Skip to main content

Goedel applied to emergence: Lower-level indeterminism

Goedel's theorum may be good for more than AI-bashing: we may be able to apply it to emergence (understood broadly enough to include my Aristotelian or rather neo-Platonic conception of higher/lower levels of being/operation).

Think of how we can posit a set of mathematical operations and terms and use these operations and terms to formulate rules/algorithms that can be used in term to determine the truth values of the expressions that use those terms. Goedel showed that the set of all possible rules that we might formulate will be able can determine the truth values of SOME BUT NOT ALL of the expressions that could be created using those terms and operations (I'm not sure I said the Goedel thing 100% right but hopefully closely enough)...

If you keep the above in mind, then you might consider how all of that math stuff might have the following analogy in nature: i.e., the laws or properties that attend a lower level of being can somewhat determine many but not all of the possible behaviors/arrangements/interactions at that lower level. These laws of nature attending lower levels of being are like algorithms: they underdetermine the lower level states of affairs in a manner analogous to how the rules/algorithms in a given math system unable to determine the truth values of all of the possible expressions using operations available. In both cases there is something law-like that underdetermines.

Just as mathematical rules within a system can at least exclude some expressions as impossible or false but cannot establish the truth of all equations that could be expressed using those terms, .... so too, lower-level properties exclude certain things as impossible at the lower level but do not comprehend all possible states of affairs. The lower level rules are open ended, open to influence of a possible higher level.

This indetermination is an openness to determination at the higher level.
This indetermination is NOT freedom. But acknowledging that it is there will utterly undercut reductive materialist arguments against the very possibility of freedom.

Comments

Post a Comment

Popular posts from this blog

Dembski's "specified compexity" semiotics and teleology (both ad intra and ad extra)

Integral to Dembski's idea of specified complexity (SC) is the notion that something extrinsic to evolution is the source of the specification in how it develops. He compares SC to the message sent by space aliens in the movie "Contact." In that movie, earthbound scientists determine that radio waves originating in from somewhere in our galaxy are actually a signal being sent by space aliens. The scientists determine that these waves are a signal is the fact that they indicate prime numbers in a way that a random occurrence would not. What is interesting to me is the fact that Dembski relies upon an analogy with a sign rather than a machine. Like a machine, signs are produced by an intelligent being for the sake of something beyond themselves. Machines, if you will, have a meaning. Signs, if you will, produce knowledge. But the meaning/knowledge is in both cases something other than the machine/sign itself. Both signs and machines are purposeful or teleological
Post a Comment
Read more

continuing the discussion with Tim in a new post

Hi Tim, I am posting my reply here, because the great blogmeister won't let me put it all in a comment. Me thinks I get your point: is it that we can name and chimps can't, so therefore we are of greater value than chimps? Naming is something above and beyond what a chimp can do, right? In other words, you are illustrating the point I am making (if I catch your drift). My argument is only a sketch, but I think adding the ability to name names, as it were, is still not enough to make the argument seem cogent. For one can still ask why we prefer being able to name over other skills had by animals but not by humans. The objector would demand a more convincing reason. The answer I have in mind is, to put it briefly, that there is something infinite about human beings in comparison with the subhuman. That "something" has to do with our ability to think of the meaning of the cosmos. Whereas one might say"He's got the whole world in His han
2 comments
Read more

particular/universal event/rule

While listening to a recorded lecture on Quine's Two Dogmas of Empiricism, it occurred to me that every rule is in a way, a fact about the world. Think about baseball: from the p.o.v. of an individual player, a baseball rule is not a thing but a guide for acting and interpreting the actions of others.  But this rule, like the action it guides, is part of a concrete individual --i.e., part of an institution that has come into existence at a particular place and time, has endured and  may eventually go out of existence.  The baseball rule, as a feature of that individual, is likewise individual.  The term "baseball rule," on the one hand, links us to a unique cultural event; it can, on the other hand, name a certain type of being.  In this way, it transgresses the boundary between proper and common noun. If there were no such overlap, then we might be tempted to divide our ontology between a bunch of facts "out there" and a bunch of common nouns "in here.&qu
Post a Comment
Read more