How is it empirical? Does a number exist in a physical world?Quote:
Originally Posted by Tellos Athenaios
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How is it empirical? Does a number exist in a physical world?Quote:
Originally Posted by Tellos Athenaios
A number is a quantity, nothing more.Quote:
Originally Posted by rvg
A quantity is a quantity, seems like numbers just don't cut itQuote:
Originally Posted by Tellos Athenaios
How?Quote:
Originally Posted by Fragony
From your link, a cube can apparentlty by devided into two cubes, that is not possible yet can be proven mathematicallyQuote:
Originally Posted by Tellos Athenaios
A cube cannot be partitioned in this way, that is exactly what Fermat's Last Theorem states (when considering cubes n = 3, therefore n > 2) and it is mathematically proven to be impossible. I think you misread?Quote:
Originally Posted by Fragony
Possibly, but I think you misunderstood, read againQuote:
Originally Posted by Tellos Athenaios
Which bit? From "my link":Quote:
Originally Posted by Fragony
Quote:
It is impossible to separate a cube into two cubes, or a biquadrate into two biquadrates, or in general any power higher than the second into two powers of the like degree; I have discovered a truly remarkable proof which this margin is too small to contain.
For the "biquadrate" (fourth power) case, Fermat's earlier assertion is sufficient to imply the later one: if two fourth powers cannot sum to a perfect square, they cannot sum to a fourth power either (since any fourth power, say w4, is also a perfect square, namely, the square whose side measures w2). But Fermat was asserting much more. In modern notation Fermat's assertion – known to mathematicians as Fermat's last theorem, or FLT for short – states that the equation xn + yn = zn has no solution if x, y and z all are positive integers and n is a whole number greater than 2.
That's too hard for me, you are talking to a mavo c here. But it's pretty obvious that it are the actual methods that are on trial here. If you can be a wizard with the numbers the numbers are wrong, pure and simpleQuote:
Originally Posted by Tellos Athenaios
Where in nature can I find 731?Quote:
Originally Posted by Tellos Athenaios
I see it on my screen right here.
Can you weigh it?Quote:
Originally Posted by Montmorency
Some multiple of 9.10938188 × 10^-31 kilograms, presumably.
And that's the weight of what?Quote:
Originally Posted by Montmorency
Lies.
Indeed.Quote:
Originally Posted by Montmorency
Electrons, my mistake.
Lies are heavier.
They make baby jesus cry.
Weigh baby Jesus for me.
Also, God.
This is a fundamental misconception of what mathemathics is. An extremely common one, but still fundamentally wrong.Quote:
Originally Posted by rvg
Mathematics is not abstract. Not in any way whatsoever. One can use abstract thinking to solve problems, like in every other scientific field, but the basis of mathematics will always be the natural world. Numbers exist because they are the names we have given to sizes we find in the world.
731 is easily found, just buy 731 apples, put them on the table before you and voila.
No, no. I'm not looking for 731 apples, or 731 electrons or 731 widgets.Quote:
Originally Posted by HoreTore
I'm looking for 731.
Then you are looking for something different than what mathematicians look for.Quote:
Originally Posted by rvg
It's like saying astronomy is unscientific because you can't see any stars in your waste basket.
I'm sorry, I didn't realize that all this time mathematicians had apples in mind. Thank you for enlightening me.Quote:
Originally Posted by HoreTore
No problem!Quote:
Originally Posted by rvg
Weight is irrelevant. The photon, for instance, has no mass at all. Still exists.Quote:
Originally Posted by rvg
Love also exists, but it's not an empirical object. Anyway, the idea of numbers being anything but abstract is so stupid, I'm not even gonna discuss it. Next thing I'll be hearing is that the Earth is flat.Quote:
Originally Posted by Populus Romanus
numbers aren't abstract, they're an abstraction - they are a sign used to represent a concrete reality.Quote:
Originally Posted by rvg
No need for me to say much more, I'll hand the microphone over to PVC:Quote:
Originally Posted by rvg
Spot on.Quote:
Originally Posted by Philipvs Vallindervs Calicvla
Numbers are a generalization of a concrete reality.
Everything else is stamp collecting...Quote:
Originally Posted by HoreTore
Ugh.Quote:
Originally Posted by Papewaio
At least you're being an equal-opportunities knucklehead.
Lets go through the hierarchy of Philosophy again: we progress downwards, each branch being a descendant of higher branches. So, at the top we have metaphysics, of which the highest part is epistemology - once we have decided that we accept that we can now things, even though we can't conclusively prove them guess what comes next?
Mathematics - without the basic principles of which we could not operate logic.
Paraphrase was from Rutherford and I normally sig when I'm whimsical.
Philosophy isnt science neither is mathematics.
Mathematics is a subset of philosophy.
Science a subset of mathematics.
However a container is not the fluid and not all rectangles are squares.
If a superset = a set 1:1 then they are the same. Maths is science plus something more.