immanentism and transcendentism of physical theory

Like Newton, Einstein held that physicists study what is physical, and find within the formal apparatus used in its description some elements that remind them of geometrical theory.  Einstein in fact  entertained some radical doubts concerning whether geometrical theories would continue to prove themselves availing in the science of physics.  But up to the present time at any rate, physicists have found among the features of the total structure that they are describing dimensionality, continuity, connectedness, etc., familiar from the science of geometry.  Some of these features, to be sure, are “geometrical” only by dint of the past broadening of the scope of that science.  The metrical structure for example that physics describes to us, fails to respect the classical condition of positive definiteness.  Whereas classically we think that the magnitude of the separation of any two things is non-negative, and zero only if the two things are one and the same, this condition is not respected within modern physical theory.  Moreover, classically we think of metrical structure as homogeneous, that is, everywhere the same, yet this too is not respected within modern physical theory.  Still, because geometers themselves had seen fit to relax the conditions of positive-definiteness and homogeneity, because the structures that the geometers themselves were thus led to survey were sufficiently like classical geometrical structures in other formal respects still to be thought of as geometries, the aspect of physical structure that is formally rendered as an inhomogenous non-positive-definite metric, can still be called geometrical structure.  According to Einstein, we then identify that part of physical theory, as our theory of space and time.  But really that part of physical theory, fits with the rest of physical theory seamlessly.  And that part of physical theory is, moreover, no less subject than other parts, to thoroughgoing reconceptualisation and correction if such becomes called for as a condition for theoretical physics to progress.

Conventionalists about spacetime structure have long (and thoroughly, and no doubt really very successfully) explored the fact that spacetime doctrines connect seamlessly with the rest of physics.  For many conventionalists, the purpose of this work is to warrant the conception that spacetime structure is merely immanent in material goings-on.  Their view seems to be that conventionality signifies immanence.  I believe however that this view is groundless.  It is true that in the most measured understanding of spacetime there is a kind of conventionality.  There is something stipulational, and a stipulation is partly conventional.  What is stipulated can have regard however for idealised phenomena rather than just the actual material goings-on.  And when this is so it would be wrong to think that conventionality signifies immanence.

Opponents of conventionalism mostly hold that spacetime structure transcends material goings-on, i.e. that spacetime structure is prior to such goings on and in its form helps determine their form.  In other words, spacetime structure should be thought an explanation for, not merely a way of representing, various patterns which physics notes within the material goings-on.  Defenders of this point of view consider the spatiotemporal structures that are needed before the patterns which physics notes can be represented, and they question whether immanentists are able on their own methods really to lay hold of these structures.   Thus this traditional way of opposing conventionalism is essentially realist.  It holds that spacetime structures are objective, precisely because they possess an independent reality.  The warrant for postulating them is that they are needed as an explanation for physical phenomena.  The target of this traditional response is less conventionalism per se, than its associated immanentism.

Immanentism about spacetime structure opposes transcendentism also in the debate between relationalists and absolutists.  Relationalism as a thesis about the ideology of spacetime theories is scarcely any other than the thesis of immanentist conventionalism.  Relationalism as a thesis about the ontology of spacetime theories is however a distinctive position from this.  Absolutists oppose ontological relationalists about space or time or spacetime by positing space or time or spacetime as an independent existent.  The warrant for the posit is supposed to be that it alone best allows one to explain what we see.  According to the absolutists, the relationalists are quite without the wherewithal adequately to explain observed phenomena.

When Einstein commented that spacetime is a “structural quality of the physical field”, he showed, as it seems to me, how to hit the line between immanentism and transcendentism, rather than siding with one or the other.  This middle position follows given the methodological demand to add nothing further to the doctrine of spacetime than is required to comprehend the facts of materiality, yet also to include nothing less.  It is, in short, if it can be made out, the most measured understanding possible of spacetime structure.  It is neither an explaining away of spacetime structure in terms of other facts of materiality, nor an explaining of other facts of materiality in terms of spacetime structure.

To understand this middle position, it is important to see why Einstein’s “structural quality” idea is epistemological.  This is because Einstein’s doctrine of spacetime structure is in its way stipulational.  Einstein denied that spacetime structure should be thought a separate explanation for patterns which physics discerns in material goings-on.  He complained forcefully against the idea of spatiotemporal structures being the cause of any such patterns that we meet with.  His most-measured understanding of spacetime structure was thus not transcendist in any way.  Nevertheless it idealised, since its stipulated coordination of spacetime concepts was not to actual measurement operations, but to physical laws, specifically those found in the rest of physics.  It was not at all immanentist, just as it was not at all transcendist.

