Our world is spatial. In particular there are 3 dimensions and we can measure lengths of objects in either of them.

However, when thinking about metaphysics I came to the conclusion that there might be a non-spatial world, a world where the notions of figures, points, lines, positions, angles, etc. are meaningless. Information does not need to be arranged in space. Instead, information precedes space (in my view).

I agree it's hard to think of a non-spatial world just as it's hard to think about colors you never can experience, e.g., colors seen by other species. Nevertheless, this hardly discards the idea that such colors exist. And I'm not speaking about wavelengths but about perception. The same reasoning I apply to the idea of non-spatial world.

But is this idea recognized within philosophy? Is there an established term for what I call "non-spatial world"?

  • I don't know about "in philosophy", per se, but "in physics" there's lots of stuff like arxiv.org/abs/1504.00464 (with link.springer.com/article/10.1007/BF02724247 from 1986 the earliest I'm personally aware of, although I'd bet there's plenty of earlier stuff, too). – John Forkosh Aug 4 '18 at 9:37
  • You seem to be talking about the Unmanifest. It is well recognised in philosophy and plays a crucial role in metaphysics. Such a 'world' is necessary unless we reify time and space. – user20253 Aug 4 '18 at 11:24
  • Another "dimension" to this question you may like to explore is if there is information then you can have information based entity to process it, maybe many. Now consider how two humans with different languages would communicate: At first there would be a lot of pointing, pointing at the ground to establish the universally experienced direction 'down', pointing up to establish 'opposite' and 'up' and so on. So it seems that communication needs the creation of direction (and space). Maybe you can think of another way the 'information entities' can establish communication? – christo183 Sep 4 '18 at 13:33
  • @rus9384-I think the platonists view in philosophy takes up some issues of abstract properties. propositions etc..which can build a non-spatial object of enquiry..see-plato.stanford.edu/entries/platonism/#1 – drvrm Sep 11 '18 at 19:39

Whereas philosophy was once closely associated with nature this is less so in the modern era; for example, Newton thought of himself as a natural philosopher and not as a mathematician or physicist though these are the names we retrospectively use to describe him.

This break was occurred in the early part of the 20C. It was quite common then for scientists to be versed in philosophy - for example Heisenberg read Plato and considered the elementall nature of the world to be akin to fire (ie energy) - whereas in the modern era this is very much less so and increasingly so; Feynman in his popular books, for example, ridicules philosophy whilst at least having the grace to attempt to understand it; and Sabine Hossenfelder in her popular book ridicules philosophy without showing any evidence that she has read any philosophy of worth.

It's plausible that this this is merely an artifact of the increasing specialisation of the various disciplines. Even in a discipline traditionally closely associated with physics - that is mathematics - the prominent British mathematician, Sir Michael Atiyah pointed out that mathematics increasingly had different questions that it pursued apart from physics; nevertheless, he noted that on occasion - and he points out the 70s - the two disciples cross-fertilised each other (in his example, the theory of fibre bundles and QFTs) and then again in the 90s, with the advent of string theory. Likewise we might posit an eventual reconciliation between philosophy and physics - on occasion and perhaps more permanently.

Metaphysics, as considered by Aristotle, was prominently concerned with the nature of the physical world; so he posited difficult questions about space, time, change and continuity; he also theorised about a first mover, which was later identified by the Islamic and Christian philosophers with God and it's this which tends to more prominent when people hear the word, metaphysics.

Space and time are naturally considered as determinate - we can measure the metre and we can measure the second - but in early physical theories, space and time emerged from an indeterminate something; in the classical period, this determinateness was taken as the background stage in which physics actually occurred - the absolute space and time of Newton; this determinate sense was retained even in Einsteins revolutionary theory of space, time and energy. However, QM has forced us to look at again at these concepts and recognise a quality of indeterminateness. This returns us to earlier physical speculations about the place of the indeterminate in physical theory. One might posit that if the fundamental reality is indeterminate then in its determinate unfolding we should still see some aspect of this indeterminateness in our everyday experience of determinateness.

In the modern speculative theories of QG such as Loop Quantum Gravity (LQG) and String Theory it's generally expected that space and time, in the usual sense, are emergent concepts.

