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# Metaphysical infinity between two points

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According to Ayn Rand, infinity does not metaphysically exist, rather it is only an epistemological measurement construct.

One place where we use infinity epistemologically is the space between two points. If I look at a number line, there are technically infinite points between the number "1" and the number "2" because I could theretically always add more digits onto a demimal point between them. For instance, 1.0000000000000000000000000000000000000000009 is a single point between the two points, and by adding more digits, I can infinetely find more points.

My question is: how does this apply metaphically?

If I draw a line on a pierce of paper with a pencil, it make look like a single, solid line, but I know that it is not. Instead the line is made up of specs of graphite which are in turn mae up of molecules which are made of atoms, which are made of quarks, which are made of something, etc. Aren't there infinite points between the two lines? Can you break any metaphysical entity down infinitely?

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You can only continue to break it down metaphysically until you cannot.

Mathematics seems to get around this, as an epistemological tool, by giving us the sense that we can extend or subdivide indefinately, because we know how to add another place holder on either side of the decimal.

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Is there actually a point at which something can't be broken down? What would be the scientific basis for such a point?

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The scientific basis is the Law of identity.

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A Randian answer might be that points are not entities, only abstractions that require you to recognize them.  You could go on indefinitely finding a new point between any two you'd already found, and this is a case in point of what Aristotle and Rand meant by saying that infinity is potential, not actual.

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That is also the point in identifying that mathematics gives us the impression that we can extend or subdivide indefinately, because we know, mathematically, how to accomplish it.

While the law of identity does cover this, the other imposed limit is what we can actually subdivide down to. Until we discover a method that allow us to subdivide subatomic particles is discovered, we are limited in our knowledge and abilty to going further at this point. Discovering such a method is how the law of identity is extended to new or previously undiscovered entities and methods.

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Is there actually a point at which something can't be broken down? What would be the scientific basis for such a point?

If you want a scientific answer, you'll need to at least define your terms a little better (i.e. broken down), but also ask a more specific question. Science doesn't really deal with terms like "something" and "can" (where no further context is specified, i.e. what tool you'd be using to try to do this "breaking down"). Edited by Nicky
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Does anyone here know how to take an electron apart?

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Can electrons be taken apart?

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Is there actually a point at which something can't be broken down? What would be the scientific basis for such a point?

What would be the scientific basis for assuming something can be "broken down" indefinitely?

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What would be the scientific basis for assuming something can be "broken down" indefinitely?

I won't claim to understand the science behind any of it, but it seems logical that with enough precision, one could continue cutting or smashing something into smaller pieces.

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A metaphysical infinity is logical ?

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I think the OP is a good example of what Reidy pointed to as Rand's and Aristotle's meaning, infinity is a potential not an actuality. You simply add another placeholder indefinately(potentiality), but the number of specific placeholders at any one time is the actual amount you have(actuality).

As to subatomic particles and the smashing thereof..smashin' em is probably easier than countin' what you get

Wait on second thought perhaps the points and line example is not good. Numbers refer to quantities of existents, just saying you can ascribe a number doesn't mean there is actually a quantity to refer to, even you want to. Infinite points on a line does not actually refer to an existent quantity outside of the maths. (??)

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Infinity isn't only the horizon you can never reach... it's also the amount of time you can walk toward it.

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I am satisfied with Reidy and tadmjones's responses.

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