On the limits of our knowledge, again.

By the way, I have to write another on. The talk I just discussed on limits of science. I have another interesting idea about the limits. There seems we are trapped within the big and the small. At large scales we are ultimately captured by the speed of light. On the small scale we are ultimately captured by quantum resolution. Now this to me looks like some tough limits on what we can know. Does it also indicate that someone trapped us...?

On scientific knowledge

I was watching this very interesting debate between some great thinkers of our time. And of course I was thinking: "no, that have to be wrong"!
The question at hand is: is all knowledge empirical? Kruass is strongly advocating thing line. Dennet and Pigliucci is a bit more vague, but at the end seem to lean to the same conclusion. I would claim that this is wrong. There is knowledge (if we even can define the term!) that is not empirical. My example of this is basically mathematical knowledge. Krauss is claiming also mathematical knowledge is empirical since the basis (the axioms) is empirical to their nature is not correct. There can be many axioms not at all connected to any empirical facts - in fact ZF is an excellent example of this. Even the designers of the damn thing did not like it since it was counter intuitive with all these axioms. Nevertheless we would all agree that "the integral of 1/x is ln(x)" is knowledge. Or an even better example, the properties of the monster group constitute knowledge.

I think I would rather go further actually and say that all knowledge is of non-empirical nature. Empirical stuff is what can be observed. However observations can never be trusted. Never. However, deductions (which might be based on observations) can be trusted and render knowledge. But all that knowledge is of the for "if a the b". If a is observed, that b can be deduced. Thus, the knowledge does not depend on the empirical fact, but is only claims something about logical consequences given the empirical fact.

On free will

There is an exciting talk by Daniel Dennet about free will. His take is a very interesting one, being a compatibilist. But I would like to take another stab at this case. Not that I know much of it, I must admit. But of course it is one of the tricky ones. So, my take, here goes.

I think one should be able to give a more detailed account for what free will is than with guys like Daniel Dennet is doing. The problem is that there is a quite large gap between discussing determinism and free will. Determinism can be described like
F = m a
or is many other ways ans mathematically well formed laws. This is not a consequence of determinism. It is determinism, and it is how we can understand it.
At the other end of the spectrum, there is randomness. This is just as nice as determinism. It can be described using pure mathematics. We can say that the random variable X obeys the distribution A(P₁, P₂, ..., P_n), where the P's are parameters.
Now, the problem is that non of these descriptions fit free will, and at the same time it seem free will is something similar to these concepts. Could it be that one can define free will as: An entity has free will if, via communication, it can be made to obey either a deterministic law or any stochastic. Thus, my definition require that the entity can communicate some way.

Anyway, back to work. Let's elaborate more on this later.

On " the unreasonable effectiveness of mathematics in the natural sciences"

There is allot of fuzz on this question out there. E.g. on fqxi. To me this is not so strange. If we assume nature has structure, and is not only chaos, then why would not any attempt to capture that structure succed?

The point is that any modeling structure that you can come up with will be sufficient to describe (that is, model) at least a part of reality (in  approximation). And from there it is just refinement. Science is an optimization process, or a search if you want. An optimization to minimize the error between model and measuremen.

Thus we (the humans) could have started from any mathematics and enevideble would have ended up with a physical model that will capture some part of reality.

Börja med det lättaste

När man ska ta sej an en uppgift ned flera delar har jag lärt mej en sak som ofta gäller: Börja med de delar som är lättast.

Det finns många anledningar till att göra så. T.ex så blir det lättare att avgöra hur mycket tid man har på sej å dom svåra. Sedan har man ju i alla fall något att visa upp. Och man blir nöjd över att fått något gjort. Och det svåra blir lite mer strukturerat när det lätta är undanstökat.

Men dessa insikter har tydligen inte nått stadsministern med tanke på att han bara tjatar om åtgärder till de som står längst från arbetsmarknaden.