Question on Ockham's Razor

[Nex]

OK, I've done a few forum and Google searches and come up with squat, so if anyone can help I'd really appreciate it.

I'm in a debate on a woo board about human consciousness, and oh bob I have a headache! Aside from that, according to one of the members there:

In Occam's Razor, one "unnecessary" hypothesis is always needed.

I'm not sure what he's saying, or where this came from. He keeps referencing Gödel's Incompleteness Theorem and the Copenhagen Interpretation in order to support his claim about Ockham's Razor.

Has anyone run across this before? It seems patently absurd to me, and try as I might, I don't understand what he's saying.

 

[Eleatic Stranger]

It's nonsense. He probably knows a few big words and has seen them used to great effect in the past, though he doesn't quite grasp how.

 

[Nex]

It's nonsense. He probably knows a few big words and has seen them used to great effect in the past, though he doesn't quite grasp how.

That's exactly what I think, but he's just not letting go of it.

If I thought there were a god, I'd ask him to deliver me from this stupidity.

 

[c4ts]

OK, I've done a few forum and Google searches and come up with squat, so if anyone can help I'd really appreciate it.

I'm in a debate on a woo board about human consciousness, and oh bob I have a headache! Aside from that, according to one of the members there:


I'm not sure what he's saying, or where this came from. He keeps referencing Gödel's Incompleteness Theorem and the Copenhagen Interpretation in order to support his claim about Ockham's Razor.

Has anyone run across this before? It seems patently absurd to me, and try as I might, I don't understand what he's saying.

Ockham never said an unnecessary hypothesis was always needed, just that given two different hypotheses which, when taken together, created a totally messed up system like dual realities, you take out the more complicated one, and that will give you a more likely result.

 

[Mercutio]

My guess is that what he means is that, when comparing two hypotheses and rejecting the less parsimonious of the two, the rejected one must have at least one element that the other does not, a superfluous step which is to be carved away by Ockham.

If they are both equally parsimonious, O does not tell which is preferred, so perhaps your opponent uses "hypothesis" where others might use "assumptions" or "steps" or some other word.

 

[T'ai Chi]

I view Occam's Razor like so:

Let H be a hypothesis with n assumptions, and let ~E be "explains the event E".

If

H1(n1) ~ E and H2(n2) ~ E,

we 'go with' the H with that has the smallest n as our 'best' hypothesis for explaining event E.

 

[Lord Muck oGentry]

Nex,
Is it possible that the chap is challenging you to say which hypothesis ( assumption, postulate or whatever) in his argument is unnecessary?
Just a guess, of course.
Regards

 

[c4ts]

Really, if you read William of Occham's work, his razor doesn't look like much. You have to stop and think about what he's saying, before you realize he's used the razor. He doesn't actually say "the simplest possible explanation is the most likely." That's a summary of what he does with dual realities, not a translation. Usually anything along the lines of "keep it simple, stupid" ignores a major problem, but in this case, it really works.

 

[The idea]

[...] according to one of the members there:

quote:
---------------------------------------------------
In Occam's Razor, one "unnecessary"
hypothesis is always needed.
----------------------------------------------------

Have you tried asking in what sense the hypothesis is "unnecessary" and in what sense it is needed? Without more explanation, it sounds like a contradictory claim.

He keeps referencing Gödel's Incompleteness Theorem [...] in order to support his claim about Ockham's Razor.

Maybe he has some kind of point. Gödel's Incompleteness Theorem seems to indicate that Ockham's Razor doesn't apply to mathematics. If a true and complete theory of numbers is already infinitely complicated, then a true and complete theory of reality either excludes the theory of numbers or already includes an infinite amount of complexity. If a theory is already infinitely complicated, then what's the benefit of reducing the complexity by some finite amount?

One approach could be to restrict the mathematical part of physical theories to a system in which there are only finitely many different values. Alternatively, one could exclude the mathematical aspects of theories when comparing the complexity of different theories.