For example, in LQG, the spectra of an area operator gives the basic quanta of area. The same does not hold for string theory - as there the background is still a given - so in some ways, LQG is more revolutionary than string theory where space and time remain a background stage and are not reworked conceptually.

Hence in the LQG context, we have a non-spatial fundamental reality (but which does not negate spatial reality) since spatiality is implicit and emerges in its unfolding.

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This is a second answer. My first answer considered the natural numbers as an algebraic system without a distance relation between the natural numbers. This would be a form of reality for a realist philosophy of mathematics.

This answer goes further and considers all propositions for which one can potentially try to assign a truth value as a form of reality that is not located in space, nor for that matter, time.

I will be using arguments presented by Frederick Fitch in Symbolic Logic: An Introduction to establish that this idea is "recognized within philosophy".

First, Fitch defines "sentences" (page 5):

2.1 Certain combinations of words constitute word groups called "sentences".

He claims every sentence has one or more "meanings" and these meanings are "propositions" whether "verbalized" or "unverbalized" (page 6):

2.3 Meanings of sentences may also be called "verbalized propositions". Every verbalized proposition is the meaning of some sentence. Roughly speaking, a proposition is anything that might conceivably be the meaning of some sentence, whether or not the requisite sentence has ever been formulated or uttered, and hence whether the proposition is verbalized or not. We often have vague feelings or premonitions that we cannot easily express in words. These are unverbalized propositions.

The propositions (meanings) are the "objects of belief and disbelief". They may be necessarily or contingently true or necessarily or contingently false or indefinite.

It is this reality of meaning or propositions that is non-spatial and even non-temporal (page 8-9)

Propositions are not to be thought of as located in space and time. Consider, for example, the true proposition, or fact, that the earth revolves around the sun. The sun has a location in space and time, and the earth has a location in space and time, but the fact that the earth revolves around the sun does not have any genuine location in space and time. If we were to try to assign this fact to some specific region of space time, the exact limits of such a region would be impossible to specify. Similarly, the fact that grass is green is not located anywhere, though grass itself and other green things do have location. Just as facts or truths have no space-time location, so also counterfacts or untruths have no location in space and time.

And finally to make sure one does not think of propositions as "merely mental" he notes (page 9):

Propositions, finally, are not to be thought of a "merely mental" things. The fact that the earth goes around the sun is not just a mental thing. In other words, propositions are no more "located in the mind" than they are located in space and time. But the mind may be in relationship to various propositions as when it believes or disbelieves them. The mind may also be in relationship to various objects that do have space-time location.

Here is something more general than the natural numbers. Meaning or propositions whether verbalized as sentences or unverbalized are a form of "non-spatial reality in philosophy".


Fitch, F. B. (1953). Symbolic Logic; an Introduction.

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Wikipedia describes the philosophy of mathematics as

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives. The logical and structural nature of mathematics itself makes this study both broad and unique among its philosophical counterparts.

In particular mathematical realism is described in that article as

Mathematical realism, like realism in general, holds that mathematical entities exist independently of the human mind. Thus humans do not invent mathematics, but rather discover it, and any other intelligent beings in the universe would presumably do the same. In this point of view, there is really one sort of mathematics that can be discovered; triangles, for example, are real entities, not the creations of the human mind.

Let us consider the question in the title:

Is there an idea of non-spatial reality in philosophy?

If we consider the natural numbers from the perspective of mathematical realism which is a position in the philosophy of mathematics these objects would be kind of objective reality which "exist independently of the human mind." They have a certain algebraic structure perhaps and even an order relationship. However, the natural numbers need not have a metric relation although one often thinks of the natural numbers as embedded within the real number line. The real number line has a metric based on the difference between two points on that number line.

The natural numbers are, without that real metric, or for that matter any metric relationship between two natural numbers, a kind of reality that is non-spatial.

As the OP notes:

Information does not need to be arranged in space. Instead, information precedes space (in my view).

This would be illustrated by the natural numbers given a philosophy of mathematical realism where the natural numbers are not assigned a metric.


