Physical laws of nature, so to speak, which are mathematical in their nature, can be considered to have a platonical existence, which makes sense, because after all they have no physical form of their own.
However, so-called “number-ness” is something different – it refers to the idea that things such as numbers have an independent abstract existence, existing not as laws of reality, but as meaningful independent abstract objects.
Quantity exists in our reality – imagine if only three physical things existed in the universe, such as three apples, and then those three apples somehow vanished out of existence – the idea is that the so-called three-ness is not actually dependent on three things existing – it is supposed to exist even if nothing at all physical exists in the universe.
One aspect (extension) of this platonic existence is the assertion of quantitative infinite existence, i.e., completed infinities (i.e., contained, e.g., in a set) of different sizes.
It would seem to follow that other aspects of physical reality must have their own independent abstract existence. Numbers can be thought of as having a static existence as opposed to a changing existence – other examples of static existences are: - shape, size, and even position.
Even though it's inconsequential, why should: “shape-ness”, “size-ness” and “position-ness”, be any less likely to have a platonic existence, than “number-ness” is?
Keep in mind, “three-ness” (supposedly) (or any other number-ness value) is not a physical law so to speak, i.e., it is its own independent abstract object, or thing, if you prefer to think of it that way.
Platonic velocity or acceleration independent of physical laws would violate them.
Example: velocity which is limited to light speed as in accordance with relativity theory, would be violated by – some finite distance / an infinitesimal period of time = infinite platonic velocity.
Therefore, the idea of platonic motion seems even stranger than the existence of platonic objects.
Bizare: why should it be possible for an abstract shape to exist (such as a sphere, that maybe also has abstract density) that cannot move?
If platonic motion supposedly does exist, and assuming it does not violate the laws of physics, then combined with number-ness, and all other possible types of “ness”, it seems as if all possible physical reality must have a platonical existence, even in a completely empty universe – seriously?
Therefore, although it seems reasonable to consider the laws of physics to have a kind of platonical existence of their own, it is also inconsequential, and such an idea does not try to assert infinite numerical values, which is explained in more detail in the next two sections.
A platonic numerical value must still be a number – by adding 1 to it, we prove it isn’t infinite.
Some paradoxical examples: Infinitesimal Paradoxes Identified – a link to the “Potential infinity disproven” page.
Asserting that numbers have a platonic existence in an attempt to justify the existence of infinitesimal and infinite values, doesn’t work.
The problem is simply that infinity is not a numerical value, and therefore platonic infinity is not a numerical value. Obviously, infinity cannot just be 1 single value, which ultimately, is exactly why! infinity is a misconception – e.g., there cannot exist two or more separate (or even just one) locations infinitely far away.
By asserting numerical platonic existence, it means that numbers can exist abstractly, instead of simply representing some quantitative state of physical existence. E.g., 5 cherries do indeed exist, which each consist of trillions of molecules, atoms, and subatomic particles, but platonically however, all quantities already exist, even without cherries.
When someone is thinking about platonism for the first time – simply accepting abstract existence, might result in trying to imagine that infinite numerical values actually do exist.
But consider: 1, 2, 3, 4, 5, all supposedly existing as abstract objects – and therefore so do the numbers: 1000000, 1000001, 1000002, etc., and so on – but why should this trend ever change?
In other words, when exactly does a sequence of numerical values transcend into something else? Whatever would that “something else” be?
Therefore, it stands to reason that the above “trend” is all there is to “numerical platonic existence”, i.e., only numerical values can exist platonically – therefore how is it possible for some platonic numerical value to not be finite? ... i.e., a numerical value by definition is not infinite – it can always be used coherently in arithmetic such as addition and subtraction.
The answer is of course: “it is not possible”, and therefore all supposed platonic numbers must be finite – an argument which proves platonic numbers do not exist, because if they did, there clearly would have to exist an infinite platonic value (number), which we have just established is impossible.