Has anyone run across this before?

I can't recall hearing any suggestion that Gödel's Incompleteness Theorem is relevant to Ockham's Razor or vice versa.

 

[The idea]

Alternatively, one could exclude the mathematical aspects of theories when comparing the complexity of different theories.

On second thought, this would be an attempt to solve a problem that doesn't really arise. Any actual theory of numbers is an incomplete theory that has a finite complexity. A true and complete theory of numbers is simply an imaginary ideal.

Nevertheless, if a true and complete theory of numbers would have to be infinitely complicated, then one would expect that, as the actual theories become better and better, they would also tend to become more complicated.

In other words, Gödel's Incompleteness Theorem provides a reason to question Ockham's Razor. There could be an infinite sequence of theories, all of them true. In this scenario, greater complexity is not a flaw suggesting falsehood but a necessity to achieve greater completeness. However, all of the theories would still be incomplete.

 

[Eleatic Stranger]

If a true and complete theory of numbers is already infinitely complicated, then a true and complete theory of reality either excludes the theory of numbers or already includes an infinite amount of complexity. If a theory is already infinitely complicated, then what's the benefit of reducing the complexity by some finite amount?

Er, I'm not sure what exactly Godel has to do with the above bit at all, honestly, but I should point out that even if it goes through that's still not a valid application of Occam's razor.

All that Occam's razor amounts to is "do not multiply entities beyond necessity" - so, for example, if all divine phenomena can be explained with reference to a single omnipotent diety, then one only has evidence for a single omnipotent diety, and not three omnipotent dieties and a whole host of lower beings, etc etc etc. It really doesn't apply to 'infinitely complicated theories' or whatever you're trying to make it do there in any reasonable way.

--
Addendum - I may have been harsh there, as rereading it indicates you were probably trying to make sense of something the other person might have been saying and not advancing an idea of your own. If that is what he's after, though, it's still really muddled.

 

[Kopji]

"muddled"
8 out of a possible 10

Gödel's incompleteness theorem is usually dissed by atheists as being meaningless for philosophical debate. I tend to disagree but what do I know...

Everyone agrees that the idea of God exists. Quite a lot of religious thinking has gone into trying to show that if the idea of God exists, God must exist.

What Gödel proved, is that in ANY complex enough system there is always a mystery like God. (My words). Gödel pulls the rug out from under the case that the idea of God occurs because of some unique activity.

The incompleteness theorem is not an attack on God, it is an attack on the idea that 'God' must have come about due to some kind of event. Ideas like God come about as a mathematical certainty.

 

[T'ai Chi]

[BWhat Gödel proved, is that in ANY complex enough system there is always a mystery like God. (My words).
[/B]

Sorry to say bluntly, but that's absurd.

Godel's theorem only refers to arithmetical systems, say using the operations + and * on whole numbers. In these systems, he showed there exist propositions that can never be proved nor disproved inside the system (and if you prove or disprove them using another system, Godel's theorem applies to that system as well, so that doesn't work).

 

[Bodhi Dharma Zen]

Nex

Can you give us the link to the original discussion? to see the context.

 

[Nex]

Nex

Can you give us the link to the original discussion? to see the context.

Sure.

I've bowed out of it already (pg. 4), as I don't have the knowledge of Gödel to even rebut what this guy is saying, and honestly, he's getting a bit pushy. I also don't feel it necessary to deal with their snide comments about "materialists."

Here you go.

As an aside, if any of you could let me know what mistakes I've made in the debate, I'd be grateful. I know I've probably made a couple, like letting him take us away from the OP's subject.

 

[Nex]

Oh, and thank you to everyone else for your replies.

When I have more time, I'll go back over it to see if and how they apply to his argument. I'll probably also PM him in that forum to see if he can clear it up.

Thanks!

