Philosophy Now Forum

Does math need to be 100% consistent? What makes this challenging is the concept of infinity because, if real, then how would one establish the (total) consistency of math?

A Wiki article helps to explain here: http://en.m.wikipedia.org/wiki/Consistency

PhilX

Philosophy Explorer wrote:Does math need to be 100% consistent? What makes this challenging is the concept of infinity because, if real, then how would one establish the (total) consistency of math?

A Wiki article helps to explain here: http://en.m.wikipedia.org/wiki/Consistency

PhilX

I don't think it is possible to get infinities to be part of an overall consistent mathematics, because mathematics is probably not consistent anyway. Consistent in terms of the link you have posted, that is. Given the fact that mathematics since, the time of Godel has show that such a consistency is not possible. Certainly, quantum mechanics (uncertainty principle) lends supports to Godel's idea of there being limits to what we can measure in mathematical terms.

Ginkgo wrote:

Philosophy Explorer wrote:Does math need to be 100% consistent? What makes this challenging is the concept of infinity because, if real, then how would one establish the (total) consistency of math?

A Wiki article helps to explain here: http://en.m.wikipedia.org/wiki/Consistency

PhilX

I don't think it is possible to get infinities to be part of an overall consistent mathematics, because mathematics is probably not consistent anyway. Consistent in terms of the link you have posted, that is. Given the fact that mathematics since, the time of Godel has show that such a consistency is not possible. Certainly, quantum mechanics (uncertainty principle) lends supports to Godel's idea of there being limits to what we can measure in mathematical terms.

I would think that math could be consistent enough, it's the Quantum Mechanics (physics) that is causing the problems.

Not really it is the most successful theory in history at least in physics. What is causing the problems is not quantum mechanics, but our inability to render it sensible to linear maths. As Bohr said we may just have to accept that there is no exact complentarity with quantum mechanics and the weakness of humans and their unjustifiable perceptions.

Blaggard wrote:Not really it is the most successful theory in history at least in physics. What is causing the problems is not quantum mechanics, but our inability to render it sensible to linear maths. As Bohr said we may just have to accept that there is no exact complentarity with quantum mechanics and the weakness of humans and their unjustifiable perceptions.

Perhaps I should have said, "it's our understanding of Quantum Mechanics that is causing the problems".

Philosophy Explorer wrote: ↑Fri Mar 13, 2015 9:30 am Does math need to be 100% consistent? What makes this challenging is the concept of infinity because, if real, then how would one establish the (total) consistency of math?

A Wiki article helps to explain here: http://en.m.wikipedia.org/wiki/Consistency

PhilX

PhilX you are one of the few philosophers here with really valid questions...as I go through this section of the forum.

Presented argument:

If number is viewed in an individual manner (not a whole), but rather a particulate which composes further number which in turn are "particulate" it may simultaneously be viewed as probabilistic in certain respects (not all).

This is considering that particulate are composed of further particulate with these particulate in themselves strictly being "relations". In these respects, as relations, particulate manifest a dual role of "actuality" and "potential" with both actuality and potentiality in themselves being "relations".


It is through the relation of actual particle relations (which in themselves can be argued as "actual" particles considering particles are strictly "quantums of relations") and further actual particle relations that the nature of mathematical multiplication is "embodied" as the production of "potential particle relations".

In turn the relation of potential particulate and actual particulate that the nature of mathematical "division" is "embodied" as the production of further actual particulate.

In these respects multiplication and division are inherent duals through 1 in the same manner + and - is a dual extension of 1.


It is in these respects that time is strictly a cycle of multiplication and division that moves particulate towards a "unity" as it relates towards the stable ethereal space. Multiplication and Division are dual cycles of flux that cycle through each other and in this respect all "time" is equivalent to "cyclical flux" between dual "poles" of actuality and potentiality.



example: 4x2 = 8
with φ = "actual particulate", ω = "potential particulate", and ∫ = "relations of"

∫(4φ, 2φ) ≜ 8ω



example 8/2=4

∫(8ω, 2φ) ≜ 4φ