DiSalle on spacetime theory as physical geometry. 

I have carefully expressed myself in terms consonant with Robert DiSalle’s recent and insightful treatment of spacetime theory as physical geometry.  DiSalle discusses the stipulational yet empirical nature of the sorts of coordinations to physical laws of geometrical concepts like ‘length’ and ‘rotation’.  He concludes from his discussion that the nature of spacetime is a question, not of whether a theoretical entity provides a causal explanation for appearances, but of whether the physical processes of measurement conform to geometrical laws.  ... To claim that space is Euclidean only means that measurements agree with the Euclidean metric; Euclidean geometry, if true, can’t causally explain those measurements, because it only expresses the constraints to which those measurements will conform.  This clearly does not imply that the content of spatial geometry somehow reduces to measurement operations.  For Euclidean geometry systematises those measurements and exhibits them as aspects of a formal structure, something more abstract and more exact than the appearances could express by themselves.  To claim that that formal structure is really the structure of actual space, is not to posit an underlying cause of the appearances.  It is only to claim that, modulo the initial coordination, the appearances conform to the laws of that structure.

In my own view this passage points to a middle ground between conventionalism and realism, relationalism and absolutism, immanentism and transcendentism. Einstein’s philosophical development was complex, and I hope to remark some of its complexities in a moment.  But Einstein’s mature position was, I believe, clear.  It can, by a close paraphrasing of DiSalle’s remarks, be stated as follows.  Einstein coordinated to his own field equations of general relativity theory the various geometrical concepts, in such a way that spacetime is stipulated to have a structure depending, in just the ways specified by those laws, on the distribution of matter-energy. 

... To claim that spacetime is this structural quality of the physical field, only means that measurements agree with the relevant metric; the relevant geometry, if true, can’t causally explain those measurements, because it only expresses the constraints to which those measurements will conform.  This clearly does not imply that the content of spacetime geometry somehow reduces to measurement operations.  For the relevant geometry systematises those measurements and exhibits them as aspects of a formal structure, something more abstract and more exact than the appearances could express by themselves.  To claim that that structural quality of the physical field is really the structure of actual spacetime, is not to posit an underlying cause of the appearances.  It is only to claim that, modulo the initial coordination, the appearances conform to the laws of that structure.

In short, our spacetime concepts derive their content by being coordinated to physical laws.  Such coordination is stipulational, but then it proves its mettle in an empirical way.  This position is altogether on the line between conventionalism and realism.  It is not itself conventionalist and it is not itself realist, because it implies that the division between these positions cannot really open up.

Objections to this conception considered and rejected.

It may be objected that, because, in Einstein’s general relativity theory (GR), spacetime structure is itself dynamical, and because it assimilates gravitational phenomena to inertia, the account just offered of the status of spacetime structure will not work for it.  For, as is well known, GR implies that energy-momentum can be carried in the geometry of spacetime.  GR is both a local theory and a non-linear one.  It implies that there can be gravitational waves, as massive as all get-out.  It implies, in its way, that gravity itself gravitates and to this extent presents itself to us as something itself real.  Yet the position that I have outlined seems to deny reality to gravity, which it assimilates to a stipulated inertial structure, to stipulated ways in which various concepts concerning trajectories etc. will be used.  What can it say, then, concerning the case where, as we might say, a massive gravitational wave disturbs things?  What can it say even concerning the planets in their motion about the sun?  For because GR is a local theory, the planets cannot be supposed to take their marching orders, as it were, from the sun.  They move inertially, and so ¾ as proponents of GR generally explain things ¾ they take their marching orders from what is local to them, viz., the local geometry of spacetime.  Do these considerations not heap reason upon reason to treat spacetime as something in its own right real?

Without a doubt, Einstein himself sometimes chose ways of talking which imply that they do.   Yet the mooted standpoint is also one which Einstein overtly resists, for example in his maintaining as he did his professed determination to understand spacetime as a structural quality of the physical field.  To appreciate Einstein’s position I believe that one needs to remark two further features of GR, first of all that it directs itself beyond an efficient-causal to a more purely formal mode of comprehending the facts which it embraces, and secondly, that it is quite evidently not a final theory, but rather quite evidently stands in need of further generalisation and refinement.

