few remarks. First, as we saw, the acceptance of the existence of an entity does not involve any commitment to the belief in its existence “in itself” with the properties we attribute to them. The acceptance of the truth of a statement does not commit one

20 Whether Ptolemy himself believed in solid spheres or not is a controversial issue, but Adrastus of Aphrodisias and Theon of Smyrna did (Duhem 1969). However, we are not concerned here with what they actually believed but rather with what they were entitled to believe. 21 This notion of approximate truth is also discussed in Ghins (1992).

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to the belief in the existence “in nature” of some state of things that makes the statement true, nor to his unrevisable and absolute truth. To that extent, the realism advocated in this paper is moderate. Second, we are not allowed to accept the truth of all statements of currently accepted scientific theories. For example, we cannot accept the truth of statements about the global topology of the universe since empirically indistinguishable but non-isomorphic spacetimes with distinct topologies occur in the framework of Robertson-Walker cosmology (Glymour (1977) and Malament (1977)). (It may be pointed out however that current “standard” cosmology is far from being well-established). Thus, the brand of scientific realism we favour is selective. Third, in the same way as objectivity comes in degrees, reality also comes in degrees and is proportional to the size of the invariance group. The same line of reasoning was followed by John Locke (1690) when he defended that primary (geometrical) qualities belong to the things themselves, while secondary qualities (colour, texture, smell, etc.) depend on the interaction of the objects with our sensory organs. Geometrical qualities (shapes) are, according to Locke (1690, Book II, §19), invariant under a larger variation of observational conditions than secondary qualities (like the colour of porphyry). I do not want to maintain that any property or quality, be it mathematical or not, belong to the things “in themselves” and to endow some privilege to mathematical properties on this respect. I only wish to say that a physical, theoretical, mathematically represented entity is more real than another to the extent that it is more invariant. For example, in the theory of general relativity, the scalar curvature of spacetime is more objective, and real, than the velocity of a particle in some reference system.

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