John Platko wrote:There certainly were elements of Newton's laws that existed before Newton. But perhaps more to your point, reality existed before Newton provided certain models for approximating that reality, but those models no more existed before Newton came up with them then this sentence existed before I wrote it. Surely this is obvious.

John Platko wrote: my claim is knowledge, and knowledge is an abstract constructor capable of physical transformation.

John Platko wrote: How would you go about demonstrating the truth of a circle existing before someone imagined a circle?

John Platko wrote:I can see how the concept of angels can nicely fit into very modern physics.

JamesSS wrote:
If I specify an infinite set of apples and another infinite set of oranges, together I have an infinite set that is twice the size of either original infinite set. That is a set that has a cardinality between the set of all integers and that of all reals. And the reason that works is that by stating a set of all of a physical item, I have specified a specific infinity:

InfiniteA == [A,A,A,...] numbering a quantity equal to [1+1+1+...]
InfiniteB == [B,B,B,...] also numbering a quantity equal to [1+1+1+...]

And then the sum of them has twice the number/quantity of elements:
[A,B+A,B+A,B+...A,B] numbering a quantity equal to;
[1+1+1+...] + [1+1+1+...] = [2+2+2+...] - as a total quantity of elements thus a cardinality.

Greyman wrote:

JamesSS wrote:
If I specify an infinite set of apples and another infinite set of oranges, together I have an infinite set that is twice the size of either original infinite set. That is a set that has a cardinality between the set of all integers and that of all reals. And the reason that works is that by stating a set of all of a physical item, I have specified a specific infinity:

InfiniteA == [A,A,A,...] numbering a quantity equal to [1+1+1+...]
InfiniteB == [B,B,B,...] also numbering a quantity equal to [1+1+1+...]

And then the sum of them has twice the number/quantity of elements:
[A,B+A,B+A,B+...A,B] numbering a quantity equal to;
[1+1+1+...] + [1+1+1+...] = [2+2+2+...] - as a total quantity of elements thus a cardinality.

No. Assuming a countable infinite number of each, then the set of all apples and all oranges has the same cardinality as the set of all apples.

Cardinality_of_the_continuum

Wiki wrote:In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

JamesSS wrote:
Again, as I originally stated. This is an issue of how one defines "cardinality".

ScholasticSpastic wrote:

JamesSS wrote:
Again, as I originally stated. This is an issue of how one defines "cardinality".

Exactly. When one defines "cardinality" contingent upon one's desired outcome, or based upon one's ignorance of mathematics, rather than using standard definitions, one finds that one gets different results. And now my nipples are hard. Because I said "ignorance."

JamesSS wrote:
I quoted it from Wiki, ignorant one.

JamesSS wrote:babbling gadflies

ScholasticSpastic wrote:

JamesSS wrote:
I quoted it from Wiki, ignorant one.

You quoted some correct bits from wikipedia, and then went an incorrect direction with that information all by yourself.

ScholasticSpastic wrote:I can say that you are ignorant in a certain subject, and if I back this up with examples, it becomes a statement of fact, rather than a personal attack.

ScholasticSpastic wrote:However, if I were to say that you are ignorant, full stop, as you just said to me, that is a personal attack in contravention of the FUA.

JamesSS wrote:

ScholasticSpastic wrote:

JamesSS wrote:
I quoted it from Wiki, ignorant one.

You quoted some correct bits from wikipedia, and then went an incorrect direction with that information all by yourself.

No. I did not. And neither have you shown that I have. Thus your continued ad hom pestering is just as fallacious and malicious as always:

ScholasticSpastic wrote:I can say that you are ignorant in a certain subject, and if I back this up with examples, it becomes a statement of fact, rather than a personal attack.

And yet you have not.

ScholasticSpastic wrote:However, if I were to say that you are ignorant, full stop, as you just said to me, that is a personal attack in contravention of the FUA.

As you just did .. full stop.

ScholasticSpastic wrote:This is no kindergarten for babies !

scott1328 wrote:Apropos of nothing, and not impugning the reputation of any of the commentartiot... But is anyone else aware that Seth is currently suspended at Rationalia?

JamesSS wrote:

Cito di Pense wrote:

JamesSS wrote:
Can I take it that none of you are familiar with Edwin Hewitt and hyperreal numbers?

Read it and weep, JamesSS: From 2010, by somebody who's in this thread with you:

http://www.rationalskepticism.org/post5 ... eal#p50074

There is nothing to weep about. Do I need to explain it to you?