Why do the planets fall about one another and the sun the way they do?    This question seems to demand a causal answer, but I believe that it actually is a mistake to give it one.  To some extent the question should be resisted as ill-formed, for it is not even clear that falling is actually something that the planets do.  The question in front of us strikes me as similar to the following: why are the planets spaced?  That is to say, why do they take up positions outside one another, in a richly geometrically structured array of such positions?  There are two things to note about the question why the planets are spaced, each of which in my view makes it like the question why the planets fall about one another and the sun the way they do.  First, it is problematic whether the planets are spaced.  We in fact have learned that, absolutely speaking, they are not — that is, it is only in a reference-frame-dependent way that the planets are spaced, and what is absolute are arrangements that are ineluctably spatiotemporal.  And second, it is best not to view the question of why the planets are spaced, even insofar as we take this question to be well formed, as seeking knowledge of a cause.  That the planets are spaced (to the extent that they are) concerns simply a formal feature of physicality generally.  To the extent that it is either necessary or possible to understand it, the understanding of why the planets are spaced will be formal rather than causal.  The planets are spaced (to the extent that they are) because that is an aspect of the form that physical reality in general takes.

Why then, do the planets fall (to the extent that they do) as they do about one another and the sun?  This question deserves, in my view, an identical answer.  It is appropriate to correct the question as well as answering it.  And the answer is not in terms of a cause, but rather in terms of something formal.  Precisely by the trajectories of the planets being as they are, a certain formal, geometrical condition is satisfied.  It is a mistake, I believe, to say instead that the planets move as they do, because they are caused to do so.  It is a mistake to think that they pick up marching orders from anything, either the sun or the local geometry of spacetime.  The motions are as they are for formal not causal reasons.

I accept that something more does need to be said.  I cannot just say that a certain formal, geometrical condition is satisfied, and leave it at that.  There is still something further to explore, concerning — in some sense — why this condition is satisfied.  For GR does not allow us to understand inertiality itself.  And to this extent the understanding from GR of spacetime structure is less measured than we need it to be.  In merely invoking inertiality as it does, GR is a bit more like an inference to a metaphysical explanation, and a bit less like a formal understanding that has been deduced from phenomena, than would be ideal.  Note however, that the question why there is inertiality, itself need not be directed towards delineation of a cause.  Einstein himself expected that by comprehending electromagnetism structurally, just as he had already comprehended gravitation structurally, he would be led to an understanding of inertiality itself.   That is to say, Einstein expected that he might discover a formal rather than causal explanation for inertiality.  It was by a generalisation of the kind of (purely formal) understanding met with in GR, that Einstein hoped to understand what inertiality itself is.

I have argued that the most measured understanding of spacetime involves something less than transcendentist commitments.  For this reason I believe that on the most measured understanding of spacetime, it is impossible that spacetime structure should be a cause of anything.  What then can I say concerning the physical disturbances which would register the arrival of a massive gravitational wave?  I think that it is actually not difficult to give an account of this.  The concepts concerning trajectories which I say are merely stipulated, must also, I say, prove their mettle empirically.  To stipulate in the way encouraged upon us by GR is to imply that, potentially, there can be complexities in local inertial structure, complexities which may aptly be described as the local passing through of a gravitational wave.  To accept GR is to stipulate uses for the terms in which we reckon inertiality in a way which implies a kind of non-linear deformability in inertial structure.  To this extent, to accept GR is to accept that “gravity gravitates”.  Yet — as Einstein himself forthrightly insisted — GR in no way faces us with a hidden cause for physical events, but directs us rather to a general formal feature of them.

 Einstein confused about his relationship to Newton.

Newton is usually taken to have held that spacetime is physically more fundamental than matter itself.  Prior to the work of Howard Stein, at any rate, the orthodox view of Newton was that he treated spacetime as structured in a certain way prior to there being any material things or processes in it at all, and that he simply started with a doctrine of spacetime structure, before he proceeded to a discussion of the physics of matter.  In fact, however, as Stein, and more recently DiSalle, have eloquently argued, Newton developed his doctrine of space and time in order to account to himself (with exceptional philosophical care) for the conceptual presuppositions of his dynamical principles.  Thus Newton in fact prioritised the physics of matter to the structure of spacetime.  Newton had, moreover, like Einstein, a very physicalised understanding of the status of geometry itself.  Newton had a profound understanding of the art of measurement, and accompanying this, a singularly clear and searching grasp of the relationship between physical theory and experimental practice.  In his doctrine of space and time, and in his work as a physicist generally, he can be regarded as having set an epistemological example which Einstein then very much followed.

