This is absurd. "Nothing is bigger than X" doesn't mean "there's a thing which is bigger than X". It means "the set of things bigger than X is empty".
It's not a relationship that can be directly described using the symbol "<". If you tried using similar reasoning to this post, the closest you'd get is "every member of the empty set is smaller than every member of the empty set". This is of course true.
Si, it is absurd. I take that to mean some kind of error has been committed. On cursory examination, it seems I've made the blunder the Greeks were weary of: considering nothing to be something. Only something can be greater/less than something else. Yet in math we regularly encounter statements such as or , etc. Aren't these instances of comparing something to nothing and deeming this a valid comparison? Am I not doing the same when I say nothing is greater than , which in math becomes ?
Am I not doing the same when I say ...
No.
"0 < 0.5 is a statement about the numerical value indicating nothing. "Nothing is greater than X" is a statement about the size of the set containing things greater than X. You are using "nothing" with two different meanings.
So you mean to say ... supposing there are no dogs and 3 cats and n(x) returns the numerical value of x that what 0 < 3 means is n(dogs) < n(cats) i.e. n({ }) < n({cat 1, cat 2, cat 3})? There must be some quality (in this case quantity :puzzled:) on the basis of which a comparison (here quantitative) can be made.
Do you also mean that we can't compare nothing to something, like I was doing above? Gracias. Non liquet, but gracias.
Just a thought, but what if our ancestors had used an infinitesimal (sensu amplissimo) wherever they had to deal with n(nothing) = 0. They could've surmounted their philosophical/intuitionistic objections to treating nothing a something. For example if they ran into the equation , they could've used s (representing a really, really, small number) and "solved" the equation thus: . It would've surely made more sense to them than , oui?
There must be some quality (in this case quantity :puzzled:) on the basis of which a comparison (here quantitative) can be made.
There is sometimes a quantity on the basis of which a comparison can be made.
This quantity exists in 0 < 3. It doesn't in "nothing is bigger than X".
I think you misunderstood what Questions on LW are for. They are not to solve your small problem but pose big or otherwise of wider interest issues. You could have asked your question as a Shortform without downvoting.
LW is huge and I've just joined (it's been less than a year). I didn't realize ... apologies. I will be mindful of what kinda questions I ask. Gracias
I would've downvoted OP even if it were a shortform. Would that transgress a community norm I'm unaware of?
Also, I was unaware of any norm against small questions and doubt the value of having such a norm.
You can of course downvote anything that you think is not valuable. But usually, the standards for posts and questions are higher than for shortforms or comments.
I can't seem to trace it but there's an interesting article on nothing on Wikipedia. The gist of the article is that people have deemed inquiring about nothing a fool's errand, bound to fail!
By nothing I refer to that which the fundamental question of metaphysics, "Why is there something rather than nothing?", queries and that which baffled the Greeks who asked of 0, "How can something be nothing?"
That out of the way, I would like clarifications/answers/comments to a puzzle that's become somewhat of a staple of jokes.
Imagine a world of 2 objects, viz. and . We can see that is greater than or that is less than (size-wise). In this world nothing is smaller than x and nothing is bigger than X. In mathematical terms: . By the transitive property of greater/less than we have . Isn't this a paradox, that something is both greater than and less than itself?
Are there 2 types of nothing here? Is the nothing that's less than the same nothing as the nothing that's greater than ? This would be my feeble attempt to resolve this paradox.