When I say that a tennis court is a rectangle, I simply mean that there is a certain spatial relationship between its edges which match the concept of a “rectangle”.
This implies that the concept of “shape” only applies to physical objects, things with boundaries.
Boundary is a concept which applies to entities, things that have physical extension. But the term universe is not an entity and has no physical extension, therefore no boundaries.
He then proceeds to point out that the term universe refers to everything that exists. And is therefore not a physical entity. As shape applies to physical entities, the universe cannot be said to have a shape.
He then points out that it is not infinite. And that because it is not a physical entity, it cannot have any spatial measurements and thus it is neither finite nor infinite.
Indeed, the concept of “size” has no relevance to the concept of “the universe”.
Infinity refers to a certain kind of potential to progress in a mathematical series. It does not refer to size. So, even if the universe was an entity, infinity would still not apply to its size.
Since the universe has no size, does this mean that the universe is not finite either?
No. The universe is finite. In the sense that it includes so many entities and no more. Let me explain…
The universe includes everything that exists. Only a certain number of entities. It may be a very large number of entities, but it is some number of entities.
The universe is therefore limited in as far as the number of entities it includes. So, in that sense it is finite.
Before we move on, I have a few further comments.
I do not agree that shape must be measured in three dimensions. For instance, you can identify a drawing and identify it as a circle. You can do so by only considering two dimensions and ignoring the third.
In an earlier chapter, he discussed the axioms. This is a good chapter and it is rare that such things are properly covered in any kind of philosophy book.
We have not covered this essay and probably will not do so in this series.
We will cover the axioms. But, not his coverage of it, as it is mostly not all that interesting.
However, there is this bit from that chapter which I would like to quote from page 9:
“The third corollary of identity: Anything that exists must have some relationship to everything else that exists”
The author had also said, quoted earlier in our discussion, that “ A relationship is an interaction”.
If a relationship is an interaction, then how is this a corollary of identity? How does the fact that to exist is to have a specific nature imply that everything must interact with everything else that exists?
Obviously, it does not. The axiom of identity in no way implies this. In fact, whether all things interact is not a philosophical issue. It is an issue of physics.
I have to wonder if he is using “related” in two different senses, without clearly indicating this. I would not have mentioned it, but unfortunately, it does make one curious whether he is overreaching as to what the axioms and their corollaries are.
Alright. That brings us to the end of this episode. Thanks for listening!
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