Are number theory and set theory the only branches of math where speaking of truth is permitted?

[Boojatta]

If those are the only two areas where it is permissible to speak of truth, then what is it about them that creates this situation?

Would it be possible that in future mathematicians might invent, in addition to existing branches of mathematics, a new branch that would be the third one in which we can talk about truth? Alternatively, is there some way to show that there can be no such third branch?

[immoderate]

1. No.

--imm

[Lionel Mandrake]

7. Of course not.

Mathematics is all about the search for truth. So are all other academic subjects, e. g., physics, chemistry, biology, history, classics, philosophy, economics, anthropology, psychology, sociology.

Speaking of truth is always encouraged, never forbidden.

[Xipe Totec]

2. Can you cite an example of a branch of mathematics where speaking of truth is not permitted?

Truly curious.

[Boojatta]

4. Perhaps it will be clearer if I begin with number theory and set theory.

In each of those two branches, it's acknowledged that there are meaningful ideas involved and that new axioms could be discovered and recognized as being true. Thus, existing systems of axioms could be expanded.

In other branches, there is some motivating idea, but people insist that the idea is merely a heuristic aid, and that the only thing we can truly rely upon is a definition that consists of a fixed list of properties. Each such property might superficially resemble an axiom, but the list of properties is always fixed by the definition. The list of properties isn't to be expanded by adding new properties. In contrast, a list of axioms of number theory is open-ended, as is a list of axioms for set theory.

[Xipe Totec]

6. I'm not following; You'll have to cite an example for me,

Because as far as I know, every branch of mathematics connects to number and set theory.

Now set theory has it's own problems, such as Cantor's paradox, and Kurt Gödel punched a whole in number theory with his incompleteness theorem, establishing inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.

[Boojatta]

5. The connection with truth is ...

that in number theory and set theory it is acknowledged that an open-ended process of discovery is possible, and that the goal is to discover the truth.

For other branches of mathematics, we can think of an analogy: the experimental investigation of allowing one's mind to interact with the actual mathematical structures isn't permitted. Instead, one relies upon theory alone in the sense that the genuine but intangible concepts are replaced with something like dogmatic conventions. One might make discoveries within the system provided by such theory, but one cannot make any discoveries that go beyond the framework.

[saras]

9. Statistics and college algebra come to mind.

[Xipe Totec]

10. Lol! That's hilarious!

I prefer to call them sadistics.

[TheMadMonk]

3. Boolean logic? /nt

[izquierdista]

8. Those are the areas where truth gets a mathematical definition.

The reason truth is discussed in those areas (and in the area of mathematical logic) is because they deal with fundamental definitions (i.e., "truth&quot . And in answer to your post#4, axioms are not discovered, they are postulated. They are suppositions upon which all else is based.

If you really want to untangle all the details of this, it's time for you to read Russell's Principia Mathematica.

[MarkCharles]

11. Why do I think this thread was only started to...

get some attention?

I think that. I do!

[Boojatta]

12. Would you be so good as to recruit some DU members

for me? I want people who are willing to receive private messages from me, and who will respond within seven days to indicate one of the following:
1. They might be willing to post a message on the public boards depending on what editing I consent to;
2. They definitely won't post the message on the public boards; or
3. They are willing to post the message, in its current form, on the public boards.

Of course, if they select option 3, then they will have to wait for me to give them authorization before they proceed. Otherwise, the same message might be posted more than once by several people. I don't want to contribute in any way to spamming of the DU message board.

The idea is to allow me to find out what people think on various issues without allowing my username to influence their reactions.

Another benefit is that nobody will mistakenly believe that I am looking for attention. Of course, I do want people to share their thoughts with me, and I suppose that they are unlikely to think very deeply about something if they aren't even paying attention. However, if they're paying attention to my username, then they are being distracted. I prefer that they not be distracted. That's why I already thought of this scheme of having others post my messages without mentioning me. Yes, I'm basically repeating myself here. Why? Because you have given me an opportunity to ask you to volunteer your services.

We share the same goal, and I cannot achieve this goal without help. Will you help, or are you participating in this thread for no constructive purpose?

[HopeHoops]

13. FUCK NO! Mathematics is absolute. It doesn't always describe the subject accurately...

But it is still absolute. It's the only science that is. Right or wrong, the rules stand on their own. They don't impose themselves on physics, chemistry, astronomy, optics, or any other branch of science. The rules are used by the others but not the master. All of mathematics is truth. Right or wrong, it is truth because there isn't another way to express it. There aren't two branches, or more branches, there is only one. And yeah, I'll get pissed about this if necessary.