Statements about statements about society

It’s pretty easy to communicate “London is a city”, “I know London is a city” or even “I know that you think that London is a city”.

But statements like “Everyone knows X and everyone knows that everyone knows X” start to make it much harder

This happens to be the strong version of ‘group knowledge’ of X:

‘I know that nobody thinks that everyone knows X” is harder still. If you aren’t convinced, just try building up to your own limit. The point isn’t that it’s hard to do, it’s that it’s hard to communicate.

If the top sentences were to be written in a more formal notation (where all the references are clear)  it would be something like:

1: “London is a city”:   is_a(London,City)

2: “I know London is a city”:  Know[I, is_a(London,City)]

3: “I know that you think that London is a city”: Knows[I, Think[you, is_a(London,City)]]

I tend to label 1, 2 and 3 as ‘first’, ‘second’ and ‘third order statements’ respectively. This is because the first one is simply a statement, the second is a statement about a statement and the third is a statement about a statement about a statement etc.

The complexity builds up pretty quickly even when all the markers are present. The problem is that there are so many social abstracts that depend on second and third order concepts like “what people believe that  most people believe” and “what people believe that almost everyone thinks”

Here are just a few examples:

Most racists in the BNP believe that most BNP members could tell ‘white’ from ‘non-white’ [second order]

Does everyone think that everyone thinks that ‘the Tories’ will win the next election? [third order]

Does everyone believe that everyone knows that the value of Jewelry is based only on other people over-valuing it ? [third order] {This nearly made a famous British Jewler go bust}

Christians believe that God exists [second order]

Christians believe that they know God exists (because God tells them so) [third order]

Scientists know that they don’t know God exists (because their methods cannot test him) [third order]

How do scientists know that they can’t know God Exists? (because God is unfalsifiable) [third order]

At the very least I hope you can agree they are a mouthful, where the question “Do people have ‘Group Knowledge’ of the fact Jewelry is overpriced?” is less so.

Politicians try to imply statements in the third and fourth (comment highlighted) orders all the time and many such statements are genuine open questions. As we explore increasingly sophisticated ideas in the social graph we need to popularize terms like ‘Group Knowledge’ and create new ones for similar phenomena so we can have a richer debate about the mechanics of politics, economics and society.

MIT’s Stephen Pinker explains why this all matters and how it relates to indirect speech acts (like offering bribes) in one of his fantatstic ted talks:

For a much more academic treatment on Group Knowledge see Group knowledge and group rationality: a judgment aggregation perspective  C List – Episteme, 2005 – Edinburgh Univ Press

B