**Links to**: [[Mathematics]], [[Computational irreducibility]], [[Incompleteness]], [[Uncertainty]], [[Choice sequences]], [[Suspension of disbelief]], [[Hegel]], [[Bertrand Russell]], [[Logic]], [[Set theory]], [[Derrida]], [[Zizek]]. ### [[000 Postulate]]: For now, let us say that _infinity_ is the concept we tend to use for the suspension of disbelief (“...”). For construction’s sake. %% "The bad infinite now is a concept of the infinite which inevitably leads to a thought of the finite (BTL 117). In the schema, this is basically the third statement (c). But the structure of the bad infinite also covers the other direction, a thought of the infinite leads to a thought of the finite (BTL 117). In the schema, this is the fourth statement (d). What we eventually get here is what Priest calls a ‘flip-flop’ which amounts to the following: ‘another thought of the finite, if x is a thought of the infinite; another thought of the infinite, if x is a thought of the finite’ (BTL 118).35 This is analogous to the ‘badly infinite’ position Žižek ascribes to Derrida (cf. supra), but gets a more precise meaning than the one he ascribes to it himself: ‘another metalinguistic utterance, if x is an utterance of the non- existence of metalanguage, another utterance of the non-existence of metalanguage if x is a metalinguistic utterance’. What is the true infinite then? It is simply an object whose finitude is its infinitude. This object is precisely the totality of all thoughts. Once we consider it as a finite totality, we can apply the diagonalizer to it and get something beyond that finitude t(T)T. But this infinitude is again part of that totality, being of the same kind: t(T) ∈T. Likewise, in the case of the Russell paradox, the true infinite is the universal set of sets that are not a member of itself. Once we have it, we can say that it is not a member of itself but, as it is defined as the set of all sets that are not members of themselves, it is a member of itself. In the case of Derrida we can say that the true infinite is just the conjunction of the fact that the utterance of the non-existence of metalanguage is metalanguage and not metalanguage. But we will come back to this later on (section 9)" [[Johan Vandyke]] [[Spirit]] p320 ______ [[Attractor]], [[Delusions and models]] When we model something we unavoidably abstract. This abstraction, ultimately, rests in the belief in the possibility of zero, or infinity. Why so? For something to be separated off, whether in a differential equation or in a conceptual linguistic model, it has to be "put on pause" for an indefinite moment, it has to [[Rest]], in order to become a vantage point. How does this work in the context of PP? An attractor that gives many other attractors ________ The inconsistency of infinitude, its incoherence: if you take the real numbers 0, 1, 2, 3, 4, 5 and you take the even numbers 0, 2, 4, 6, 8; there should be the same amount of them, but that makes no sense, because the even numbers are missing half of them. Cantor showed how if you remove things from a finite set, that's what makes it _finite_, it makes it smaller, but an infinite set is precisely a set which doesn't get smaller as you remove things. Things seem incoherent because we don't have adequate understandings of infinity, we only reason in finite quantities. What [[Ludwig Wittgenstein]] called reasoning which doesn't work because of an "inadequate diet of examples". _______ [[Gödel]] and incompleteness: if you've got a mathematical theory it must be either incomplete or inconsistent. [[Foundations of Philosophy]] van mieses? Probability is approaching infinity ________ ### Infinity-nothing Cormac Gallagher "The title he had given to the fragment known as the Wager was in fact 'Infinity-nothing' and this can obviously be cast in mathematical terms." (see source in [[Pascal’s wager]] note). _______ James Williams Diff Rep p. 40 ![[diffrep 8.png]]