Where can I actualy read anyone explaining the concept of numbers that way? — TonesInDeepFreeze
Where can I actualy read anyone explaining the concept of numbers that way?
— TonesInDeepFreeze
Didn't you just read it? — Metaphysician Undercover
The notion of an actual infinite makes zero sense if, as per my assumption, actual means what it seems to mean to wit, completed in one sense or another for it flies against the definition of infinity as being necessarily that which can't be completed.
Maths, set theoretical infinities, kind courtesy of Georg Cantor, is an altogther different story as maths is essentially an axiomatic system, anything goes so long as you don't contradict yourself within one. — TheMadFool
There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity. — Metaphysician Undercover
I have another idle thought ... that the next revolution in physics will be the discovery of the actual infinite in the real world. By analogy, non-Euclidean geometry was thought to be a mathematical parlor trick of no use to physicists. Then Einstein came along and non-Euclidean geometry became real to the physicists.
Physically realized actual infinity has the same status in physics today as non-Euclidean geometry had in physics in the 1840s. The future genius to make this next breakthrough hasn't been born yet. Perhaps. — fishfry
What's interesting about this is that whereas it is quite easy to see how mathematics (at its extremes) makes no sense — synthesis
I thought you meant that there is a fundamental problem with:
"The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well."
And that your supposed solution to the supposed problem is:
"[...] we have to allow that "1" represents a different type of unity than "2" does [...]" — TonesInDeepFreeze
Or perhaps you would make clear which parts of your passage are ones you are critiquing and which parts are ones you are claiming. — TonesInDeepFreeze
I am claiming that there is a fundamental problem with numbers. If "1", "2", "3", etc. , are used to represent unities, — Metaphysician Undercover
Yes, as I thought, you find that there is a problem with the notion (whatever it means) that 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". — TonesInDeepFreeze
But (aside from even trying to parse the broken phrases) I don't know who says anything along the lines of 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc". So I don't see why you think it is a problem that needs to be addressed. — TonesInDeepFreeze
I see no problem with that in itself. The problem is when we want to say that, and also that "2" and "3" represent a type of unity. — Metaphysician Undercover
I understood that; I thought you meant that you do want to take '2' and '3' as representing a type of unity, while you think that that is contradicted by 'the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" so that it needs correction .
Am I not correct that that is your view? — TonesInDeepFreeze
More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual. — TonesInDeepFreeze
In sum, I can't make sense of what you're trying to say. — TonesInDeepFreeze
Suggestion: You could reference some actual piece of mathematical or philosophical writing that you disagree with and show how you think you can correct it. — TonesInDeepFreeze
More basically, I don't know why one would fret over any of this, since I don't know anyone who claims "the numeral "1" represents a basic unity. an individual.
— TonesInDeepFreeze
I find that very strange I hear them used that way all the time. — Metaphysician Undercover
"the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" — TonesInDeepFreeze
You haven't really ever thought about such fundamental issues as how we use numerals, and you don't really understand why anyone else would. — Metaphysician Undercover
But neither P nor Q are stated coherently by you. And there's no reason to think anyone wants P or Q anyway. — TonesInDeepFreeze
Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity". — TonesInDeepFreeze
t would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. — TonesInDeepFreeze
1 (one, also called unit, and unity) is a number and a numerical digit used to represent that number in numerals. It represents a single entity, the unit of counting or measurement. For example, a line segment of unit length is a line segment of length 1. In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer.[1] It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0. — Wikipedia
In the very most basic example, we can ask whether the number -2 is prime. The question may seem nonsensical, but it can motivate us to put into words the unique role of 1 in the whole numbers. The most unusual aspect of 1 in the whole numbers is that it has a multiplicative inverse that is also an integer. (A multiplicative inverse of the number x is a number that when multiplied by x gives 1. The number 2 has a multiplicative inverse in the set of the rational or real numbers, 1/2: 1/2×2=1, but 1/2 is not an integer.) The number 1 happens to be its own multiplicative inverse. No other positive integer has a multiplicative inverse within the set of integers.* The property of having a multiplicative inverse is called being a unit. The number -1 is also a unit within the set of integers: again, it is its own multiplicative inverse. We don’t consider units to be either prime or composite because you can multiply them by certain other units without changing much. We can then think of the number -2 as not so different from 2; from the point of view of multiplication, -2 is just 2 times a unit. If 2 is prime, -2 should be as well.
*This sentence was edited after publication to clarify that no other positive integer has a multiplicative inverse that is also an integer. — * reference above
near complete denial of the relation between one and unity — Metaphysician Undercover
Then I conclude that what needs to be discussed is clarification of P and Q. — Metaphysician Undercover
Count the books on the shelf for example. "Book" signifies the type of unity being counted, "1" signifies that a unity called "a book" has been identified, and a first one has been counted , "2" signifies two of these units, etc.. — Metaphysician Undercover
I assume you know how to use Google or some other search facility. You could simply search this if you need such a confirmation, instead of asking me to do your research for you. — Metaphysician Undercover
Here's the first entry I get when I Google that question, is 1 a prime number — Metaphysician Undercover
Of course the notion of 'one' is related to that of a unity. But even aside from parsing, I don't know who in particular you think holds that "The "2" represents two of those individuals together, and "3" represents three, etc". It would help if you would cite at least one particular written passage by someone that you think is properly rendered as "the numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc" and "'2" and "3" represent some kind of unity". — TonesInDeepFreeze
There is a fundamental problem with the concept of numbers. The numeral "1" represents a basic unity. an individual. The "2" represents two of those individuals together, and "3" represents three, etc. But then we want "2" and "3", each to represent a distinct unity as well. So we have to allow that "1" represents a different type of unity than "2" does, or else we'd have the contradiction of "2" representing both one and also two of the same type of unity. — Metaphysician Undercover
The spaceship can keep going, because the universe is expanding faster than the speed of light. The spaceship won't catch up with the expansion of the universe. — Down The Rabbit Hole
1 is the count at the first member of the set, a particular unity (whatever it is). 2 is the count at the second member of the set. Etc. And '1' and '2' name different individual numbers. And 1 is the count of the members of the set with one unit. And 2 is the count of the members of a unity that is a set with two members. And a set with one member is a different kind of unity from a set with two members. — TonesInDeepFreeze
'2' denotes the number 2. The number 2 is the count of a set with two members. And a set of two members is itself a unity as a set. But '2' does not denote a unity; it does not denote the set that it counts. It denotes the COUNT of a set that is itself a unity. When we say that a set is a unity, we mean that it is one set, while we recognize that the number of members of the set may be greater than one. — TonesInDeepFreeze
The universe is not expanding, objects in the universe are simply moving away from each other and the space within which they are moving, in is infinite. — Present awareness
Let's say that "1" refers to the number 1, which represents the count, and is also the thing counted — Metaphysician Undercover
Since Aristotle, the philosophers say that there is only the potentially infinite. — spirit-salamander
do you agree that it is necessary that there is a thing counted — Metaphysician Undercover
If "1" does not refer to the book, as well as what you call the number, then there is nothing being counted — Metaphysician Undercover
we cannot dispense with the fact that "1" must refer to the object being counted, a book — Metaphysician Undercover
To have a true count, "1" must refer to the first book, "2" refers to the first and second together — Metaphysician Undercover
So there wasn't a big bang that started an expanding universe? — Down The Rabbit Hole
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