Time And Space: The Difference Between Relationalism And Substantivalism

Reality is a concept often explored by philosophers through the study of space and time. Key to defining one of these key themes, space, frequently comes down to an argument about its very existence. Whether or not we are objects existing with and of each other or within the conceptually manifested idea of ‘space’ has been a hotly contested discussion in history throughout science, physics and philosophy. Encompassing these ideas are the theories of substantivalism and relationalism, and despite both being vastly different showcase a plethora of arguments accentuating their philosophy, whilst both having extremely contentious objections not fully solvable.

Although many of the objections can both be solved by superstantivalism, it will be proved throughout this essay that pure Newtonian substantivalism is the least quarrelsome and most sensical space theory. What is space in this essay? For the purposes of this essay when space is discussed specifically in substantivalism, it refers to a separate entity other than materials, objects or people. Ignoring arguments of whether it exists or not or arguments about temporal flow, we will assume that space exists outside of the mind and is real. Finally, space can be pictured like a hollow sphere, with the empty interior being filled with objects. Key to this is the idea that the area around the objects is an entity itself, being the concept of space. Inside this sphere the objects move around freely, manipulating the space but not hindering its existence. This dualist view of space and objects is the foundation of the space theory substantivalism.


Substantivalism argues for the existence of space as its own, in simplest terms, ‘thing’ in space theory, that being an entity with characteristics alongside objects. One of the main ways this is argued for against its counterpart relationalism is that substantivalism believes that if you removed all materials from the existing universe, space would still be existent independent of this fact. Originally put forth by Newton, substantivalism views space as a fundamental characteristic of spacetime discourse (Ray, 1991). This space theory is a much more logical and gives a simpler account for providing a sensical world for other defined theories such as absolute motion and inertia, explored later in objections to relationalism. Important to this theory is that by just including the possibility of existence of space allows substantivalism to dismiss plenty of relational arguments as that theory suffers most of its objections through its rejection of space as an entity.

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Objections; Leibniz argument

Before tackling relationalism however, substantivalism has some questions that need justification to be a solidified option as a space theory. Leibniz and his perpetuation of relationalism lead him to be the key disputant against substantivalism. His arguments centralise around the fact that if substantivalism be true, it preserves the idea that there is a “proliferation of possibilities” (Dasgupta, 2015). Inherently a side-effect of this in his argument was an immediate explosion of hundreds of eventualities because of this endless possibility ideal substantivalism proposes. How does it do this? Leibniz encompasses the argument through a multi-world theory. If there is a world 1 that has the exact same intrinsic properties as our existing one and then a world 2 that is the exact same bar taking place exactly 10 meters below that, the substantivalist would see this as a real difference (Dasgupta, 2015). Despite 2 and 1 having the same events occurring, they are in completely separate spatial regions, and substantivalism implicates that these shifted worlds can become infinite. Similarly, for an example of two worlds where the events unfolding at the same time, but one is travelling around the sun slightly quicker than the other, relationalism doesn’t perpetuate this possibility, but substantivalism promotes this possibility because there is a spatial difference in these worlds too (Dasgupta, 2015). Assuming endless possible worlds isn’t itself a problem, but Leibniz saw two reasons for this to be awkward for substantivalism.

First was his axiom for God making the world in any other way than it was, and of course any world that is similar to but not exactly our one contradicts this axiom easily (Khamara, 2006). Similarly, Leibniz’s second reason for thinking the “proliferation of possibilities” was troublesome for substantivalism is that all of these worlds in relationalism would be indiscernible. Again, this argument only stems from his own principle that no two objects can be indiscernible from each other.

Personally, Leibniz being a relationalist and using arguments from his own logic against the countering space theory seems weak at best but must be considered to help our comprehension going forward into our discussion of relationalism (Khamara, 2006). Despite its strong objections, it is useful to enhance our understanding of previous thinkers in this topic and opens the door to the discussion of superstantivalism as a middle ground for space theory.

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Relationalism is the complete countertheory to subtantivalism insofar as it negates any idea of space and doesn’t count it as its own entity, rejecting any dualistic theories. In this theory, space doesn’t exist, and all that we have to define space theory is the distance relative to objects. The best way to contrast the theories is imagine the same sphere from substantivalism and all the objects within it, then remove the sphere. We are only defining our space in this theory by how all these objects relate to each other, via distance and direction (Dasgupta, 2015). Patently, this theory elucidates how Leibniz’s multi-world theory doesn’t have a problem in relationalism, as all these worlds are the same as the objects are all the exact same relative to each other in world 1 and world 2 (Norton, 2018). Relationalism, through Leibniz’s shift argument covers more grounds for being possible and parsimonious in space theory but isn’t as logical and intuitive as its counterpart. And this is where its objections lie; scientific preapproved theories and Newtons famous bucket experiment.