Wikipedia, "Philosophy of mathematics" https://en.wikipedia.org/wiki/Philosophy_of_mathematics

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  • Interesting approach, but at the same time mathematics does not seem to assert there is reality that lacks space. Mathematics only examines what could be in non-spatial reality, doesn't it? – rus9384 Oct 4 '18 at 18:46
  • @rus9384 If you accept a realistic philosophy of mathematics then the natural numbers without the real-line metric would be an example of a mathematics that does not have space associated with it. Not all mathematics would be like that. There are metric spaces which imply the existence of space. – Frank Hubeny Oct 5 '18 at 0:19

We interact as individuals within us and the environment inside this context that is spacetime. A non-spacetime reality implies even the loss of causality: causality demands the existence of time, because causality is a sequential mechanism, action first, reaction last. And you cannot separate time from space. They're interdependent.

Having said that, I assume there's no philosophical approach of a non-spatial reality. In fact, it would have not logical rules. But perhaps I'm wrong.

Personally, I think there's one possibility: the systems theory. What I'm going to describe are personal ideas.

The systems theory describes systems, and a subset of all systems are physical systems, or simply things, subject to spatio-temporal rules. Systems perform interactions between them, and physical systems follow the same behavior. Except that physical systems are subject to interact under the rules of spacetime. Nevertheless, spacetime interactions are just a subset of systemic interactions. Systemic interactions would define physical interactions. Systemic interaction is precisely the topic of my last book (check my profile).

In consequence, the systems theory would be a generic description of how all entities (not only physical entities) behave. Systems could be the real bricks of the universe: they don't really depend on space and time.

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  • "causality demands the existence of time" - non-spatial does not mean timeless. The idea is about causation without space, the change within information. "And you cannot separate time from space" - well, I don't think so. People minds are so constrained that they in some context refer to thoughts as points and positions. No wonder they think of time in spatial sense. – rus9384 Aug 4 '18 at 1:52
  • Of course, I do not argue causality in our world is not spatial. However, it always was my position: arrow of time - the speed of energy exchange - is connected with space. But the time itself is not. "Behave" implies change and objects to change, thus causation and finally time. – rus9384 Aug 4 '18 at 2:01
  • Following up @rus9384 "causality demands the existence of time" is wrong. Causality "demands" ("corresponds to" would be >>much<< better wording) a partial order structure on events, e.g., en.wikipedia.org/wiki/Causal_sets Although that particular page's wording suggests spacetime is foundational, other causal set papers/discussions (google "causal sets") treat the poset structure as fundamental, with spacetime emergent from it. That would be my guess, though it may be "six of one..." -- I'm not well-versed enough to be sure whether or not they're (in)equivalent. – John Forkosh Aug 4 '18 at 9:51
  • There are philosophical and physical approaches to define causality. Here, philosophical causality is under discussion. There are attempts to give causality a physical definition (arguable!), that's OK, OK, OK, but any physical approach has nothing to do with the OP's question. There is no "reality", "world", etc. in physics! Such fallacy is called "moving the goalpost". I cite the OP: ..."I'm not speaking about wavelengths but about perception". – RodolfoAP Aug 5 '18 at 4:14
However, when thinking about metaphysics I came to the conclusion that there might be non-spatial world.

Not really sure what you mean by non-spatial, but let's first explore a spatial world. Let's model a cubical room using finite elements; in particular, we might divide the room into, say, 10K by 10K by 10K cubical voxels, with a cube packing arrangement. Pick out a single central voxel and let's explore the local space. It touches other voxels in six directions (we count arbitrarily face to face connections only); up, down, left, right, forward, back. In this model, I'd like you to imagine that up simply means a direction you can "go" in; and down is simply another direction you can "go" in. Two nodes touch if you can go from one node to another node along some direction in a single step. In other words, our room model forms a directed graph.

This model is similar to one that Stephen Wolfram discusses in this blog post; I'm simply emphasizing a directed graph view. Our room model then is simply a particular kind of graph. Our particular graph has a set of properties, including:

  • For every edge x from A to B there is a corresponding edge y from B to A
  • There are six families of edges decomposable into three pairs of families such that the two families within each pair can be called "inverses"; call each family a direction and its pair an inverse direction.
  • Given a path from X to Y such that for all three family sets, if and only if for all three direction sets, there are the same number of edge traversals along this path in one direction as there are its inverse, then X and Y are the same node.

