we cannot dispense with the fact that "1" must refer to the object being counted, a book
— Metaphysician Undercover — TonesInDeepFreeze
I'm not saying a number is a book — Metaphysician Undercover
the number 5 loses its meaning if it does not refer to five of something counted, — Metaphysician Undercover
if we remove "War and Peace", there is no longer two books, and the pairing is invalidated — Metaphysician Undercover
You might still use "2" to name the book — Metaphysician Undercover
neither Portnoy's complaint nor "War and Peace" need to be paired with either 1 or 2, for there to be a valid count of 2 — Metaphysician Undercover
We can have a count of 2 [electrons] without establishing the principles required to distinguish one from the other — Metaphysician Undercover
we can talk about 12 volts, without the need to distinguish and label each unit of electrical potential — Metaphysician Undercover
You look at your bookshelf, number "Portnoy's Complaint" as 2, and bring it in to me, telling me you have two books in your hand, because "Portnoy's Complaint" is identified as two books. — Metaphysician Undercover
At the moment of conception, there is a rapid expansion of cells, like a Big Bang, only on a biological scale if you will. Looking at our observable universe, we see what conception looks like on a cosmic scale. Since space is infinite, there may be an infinite number of Big Bangs, but we’ll never observe them from earth because of the enormous distances involved. The light from a universe 100 billion light years away, won’t arrive on earth for another 86 billion years. — Present awareness
Oh I see I missed your point the other day and this is a good point. Yes even hard science is ultimately nonsense. — fishfry
Nothing within the universe is supposed to be able to travel faster than the speed of light - it's called the cosmic speed limit. As galaxies are moving away from us faster than the speed of light, physicists say that as nothing within the universe can move faster than the speed of light, it is the universe itself expanding. — Down The Rabbit Hole
If I'm not mistaken, in another thread, you were using the word 'refer' in the sense of 'denote'. So if not 'denote' what exactly do you mean by 'refer' in this thread? — TonesInDeepFreeze
The numeral '5' has meaning. The number 5 is not the numeral '5'. — TonesInDeepFreeze
The fact that 5 is a count doesn't contradict that 5 also is a number no matter what it happens to count. — TonesInDeepFreeze
5 is the successor of 4. 4 is the successor of 3. 3 is the successor of 2. 2 is the successor of 1. 1 is the successor of 0.
No matter what the numbers count, they exist by virtue of successorship or by being 0. — TonesInDeepFreeze
of course are different, but nothing is "invalidated". Saying the pairings are "invalidated" is not even sensical. — TonesInDeepFreeze
You're doing it again! We do not use '2' to name a book. '2' does not denote a book. — TonesInDeepFreeze
We can switch them so that we have:
{<'Portnoy's Complaint' 1> <'War And Peace' 2>}
But the greatest number in the range is still 2. — TonesInDeepFreeze
That doesn't contradict that when we see discrete objects then we may count them. — TonesInDeepFreeze
How we use the concept of counting is a matter of practical approach, such as putting the water in a beaker with lines and counting the lines in the beaker to the point the water level ends or whatever. Whatever difficulties there may be conceptually with that, they don't negate the more basic notion of counting by bijection. — TonesInDeepFreeze
You present as so confused that I wonder whether you are posting as some kind of stunt or dumb cluck character. — TonesInDeepFreeze
"Refer" [...] means that we must direct our attention toward whatever it is which is referred to, — Metaphysician Undercover
You might still use "2" to name the book — Metaphysician Undercover
Which pair is the true representation of the count? — Metaphysician Undercover
Imagine not having the pressure of trying to figure everything out, instead, just going with the flow of ideas, allowing them to come and go as do all things — synthesis
In everyday understanding, when we count, we associate one thing with 1, then the next thing with 2, etc. Literally. We say the numbers, one for each object as we count the objects. Mathematically. this is expressed as a function from the set of things counted to a set of numbers: — TonesInDeepFreeze
It is the very point that you can count more than one way.
You can count 'War And Peace as the first, then 'Portnoy's Complaint' as the second. Or you can count 'Portnoy's Complaint' as the first, then 'War And Peace' as the second. In either case, both counts show that there's a first and second, thus there are two. — TonesInDeepFreeze
The sequence a,b,c,d,e is a sequence of five letters. e is letter five. — jgill
The sequence a,b,c,d,e is a sequence of five letters. e is letter five. — jgill
That's an arbitrary designation, dependent on a stipulation that there is a left to right order to the sequence. "a" could just as easily be letter five, or we could assume an ordering which makes any of the letters number five — Metaphysician Undercover
This is simply not true. Numbers are defined by quantity, not order. — Metaphysician Undercover
The point is that to describe a count as a tuple is not a correct description of a count. You just don't get it. — Metaphysician Undercover
You're failing to distinguish between cardinals and ordinals.
Let me give you a standard example. Consider the positive integers in their usual order: — fishfry
Now the quantity of positive integers is exactly the same in either case, since the ordered set ({1,2,3,…},<)({1,2,3,…},<) and the ordered set ({1,2,4…,3},≺)({1,2,4…,3},≺) have the exact same elements, just slightly permuted. There is a one-to-one correspondence between the elements of the two ordered sets. — fishfry
You don't even know what it is that you don't get. — TonesInDeepFreeze
It's almost an admirable trait . . . but not quite. — jgill
maybe after you explain an infinite number of times, I'll get it — Metaphysician Undercover
we were talking about a count, which is a measure of quantity, not an order — Metaphysician Undercover
the number is excluded by the infinite order which must occur prior to it — Metaphysician Undercover
lack of knowledge is innocence — Metaphysician Undercover
The point is that we were talking about a count, which is a measure of quantity, not an order. To use numbers to indicate an order is a different matter. So to demonstrate the use of numbers in ordering now, is to equivocate, because an order does not necessarily imply a count — Metaphysician Undercover
That is not true. These sets do not have the same elements. — Metaphysician Undercover
If "..." implies an infinite extension of the order, then 3 does not exist in the second set. Therefore they do not have the same elements. The symbol "3" is there, but the number is excluded by the infinite order which must occur prior to it. That's an obvious problem with your mode of equivocation, and conflating counting and ordering, it allows for contradiction. You can describe an order which is never ending (infinite), then say that there is a 3 after the end of it. And for you, that 3 is there. But of course you've just accepted the contradiction. — Metaphysician Undercover
In this context, there are two senses of 'count':
(1) A count is an instance of counting. "Do a count of the books."
(2) A count is the result of counting. "The count of the books is five." — TonesInDeepFreeze
A count(1) implies an ordering and a result that is a cardinality ("quantity", i.e. a count(2)). — TonesInDeepFreeze
If lack of knowledge is innocence, then you are a saint. — TonesInDeepFreeze
You wrote: "Numbers are defined by quantity, not order ..." If you didn't mean that you should not have written that. — fishfry
My God, you wield your ignorance like a cudgel. I could have just as easily notated the two ordered sets as:
* ({1,2,3,4,…},<)({1,2,3,4,…},<) and
* ({1,2,3,4,…},≺)({1,2,3,4,…},≺)
which shows that these two ordered sets consist of the exact same underlying set of elements but different linear orders. Remember that sets have no inherent order. So {1,2,3,4,...} has no inherent order. The order is given by << or ≺≺. — fishfry
On the contrary, sets have no inherent order. — fishfry
Why don't you have a look at the Wiki page on ordinal numbers and learn something instead of continually arguing from your lack of mathematical knowledge? — fishfry
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