John Platko wrote:Soooo. If I have a rock. An actual rock with all of it's behaviors intact. And then I "conceptually remove it's behavior"(s) I'm still left with the knowledge of the original rock.

The "knowledge of" the *former* rock, is not the rock.

My point was that if you say that a rock is not equivalent to its behavior, then you should be able to conceptually remove its behavior and still have something left, yet you don't

Nor is such knowledge a property of the rock, but rather a property of you.

The fact that you know that there used to be a rock does in no way imply that the rock still exists (else we should probably all go have a talk with our bankers).

Not "know that there used to be" - there still is a rock! I can't change the rock by changing my conception of the rock.

John Platko wrote: (not to mention the actual rock because conceptually removing behaviors doesn't do dick to the actual rock.

Again missing the point. What is left of the rock once you remove its properties/behaviors?

John Platko wrote:Maybe it would help if you explained this a bit more slowly - perhaps showing how one conceptually removes the behaviors of a rock - one by one.

Well, I did that already. I first ("conceptually") removed the rock's inertia such that it cannot block anything from moving through that space. Then I also removed the rock's gravitational effect (not that it wouldn't have already been removed with the inertia).

Once the rock has no inertia and no gravitational effect (no weight), it no longer affects anything at all.

The fact that you knew that it used to be there is irrelevant. The rock IS not affecting anything any longer, thus the rock does not exist. You could run any kind of scientific test you like and the conclusion will be that there is no rock there.

John Platko wrote:But I still have the rock

John Platko wrote:That's why I'm not left with nothing when I conceptually castrated the rock. I still have my knowledge of the rock- even if I toss the rock. And that knowledge is my property.

JamesSS wrote:

John Platko wrote:But I still have the rock

In what way do you still have the rock? The knowledge of its prior existence is irrelevant.

John Platko wrote:That's why I'm not left with nothing when I conceptually castrated the rock. I still have my knowledge of the rock- even if I toss the rock. And that knowledge is my property.

I didn't say you were left with nothing at all. I said that you no longer have a rock.

JamesSS wrote:Again, as I originally stated. This is an issue of how one defines "cardinality". When given the definition that "cardinality" denotes the number of elements in a set:

Wiki wrote:In mathematics, the cardinality of a set is a measure of the "number of elements of the set".

then any element added to an existing set increase that number. That is what "adding" means.

So if you can add two independent infinite sets and get no more than what you originally had, then by definition, you did not add anything.

But "cardinality" is merely a word and words get used differently by different people.

logical bob wrote:
Two sets have the same cardinal if and only if there is a 1:1 correspondence between their members. That's how cardinality is defined, as that wiki page no doubt tells you. You can use the word differently, but you can also use the word hedgehog to refer to a teapot.

For finite sets the cardinal is the number of elements, but there isn't a "number of elements" in an infinite set.

So take a countably infinite set of apples {A1, A2, A3, ...} and a countably infinite set of oranges {O1, O2, O3,...}. Take their union {A1, O1, A2, O2, A3, O3,...}.

Now map A1 to the first term of that list, A2 to the second, A3 to the third and so on. Explicitly, for each integer n, A(2n-1) n the set of apples corresponds to An in the union and A(2n) in the set of apples corresponds to On in the union. This is a 1:1 correspondence, so the union and the set of apples have the same cardinality.

JamesSS wrote:The concept of infinity would make it appear as though the "largest number" is a definite oxymoron, because infinite MEANS no largest number. But I don't know that I could personally ever prove that there isn't a largest "prime number", even though it seems intuitive that there wouldn't be. Although I seriously doubt it, perhaps there is some phenomenon that happens concerning extreme prime numbers.

logical bob wrote:

JamesSS wrote:The concept of infinity would make it appear as though the "largest number" is a definite oxymoron, because infinite MEANS no largest number. But I don't know that I could personally ever prove that there isn't a largest "prime number", even though it seems intuitive that there wouldn't be. Although I seriously doubt it, perhaps there is some phenomenon that happens concerning extreme prime numbers.

Suppose there were a largest prime. Then there would be a complete list P1, P2, ..., Pn for some integer n. Multiply all n primes together and add 1. Call that number K. For any integer a up to n, dividing K by Pa yields a remainder of 1. Hence K is not divisible by any prime number. Hence K is prime. But this is impossible since K is bigger than every number on the complete list of primes. Therefore there is no complete list of primes and hence no largest prime.