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If one is to postulate an entity that has a complete or absolute lack of height, depth, and width, can such an entity be located anywhere? Or does attribution of location to an entity entail length, depth, or width (assuming a three-dimensional world)?

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  • In Geographic Information Systems (GIS) entities are surfaces (having width and length), lines (having length) and points (not having a size). Points are used to represent certain entities, and don't need a size (WxHxL). If you reach the point that correspond to a monument, city, building, historic place, etc., the entity will be located over/above/below it.
    – RodolfoAP
    Oct 26, 2023 at 2:59
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    The set containing you as the only element has no height, depth, or width. It is located where you are. Same with your mood or dignity. Generally, on location of abstract objects see SEP.
    – Conifold
    Oct 26, 2023 at 8:25
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    Can you take a step back and consider how anything lacking height, depth and width could exist? Doesn't the smallest, as-yet-undiscovered sub-atomic particle have height, depth and width? Oct 26, 2023 at 21:25
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    @RobbieGoodwin particle physics treats elementary particles as being pointlike (having zero volume).
    – Sandejo
    Oct 27, 2023 at 3:43
  • @Sandejo Thanks and how is this about any particular branch of physics, rather than Philosophy? In my book, 'entity' implies 'living being' while very differently, you're looking at an 'object'. I'd like to hear how MaxMaxman thinks that bears on the Question. If you went with point-like objects having zero volume, how would that avoid the - philosophical - question of whether 'zero' means 'no'… which I suggest it doesn't. Oct 28, 2023 at 19:10

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David Gudeman rightly points out that your entity is called a point. A point by definition has no extension. How that is possible is that Euclidean space is concerned with having dimensions that are mapped to a real sequence. Thus, a point can have a triple that describes it's location (x,y,z) even though it has no length, breadth, or height ([x1,x2],[y1,y2], [z1,z2]). In more advanced models of space, points can have more complex definitions other than no extension or ranges.

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  • @J D What I cannot seem to wrap my head around is that we are assigning a location to this point, yet it dosen't have length, width, or height. To make this clearer, let us use the triple x,y, z. Let z be the plain of depth, y the plain of width, and x the pain of length. How would I be able to describe something in terms of these plains when it dosen't have any extension? How can it, for example, be assigned a position in the plain of depth when it clearly has no depth? It seems as if a non-physical entity (given its lack of extension) is being prescribed a location, which seems absurd.
    – Max Maxman
    Oct 26, 2023 at 4:27
  • @MaxMaxman But surely you can see that on any of those planes, you can still consider individual points. Imagine the number line, it may extend infinitely in two directions, but we can still recognize the number 1 as a distinct point on the line, and doing so has a lot of uses. And just because a physical object is more than a point, it doesnt mean points arent useful for physical objects. For example, how would you describe the location of a corner of a cube without a point to represent it, and why would it be better than just using a point?
    – JMac
    Oct 26, 2023 at 13:24
  • @JMac I think of a number line as a mere sequential representation of numbers, not a model of space. It seems to me the corner of a cuber would in fact be represented by an infinitesimally small range, not an unextended point.
    – Max Maxman
    Oct 26, 2023 at 15:38
  • Okay Max. So here's the thing about space. It's not real. That's a conclusion that comes directly from Kant. Space as you have intuitions are expressed by the Metaphor of Containment, which is to say that intuitively, you treat space as if it has the properties of a container. And daily, that works for us, but when you get deep into the philosophy, space doesn't have a physical existence. You can't touch it. You can't weigh it. You can't see it. Space is an abstraction... whenever you examine discussion of space, you inevitably are led to the phenomenological objects of space... things that...
    – J D
    Oct 26, 2023 at 16:35
  • @MaxMaxman And what benefit does representing it as an infinitesimally small range have over representing it as a point? I'd say that in most circumstances, representing it as a point is reasonable. Also, what is the difference between a "representation" and a "model" to you? And we already use numbers to represent spaces all the time. What is the issue with extending that model to represent a point, the same way we can represent a single number even though the number line isnt a discrete representation.
    – JMac
    Oct 26, 2023 at 16:36
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Judging by your response to JD's excellent answer, what you seem to be asking is whether it makes any sense to talk about an unreal object having a location. I think the answer is generally no, it doesn't. Incidentally, even objects which we do consider to be real and to have a finite extent, such as electrons, don't always have a well-defined location, since according to quantum theory their position is essentially a matter of probabilities. That all said, there is one type of non-physical object, namely a point in space, which we imagine expressly for the purpose of allocating a location to it. If you are struggling to come to terms with that idea, imagine that we use a small sphere to mark a position in space. Presumably you are OK with that idea, because a sphere has a length, breadth and depth. But how do you allocate a location to a sphere? Conventionally, we do so by associating coordinates with its centre. Its centre is a point that has no length, breadth or depth, yet you should be able to feel Ok giving it a definite location in space because you are happy with the idea of the surrounding sphere being a real object.

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    It is utterly commonplace to describe the location of unreal objects that lack breadth in one or more dimensions. The equator, national boundaries, a line of scrimmage, a line of sight, and the center of the earth are all conceptual entities that are not real 3-dimensional objects, but are instead planes, lines, or points. I totally disagree that it doesn't make sense to talk about the location of a national boundary simply because it is not a "real object". Oct 26, 2023 at 14:16
  • @NuclearHoagie, sure- I agree with you in general. Some of the things you mention are properties of physical objects, but leaving that aside, you can definitely associate locations with some conceptual objects, but there are more that you can't meaningfully locate. Oct 26, 2023 at 14:24
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    @NuclearHoagie It seems to me that what you refer to as entities such as the equator, national boundaries, a line of scrimmage, a line of sight, and the center of the earth, are all concepts that simply name some areas so as to distinguish them from others. They do not seem to have any existence outside the area they denote...
    – Max Maxman
    Oct 26, 2023 at 15:48
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    @MaxMaxman: The center of the earth does not name any area, nor any volume or any other higher- or lower-dimensional measure. It is simply a point.
    – Kevin
    Oct 26, 2023 at 22:03
  • +1 For my favorite kind of flattery.
    – J D
    Oct 28, 2023 at 7:32
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In a three-dimensional world, location is defined as a point that is represented by 3 numbers; one for each dimension; ex. height, depth, and width. So, if an entity does not have height, depth, and width, it cannot be represented in a three-dimensional world, which means that location cannot be assigned to it.

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    If something exists in a 2-d world or less, then it is out of scope from a 3-d world perspective; it is conceivable only through imagination; it cannot "act" on the 3-d world. Nov 5, 2023 at 10:41

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