Излишние сущности. 2

[shkrobius]

Мне столько раз повторяли, особенно в последние недели, что сущности не могут превышать необходимости, что (если бы я точно не знал, что имею дело с рациональными существами, у которых не может быть предрассудков) мог бы подумать, что на мне применяют магические заклинания

Comments

[chaource]

Somehow I always had a different view of Ockham's razor. Parameters in the model are quite different from "entities" in the theory. Simplicity is not at all synonymous with fewer parameters or fewer equations.

Here is an example of how I would use Ockham's razor. Suppose we have data points {x_i,y_i}, and we fit them with a curve y=f(x). We can fit with 3 parameters y=f(x,a,b,c) or with 5 parameters y=f(x,a,b,c,d,e). Of course we can fit better with 5 parameters, and it is not true that 3 parameters will always give a "more correct" theory just because it is simpler. If we need to decide between 3 and 5 parameters, we cannot just decide on "simplicity" - we need other, more significant considerations.

Ockham's razor will be used in the following way. Suppose I'm fitting the curve y= f(x,a,b,c,d,e) with 5 parameters and also I'm saying: there is a very important function g(x,y) which we also need to compute. I spend a long time explaining how to find this function; it needs to have certain properties. It has to be such that g(x,y) is monotonic in x, when evaluated on our data points. It has to grow at least as fast as x^n for some n>1. And so on. This function is called "g" because it is the Grand Transcendental Essence that "truly expresses the character of the data points". The values of g(x,y) are not observable and not used in any other way; we first do the fitting and then compute g(x,y).

So actually this function g(x,y) has nothing to do with fitting the curve or with any other calculations. Therefore, the function g(x,y) is an extra entity that we should discard from the theory. This is how I always understood Ockham's razor.

As another example, the concept of "ether" was discarded from electrodynamics and special relativity theory because it is an extra entity that does not contribute to any formulas or observations, once electrodynamics and relativity were formulated in modern terms.

But this is not how these people discuss it...

[shkrobius]

Thank you for lucid exposition of your objections.

I cannot go in detail right now. The brief answer is that you are using a different principle to exclude this function, viz. the principle of sufficient reason. These two principles are fully identical only in Leibnitz.

Electrodynamics and relativity do not exclude relativistic aether. That it is not observed does not follow from either one of these theories. If it is observed tomorrow (an we do have a kind of aether in the microwave background) they strongly imply that this aether should be relativistic. That is all they can say.

[chaource]

It's comforting to think that Leibnitz already said what I wanted to say :)

Of course, electrodynamics does not exclude "ether". But electrodynamics is formulated without the assumption of "ether". Cosmic microwave background is observable but it consists of electromagnetic radiation, so CMB is quite different from what "ether" would have been (a substrate for the EM radiation itself).

[shkrobius]

I remind that coherent and all-inclusive application of this very principle is the very basis for Leibnitz's proof of the existence of G-d. Incidentally, it is also the basis for his rejection of the absolute time and space, which is the intellectual foundation of relativity. I have nothing against this principle per se, but invoking it in the context suggested by the commenters would be really something remarkable, given its explicit purpose and history. This is the chief reason why people are so careful in separating these two principles. They know.

[chaource]

I am not a philosopher, in part because I do not believe in applying philosophical principles in an "all-inclusive" manner, because I think that our human language is too imprecise for us to do "follow a principle to the very end" without arriving at utter nonsense.

[shkrobius]

And in that you are agreeing with Leibnitz once again, as he was developing his Logical Calculi (= calculus universalis) to address this very problem. However, his principle was the basis for that endeavor, too, so this does not resolve this particular conundrum. Incidentally, the Ockham razor itself was suggested in the context of disproving of the rational proofs of G-d's existence a la Leibnitz. Ockham was a fideist who went to the extreme in his philosophical views (which you do not like). Roughly, his intent was to demonstrate that rational proofs for G-d's existence are impossible and fallacious, because these would make it necessary for a rational creature to believe in G-d's existence violating the doctrine of the free will. Ockham's razor is derived from the theology of this sort. It cracks me when it is used as a rational argument AGAINST G-d's existence, because it is derived from the revelation rather than reason.

[nighteagleowl]

I can be wrong, but how the principle of sufficient reason or the Ockham razor will help here?
Physics deals with models, it says nothing about reality (well, a bit hard to tell what is reality...). That is, the principles would/could help to build a good model, but even if e.g. there is no angels in this model it does not mean there is no angels at all. 10 minutes later the reality could give us some other evidences and the model would be completely re-shaped.

How could one dare to do a step from as-is model describing what we can measure with our current technique
to the statements about reality in general.

[shkrobius]

That is why you would not find any philosopher worth his guns using the Occam's razor to such an end. It is total mystery wherefrom this talk about the razor originates.