The smallest non-interesting number

[Ramanujan]

@septimus

Didn’t you once tell us how interesting 1729 was?

proof by contradiction!

[Indistinguishable]

@Ramanujan

this is not strictly true. consider, for example, any infinite, but not well-ordered set. there is no guarantee that you will ever hit a false. in fact, even for well-ordered sets, consider, maybe, the set of numbers which have been enumerated.

Re-read what you have quoted. I explicitly specified the natural numbers as the domain.

(Just dropped in to reply to this; TriPolar, I’ll happily expound more on intuitionistic logic later, when I have a little more time)

[TriPolar]

@Indistinguishable

I would say there can be a formal logic for undecidable or ambiguous predicates, able to treat oceanhood without the supposition that every particular instance either definitely is is or definitely isn’t an ocean; for example, though I wouldn’t consider it the relevant logic to use in this instance either, there is formal intuitionistic logic which denies the automatic truth-hood of “P or not P”, and in that sense allows one to define predicates without the supposition that there must be a clear YES or NO answer to their holding in any particular case.

Ok, I see you’re talking about non-binary logic allowing a result that is neither “P” or “not P” (my way of describing it, not arguing yours), and as you say isn’t really applicable to the idea of agreed upon definitions of what is or is not an ocean, but it could apply where the definition of oceans and not oceans are not agreed upon.

[Mijin]

@TriPolar

Ok, I see you’re talking about non-binary logic allowing a result that is neither “P” or “not P” (my way of describing it, not arguing yours), and as you say isn’t really applicable to the idea of agreed upon definitions of what is or is not an ocean, but it could apply where the definition of oceans and not oceans are not agreed upon.

Well, the definition of an ocean does not specify a precise volume, so you can consider it “not agreed upon” for our purposes here.

I assumed that Indistinguishable was alluding to fuzzy logic.
For my mind, the sorites paradox is effectively solved by fuzzy logic, though I appreciate that there is not universal agreement on this.

Each drop of water increases the “ocean-ness” of a body of water.
From a practical point of view, what this means is that above a certain threshold*, each additional drop will slightly increase the chance of a human judging that this body of water is an ocean.

• And note that this threshold does not have the same problem as the sorites paradox. There is no theoretical problem with setting a threshold below which “everyone agrees this is not an ocean”.

[Bryan_Ekers]

Earlier today I saw 1729 on a taxi’s licence plate.