Why do you ask?
But no, people trying to change the subject and avoid addressing points I made doesn't hurt my feelings. Makes me wonder who they are trying to convince, though - me or themselves.
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KCfromNC, would it hurt your feelings if I said you have faith in secular presuppositions and axioms like a religious fundamentalist has faith in his deity?
Mathematics is the language of science.
It's just a useful mental construct.
More than that.
... mathematical reality lies outside us, ... our function is to discover or observe it, and ... the theorems which we prove, and which we describe grandiloquently as our creations, are simply our notes of our observations. -- G. H. Hardy
Mathematics are descriptive, they describe the relationships between measured and measurable units.
More than that, as I said.
All of mathematics would remain true, even if the Universe was devoid of measurable objects.
I'll take G.H. Hardy's understanding of mathematics over that of some happy cat, I think.
Mathematics are descriptive, they do not exist on their own.
I disagree, as do most professional mathematicians.
For one thing, there are only about 10^80 particles in the Universe. Any statements about numbers larger than that is not "descriptive" of anything physical.
Theoretical numbers are extrapolations.
I can extrapolate logically in any language to unreal ideas (it is the nature of abstraction), this doesn't mean that language can or does exist independently of the thing it describes, and certainly not independently of any object..
Theoretical numbers?
The largest known prime number is 2^57,885,161 − 1, which is about 10^17,425,170 and so is enormously larger than the 10^80 particles in the observable universe.
Consequently, the number 2^57,885,161 − 1 doesn't describe anything physical, but it's a perfectly real number. In particular, it really is prime.
It doesn't exist in the universe where it has nothing to describe.
True, but mathematics is a lot more than that. For a start, it was around long before science, telling us truths about numbers and about Euclidean geometry.
And about non-Euclidean geometry, too.
Let's just agree to disagree. But I have virtually all professional mathematicians on my side. The quote from Hardy would be typical.
Perfectly real in what sense? It describes an extrapolation of a relationship within a system of ideas which were developed to describe real things.
I don't doubt that you can extrapolate to any number of abstractions that don't describe specific things (aside from the relationships between abstractions for a given system with given rules) but to say they are real in any sense outside of self reference would be stretching it to say the least.
...
Mathematics is an abstraction from reality not a reality in and of itself. It doesn't exist in the universe where it has nothing to describe.
For the most part, I agree with you. There is a sense in which one can say mathematics exists only when there is a mind to think about mathematics. There is some physical construct of the numeral 1 in my mind, and so it exists in that sense.
Can't you say the same of any descriptor? "Blue" only exists in the mind as well. And yet there is something that exists even when the mental concept "blue" doesn't exist (light at specific wavelengths). At that point it becomes a matter of agreement in the way we use our language. If we agree "blue" refers not to a mental concept, but only to specific wavelengths of light, then we can say blue exists.
It seems it then becomes a matter of what satisfies a particular person. Electrons have no known subparticles, and so some may be satisfied to say an electron is the fundamental thing that exists and stop there. But electrons can be made from photons and annihiliated (with a positron) to emit photons. As such, others are not satisfied that the electron is the fundamental thing and want to go a bit further down the infinite chain of turtles.
So, given the speed of those photons in a vacuum is ~3E8 m/s, and that photons don't have a rest state, is there a sense in which the existence of a photon is dependent upon a thing we call 3E8 m/s?
To observe blue does not take any abstraction only calling it blue involves an abstraction.
Two is a completely abstract idea as it is not simply naming what one observes but requires one to consider whether there is a relationship between things that one observes.
For the most part, I agree with you. There is a sense in which one can say mathematics exists only when there is a mind to think about mathematics. There is some physical construct of the numeral 1 in my mind, and so it exists in that sense.
Can't you say the same of any descriptor? "Blue" only exists in the mind as well. And yet there is something that exists even when the mental concept "blue" doesn't exist (light at specific wavelengths). At that point it becomes a matter of agreement in the way we use our language. If we agree "blue" refers not to a mental concept, but only to specific wavelengths of light, then we can say blue exists.
It seems it then becomes a matter of what satisfies a particular person. Electrons have no known subparticles, and so some may be satisfied to say an electron is the fundamental thing that exists and stop there. But electrons can be made from photons and annihiliated (with a positron) to emit photons. As such, others are not satisfied that the electron is the fundamental thing and want to go a bit further down the infinite chain of turtles.
So, given the speed of those photons in a vacuum is ~3E8 m/s, and that photons don't have a rest state, is there a sense in which the existence of a photon is dependent upon a thing we call 3E8 m/s?
I don't think any abstractions exist outside of minds or at the least living systems and I would be hard pressed to come up with a metaphysical justification for how they could exist without one.
I'm not saying they do. Maybe I should put it this way. You described Radagast's prime (2^57,885,161 − 1) as "an extrapolation of a relationship within a system of ideas which were developed to describe real things." So, I would say most if not all abstractions have their origin in something real (are extrapolated from real things). I am further saying that extreme cases such as Radagast's prime are easy to identify as an abstraction, but as we get closer to the real root, the actual boundary between real and abstraction is very difficult to define.
For example: Are photons real or are they an abstraction?
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