This is false. There are sets of numbers, but number themselves are not at all sets — Ikolos
the cardinality and ordinality of sets which can be put into a function with a proper subset of themselves — MindForged
Finite Numbers can be defined in terms of the cardinality of sets in just the same way. — MindForged
Of course they are. — SophistiCat
Quality is the degree of excellence of a thing. — Metaphysician Undercover
This is the 'singoletto'(I don't know the English word, kind of 'single set') not of a number. — Ikolos
If Zero is defined as the empty set — MindForged
I'm still confused about what you meant when you said I had a medieval theologian type of thinking... — MindForged
This is the condition to CONSIDER the 'singleton'(I trust you on the term) as the number one, but not to DEFINE it. Numbers are defined by a postulate and succession: see Peano Arithmetics( 0 is number(POSTULATE). If n is a number, then n+1 is number.(AXIOM) Then 1 is a number, as 0+1=1.) — Ikolos
Thinking infinity has THE QUANTITY OF WHICH NO QUANTITY IS GREATER is the MEDIEVAL conception of infinity. — Ikolos
↪MindForged Our cranky and inarticulate friend has a point in that there is a difference between a conceptual definition of a number, which describes the properties that anything fitting the definition of a 'number' ought to have, and its particular theoretical construction, such as von Neumann's (which was designed to meet the requirements of the conceptual definition). — SophistiCat
Frankly, a definition so senseless as all the medieval definitions were. You are deeply confused. — Ikolos
Now, if something is to be selected as a discrete unity, as you say, it presupposes a quantity on which this selection is operated. Or do you think we actually create quantity by itself, against the basic postulate of physics? — Ikolos
Hence as the scale of degrees(quality) relies on a spatial property, than the degrees do rely on that to. — Ikolos
But neither Space nor matter presupposes any detectable quality by themselves. Quality, furthermore, presupposes a RELATION between space and something, which renders possible to detect some spatial properties or, as you seem to prefer, to select from that properties units, in respect to which establish a scale of measuring. This something is matter. Matter does not imply quality(degrees) but the distinguishability of degrees implies matter. But matter presupposes space. Then quality presupposes space. Either you identify space with the properties we can distinguish and classify under the kind 'spatial' and name IT quantity, or you do not identify space with those properties and call those properties 'QUANTITY' it is the same for our question: quantity it is presupposed by quality. — Ikolos
everything is a set in the set theory construction of mathematics - obviously) — SophistiCat
how we measure, by units — Metaphysician Undercover
Which basic postulate of physics states otherwise? — Metaphysician Undercover
"the degree" may be arbitrary. The premise of "the distinguishability of degrees" misleads you. So we commonly divide space by degree — Metaphysician Undercover
Aleph-null is definitely not a quantity above all others, for instance. — MindForged
How is this different from what I said? — MindForged
that's not just the singleton of a set. It was the DEFINITION of the number one in set theory. — MindForged
Yes, and what do you measure my friend? Quantity. Hence there is quantity yet, and you measure it. That fact that the methods and units of measurement may be relative(as you correctly say) does not make this less true, i.e. quantity is presupposed REALITER as what is to be measured. — Ikolos
Independently existing matter, independently from particular modes of perceiving it, and that actually causes any perception to happen. — Ikolos
No one divide space by degree man, that is nonsensical. — Ikolos
The units of measurement, which are counted as a quantity, are very often created by the human mind, for the purpose of measurement, they are artificial. So "quantity", as the thing measured, is not necessarily presupposed. In the cases where we cannot find individual units to count, we simply create them, giving us the capacity to measure without there being any real quantity which is being measured. — Metaphysician Undercover
That number of degrees around a circle is complete arbitrary. The circle could be divided into an infinite number of degrees, and there could be an infinite number of degrees between each of the four right angles, — Metaphysician Undercover
1. Infinity is a never ending quantity.
2. Infinity is not a number. — Emmanuele
Btw, countable and uncountable infinity is counterintuitive, insane and nonsensical. Cantor was a lunatic. — Emmanuele
First of all the new number has conditioned itself to be infinitely different from the one on the list. In no possible way can the number be the one on the list, however the same can be said by the number on the list ever actually being a quantity. It has and will never end. Thus they're both infinite numbers, and thus they both have the same length. The only difference is the rate at which they grow. — Emmanuele
Second of all the rate of growth in infinite numbers is not a valid argument to define N (aleph-null) as an ordinal 'uncountable infinite'. This is because the rate of growth can still be achieved without ever actually having the list to being with. This new number N is in no way different or special from the numbers on the list. — Emmanuele
Third of all the rate of growth to infinity does not change at all the fact that they're both infinite. Saying that some N1 is infinite will then have an N2 being infinite proceed from that one makes no sense and is mathematically possible but absolutely irrational, and a waste of time for your brain to acknowledge. But people don't understand these three simple concepts. — Emmanuele
Planck Length, Planck Scale, speed of light (which is basically a scale constant) are not in any sense arbitrary. Unless Im mistaken, the SI system is based on non-arbitrary physical constants not this nonsensical notion of "qualities" or whatever. And even if it isn't, such a thing is possible but the gain is little for all the work required. See Natural units. — MindForged
That something could be done a different way does not make something arbitrary. There are perfectly sensible reasons to put the number of degrees at 360. It's a highly composite number allowing us to avoid fractions (which are hard for humans to do, hence the preference for decimal expressions), it's not a large whole number so it's fairly easy to do basic math with (particularly division), etc. I'm thinking you're using a weird definition of "arbitrary" or not explaining why it is (supposedly) so. — MindForged
As I said, and provided examples for, some divisions of degree are arbitrary, I didn't say that all are arbitrary. But the fact that some are, is all that's required to disprove Ikolos' claim that quantity is what is measured. Actually, quantity is the measurement. — Metaphysician Undercover
That's not even an argument, the number of degrees in a circle is not arbitrary, it was chosen because it's "easy to do basic math with". — Metaphysician Undercover
Logically I would state that the reason why aleph-null makes no sense is because like both aleph-null and the numbers on the list are infinity, then to say that aleph-null is in any way different from the numbers on the list is to state that the numbers on the list have an ending. This is because for them to actually be different is for both numbers to end in a difference. Such statement may sound illogical at first glance because no matter what number appears it will always be different, however the point is that if we think about it aleph-null is still impossible to fully become different. — Emmanuele
That does not follow. For one to be larger than the other all that need be true is that one set has a greater cardinality. What this will mean is that when you try to place them in a one-to-one correspondence with each other, it fails to be possible to do so. After all, sets that can be mapped together in this way are the same size. What Cantor showed was that it's impossible to map the naturals with the reals on pain of contradiction, it turned out the reals were larger not that the naturals had an end (in the sense of a final member). That's what makes them different, despite being infinite. They're different levels of infinity. — MindForged
Incorrect, their argument was that some were not "qualities" as you deemed them because they are part of reality. Pointing out that some aren't (as that user already admitted) is very much besides the point when they already admitted so. — MindForged
How is that not an argument? Ease of use is a perfectly legitimate reason to do prefer something. — MindForged
Also, try to do set a circle equal to 4 degrees and see how the math works out for you. — MindForged
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