On one level, the relationship between Einstein and Newton is complicated.  Einstein understood Newton to have been a poor epistemologist.  There seem to have been two conflicting reasons why Einstein thought this, both of them based upon an inadequate appreciation of Newton.  One reason was that Einstein supposed that Newton proved himself rather incautious epistemologically, rather too ready in his work to undertake the tasks of a metaphysician.  Another reason was that Newton, in Einstein’s view, was mistaken to think that epistemological caution is possible: theoretical conclusions cannot, he said, be directly “deduced from phenomena” as Newton claimed that they could.  The curious thing here is that Einstein actually very forthrightly urged epistemological caution himself and in fact achieved it in his own work precisely by employing the method of Newton’s which he said could never work.  (This fact about Einstein was first studied systematically by Jon Dorling.  Since then, in works cited among the references below, Clark Glymour, John Earman, John Norton, William Harper, Robert DiSalle, and my former PhD student David Gunn, have added to the case which can be made in its support.)  Moreover Newton was not the epistemologically incautious figure that Einstein supposed that he was, for he too employed the method of deductions from phenomena, just as he claimed to have done.  (Again Dorling was early to point this out, and Glymour and the others have added to our understanding of this.)  In particular, Newton never undertook in his work the metaphysical tasks which Einstein thought he saw there.  Epistemologically Einstein followed the very path that Newton had blazed, without realising however that Newton had been there before him.  Thus on another level Einstein’s relationship to Newton is simple.  They each developed essentially the same understanding of the way to be an epistemologically responsible physicist.  I have extracted above from this understanding an answer to my question, how can it have been epistemological, for Einstein to have held that spacetime is just a “structural quality of the physical field”?  And we have also seen that the way Einstein steered a middle course between immanentism and transcendentism, was also actually Newton’s way.

Newton in effect determined by a deduction from the phenomena of inertiality what his views must be concerning the structure of spacetime.  Significantly, however (as DiSalle has emphasised), Newton then located his conclusions concerning the structure of spacetime in the scholium to the e definitions.  The theoretical convictions which Newton had concerning space and time, essentially s tipulated what was to be meant by the terms he used to express these convictions.  Yet they were not the less empirical because this was so.  On the contrary, the proof of their worth was that, without them, sense could not be made of empirically based dynamical laws.

Newton’s method of deductions from phenomena was as I have acknowledged in all instances a fallible one.  Nevertheless, Newton employed this method in an extraordinarily exacting, epistemologically most-cautious way.  For first, Newton carefully restricted his theoretical starting points to a very few, just Euclidean geometry plus the three laws, or axioms, of motion.  Second, the very few theoretical starting points which Newton did employ were such that no-one in that day would have raised the slightest complaint against them.  They were, at least from the contemporary vantage point, as innocuous as any theoretical starting-points could be.  And third, Newton demanded of these theoretical starting-points that they could afford not only one but rather many and varied deductions from phenomena, all to highly consequential and thus multiply intersecting theoretical conclusions.  Newton’s method, because it was an exacting, epistemologically cautious one, very effectively eschewed the metaphysical largesse of inference to the best explanation on the one hand, even while it also avoided the impossible restrictions of an operationalistic empiricism on the other hand.  It was a method which combined the rationalist demand for unification with the empiricist demand that theoretical conclusions be induced from the evidence.

Moreover, Einstein himself followed exactly this method.  Einstein failed to articulate this method with as much care or accuracy as Newton did, and officially, of course, Einstein threw his support behind conjecture-and-refutation-type, i.e. inference-to-the-best-explanation philosophy of science.  Einstein, with Popper’s help, muddied the understanding of induction.  He falsely professed himself to be anti-inductivist.  But like Newton, Einstein’s method was in fact carefully to deduce from phenomena principles which he would then render general by induction.  He like Newton used induction, not naively, but in a way which cleaved simultaneously to the rationalist demand for theoretical unification, and to the empiricist demand for the evidence to lead the way.  And by working in this way, Einstein, like Newton, steered a middle course between on the one hand the laxness of inferring to something just because of the way it explains things and on the other hand the stringency of an excessively strict empiricism.

 Einstein’s “structural quality” idea tolerates very considerable scepticism concerning current spacetime doctrines.

