Are there an (actual or potential) infinite amount of propositions and counter propositions?

Question

maybe this should have gone in the philosophy category.

well : what constitutes a relevant proposition

WTF??????????????????

you are almost using a circular definition. what is interesting in this context.

I was wondering what relevant meant and i thought you saying: 'something intresting' wasn't conducive to clarity. How can anyone know what is relevant?
I can see how for example: the proposistion kermit is green would almost certainly be of no use to someone working towards building a quantum computer. I will think about this a bit more. hmmmm.........

how can mathematicians sense what is usefull.

Answer 1

yes, i believe so
A better question: Are there an (actual or potential) infinite amount of relevant propositions and counter propositions?

what constitutes a relevant proposition?
something that is interesting enough

You can have a computer that given some math concepts will sort out an infinite number of propositions. Most of them will be uninteresting.

Presently there is a finite number of relevant propositions. Even if it huge and no living person can read it all. But since science evolves, math will evolve too and thus new theories will provide a potential infinite number of propositions.

you are almost using a circular definition. what is interesting in this context.
Something that is interesting for mathematicians. Something that is useful, a breakthrough. Mathematicans have a sense for this. This is why there are good journals and ...the others.
You can create definitions, propsitions and theorems but they are not useful for the theory and they will not get attention. It is easy to create uninteresting stuff. The interesting stuff requires more experience, intelligence and creativity.
I don't create a cycling argument. I thought you didn't know what "relevant" means.

Answer 2

To pluck one at random, for all n > 0 "n^2 > 5"

In the jargon that gives you a countably infinite number of propositions, true for all integers > 2, false for n=1 or n=2.

How do mathematicians sense what is useful? By what has worked or proved useful in the past.

If you wanted an absolutely rock bottom minimum, you could, in theory(!), deduce the whole of mathematics from the ten axioms of ZFC set theory. (More accurately, axiom schemas of ZFC set theory.)

According to Godel's incompleteness theorem, there must be some propositions in mathematics which are neither provable nor disprovable. However, unless it turned out that something pretty fundamental was unprovable, a pure mathematician would not accept something as true unless it could be proven to be true. He wouldn't be happy with the physical scientist's approach that something is true if it is more likely than not to be true. An applied mathematician I suppose has a foot in both camps. He can't give up on mathematical rigour without surrendering his claim to be a mathematician; on the other hand he has to work with physicists.

At the beginning of the twentieth century it was hoped that all mathematical propositions would be either provable or disprovable, but that is now known to have been a forlorn hope.

Answer 3

Of course there are, if you count propositions about specific positive integers and such-like.

E.g., for all N, "N is divisible by 7" is a proposition, and the number of propositions of that form is countably infinite.

Or look at moral claims. Pick a finite set of possible events that can be time-stamped, and a finite set of choices. Look at the set of all claims of the sort "If A happens first, and B happens second, and C happens third, and ... , then Z is morally justifiable." Each one is a different proposition, and as long as you don't limit the length of the chain of events, there are infinitely many of them.

Answer 4

Maybe, but that would simply help to answer your own question.

It is infinite.

I mean, if you were to only use the same question each time, by the time you had gone round the world once asking all eligible woman, then new women would be waiting back at the start.

Then add the different ways you could ask, languages, wording, etc...

Yeah, infinite.

But, for you (and I) no.

But there are still an infinite amount of ways to be slapped in the face.

Good luck son.

Answer 5

I believe that if the propositions are sufficiently organized
and generalized wherever possible, then a finite number
should suffice to explain a science like mathematics, even
a very large number of propositions , but not so large a number that they lose their explanatory efficiency.

Answer 6

The work of Gregory Chaitin has shown that you would actually need an infinite number of axioms in mathematics. Indeed it suggests that there are only small islands of proveable statements in vast seas of unproveable ones. Not only that there is no mechanism for deciding whether a statement is proveable or not. (Turing halting problem)

Answer 7

Who's he?