Objections; absolute motion and the bucket argument

The first objection for relationalism is more of a pro-substantivalist argument rather than an anti-relationalist perspective. This is the argument for absolute motion. The premises for this argument go as follows;

  1. Relationalism only views motion comparative to corresponding objects, therefore there is no absolute motion.
  2. We know there is absolute motion.
  3. Hence, relationalism needs to disprove this, otherwise it is false.

Unfortunately for relationalism, absolute motion occurs often in day to day life. Most obviously when on a train, the inertia you feel as you a propelled forward whilst simultaneously pushed back on your seat. Although you are moving comparative to other objects, you are still solely acting in absolute motion. Feasibly there is merit in arguing premise 2’s validity, such as comparing the motion of you on the train to something not on the earth and claiming that this is what you are moving relative to (Hawking et al, 1973). Known as Mach’s principle where he uses fixed stars, this is easily disputable as you can argue for a world without this otherworldly object or claim this is too extraneous to be a rational argument. Expanding on this is Newton’s absolute rotation extension of the objection, centralised around his bucket argument. Again, being a case for substantivalism more than an outright objection to relationalism (but doing a thorough job of disproving it regardless), the bucket argument systematically explains how and why absolute space is indeed existent. Newton devised that the behaviour of accelerating bodies was a good example of proving substantivalism and formulated the bucket argument to prove his premise (Dasgupta, 2015).

The experiment involved hanging a bucket full of water with a rope and spinning said bucket. Starting with a flat surface, as the water begun to pick up speed and spin with the bucket, the surface area would dip and become concave. Even after stopping the bucket, the water would spin, and surface remain concave. As the bucket and water have differing instances such as a stopped bucket having concave water or a spinning bucket having a flat surface (before the water starts to spin), Newton theorised there must be an external force in play here (Dasgupta, 2015). This is how the bucket argument disproves relationalism, as there is no possibility in that space theory the two parts are moving relative to something. Rather, the substantival space is what the water has the ability to accelerate through, and the best part of the argument is that it is characterised on the relationists terms; we used the relative motion of water and bucket but still ended up with a much needed third factor, space (Dasgupta, 2015). Again however, Mach’s principle depicts the bucket argument as challenging to prove. Again, using a fixed star, Mach argues in am empty universe the water would go concave regardless (Dasgupta, 2015). But this is almost a straw man type of response, as we are observing a real bucket with real water, and Mach is perpetuating a thought experiment in an unrealistic scenario (Dasgupta, 2015).

Due to this being the best proposed argument against the bucket experiment and its unfeasibility in practise, Newton’s bucket argument provides the most substantial case not only for disproving relationalism, but also promoting substantivalism and the existence of space as its own entity. Does superstantivalism have enough merit to dethrone the others? Previously mentioned in this essay is the case for a somewhat mix of the theories and how it can combat some of the objections to both. This space theory is known as superstantivalism and encompasses a spacetime view that space is an entity and objects are spatial regions themselves. This highlights the space as an entity viewpoint of substantivalism and the non-dualism of relationalism. This space theory is important to distinguish and discuss as it provides some arguments that neither of the original theories can solve. Superstantivalism monopolises the existence of objects location and justifies how they can’t be in two locations due to encompassing a spatial region itself, and furthermore it can maintain how objects exist without a location (as they are spatial regions). Normal substantivalism doesn’t do this.

Also, by providing a theory with space involved but justifying relationalism objections creates a perfect dualization of the theories. There are some sole theory objections it struggles to oppose however, such as vindicating its ideal that spatial regions don’t move, unlike material objects. As a spacetime theory it has to accommodate for temporal parts and time-based theories and struggles to answer issues like this.

Conclusion and preferred view

This coupled with the arguments provided in this essay show that the bucket arguments lack of proper objections and clear explanation for the water accelerating through space proves space is an acting force in our universe and disproves relationalism. Despite the alluring view of superstantivalism, the logical and sound arguments provided for substantivalism such as explaining inertial effects makes it the most realistic space theory to follow.

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