We can imagine other kinds of symmetries. If there are only two sets of inverse direction pairs instead of 3, our graph models a 2D space. We can imagine a 2D space such as a Mobius strip or a torus, which still has the invertible feature but destroys the "and only if" part of inverse paths (i.e., there are more ways to arrive back at the same point than having exactly as many inverse steps). We could model 12D spaces if we like by creating twelve distinct pairs of invertible directions.

But we can also completely remove these symmetries, even at small scales. Going from A to B need not allow you to go from B to A in one step, or even at all. We could have more incoming nodes than outgoing nodes for a particular node, or vice versa. Given the graphs that are possible we can get rid of any sensible notion of dimensions or directions. And this is just for starters; if we add objects, we can have "buttons-and-trapdoors" (alluding to old puzzle games)... that is, rules where the very connectivity of space depends on how objects traverse. This need not even be something comprehensible; an object going from A to B could lead to an arbitrary rescrambling of connections. Note that for example particular graph symmetries give rise to basic concepts such as dimensionality of our space... so by removing these symmetries we compromise the ability to easily describe space with such connections.

These are merely "possible ideas" I have; I'm not sure if there's a lot of in depth discussions of these particular kinds of alien spaces or not. Wolfram's ideas reflect some of the points being discussed here, but he seems much more focused on potentially describing graphs like this as models of the space we live in, where objects themselves are modeled by topological "defects" and how this may connect to general relativity... whereas it seems you're after simply models of arbitrarily mixed up hypothetical spaces. Maybe, though, in some sense these conflicting goals actually overlap; exploring relations about what's conceivably possible helps formulate ideas about what might be fundamental, in which case you might find interest in Wolfram.

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Is there an idea of non-spatial reality in philosophy? ....A world where the notions of figures, points, lines, positions, angles, etc. are meaningless.

There is only one 'thing'...but you cannot call it a world, because to call it a world, you should see a second thing...at least 'you' and 'the world'. (Even you deny all the terms given above.) Even though you were not ready to deny, it is 'The one without a second'...always.

Here you should note one more thing--You can't use any other tense forms except 'is'.


I agree it's hard to think of non-spatial world.

Of course, mind cannot catch it.

If it is as you mentioned, all your doubts must end by its realization.

Now I believe you understood whether this idea is recognized within philosophy.

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  • Well, outside of our reality there is non-spatial one with different laws of logic (but it can implement our logic). However, it also contains organized information processes - conscious entities. I believe there is something even further outside of that world. – rus9384 Aug 4 '18 at 8:53
  • If you realize it you won't try to ask or think about another world. I think you will try to understand more about it from other websites. britannica.com/topic/brahman-Hindu-concept – SonOfThought Aug 4 '18 at 13:50
  • I honestly do not understand this answer at all. You posted a link to Wikipedia but that doesn't really answer the question nor do you explain what it has to do with your answer. Also, what do my "sorrows" have to do with non-spatial dimensions? – syntonicC Aug 4 '18 at 15:17
  • @rus9384Please refer SEP and see: "If Brahman is all there is, for example,then there is nothing outside Brahman that could serve as an object of its knowledge." – SonOfThought Aug 5 '18 at 14:15
  • @syntonicC I have given one more link in the 'comments'. I have replaced that word (although it is correct). To feel sorrow about something, there must be at least a second thing--'the person who feels' and 'a world'...actually you can replace it (doubts) by sorrows. As you mentioned, sorrows have nothing to do with non-spatial dimensions. FYI see: 1. sivanandaonline.org/public_html/… 2. hinduwebsite.com/brahmanmain.asp Now try to understand the ideas given in the link. – SonOfThought Aug 5 '18 at 14:20

The idea of a non-spatial world is as old as metaphysics. Plato's realm of forms is the domain of abstraction. Descartes saw there being a dualism of physical 'extensible' world, and mental 'inextensible' world, which meet somewhere in the human brain. Liebniz proposed a monadology, to explain the arising of material particulars from increasingly abstract and less material unities.

The idea of a non-spatio-temporal world is proving essential to physics, in order to have a picture of how space & time might be quantised, and the 4 fundamental forces unified. Carlo Rovelli talks about an underlying layer from which time and events emerge.

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