When Einstein articulated the “structural quality” idea about the status of spacetime, he was working, as he believed, towards a “unified field theory”.  He was working, that is, as he believed towards a correction, as well as explanation, of his own earlier doctrine of spacetime structure.  It is important to consider how radically Einstein expected that a satisfactory theory of the unified field might correct general relativity theory.  For this shows that Einstein’s “structural quality” idea tolerates very considerable scepticism concerning whether the geometrical affections of the world are ultimate at all.

By some sort of generalisation of the structures which he had laid before us in the theory of general relativity, Einstein hoped to comprehend the electromagnetic force together with gravitation in a unified way.  Physicists at that time had no further forces yet in mind besides gravity and electromagnetism.  And Einstein had already comprehended gravity as inertia.  That is to say, within his general theory of relativity, Einstein had successfully assimilated gravity to the affine structure of spacetime.  Yet general relativity theory also very much heightened the importance of the question, what is inertia?  Whence arises a body’s tendency to travel the straightest path?  There were many reasons why Einstein expected that electromagnetic theory would ultimately yield the clues that are needed in order to answer this deep-lying question.  Once already within Einstein’s own lifetime, electromagnetic theory had yielded the beginnings of an understanding of mass or inertia — it had, in the late-nineteenth-century heyday of the so-called “electromagnetic world-picture”, come some way towards explaining, wholly electromagnetically, the resistivity to acceleration, that is to say, the inertia, of the electron.  Moreover, electromagnetic theory was already deeply implicated in Einstein’s theory of gravity.  For general relativity theory was a generalisation of special relativity theory, and special relativity theory described the kinematical conditions under which alone may electromagnetism respect the so-called principle of special relativity which mechanics respects, a principle which, in its way, structures the very notion of inertia.  Thus it is unmysterious why Einstein worked as he did, attempting to generalise general relativity theory into a theory of a unified field.

Einstein was at the same time of course profoundly aware of the “problem of the quantum”, which he had himself in large measure helped to discover.  Einstein in fact devoted himself from his earliest researches to the end of his life to studying and attempting to surmount the “deep-going opposition” in physics between fields and particles.  As a number of historians of physics, particularly Martin Klein, have helped to show, Einstein’s endeavour to surmount this opposition inspired really all of his great work. Whereas the quantum theory ultimately accepted as insurmountable the opposition which he had sought to overcome, Einstein had excellent grounds to think such acceptance stultifying: for in his own work, it was precisely the effort to overcome this opposition that had fostered all his great discoveries.  Nevertheless, Einstein had himself hugely contributed to the early development of quantum theory.  Moreover, the “problem of the quantum” exercised him keenly throughout his life.  As John Stachel has very nicely documented, this “problem” in fact led Einstein in his later years to entertain some very radical doubts concerning how he ought to conceive of the unified field.  In particular, Einstein doubted whether the mathematics of the continuum would ultimately prevail in physics.  Significantly, however, Einstein was not able, even for purposes of speculation, to make out at all successfully to himself what an alternative mathematical approach in physics would be like.

Einstein’s uncertainties about the continuity of spacetime were of course eminently reasonable.  Not only did he have the problem of the quantum to worry about, but also he like anyone else was without any adequate warrant for the idea that the universe is inwardly infinite.  This idea is for all we know perhaps not even mathematically coherent.  Indeed (from Gödel’s work) we know that it is mathematically impossible that we should know that the idea of the continuum is mathematically coherent.  Supposing that mathematically the idea does make coherent sense, however, we are in that case in coherent possession of the concept of infinity.  And in terms of this concept, we are bound to admit that, whatever the physical evidence, it is an infinite leap beyond this evidence it to suppose that the universe is inwardly infinite.  We might have good empirical grounds for thinking that differences out at an eleventh or twelfth decimal place are physically significant.  It is however an infinite leap to conclude from this that differences out at the ten-to-the-ten-to-the-tenth decimal place are physically significant, and so on, out as far as you please.  Thus, simple scientific caution helped make eminently reasonable Einstein’s uncertainties about the continuity of spacetime.  It was simply an additional reason for Einstein to doubt the continuum, that he hoped possibly to discover a better way to represent quantum phenomena by doing so.

