notes-philosophy-freeWill

i had an idea today and upon looking it up i found that Popper had it first:

"Karl Popper did make an attempt to explain free-will in term of "self-diagonalization" indeed. The basic and simple idea is that IF I can totally predict myself, then I have the opportunity to refute such a prediction." -- Bruno Marchal

also, http://en.wikipedia.org/wiki/Karl_Popper#Free_will makes it seems that Popper likes the generate-and-test model of thought.

to go on about it a little more:

an agent can be said to have free will iff: (a) the agent understands the concept of self (b) the agent understands the concept of action (c) the agent understands the concept of prediction (d) it is possible for the agent to be in a state such that no matter what information that they receive (and understand) which predicts that they will take a certain action, then they will in fact take a different action

of course this isn't very satisfactory because it contain the difficult-to-define concept of 'understanding'. (a), (b), and (c) are just pre-requisites for the agent to be able to "receive (and understand)" "information...which predicts that they will take a certain action".

note that when these conditions are satisfied, we can prove through a diagonal argument that it is possible for the agent to be in a state in which it is incapable of knowing what it will do.

note that these conditions can be satisfied even in a deterministic world.

note that these conditions are loose enough to allow the agent to have free will in certain subsets of circumstances and not in others; e.g. if the agent finds a crystal ball which predicts without fail what it will do, then with respect to all those actions which it can see in the crystal ball, it is not free.

interestingly, "the stock market" has something similar but not identical to free will, if define the stock market to "understand" something if any of its participants understand that thing, and if we define an 'action' to be a price level. Because, if there are certain kinds of predictable regularities in the future prices of the stock market, then it is possible for participants to trade on this prediction. This will have the effect of removing the regularity. However, there are other kinds of regularities which are not removed by trading; e.g. if a central bank says, "i will buy an arbitrarily large amount of bonds in order to keep their yield below a certain level", then it is guaranteed that the yield of those bonds will not rise above that level.

hmmm... that's not quite it because who is to say when it is being 'predictable'..