The Theory Of Relativity: Anticipated At The Turn Of The Seventeenth Century By George Berkeley

by Philip Pilkington

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Bishop George Berkeley is, in my opinion, the most profound philosopher ever to have written. He came up with many ideas in the early modern period – that is, around the beginning of the 18th century – that were only integrated into modern science around the beginning of the 20th century. What is more, most Anglophone philosophy today still operates under notions that have been stale in scientific discourse since Mach and Einstein and which should have been overturned by Berkeley nearly four hundred years ago.

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Modern Anglophone philosophy, for example, usually operates under Kantian notions about space and time as a priori givens. Later in a philosophy course it is often admitted that Kant was operating in a Newtonian paradigm that has since been overthrown but this is simply a handwave; it is rarely, if ever, integrated into the teaching of philosophy. Thus Anglophone philosophy today operates in a strange slipstream: these philosophers at once know that absolute notions of space and time are incorrect but they nevertheless teach philosophy as if they were not.

Here I present a particularly clear exposition of the relativity of space and time as given by Berkeley in his seminal Three Dialogues Between Hylas and Philonous. In the dialogues Hylas is representative of Newtonian ideas together with a belief in the existence of matter whereas Philonous is representative of Berkeley’s position on the relativity of space and time together with an affirmation that matter does not exist. These two ideas are inherently tied up with one another.

In what follows I use a version of the Three Dialogues Between Hylas and Philonous that has updated it by translating it into modern English. Such a translation is perfecttly in keeping with Berkeley’s common sense view of how thought should be structured.

So, first let us turn to to the relativity of space. Here is the relevant part of the dialogue in full,

Phil: A tiny insect, therefore, must be supposed to see its own foot, and other things of that size or even smaller, seeing them all as bodies of considerable size, even though you can see them – if at all – only as so many visible points.

Hyl: I can’t deny that.

Phil: And to creatures even smaller than that insect they will seem even bigger.

Hyl: They will.

Phil: So that something you can hardly pick out because it is so small will appear like a huge mountain to an extremely tiny animal.

Hyl: I agree about all this.

Phil: Can a single thing have different sizes at the same time?

Hyl: It would be absurd to think so.

Phil: But from what you have said it follows that the true size of the insect’s foot is the size you see it having and the size the insect sees it as having, and all the sizes it is seen

as having by animals that are even smaller. That is to say, your own principles have led you into an absurdity.

Hyl: I seem to be in some difficulty about this.

As we can see, Berkeley overturns the idea of absolute space by reference to the fact that the world we experience is always based on our relative position within it. Thus the notion of space as existing ‘out there’ as some objective given becomes meaningless. In the appendice to his Relativity Einstein makes a similar point – although he wrongly attributes the overthrow of absolute space to David Hume. He writes,

Mach, in the nineteenth century, was the only one who thought seriously of an elimination of the concept of space, in that he sought to replace it by the notion of the totality of the instantaneous distances between all material points.

For more information on Mach’s theory of space the following article is a good summary. As can be seen his concerns are identical to Berkeley’s.

Let us now move on to Berkeley’s criticisms of the notion of absolute time. Again, I quote in full the relevant section of the dialogue.

Phil: Can a real motion in any external body be at the same time both very swift and very slow?

Hyl: It cannot.

Phil: Isn’t the speed at which a body moves inversely proportional to the time it takes to go any given distance? Thus a body that travels a mile in an hour moves three times as fast as it would if it travelled only a mile in three hours.

Hyl: I agree with you.

Phil: And isn’t time measured by the succession of ideas in our minds?

Hyl: It is.

Phil: And isn’t it possible that ideas should succeed one another twice as fast in your mind as they do in mine, or in the mind of some kind of non-human spirit?

Hyl: I agree about that.

Phil: Consequently the same body may seem to another spirit to make its journey in half the time that it seems to you to take. (Half is just an example; any other fraction would make the point just as well.) That is to say, according to your view that both of the perceived motions are in the object, a single body can really move both very swiftly and very slowly at the same time. How is this consistent either with common sense or with what you recently agreed to?

Hyl: I have nothing to say to it.

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.