The implication being 'people like this only recite what they're learned in class, they're not really capable of philosophy'. — Wayfarer
As I just finished practicing piano, I observed that the notes that I was playing as I read them off paper was can awful representation of the music that I was creating. — Rich
So are mathematical symbols and equations an awful representation of nature. — Rich
It is interesting that Bergson used music as his analog for duration ... — Rich
I am not suggesting that musical notes are not useful. What I am saying is that they, as are all symbols, are an absolute awful representation of the experience itself. — Rich
We must put mathematical equations in proper perspective and not get carried away by them. — Rich
What I am saying is that they, as are all symbols, are an absolute awful representation of the experience itself. — Rich
You are very sensitive. I apologise if you have feelings that are easily hurt. But is this my problem or your problem? — apokrisis
what I am looking for from you is a genuine counter-argument, — apokrisis
a restatement of a particular institutional view that is widely held for the pragmatic reasons I've previously stated. — apokrisis
I have never and I repeat never said that I think mathematics has the slightest thing to say about reality. — fishfry
Is there an a posteriori way of determining whether there are any real continua vs. everything (including space and time) being discrete? — aletheist
As a structural engineer, I analyze continuous things using discrete models (i.e., finite elements) all the time, and it works just fine for that purpose. Of course, I also apply safety factors to the results, since I am not interested in having the underlying theory falsified. — aletheist
How does it fail to provide the whole story? If "things" don't really exist, and every "thing" is a network of relationships, then mathematics would describe the world, because mathematics has no objects - it's pure relationality. Think about geometry. A line in geometry isn't constituted in-itself, but always in reference to all other possible geometrical constructs - indeed to understand what a line is, one must ultimately understand all of geometry. Geometrical objects are nothing except relations, that's why they are actually impossible in the real world - for example a line has no thickness. They are constituted by the whole system - it is their interrelationships which constitute them, and in the end give them the properties they have. So "things" are illusory - reality is fundamentally relation, not thing. Scientific knowledge is merely useful, but not true, because the truth would have to be the Whole of reality, and every part of reality would be in its totality determined by this Whole. That's why we can get better and better approximations for everything, but we can never be exact, because we - as a part of the Whole - can never know the Whole completely - there will always be a residue of uncertainty.So the issue for me is that clearly maths does say something deep about metaphysics. Yet then - something which theoretical biologists have particular reason to be alert to - maths also fails to supply the whole story (for the reasons I've outlined at some length). — apokrisis
Charles Sanders Peirce likewise took strong exception to the idea that a true continuum can be composed of distinct members, no matter how multitudinous, even if they are as dense as the real numbers. — aletheist
Geometrical objects are nothing except relations, that's why they are actually impossible in the real world - for example a line has no thickness — Agustino
It is trivially true that no representation reproduces its object in every respect, and the purpose of musical notes - and mathematical symbols/equations - is obviously not to represent "the experience itself." — aletheist
Right - the real numbers constitute an analytic continuum, but not a synthetic continuum; i.e., a true continuum in the Peircean sense, which cannot be represented by numbers at all. As he put it, "Breaking grains of sand more and more [even infinitely] will only make the sand more broken. It will not weld the grains into unbroken continuity." — aletheist
Breaking sand "infinitely" yields tiny bits of sand? Please! — tom
Breaking the real numbers "infinitely" yields what? — tom
More real numbers, all of which are distinct; again, it obviously does not yield an unbroken continuum. Put another way, the set of real numbers has a multitude or cardinality, which is exceeded by its power set; but a true continuum exceeds all multitude or cardinality. It is not composed of parts, it can only be divided into parts, all of which can likewise be divided into more and smaller parts of the same kind. — aletheist
It's you. — tom
↪aletheist It's you. — tom
I might even agree with that whole post, if I am understanding it correctly. — aletheist
The values ARE equal. There is NO difference between them. — tom
We typically treat the two values as equal, but arguably there is an infinitesimal (non-zero) difference between them. As you might have guessed, the Peircean continuum is non-Archimedean. — aletheist
You cannot create a new number by adding an infinitesimal quantity. — tom
As it happens, .999... = 1 is a theorem even in nonstandard analysis. — fishfry
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