Love the argument, Tom; but I have to say I agree with Pierre-Normand that what you have shown is that the totality of facts is uncountable, not that it is impossible. — Banno

You don't understand Cantor's theorem then. The powerset is always strictly bigger than the set, as Cantor proved. This is how the various Aleph numbers are generated. Even if the set of facts was Aleph_3, its powerset would be Aleph_4.

And...?
You've still not shown a contradiction; only that the number of facts is not countable.

You've still not shown a contradiction; only that the number of facts is not countable. — Banno

No. I showed that the ASSUMPTION that there is a totality of facts leads to a CONTRADICTION. The argument works whatever Aleph number you assign to the totality.

There are various versions of 'the world is the totality of so-and-so'.

Wittgenstein: The world is the totality of facts.
Carnap: The world is the totality of physical objects and logical structures.
Quine: The world is the totality of physical objects and mathematical objects.
Lewis: The world is the totality of things in possible worlds.
Armstrong: The world is the totality of states of affairs.
.
.
.

There are various versions of 'the world is the totality of so-and-so' — quine

Presumably any totality is at time t.

I'm not a great one for totalities. If a totality is in its details unknowable - and I presume it is - how can we reasonably claim to know what it consists of? Or perhaps, what constitutes it?

Wittgenstein's 'everything that is the case' was part of a tightly-defined set of propositions about, as we would say now, a closed formal system. I take it the others are.

What of gods, individuals' beliefs that no-one knows about, expectations that might or might not come to fruition, brilliant ideas for novels or the use of graphene that are about to be imagined but haven't been yet, ideas of beauty and morality...?

My understanding is that this is definitive. It locates facts as physical, worldly affairs rather than linguistic. Statements of fact are statements about the world, and the facts are the truth makers. Thus the statement, "The world is the totality of facts." is not a fact, but a definition, a linguistic affair, for or against which factual evidence cannot be brought.

As such, it is certainly vulnerable to being shown to be contradictory or incoherent, but since there does seem to be a world, and we do talk about it both as a totality and as fragmentary facts, it is so fundamental to discourse that it might well be easier to dismantle set theory if it proves to be in contradiction with such a statement.

As such, it is certainly vulnerable to being shown to be contradictory or incoherent, but since there does seem to be a world, and we do talk about it both as a totality and as fragmentary facts, it is so fundamental to discourse that it might well be easier to dismantle set theory if it proves to be in contradiction with such a statement. — unenlightened

You will need to dismantle Relativity as well as Set Theory, not to mention reason if you want to maintain a "totality of facts".

e.g. https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument

You will need to dismantle Relativity as well as Set Theory, not to mention reason if you want to maintain a "totality of facts". — tom

I actually prefer to dismantle reason, over dismantling the world. That talk and theory and reason is in the end inadequate to the world is relatively unproblematic; we can always just shut up about what cannot be said. And that seems preferable to trying to excise it from the world.

Wittgenstein: The world is the totality of facts.
Carnap: The world is the totality of physical objects and logical structures.
Quine: The world is the totality of physical objects and mathematical objects.
Lewis: The world is the totality of things in possible worlds.
Armstrong: The world is the totality of states of affairs. — quine

What would Kripke say?

The world is the totality of every realized and unrealized modalities?

I actually prefer to dismantle reason, over dismantling the world. That talk and theory and reason is in the end inadequate to the world is relatively unproblematic; we can always just shut up about what cannot be said. And that seems preferable to trying to excise it from the world. — unenlightened

Sure, when PROVED wrong, just ignore it.

Yes. If talk proves talk wrong, stop talking. If talk proves the world wrong, talk differently. Which do you think you've done?

Thus the statement, "The world is the totality of facts." is not a fact, but a definition, a linguistic affair, for or against which factual evidence cannot be brought. — unenlightened

Yes. If talk proves talk wrong, stop talking. If talk proves the world wrong, talk differently. — unenlightened

So, what is it? Metaphysics or no metaphysics?

So, what is it? Metaphysics or no metaphysics? — Question

I think this is metaphysics: the world is under no obligation to conform itself to our talk; therefore we had best conform our talk to the world, to the extent we can.

To expect the world to conform itself to our talk is what is known as magical thinking. As if a cunning arrangement of words can oblige things to be thus and so.