Jottings III: the problem with propositions

In a previous post we discussed computational vs “biological thinking” and the question of why we assume that chunking the world in a specific way is automatically right. The outcome was that it is not obvious why the sentence

(i) Linda is a bank teller and a feminist

should always be analysed as containing two propositions that each can be assessed for truth and probability. It is quite possible that given the description we are given the sentence actually is indivisible and should be assessed as a single proposition. When asked, then, to assess the probability of this sentence and the sentence

(ii) Linda is a bank teller

we would argue that we do not compare p & q with p, but x with p where both sentences carry a probability and where the probability of x is higher than the probability of p. Now, this begs the question of why the probability for x – Linda is a bank teller and a feminist – is higher.

One possibility is that our assessment of probability is multidimensional – we assess fit rather than numerical probability. Given the story we are told in the thought experiment, the fit of x is higher than that of p.

A proposition’s fit is a compound of probability and connection with the narrative logic of what preceded it. So far, so good: this is in fact where the bias lies, right? That we consider narrative fit rather than probability, and so hence we are being irrational – right? Well, perhaps not. Perhaps the idea that we should try to assess fragmented propositions for probability without looking at narrative fit is irrational.

There is something here about propositions necessarily being abbreviations, answers and asymmetric.

Jottings II: Style of play, style of thought – human knowledge as a collection of local maxima

Pursuant to the last note, it is interesting to ask the following question: if human discovery of a game space like the one in go centers around what could be a local maxima, and computers can help us find other maxima and so play in an “alien” way — i.e. a way that is not anchored in human cognition and ultimately perhaps in our embodied, biological cognition — should we then not expect the same to be true for other bodies of thought?

Let’s say that a “body of thought” is the accumulated games in any specific game space, and that we agree we have discovered that human-anchored “bodies of thought” seem to be quietly governed by our human nature — is the same then true for philosophy? Anyone reading a history of philosophy is struck by the way concepts, ideas, arguments and methods of thinking reminds you of different games in a vast game space. We don’t even need to deploy Wittgenstein’s notion of language games to see the fruitful application of that analogy across different domains of knowledge.

Can, then, machine learning help us discover “alien” bodies of thought in philosophy? Or is there a requirement that a game space can be reduced to a set of formalized rules? If so – imagine a machine programmed to play Herman Hesse’s glass bead game, how would that work out?

In sum: have we underestimated the limiting effect on thinking across domains that our nature has? The real risk that what we hail as human knowledge and achievement is a set of local maxima?

 

Jottings I: What does style of play tell us?

If we examine the space of all possible chess games we should be able to map out all games a really played look at how they are distributed in the game space (what are the dimensions of a game space, though?). It is possible that these games cluster in different ways and we could then term these clusters “styles” of play. We at least have a naive understanding of what this would mean.

But what about the distribution of these clusters overall in a game space – are they equally distributed? Are they parts of mega clusters that describe “human play”, clusters that orient around some local optimum? And if so, do we now have tools to examine other mega clusters around other optima?

Is there a connection to non-ergodicity here? A flawed image: game style as collections of non-ergodic paths (how could paths be non-ergodic?) in a broader space? No. But there is something here – a question about why we traverse probabilities in certain ways, why we cluster, the role of human nature and cognition.The science fiction theme of cognitive clusters so far a part that they cannot connect. Styles that are truly, and necessarily alien.

How would we answer a question about how games are distributed in a game space? Surely this has been done. Strategies?