Numbers as sets

John Jones wrote:

Some writers define number as a set or multitude or plurality. ALL of these views suffer from the drawback that this concept of number will not cover the numbers 0 and 1. Moreover, these terms (sets, etc.) are utterly vague: sometimes they refer to 'heap' or 'group' or 'agglomeration' - referring to a juxtaposition in space, sometimes they are so used as to be practically equivalent to 'Number', only vaguer.

I conclude, that no analysis of the concept of Number is to be found in a definition of it as sets, etc.

These are Frege's words? Frege concluded that no analysis of the concept of Number is to be found in a definition of it as sets? If so, you ought to have attributed the quote to him.

FreeDuck wrote:

John Jones wrote:

Some writers define number as a set or multitude or plurality. ALL of these views suffer from the drawback that this concept of number will not cover the numbers 0 and 1. Moreover, these terms (sets, etc.) are utterly vague: sometimes they refer to 'heap' or 'group' or 'agglomeration' - referring to a juxtaposition in space, sometimes they are so used as to be practically equivalent to 'Number', only vaguer.

I conclude, that no analysis of the concept of Number is to be found in a definition of it as sets, etc.

These are Frege's words? Frege concluded that no analysis of the concept of Number is to be found in a definition of it as sets? If so, you ought to have attributed the quote to him.

Of course I must attribute the quote to him, so explain why if I attribute the text to myself it will not be read?

May I ask what your qualifications are to make this judgement? Do you by any chance have a degree in Math or a related field? Since I am asking you what qualifies you to have an opinion, I ought to tell you what qualifies me. I have a BS and MS in Physics. What are your qualifications? Or are you, by any chance, an utterly ignorant person talking about things he doesn't begin to comprehend?

John Jones wrote:

FreeDuck wrote:

John Jones wrote:

Some writers define number as a set or multitude or plurality. ALL of these views suffer from the drawback that this concept of number will not cover the numbers 0 and 1. Moreover, these terms (sets, etc.) are utterly vague: sometimes they refer to 'heap' or 'group' or 'agglomeration' - referring to a juxtaposition in space, sometimes they are so used as to be practically equivalent to 'Number', only vaguer.

I conclude, that no analysis of the concept of Number is to be found in a definition of it as sets, etc.

These are Frege's words? Frege concluded that no analysis of the concept of Number is to be found in a definition of it as sets? If so, you ought to have attributed the quote to him.

Of course I must attribute the quote to him, so explain why if I attribute the text to myself it will not be read?

It's universally considered improper to present someone else's writing as your own. You want to argue about universally accepted standards of behavior now?

It is also customary to cite your sources if you're going to state their ideas.

I honestly don't see what the confusion is. 0 is absence is the absence of that about which you are concerned. 1 is the thing or idea of unity (the unity makes it one idea or thing). Anything over that is ebrown said: multiple 1's.

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

John Jones wrote:

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

May one inquire what your qualifications are to opine about Mathematics?

Brandon9000 wrote:

John Jones wrote:

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

May one inquire what your qualifications are to opine about Mathematics?

We are not making a mathematical enquiry. What are your qualifications in cookery?

John Jones wrote:

Brandon9000 wrote:

John Jones wrote:

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

May one inquire what your qualifications are to opine about Mathematics?

We are not making a mathematical enquiry. What are your qualifications in cookery?

We can discuss me next if you like. Now, you are expressing opinions and drawing conclusions about Mathematics. Stop playing with words and tell me your qualifications to do this.

I'm still at a loss as to what it is you wish to discuss. What is your proposition? You agree or don't agree with Frege? Set theory is handy but loaded with paradoxes? I don't know what it is you want us to be discussing.

Brandon9000 wrote:

John Jones wrote:

Brandon9000 wrote:

John Jones wrote:

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

May one inquire what your qualifications are to opine about Mathematics?

We are not making a mathematical enquiry. What are your qualifications in cookery?

We can discuss me next if you like. Now, you are expressing opinions and drawing conclusions about Mathematics. Stop playing with words and tell me your qualifications to do this.

A mathematician does not draw conclusions from mathematics about mathematics. How could he? I think you came into the topic at the level of the rules that constitute it, and have never worked at its lower levels. If that's the case, there was never any possibility of discussion.

John Jones wrote:

Brandon9000 wrote:

John Jones wrote:

Brandon9000 wrote:

John Jones wrote:

Setanta wrote:

Quite apart from coming here in every thread with an agenda do demonstrate the superiority of his perceptions over the arduous studies of professionals, Mr. Jones now thinks to set for us the terms of management of a thread and debate. Which is, in his own term, contemptible.

Play with the duck. Or something.

May one inquire what your qualifications are to opine about Mathematics?

We are not making a mathematical enquiry. What are your qualifications in cookery?

We can discuss me next if you like. Now, you are expressing opinions and drawing conclusions about Mathematics. Stop playing with words and tell me your qualifications to do this.

A mathematician does not draw conclusions from mathematics about mathematics. How could he? I think you came into the topic at the level of the rules that constitute it, and have never worked at its lower levels. If that's the case, there was never any possibility of discussion.

You are pontificating on the subject of Mathematics without going through the preliminary step of learning the topic first. Many of us spent years in high school and college painfully climbing this mountain a foot at a time, but you lack the self-discipline to do this. You are like someone who, speaking no Russian, offers his services as a Russian translator, making up whatever nonsense pops into his head. I'm wrong? I dare you to choose your best mathematical theory and submit it to a legitimate, peer reviewed mathematics journal.

It isn't that you make statements without references; it is that you quote others out of context, without refering to them, to challenge the foundations of a subject you apparently have little actual knowledge of.

And to answer your set question from a philosophical perspective, which you seem to be emphasizing (I haven't studied mathematical set theory, but I'm off to look it up once I'm done here to have at least some idea of the topic... need to talk to a friend of mine who has studied it in depth), a set is related to its members. A set is defined by the common quality that its members have in common, and at the same time the members are related to each other as a unity through this commonality.

In set theory, a set is described as a well-defined collection of objects. These objects are called the elements or members of the set. Objects can be anything: numbers, people, other sets, etc.