It is I think a telling fact concerning Einstein’s “structural quality” idea that it tolerates even his uncertainties about the continuity of spacetime.  That is to say, Einstein could make out, in terms of this idea, how a scientist such as himself could employ, tentatively, a doctrine of spacetime structure, and yet remain agnostic on many questions, including indeed whether the world really divides into continuum-many bits (on which there literally are the differentiability etc. structures generally imputed to the spacetime manifold).  To say that a continuous spacetime structure such as that laid before us by general relativity theory is a “structural quality of the physical field” is simply to claim for it some measure of objectivity.  It would of course be ridiculous, in the face of the success of general relativity theory, to claim less for such structure than that it has some measure of objectivity.  But it is significant that Einstein was himself not willing to claim more than this.  Einstein doubted the true continuity of the field and so was open to the possibility that he would need to revise quite significantly the general conception of a field which he had inherited from his predecessors.  

In general, to say that something is a “structural quality of the physical field” is to claim simply some measure of objectivity for it.  It makes sense for example to think that gravity, although the very idea of it is not completely correct, comes out all right as a “structural quality of the physical field”.  Given an understanding in physics not actually any profounder than the one which Einstein gave us, we can of course appreciate some of the limits that there are to the accuracy of the very idea of gravity.  That is to say, we can see, in terms of a richer understanding, how to correct as well as explain this very conception of a force of gravity — as this conception occurs, for example, in Newtonian gravitational theory.  Yet as a “structural quality of the physical field”, Newtonian gravity clearly lays claim to objectivity, inasmuch as it is explained as well as corrected by superceding knowledge.  Likewise I think that there is little doubt that Kepler’s principles of planetary motion (though they stand in need of correction) concern a veritable “structural quality” of the material universe.  Likewise Maxwell’s theory of electromagnetism concerns such a quality, as does Coulomb’s theory of electrostatic attraction, and so on.  More or less limited “structural qualities” abound in physics, when you admit that they are what we thought they were only subject to correction.  Einstein’s “structural quality” idea is tolerant because it permits a healthy agnosticism concerning the extent to which any actual “structural quality” conforms to our present conceptions.  If however we have a theory which, like the theories of Newton, Kepler, Maxwell, and Coulomb, successfully “embraces a complex of phenomena” or is as we might instead say richly “bootstrap confirmed”, then it would be fantastic if it is wholly without objective significance.  Such a theory is going to concern in some way or other a structural quality of the physical field.  This is so even though the extent and nature of the theory’s claim to truth may remain significantly up for grabs.

Notice also that even if, in some sense, the programme of field theory itself proves mistaken, i.e. in need of fundamental correction as well as explanation, it could still be said that theories such as Newton’s or Maxwell’s describe structural qualities of the physical field.  For it is all right to use the concept of a physical field provided this concept possesses some measure of objectivity.  Yet it surely does possess objectivity in at least “some measure”.  As I have remarked, Einstein was fully aware that some (possibly quite thoroughgoing) correction to the field concept might ultimately be needed.

I hope it is clear then that Einstein could uphold his “structural quality” idea and be at the same time agnostic about many things.  In the face of this idea, it is unlikely that Einstein accepted a “scientific realist’s” sense of the commitments which a scientist assumes on accepting a scientific theory.  On considering, for example, his own best theory of spacetime structure, which was based upon the mathematics of the continuum, Einstein could say of it that it concerned some “structural quality of the physical field” without committing himself completely even to the need to describe this field with mathematics based on the continuum.

Evidently Einstein was modest in the commitments which he assumed on accepting physical theories, such as his own.  On Einstein’s own view, he was investigating a physical structure all right ¾ one which he called, perhaps roughly speaking, a field.  But Einstein also held that this physical structure may well be in undiscovered ways foreign to all present best conceptions.  So far as his theory of spacetime was concerned, Einstein committed himself to the following, and no more.  Among the structural features of the physical field are either dimensionality, continuity, connectedness, etc., which are familiar from the science of geometry, or at least something like these features, i.e. other features which would however explain the usefulness of such geometrical notions in our physics so far.  Wherever Einstein employed geometrical notions, he intended these to describe something physical ¾ and to describe what is physical in a way which might well require subsequent correction as well as explanation.  He therefore was certainly not investigating how to reduce what is physical to what is geometrical, nor was he committing himself to any more than the objectivity in some measure of what is geometrical.