 

[drkitten]

I've bowed out of it already (pg. 4), as I don't have the knowledge of Gödel to even rebut what this guy is saying, and honestly, he's getting a bit pushy. I also don't feel it necessary to deal with their snide comments about "materialists."

To be honest, he sounds like a standard woo-woo who can't hack the real mathematics but likes quoting scientific-sounding stuff to bolster his previously-held beliefs.

But his take on Godel is, ahem, innovative. What Godel actually proved is that, for a sufficiently complex deductive system, there will always be either a statement that can be proved both true and false, or there will be a system that can neither be proved true nor proved false. This was a much bigger deal in 1930 than it is today, and was always a much bigger deal to mathematicians than it was to physicists.

Basically, it says that "we don't know everything." Furthermore, it goes on to say that "we can never know everything." To which my only response is along the lines of, "No ◊◊◊◊, Sherlock!" Especially in physics, or other empirical sciences, this means that sometimes you're going to have to get your lazy ass off the barstool and go look at something; we will never get to the point where you can describe the entire universe ("Did drkitten have Chinese for lunch today? Will it snow in Winnipeg three weeks from Saturday? What is the mass of the neutrino?") off a single system of equations.

To some mathematicians (incl. Godel himself), mathematics is an empirical science; when we find an open question in mathematics, that simply means that we don't know enough about the underlying concepts and we need to do some more fundamental digging. (These people are usually called "Platonists.") To others, mathematics is purely an intellectual word-game, and an open question means that there are two different ways to play the game (Canadian rules vs. American rules football). (These people are usually called "Constructivists.") Neither of these people consider God to hide in the open questions.....

 

[Dr Adequate]

What Gödel showed was that at least one "unnecessary" hypothesis will always be needed.

Well this is just rubbish. Gödel's incompleteness theorem shows that there can be no complete axiomatisation of arithmetic in first-order logic. This has of course no conceivable connection to Occam's razor. Your correspondent is babbling of matters of which he knows nothing.

 

[Eleatic Stranger]

"muddled"
8 out of a possible 10

Gödel's incompleteness theorem is usually dissed by atheists as being meaningless for philosophical debate. I tend to disagree but what do I know...

Everyone agrees that the idea of God exists. Quite a lot of religious thinking has gone into trying to show that if the idea of God exists, God must exist.

What Gödel proved, is that in ANY complex enough system there is always a mystery like God. (My words). Gödel pulls the rug out from under the case that the idea of God occurs because of some unique activity.

The incompleteness theorem is not an attack on God, it is an attack on the idea that 'God' must have come about due to some kind of event. Ideas like God come about as a mathematical certainty.

It has already been pointed out that the application here is somewhat, um, nonsensical but I'd just like to note that Gödel's incompleteness theorem is not meaningless for philosophical debate -- in fact it's in itself a fascinating topic for philosophical debate. It's just not relevant to this philosophical debate any more than, say, Goldberg's knowledge arguments or Wittgenstein's private language argument, or any other famous argument that is basically irrelevant to this discussion.

---
Edited to add: And also there's a fairly significant set of arguments and positions out there that hold precisely that the 'idea of God' does not, in fact, exist.

 

[Beerina]

Really, if you read William of Occham's work, his razor doesn't look like much. You have to stop and think about what he's saying, before you realize he's used the razor. He doesn't actually say "the simplest possible explanation is the most likely." That's a summary of what he does with dual realities, not a translation. Usually anything along the lines of "keep it simple, stupid" ignores a major problem, but in this case, it really works.

For example, proposing a God created the universe adds one extra item that a natural explanation does not: an entity called "god".

200 years of science later, no reproduceable test ever demonstrated the existance of this entity. So it hangs out there as an extra thing, with no support.

At this point, one should conclude the God hypothesis is incorrect and he does not exist. However, because of emotional investment, people propose an additional property for god: He deliberately hides (presumably there is some value for some philosophical reason in us beliving not only without any proof, but without any possibility of proof. Strange being, this "god".)

:rollseyes: