Are Numbers and Mathematical Objects [whether Real or merely Formal Constructions] INTRINSICALLY "Quantized"?

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Whether we adhere to the Neo-platonistic view of Numbers and Mathematical Objects as “REAL”, or prefer the Formalistic contention that they merely represent formally constructed structures and relationships, it appears that their underlying QUANTIZED nature is ultimately inherent. ... Does this intrinsically quantized nature mean that not only our Physics but, sadly enough, even our Mathematics [as it stands today] is doomed (i.e. breaks down) when it comes to penetrating "beyond" the Planck Scale?
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Obviously, I am asking this question from a "Philosophy of Mathematics" point of view, however, should you have any physical and/or applied mathematics insights to offer, I would be eternally grateful! :-)

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Thank you for your comments.
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Answer 1

Physics or mathematics, all of them are doomed anyway beyond a point.

We used to consider energy as the "capacity for doing work" and hence it is a property of some object.
If it is at a height it has potential energy and can do work with that energy when it falls.
If it is moving it can do work when it hits something with the kinetic energy.

But the moment you say that energy is the product of the mass of an object and the square of velocity of light, the paradigm changes. Then energy is no more a quality but it IS matter. And what happens when matter is converted to energty (why convert, it is always) and no work is done with it.

These are mudane sciences, whether biology, chemistry, physics or mathematics. They all are doomed beyond a point, because they all can at the most represent what human intelligence can KNOW and not what cannot be known.

Answer 2

I don't think doomed was a very good term there. Even if it was meant as a simple adjective.

The fact that we can even attempt to quantify things that don't fit Newtonian principles is the ONLY purpose for math/physics in a "discovery" purpose so therefore I think that the only thing that could possibly happen to these fields is an EXPANSION, a growth, and ultimately, a more accurate description. Not a complete and total scrapping of the old.

Answer 3

Numbers & Mathematical Objects' intrinsic value is
colourful and inherent in Nature.

Answer 4

Some of these areas are relatively young as a science. We have always tried to quantify everything we don't understand. Therefore if there are two ways to look at it fellow the one you feels will fit your path. We can only lean that much more with two aways to go.


Live Long Live Free

Answer 5

Its the truth. It is a thought that is degrees of the state of science and state of creativity and progress of technology and freedom. Mathematics are the slit retinal restructuring that gestate the theater of the Universe and the deus machina set of the act

Answer 6

Numbers are not quantized. At least not under any traditional definition of quantization.

Something is quantized if it is discontinuous. If there are no adoptable values between any two chosen values.

It would be fair to say that WHOLE numbers are quantized - there is no whole number between 2 and 3. But it is not fair to say that ALL numbers are quantized - there is ALWAYS a number between ANY two numbers you can name.

And since your primary premise is false, your conclusion is completely unsupported.

If you believe otherwise, I challenge you to name any two numbers that do NOT have another number between them!