Einstein, friend or foe of Rationalism?

By ‘Rationalism’ here it is meant the view that we can figure out truths about things in the world through application of reason alone, without learning those truths from experience.

Rationalism is obviously connected to the possibility of what is usually called ‘a priori knowledge’, but it seems to me is better put simply in terms of understanding. I mean, it seems much better to say that we understand that whenever there are two things there is one and one more thing (and vice versa), instead of saying ‘we know a priori that whenever there are two things there is one and one more thing (and vice versa)’. Though, ‘understanding’ has the problem that we mean other things by it, like understanding a sentence, etc… But, seems to me instead of trying to figure out another word because of possible ambiguity, it will be much better to figure out why is ‘understanding’ used in both situations? Does it mean the same thing in both situations, or is it family resemblance thing… something else maybe? OK, I went on a tangent here.

Cut to 18th century, and Kant’s phenomena… Kant started Critique of Pure Reason from the point of rationalism, by asking – ‘How are a priori synthetic truths possible?’, and he included claims of math, geometry and physics in those truths. Now, Kant’s view is somewhat specific because those claims which we can know a priori are not supposed to be about the world ‘in itself’ (or “noumena”), but should only be true about the things as they appear in our experience of the world (employing what I called bad sense of ‘experience’, the sense that is still used today in philosophy), or the so called ‘phenomena’. But nevertheless, things like math, geometry and physics ARE the things over which rationalists and empiricists would tend to disagree, so I think it is non-problematic to say that Kant’s view is rationalist on those subjects.

Of course one can be rationalist about math, but empiricist about physics. And most of the discussions of possibility of a priori knowledge seem to be over the possibility of intuiting (yet another word used because of the ambiguity of ‘understand’) truths in math or logic. The idea (present in Kant) that one can intuit physical laws is probably seen as one of those ‘solved questions in philosophy’ that Richard of Et. Cetera was talking about some time ago. So, if Rationalism is to be taken as a more general stance that will include not just math and logic, but also physical laws, it is apparently dead.

As one thing which shows that our intuitions are not proper guides to how the world is, often it is pointed to the two most known physical theories of the 20th century, those of Relativity and Quantum Mechanics (QM), each of which, it is said, tell us truths about the world which are ‘unintuitive’.

Note: ‘Unintuitive’ is used often to mean that things are not as we expected. But, ‘going against expectations’ won’t really do as a claim against Rationalism. Given ‘naive thinking’, even in math one could be surprised by the fact that a square with sides twice longer will have area four times bigger (or one can be surprised that when you have multiple numbers to add, the sequence in which you add them doesn’t matter). But, for sure, this doesn’t show anything against rationalism about math. Rationalism wouldn’t claim that any idea, or any expectation (however shallow is the thinking it is based on) will be true about the world. On contrary, it will claim that only one is the real understanding, but that there is very big (even infinite) number of mistakes to which one can come through thinking or applying analogy, association etc (as sometimes it is said that something is unintuitive also if it goes against what we expected based on some analogy we applied based on experience). So when pointing to Relativity and QM, and against Rationalism, ‘unintuitive’ has stronger meaning, that not just that nobody expected it, but that nobody could expect it base on reasoning alone. (On first look there seems to be even stronger meaning of “unintuitive”, where it is to mean that the truths of Relativity and QM are simply incomprehensible, and that most we can do in forming an idea of those truths is in some positivist/ pragmatic/ instrumentalist way. But, I will try to explain later, why I don’t think this goes against Rationalism.)

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So…, back to the general topic. Kant gave few claims about the space and time, said that these were synthetic a priori truths. Einstein came and provided the theories of Relativity, which made also testable claims (more on this later), but which went against the Kant’s claims. And because the measurements were more inline with Einsteinian theory than with Newtonian/Kantian one, it is pretty safe to say that Kant was wrong. Those supposedly synthetic a priori truths, which were supposed to transcend all possible experience, don’t really do so. So, if all rationalists were to agree with Kant’s claims – if all rationalists said that they did in fact intuit the same truths that Kant ‘intuited’, this would really spell death do Rationalism. But all is not that bleak.

We can turn the whole thing upside/down and make Einstein a friend, instead of a perceived foe of Rationalism.

First let us relate to the thing that was already mentioned in the note up there – the idea that the theories of Relativity (and QM) can only be understood in instrumentalist /positivist/pragmatic way. This assumes that besides this one, there is yet another way in which we can understand notions or relations of notions present in those theories, but that this way (whatever way it is) doesn’t work here. The neat thing a rationalist can do here is this – she can deny that there is something else which is meant when we talk about space, time, movement and quantities of those, and which is unrelated from the measurements of those we can make.