Now, as it seems to me, these facts about Einstein show clearly that he would agree completely with Newton’s understanding of the relation of physics to truth.  Against the rashness, epistemologically, of making out truth as a metaphysical idea, Einstein like Newton would reflexively cleave to the most-measured point of view.  On such a view it would be irresponsible to assume commitment to any less than objectivity in some measure to structures laid before us in that present theoretical reckoning of things which is as measured as we can presently make it.  It would on the other hand be irresponsible to assume commitment to more than this.  Note how in this case Einstein agrees, quite completely, with Newton’s methodological understanding of truth.

 THEORY, PRACTICE AND THE STATUS OF SPACETIME.

People typically adopt not a cautiously methodological, but instead a fully metaphysical view of truth.  . Why this is is essentially because it takes great genius and a lucky choice of subject matter to discern the possibility of a most-measured, neither metaphysical nor merely instrumentalistic point of view.  Hitting the line between immanentism and transcendentism is difficult.  Few if any people in the world actually totally manage to do it.  It is I believe only in physics that, in science, this ideal is approached closely at all. Truth seems to us metaphysical because there is no way to reckon theoretically quite all the practical conditions that there are in order for our theories to have sense.  Thus we are inclined to view the sense which theories have as not relating purely to practice.  The failure of operationalism as a philosophy of science nicely illustrates for us the impossibility of reckoning theoretically every last practical condition that there is in order for theory to have sense.  Operationalism is the failed attempt to capture altogether completely in theory the connection which theory has with practice.

This impossibility has also been remarked in other ways.  Well-known arguments by Hilary Putnam in my view concern this limitation. If, per impossibile, a theory were to have comprehended in its own terms its entire relation to practice, then it would be something free-floating, and its truth (Putnam shows) would be automatic and therefore cheap. The really interesting element of Putnam’s argument is less the conclusion that truth would be cheap, than the hypothesis ¾ viz., of there possibly being a theory which had grown so perfect that it could comprehend in its own terms its entire relation to practice.  Truth is not cheap, and Putnam’s argument therefore demonstrates the impossibility of such a theory.  Still other arguments also demonstrate this impossibility.  In Lewis Carroll’s parable of Achilles and the tortoise, we learn that not all the elements of the practice even of logical argumentation are capturable within theoretical belief-structures. The parable teaches us to respect as insurmountable the separation of axioms from rules of inference.  A crucial way that the logician has of working, is in principle not capturable as just another theoretical element that the logician can profess.  It seems, therefore, that the impossibility that a theory should comprehend its entire relation to practice, reaches very deep; so deep, indeed, that we meet with this limitation even in logic.

In physics, a practitioner can come perhaps closer than is possible in any other inquiry to comprehending theoretically the theory’s own connection to practice. This is what has made operationalism a tempting doctrine in philosophy of physics, though, as we know, even in physics the doctrine of operationalism is not truly admissible.  Why physics has this special quality is, as I believe, that it is singularly able to achieve its insights by measurement.

Physics is a discipline within which, more than any other, ‘speculation’ functions as a term of derision.  Physics really expects its practitioners to walk the line between immanence and transcendence, and thus to eschew both the metaphysical largesse of inferences-to-the-best-explanation and yet also the sceptical excesses of an anti-realist empiricism.  I believe that only in physics is it remotely possible for practitioners to walk this line (and only the best of physicists can do it).  I believe that only in physics can truth be treated essentially epistemologically rather than metaphysically.

The point of these remarks is the following.  I think that, even if my discussion of spacetime is correct, nothing generalises from this concerning science in general.  In less lucky inquiries than physics is, and indeed in less lucky corners and interludes in physics, I suspect that speculation probably has much fuller purpose, and measurement much less.  Moreover in such other inquiries or such other parts or phases of physics, it sometimes pays to be antirealist.  It sometimes pays, that is, to muck around and see what can be done towards meeting the demand just for hypothetico-deductive empirical adequacy.  It would be just too ideal to expect practitioners in other inquiries to measure all the way in their work, and so walk the line always between immanence and transcendence conceptions.  Sometimes, I expect, an inquiry proceeds best when its practitioners assume the kinds of commitments which realists believe follow from theory-acceptance.  Sometimes, I expect, an inquiry proceeds best under the opposite condition, when its practitioners assume, say, commitment only to the truth of the empirical substructures, or what have you.  In the present article I have argued simply that, in the particular case of spacetime physics, neither the realist nor the antirealist gives the best account.  In the case of spacetime physics, the commitments which it is appropriate for a scientist to assume are, I have argued, on the line between immanence and transcendence.

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