Re: the need for relevance

Jesse F. Hughes wrote:

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

Jesse F. Hughes wrote:

So, the set of natural numbers does not contain every natural number?

THE set of natural numbers does not even exist.

Well then what the heck is N? You *do* use N as a constant term,
right? What does it mean to you?

Here's a sentence: "N is not a completed set." Is that sentence true,
false or meaningless? How about the sentence "N is a set."?

[...]

Please tell me if you agree with each of the following.
(1) When I write "N", I mean the set of natural numbers.
(2) Every element of N is a natural number.
(3) Despite the fact that N is *the* set of natural numbers, there are
some natural numbers which are not elements of N.
Or, if you prefer (though I don't):
(1) When I write "N", I mean the set of natural numbers, but this set
changes over time. (2) Every element of N is a natural number.
(3) At any time, there are some natural numbers which are not elements
of N. (4) If n is an element of N at time t, then n is an element of
N at
every later time.

Why do you insist that natural numbers SHOULD BE in A SET? I don't!

Fine. What does the term N denote?

Do you likewise insist that all infinite ordinals are in a set? Huh?

Of course not, but I do sometimes use the term On to denote the class
of ordinals. If someone asks me what On denotes, I can answer the
question.

Here we are! Now sink just one level deeper, do the same thing with N,
and we're on speaking terms. Suppose that N is the _class_ of naturals.

Happy with that conclusion? This is your method, yes?

Not happy with _your_ conclusion. But happy with my method.

Could you tell me what your method is, because I apparently don't
understand? I have a statement P and N. How do I tell if P is true
or false? Does it depend on time? There is some number n which is
not in N today. Maybe it's 10^10^10^10^...^10. Could it be in there
tomorrow?

Those questions all appear irrelevant to me.

You say you're happy with your method, but it's irrelevant what your
method is? Er, okay.

Here's a couple of questions.

Is N a meaningful term? Given a formula P with a single free variable
X, let P(N) be the result of substituting N for X throughout P. Is
P(N) a sentence (i.e., is P(N) a statement which is either true or
false?)? What is the meaning of P(N)? How do I determine whether
P(N) is true or false?

Are all of these questions irrelevant too?

No. If you are prepared to go along with me and define N as a class.

Han de Bruijn

.

Relevant Pages

  • Re: Epistemology 201: The Science of Science
    ... >>If they're meaningless symbols, don't call them numbers, ... >>there are an infinite number of naturals between any two naturals. ... I have already made my case regarding the integers and rationals. ...
    (sci.math)
  • Re: Epistemology 201: The Science of Science
    ... >>If they're meaningless symbols, don't call them numbers, ... >>there are an infinite number of naturals between any two naturals. ... I have already made my case regarding the integers and rationals. ...
    (sci.cognitive)
  • Re: Epistemology 201: The Science of Science
    ... >>If they're meaningless symbols, don't call them numbers, ... >>there are an infinite number of naturals between any two naturals. ... I have already made my case regarding the integers and rationals. ...
    (sci.physics)
  • Re: the need for relevance
    ... false or meaningless? ... Now sink just one level deeper, do the same thing with N, ... and we're on speaking terms. ... Suppose that N is the _class_ of naturals. ...
    (sci.math)
  • Re: abundance of irrationals
    ... >> The question is meaningless, since you haven't stated what program ... naturals. ... comprise a hamburger. ...
    (sci.math)