And given that we made this step, she can then point to a)the development of theories of Relativity and b)development of empirical predictions of those theories. As for (a), she can say that the theories were developed in an a priori manner based on couple of premises (invariance of physical laws from the movement of observer and constant speed of light). Being a rationalist, of course she will claim that any logic and math which are included in the reasoning are also a priori. And the rationalist can say the same for (b). That is, the predictions of the theory are good, only if they are to follow from the theory, and for them to be able to “follow” we need a priori relation. Thinking of it, (b) and (a) are instances of the same process. Starting from something which is taken to be true, new truths are deduced about the world (though they don’t include just mere logical and mathematical deduction, but also conceptual cleaning up, in relating the notions like space, time, movement and acceleration to our measurements). And for sure there will be some empiricists, which will not have problem of this. Mostly those who don’t have problem with math and logic being a priori. They will say – Well, yes, trough thinking we can get to new truths about the world, like Einsteinian relativity, but we shouldn’t forget that we have those starting premises (invariance of physical laws on movement of the observer, and the constant speed of light), to which we came through empirical research. So, that (a) and (b) were a priori, though impressive, isn’t enough for the claim of Rationalism. Let’s call this Objection One. There is also another objection, which we will call Objection Two, and that will go like this: We know that General Relativity (GR) is contradictory with Quantum Mechanics, and QM has been more empirically confirmed than GR. And while QM might not be the whole truth, GR can’t be the ‘whole truth’ also. So, GR as it is now is wrong. Hence Rationalism, even if one does away with Objection One, is wrong. And of course, there is the another kind of empiricists, that don’t believe in any a priori understanding, be it math, logic or wherever. I’m not attempting to show that empiricists view is irrational however, so I won’t give objections to that view. The goal here is much more smaller (and sounds funny) – pointing that Rationalism is rational (given the GR and QM).

Objection One: While the process of going from the premises to the theory and predictions is a priori, the premises (invariance of the laws from the movement of observer and the constant speed of light) are themselves result of the empirical research.

Now, I think that for the first premise isn’t implausible that someone could argue for it on a priori base. I won’t try to do it here, but it seems to me that invariances/symmetries present rather easy target for Rationalism. I hope that empiricist would agree at least that the invariance claim is not obviously empirical. The other premise, that of constant speed of light, is the problematic one for the Rationalism. However I think it can be dealt with, given that we make the mentioned move, to deny that we can properly think of space and time as entities, but only through the idea of measurements of those (which is, I would claim a Hegelian move – seeing time and space as abstraction from richer notions like that of change, and further of thing. I wrote about this in other posts, and I think it is important to show that this rationalist ‘response’ isn’t ad hoc, but has roots in the direct philosophical responses to Kant’s ideas. Not to mention that it may be related to Aristotelian responses to Zeno, that also go into direction of seeing positions in space and time as abstractions (or potential measurements)). The rough idea would be then this:

When an observer X moves from A to B, the observer will be at A before being at B. Observer to be at A before being at B, means that there will be possibility of quantification of time between X being at A, and X being at B. The time, measured from X, can never be 0, (even for ‘jump’, it can’t be 0 if we are to distinguish jump from A to B, from the jump from B to A, or alternatively we need to accept that X can be both at A and B at same time). Anyway, T as measured by the observer, can’t be 0, but given bigger and bigger speed, T can become smaller as much as we want. Given the distance AB, and traveler’s measurement of time, and calculate traveler’s speed St as AB/T, we will come to see a priori, that the speed St is not limited, but that it can’t get to infinity.

How will this look from third person measurements? We empirically know that what I described as impossibility for X to travel with infinite speed from A to B, from third person perspective is seen as an impossibility for X to travel with speed equal with the speed of light. However, given the first premise – invariance of the laws, and relations between the measurements of time and space among observers traveling with different speed, it is not implausible that one can translate that a priori impossibility to the one we know on empirical basis, and from there come to the conclusion that this limit is constant even for different observers. Now, I don’t know how this exactly would be done, but just so to support plausibility of the proposal, I can point to few places on internet, that seem to go in the direction of a priori deduction of Special Relativity written by people that seem to know much more on the topic than me (here or here).

Let’s turn now attention to Objection Two. The objection was that General Relativity is incompatible with QM, and QM tells us many truths about the world (empirically confirmed to great amount), so even if we expect that some new theory will take place of QM and GR, it means that GR doesn’t tell us *the exact* truth about the world.

The Rationalist response to this one is pretty easy. The claim, that the rationalist will say we come to through reason alone, is in the following form – If f is true about some X, then g is also true about that X. So, it is ‘universal claim’, and g will be true about X just so much as f is true about it. So, in terms of Relativity, because it deals with simplifying abstractions (among other things – dimensionless points of mass, if I remember right), the resulting laws of the theory will be true just so far as we can ignore other properties of things, and take them as dimensionless points of mass. One can make an analogy with math claims. For example… we can treat the shadow that a big building throws on the ground, the building itself, and the “line” which connects the top of the building and the most distant point of the shadow as forming a right triangle. And more so, we can treat that triangle as similar (having same angles) with any such “shadow triangle” formed by some smaller thing in the same time, in the same place (e.g. a stick sticked vertically in the ground) . And on base of the mathematical laws of similarity, and measuring only the shadow of the big building, the shadow of the stick and the height of the stick, we can figure out the height of the building. (Wasn’t it some Greek philosopher/mathematician who figured out the height of the Pyramids in Egypt like this?). Anyway, this is of course not *the whole truth* about the height of the real object, but it is only true in the terms of the a priori truth – For two similar triangles a1/b1=a2/b2; and us being able to treat for pragmatic purposes two systems as similar triangles. So, in same way, theories of Relativity can be a priori, and still not be “the whole truth”. (I guess the mathematical idea of limits also is important here)

I concentrated here on the theories of Relativity, in the context of more general question of Rationalism, and it’s possible “revival”. This of course is not enough. The other main ‘theory’ of the modern physics, that of Quantum Mechanics, also should be included. But, in the light of Rationalism going into “instrumentalist/pragmatic/positivist” direction, and the QM dependence on such things as invariances and symmetries, Rationalists, I think, have a right to expect that QM might show also ‘signs of apriority’.

UPDATE (Mar.31): corrected some mistakes, and rephrased few things.