The world is the totality of facts.
I'm not sure if people can look past through the profundity of this statement; but, this is essentially saying another way that the totality of facts is that and only that what an omniscient being can perceive.
For any person with a self, and with it all the limitations that having a self entails in a world of states of affairs representing facts, then this proposition itself is meaningless. The totality of facts are by essence to such a being, unknowable.
Hence, whatever cannot be said must be passed over in silence, and let the will do its job, successfully or unsuccessfully as some might argue, in face of such glaring limitations.
So, get back to work or wallow.
For any person with a self, and with it all the limitations that having a self entails in a world of states of affairs representing facts, then this proposition itself is meaningless. The totality of facts are by essence to such a being, unknowable.
Hence, whatever cannot be said must be passed over in silence, and let the will do its job, successfully or unsuccessfully as some might argue, in face of such glaring limitations.
So, get back to work or wallow.
Comments (43)
Perception of what?
That would require magic, not omniscience. Potential is an object of thought, not perception.
You hd best fill in the gaps if you want to proceed.
There is no mention of perception in "The world is the totality of facts". So it must be introduced by some other assumption. What is your hidden assumption?
This can go about two way's and Wittgenstein choose the rather treacherous/fallacious path of solipsism in the Tractatus and with it private languages if I dare say so. The other path he could have taken is to assert a dichotomy between the self and an object but instead encapsulated both in language by saying that the limits of my language are the limits of my world (as if one could not learn a new word or fact), and the rest of the Tractatus would have fallen apart in my opinion.
I think the Investigations show's that solipsism was the wrong path to take.
There are obviously infinite modalities to states of affairs and the world, after all, is not two dimensional.
I don't follow that.
Where does perception fit? Especially since the term does not appear in the Tractates.
Perception doesn't fit in with solipsism in the Tractatus, is what I'm saying.
Marchesk explained the issue.
I think I detect a change in your overall take on this from the Marchesky of yore. (Of course, I could be wrong).
That's just the ambiguity in English of "fact". Witti is very clear in setting out facts as distinct from statements of fact. Marchesk is just backtracking on that distinction.
Quoting Marchesk
Nonsense solipsism
The world is a totality of fields?
Inspired by the recent thread on Zeno's paradox, I shall prove that no "totality of facts" can exist:
Let T be the set of all facts T={t1, t2, t3, ...}
Consider, further all subsets of T, which are the elements of the power set of T, P(T) :
{}
{t1} {t2} {t3} ...
{t1, t2} {t1, t3} ...
To each element of the power set there will correspond a fact, which we construct like this:
t1 [math]\notin[/math] {}
t1 [math]\in[/math] {t1}
...
t1 [math]\in[/math] {t1, t2, t3, t4}
t1 [math]\notin[/math] {t2, t3, t4, t5}
...
Of course, there is nothing special about t1, a set of facts can be constructed similarly with any tn.
By constructing our new set of facts, we have a set with as many members as there are in the power set P(T). But, by Cantor's power set theorem, P(T) is always strictly larger than T.
Thus there are more facts than members of T, therefore no "totality of facts" can exist QED.
You've only shown there to be no infinite and denumerable totality of facts. There could still be a finite, or a non-denumerable, totality of facts. At any rate, that would not be ruled out on the basis of such a proof.
Does Cantor's theorem not work for finite sets? I thought there was a well known relation between the cardinalities of a set and its power set?
As for uncountable sets, I'm pretty sure that Cantor proved that P(T) is always bigger.
This is clearly not true. A computer is a logical space, which behavior is dictated by logical facts. Ask Turing. And as per the Church-Turing-Deutsch principle, the world is the totality of facts, not things.
But I've just proved there is no such thing as the totality of facts, and while doing so I have respected the CDT-Principle.
That really depends on the facts of physics. Your proof is a perversion of Zeno's paradox as you state.
If it were true, then no physical law can be said to be absolute in all instances, which I doubt to be true. Every problem would be a super-task, at least any non-localized problem.
Nothing to do with Zeno's paradox. It's taking the power set and Cantor's theorem, as I explained.
And, if supertasks exist, then the CTD-principle is false.
But a computer is actually a physical device that we invented to do logical things with. You have to have electromagnetism and atoms to make an electronic computer. The whole logical space, boolean algebra, and programming are all abstractions on top of the actual physicality of the machine.
But, those 'things' act in concert as logical facts.
It's nonsense to say that a tree doesn't falls in the forest if nobody is there to witness it, it just does.
Sure, and a computer moves electricity (or light) around when nobody is around to witness it.
But if something is uncountable, then by definition, counting it is impossible; and if counting it is impossible, then by definition, it is infinite; and if it is infinite, then by definition it is impossible. Just ask Metaphysician Undercover. :-}
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.
You've still not shown a contradiction; only that the number of facts is not countable.
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.
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.
.
.
.
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...?
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.
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
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.
What would Kripke say?
The world is the totality of every realized and unrealized modalities?
Sure, when PROVED wrong, just ignore it.
Quoting unenlightened
So, what is it? Metaphysics or no metaphysics?
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.