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Are Space and Time Just Relations? On Early Modern British Relationists

Date:26 January 2018
Photo by erin walker on Unsplash
Photo by erin walker on Unsplash

When you walk to the shops, or take a train to Amsterdam, you are moving through space. From second to second, you are ageing in time. Yet what are space and time? Today, there are two popular answers.

‘Absolutists’ believe space and time are giant containers, filled with everything that exists: stars, trees, people. ‘Relationists’ believe that space and time are spatial and temporal relations holding between things: Cambridge is sixty miles north of London, the thunder boomed three seconds after the lightning. For the relationist, we live in a world intricately crisscrossed with space and time relations. This post focuses on relationism (see here for more on absolutism).

Pick up any introduction to the philosophy of time, or to early modern philosophy, and you will find just one historical relationist listed: Gottfried Leibniz. I dare you to find such a book naming any other historical relationist. I’ve never seen one. And yet my research on seventeenth and early eighteenth century British philosophy of time has found several relationists – two writing prior to Leibniz.

The fact that most books only mention Leibniz’s relationism leads to two problems. The first is historical: it leaves the incorrect impression that Leibniz was the only early modern relationist. The second is philosophical. Twenty-first century philosophers of time, such as Gordon Belot, sometimes turn to history to uncover the roots of relationism. If they are under the misimpression that Leibniz is the only historical relationist, then they are missing alternative relationist theories which might contain useful philosophical ideas. I want to spread the word that Leibniz’s was not the only early modern relationism.

Let’s start from Leibniz’s more familiar relationism, before striking out into less familiar territory. The details of Leibniz’s relationism are notoriously murky, but Leibniz is widely read as identifying space and time with the spatial and temporal relations holding between things. He writes, ‘Space… [is] an Order of Coexistences, as Time is an Order of Successions’. Leibniz compares spatial and temporal relations to genealogical relations, such as ‘mother of’ or ‘sister of’. He writes that just as genealogical relations ‘express real truths’, yet are only ‘ideal’ or mind dependent things, so too are spatial and temporal relations. A question for Leibniz’s system is which things spatio-temporal relations hold between. Do these relations hold between Leibniz’s immaterial monads, or between material bodies which somehow depend on monads and may themselves be ideal?

With this background in place, let’s turn to the work of three early modern British relationists: Isaac Barrow, John Locke, and Joseph Clarke. I’ll tackle them in chronological order.

Most scholars read Barrow as an absolutist, but I think Barrow is really a relationist. My reading is based on a passage in Barrow’s Lectiones Geometricae, lectures delivered in 1664–66 at Cambridge and published in 1670. These lectures discuss ‘modes of magnitude’. A mode is a way that something can be: a pear can be green and brown. By ‘magnitude’, Barrow is considering the quantity of material body in general. Roughly, a mode of magnitude is a way that body can be. Barrow writes that ‘contiguity’ is a mode of magnitude. To be contiguous with something is to be in contact or bordering with it; for example, two clumps of ice could be contiguous with one another. Importantly, a thing cannot be in a state of contiguity by itself: to be in this state depends on a thing’s relations with other things. Considered independently of its surroundings, a clump of ice cannot be said to be in a state of contiguity, as being in this state depends on its relations with other bits of ice. In contrast, two clumps of ice considered together can be said to be contiguous. Thus, this particular mode is relational.

Barrow goes on to describe a mode that is directly opposed to contiguity. For now, let’s call this ‘non-contiguity’. To be non-contiguous with another thing is to lack contact with that thing. For example, a clump of ice in space may be non-contiguous with a nearby asteroid. This mode of being is also relational. Barrow describes this relational mode of non-contiguity as ‘space’. So, for Barrow, space is a relational mode of magnitudes – space is relational. Similarly, I believe Barrow believes that time is a relational mode of magnitudes – the bodily mode of not existing simultaneously with something else.

While the fact of Barrow’s relationism is controversial, the early relationism of John Locke is not. Although there is very little scholarship on it, Locke’s 1676–78 journal entries explicitly defend relationism. Locke is crystal clear that space and time distance relations hold between bodies. Locke describes these relations as ‘real’, by which he seems to mean mind independent; in this, Locke agrees with Barrow and disagrees with Leibniz. Yet, in another way, Locke’s relationism is very different from how I read Barrow’s. On my reading of Barrow, space is identified with modes, with ways that things can be: a particular magnitude can be square, or red, or in a state of continuity with another magnitude. Locke’s relations do not modify things in this way. He tells us firmly that a ‘pure’ relation may hold between two things but it is a ‘distinct thing’ from both of them.

Leibniz began publishing in the 1680s, after Barrow published his lectures, and Locke authored his journal entires. It’s actually possible that Leibniz’s relationism drew on Barrow’s, as Nauenberg* has shown that Leibniz used other parts of Barrow’s Lectiones Geometricae.

Fascinatingly, Barrow may also be at the root of Locke’s relationism. As Rogers** explains, Barrow and Locke met in 1672, and Barrow gave Locke an inscribed copy of his Lectiones Geometricae.

Relationism continues to make appearances in British thought after the turn of the eighteenth century. In 1733, Joseph Clarke defends relationism, writing that space is an ‘imaginary Length of SPACE… a Relation the Bodies bear to each other’. As in Locke’s 1670s texts, distance is a relation; yet where Locke describes those relations as mind independent, Clarke describes them as mind dependent. Clarke’s position is much closer to Leibniz’s than Locke’s although, unlike Leibniz, Clarke is definitely a realist about bodies. A very similar position to Clarke’s is outlined by Richard Kirwin in 1806, who concludes a lengthy discussion of space by stating its ‘true’ and ‘obvious’ nature: ‘Space is nothing more or less, than the relation of two, or more, distant bodies to each other… relations are merely mental, but the objects related are real’.

Fast forwarding to the early twentieth century, relationism is defended by Bertrand Russell and C. D. Broad. Their historical relationisms are relatively recent, yet also poorly known.

I suspect non-Leibnizian relationists are akin to yellow cars. Once you spot one somewhere, you begin to see them everywhere.


*Nauenberg reference: 

(only accessible via university licences) 

**Rogers reference: 

(only accessible via university licences) 


Emily Thomas is Assistant Professor in Philosophy at Durham University. Her book on early modern space and time theories is coming out this spring. You can follow her on Twitter: @emilytwrites


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