As Wittgenstein puts it-
But what is that discovery and why is it valuable?
Let us take a much analysed example- 'Socrates' absurd question' which is at the heart of Plato's Symposium. Here is one scholarly translation- '... is Love such as to be the love of something/someone or nothing/no-one? I am asking not if it is of a [or a particular] mother or father—for absurd would be the question if Love is love of a mother or father—but as if I were asking about the term father, “Is a father the father of someone or not?” You would have told me, I suppose, if you wanted to answer properly, that it is of a son or a daughter that a father is the father, wouldn’t you?'
Young Greek intellectuals relished this sort of argument because, like the gorgeous paradoxes of the nihilist Gorgias, it turned on a fine point of Grammar- a source of ambiguity which a suave interlocutor could exploit so as to, in a charming manner, steer his audience towards a predetermined goal. This ambiguity has to do with the subjective and objective genitive case and has no salience in English. Indeed, English speaking readers might well think Socrates was a fool and his interlocutors idiots on the basis of passages like this.
By contrast, for the Semitic languages, not just the genitive case but also the notion of Fatherhood- as in God, the Father's, consubstantiality with his Son- or Motherhood- as in 'the mother of the Book'- or daughter-hood- as in 'bat kol' the 'daughter of the voice' from Heaven- had a quite different semantic force and range of associations precisely because all genealogy led back to the univocal Godhead.
Socrates' question, as posed by Shelley- a young aristocrat at odds with his wealthy father- is indeed absurd for an English speaker because we feel very strongly that family ties don't define us. By contrast, in the Middle East, it is common to refer to a man as 'Abu' (father of) or a woman as 'Umm' (mother of) their eldest son or daughter.
For the last few centuries, Plato's trajectory in the East has been in the direction of a populist univocity and subaltern illuminationism. In the technocratic West, however, Platonism retains salience only in the Philosophy of Mathematics.
Wittgenstein, however, believed that it was a mistake to think Mathematics could have Philosophical problems. Rather Philosophy's task was to get clear of any difficulty Mathematics was making for itself so as to get a bird's eye view of what was involved without any contradiction actually being resolved.
A Mathematical treatment of what happens when a 'democratic' Social Choice mechanism treats of a multi dimensional 'policy space' is given by the McKelvey Chaos theorem. Simply put, we can show by purely mathematical means that adding dimensions to a problem means that controlling the agenda- i.e. deciding in what order to pose yes/no questions- can yield any possible outcome.
Another way of arriving at the same insight is to see Semantics as a 'Co-ordination problem'. Clearly we are all better off if we have a means to co-ordinate our actions through Language. Thomas Schelling put forward a notion of 'focal points' which 'naturally' solved the co-ordination problem under conditions of decentralized decision making. David Lewis based his theory of 'Conventions' on Schelling's insight.
Does this means there's some democratic way of getting rid of semantic problems from public discourse? No. One 'focal solution' may be more efficient or computationally less costly than another. Even without any strategic behavior, there would be some uncertainty and debate and confusion because information is costly to process and change takes time.
Factor in, strategic behavior- e.g. 'agenda control'- and there's going to be, not just frictional 'noise' creating a 'signal extraction problem' but also all sorts of 'hysteresis effects' and collectively irrational 'bubbles'- just like in the global financial system when it became 'incentive incompatible'- i.e. when politicians and money managers had perverse incentives.
Fans of Wittgenstein- or a broader philosophical 'linguistic turn', not to mention paranoid 'epistemologies of suspicion' or uncritical 'critical theory'- could pretend that by clarifying language they would be ineluctably led to some liberative insight. 'The civil status of a contradiction' might turn out to refer to some Marxian Crisis or Marcusian Lysis.
Meanwhile, on the Right, some 'neo-conservatives' allegedly believed that the elite could hang on to a clear sighted view of how things really work, and how they must be allowed to work, while writing high falutin' nonsense so as to add noise to signal as part of some soi disant 'Noble Lie'.
Both views were shallow and self serving. A little honest mathematical work- like that of John Muth- supplemented by proper empirical research could easily put paid to the notion that ordinary human beings are prisoners of Language or Culture or Gramscian 'Hegemony' or Butlerian 'Perfomativity' or Bhabha's 'hybridity' or any other such fatuous academic 'availability cascade'.
But why should this be? How can ordinary people be smarter than apple polishing PhD candidates> Well, the fact is we have evolved over tens of thousands of years to use Language strategically- i.e. lie and be lied to- and to be sensitive to the appearance of focal points as solutions to co-ordination games. In the short run, we can be fooled- but within a surprisingly short number of iterations we quickly gravitate to the focal point which would be predicted by the correct theory. 'The dead hand of the past'- or 'hysteresis'- does not dictate or render increasingly chaotic our actions in the Social sphere- provided there is a genuine collective benefit from a 'channelization' of behavior.
In practice, because we have evolved under Knightian Uncertainty, dis-coordination games and the damming up of 'capacitance diversity' also features in the relevant Evolutionary Stable 'regret minimizing' strategy.
Socrates, of course, was not a 'Social Scientist'. Even on his way to the Court Hearing where he would be condemned to death, he wished to practice the intellectual 'midwifery', or method of maieutics, which has immortalized his name.
Thus, in the Theaetetus, he puzzles over how Knowledge might have a canonical definition as 'true judgment with an account'.
The answer is that we know that the underlying co-ordination problem for agents is solvable by agreeing to be bound by 'artificial reason'- i.e. a system of endogenous protocols which may evolve on a fitness landscape but which is not itself revocable by some fact of what appears to be 'natural law' nor by a 'bat kol' or 'voice from Heaven'.
Socrates, on the brink of a fatal judgment, is, however, concerned with ultimate things. He recounts a dream which suggests that there might be an underlying 'alphabet' or (what Descartes, Leibniz et al would call a mathesis universalis or characteristica universalis) corresponding to the elementary particles or principles (stoichea) from which all Reality is built up. The trouble is these stoicheia may not be knowable, or the work of a Gnostic demiurge, so it is either futile or foolish to hope, at this early stage, that 'true judgement' can render a proper 'account' in terms of the 'alphabet of Being' or 'Theory of Everything'.
Still, one can have as many disparate ' artificial reason Dialogics' as one likes solving different types of problems. When abstract Mathematics advances enough, it can re-unite such Dialogics on the basis of greater generality. Interestingly, when this is done, Platonism (as opposed to Socratic or Stoic doubt) does not disappear, rather it re-emerges in a useful way but only because a genuine Mathematical advance hangs in the balance. By contrast, Wittgenstein's own attempt at founding his project on 'atomic propositions' came a cropper. It is not clear that his later notion of 'forms of life' is any real advance.
Why?Perhaps the answer is that Wittgenstein, unlike Brouwer, made no contribution to Mathematics. He spoke of Language Games, but unlike Von Neumann or Turing, made no contribution to the very useful mathematical theory of Games, or that of Computational complexity.
Godel's Platonism has an instrumental value for Mathematics and Mathematics, not Wittgenstein, actually clarifies genuinely open problems for the study or use of Language.
Still, Wittgenstein, like Plato, will retain salience for credentialised, as opposed to creative, literary culture by reason of some indefinable charm or appeal to the eternal entitled adolescent we all nurse within ourselves.
For a very different view of Wittgenstein's relationship to Plato there is an excellent article here by a young Professor from New Mexico which may motivate deeper discussion.