Occam's razor - quantification os Entities

[Niv]

hey all, I have a few questions about Occam's razor.

First what is considered to be a entity?
Is it any basic law of nature? (that is not a result of other laws).
A mathematical axiom/set of axioms that is needed for the theory (like Euclidean geometry for classical optics).
Basic definitions for the theory? (like mass or time in Newtonian).
A field or a particle?

Second, are all Entities are same in their "value"?
I mean, can we say that we prefer one kind of entities over another?
For example, to prefer additional dimension rather then a new particle?
Is it true, and why is it, we prefer Entities to be symmetrical?

All those questions aren't relevant when we can distinguish between the theories with a experiment.
Thank you,
Niv.

P.S.
Are there other ways except from experiment or Occam's razor?

 

[Schrodinger's Dog]

Occam's razor is not a law in that it tends to be absolutely correct when applied.

It simply states that giving equal starting conditions the simplest answer tends to be the correct one.

Now tends is not a probabilistic statement in the sense of mathematics, tends does not have a value say .9:1 so what we really have is a law but an indefinite one, and not one like say the law of gravity that provides specific results according to what variables we use.

It's rather like Murphy's law, although we say whatever can go wrong usually does, we don't mean that it is always the case that something goes wrong, just that given the general nature of events, sooner or later our errors or fate will play a role.

In essence we cannot compare such laws to the more stringent scientific laws, even though we may use them in science to make things simpler for ourselves, we still have to prove that the simplest solution is in fact the correct one.

 

[Moridin]

The principle states that the explanation of any phenomenon should make as few assumptions as possible, eliminating those that make no difference in the observable predictions of the explanatory hypothesis or theory.

It is not used so much in determining what is most likely 'true' but what does and what does not represent the current scientific knowledge.

 

[HallsofIvy]

The real point of Ockham's razor (named for William of Ockham), by the way, is this:

The point of science is to disprove theories (you can never prove a scientific theory). It's best to start with the simplest theories since they can be most quickly disproven.

 

[Niv]

The real point of Ockham's razor (named for William of Ockham), by the way, is this:

The point of science is to disprove theories (you can never prove a scientific theory). It's best to start with the simplest theories since they can be most quickly disproven.

Isn't it the Falsifiability of Karl Popper?
I think Ockham's razor is: "entities should not be multiplied beyond necessity."

Thank all of you for the answers.

I know Occam's razor is secondary to the test itself, and isn't telling (or scientific theories at all) the absolute truth.
But I still think it is critical for the scientific research because for every theory, we can invent another theory that will be equal in it's predictions, but will use more entities (that are not measurable without the theory).
And when we have a few theories that have precisely the same predictions, I think Ockham's razor is the only way out.

I'll try to focus the questions:
What is to be consider as an entity? (A law? a basic definition?...)
Do we, and why we prefer some kinds of Entities over another? (a theory with another dimension over a theory with another particle for example).

Thank you.

 

[deimors]

We seem to prefer symmetry in our theoretical entities simply because we find so much symmetry all around us, and there's a certain aesthetic to anything symmetrical. Is there any more validity in symmetric rather than asymmetric, simple rather than complex? I tend to think not, but there is something to be said for elegance.

 

[wuliheron]

Occum's razor is a philosophical idea, not a scientific one, hence all the verbage about values and entities. No doubt if someone wanted to do a statistical analysis on the idea and make it a scientific principle they could, but I've never heard of such an attempt. However, I'm sure it makes for good jokes.

 

[Moridin]

Occum's razor is a philosophical idea, not a scientific one, hence all the verbage about values and entities. No doubt if someone wanted to do a statistical analysis on the idea and make it a scientific principle they could, but I've never heard of such an attempt. However, I'm sure it makes for good jokes.

It is part of the philosophy of science, just like deduction, induction and the use of experimental data is.

 

[Niv]

We seem to prefer symmetry in our theoretical entities simply because we find so much symmetry all around us, and there's a certain aesthetic to anything symmetrical. Is there any more validity in symmetric rather than asymmetric, simple rather than complex? I tend to think not, but there is something to be said for elegance.

I agree that symmetry in our theoretical entities is much more aesthetic.
In my opinion, when we have symmetry, we prefer it because we can find a more basic theoretical explanation for it.
Like in Maxwell's equations and an approximation to the Einstein field equations.

 

[sd01g]

The real point of Ockham's razor (named for William of Ockham), by the way, is this:

The point of science is to disprove theories (you can never prove a scientific theory). It's best to start with the simplest theories since they can be most quickly disproven.

It seems to me that the point of science (the kind of science that deals with empirical reality) is not to prove or disprove, but to empirically verify. The final step of the scientific method is empirical verification.

 

[Moridin]

No, science advances by disproving hypothesis.

 

[deimors]

Karl Popper hypothesized that the ability to disprove a theorem (what he calls falsifiability) is one of the conditions of demarcation; namely, a condition by which a theorem can be tested for it's being scientific or not. Thus a theorem which is logically necessary (unable to be false in any possible world) cannot be scientific, as is found in many descriptive accounts and pseudo-scientific reasonings. The core concept here is that a proper scientific theory must have something which can be tested, and the result can either verify or disprove the theorem. Upon passing the test, the theory has validity simply because it *could* have been otherwise, whereas if it couldn't have been otherwise, there is no validity to the theory, it's as if the bases were logically loaded to begin with.

For instance, say one was to come up with the theory that they're a brain in a vat, being fed all sensory input by scientists or crazy robots or something, and this theory hypothesized that there was absolutely no way they could interact with the "real world" (because, say, they'd lost their body and were just the brain in that vat). Being that there is absolutely no test they could perform to determine whether or not the theory is true, this sort of reasoning is completely unscientific. Or, if one was to come up with an explanation for why the universe is here, say that the flying spaghetti monster created it a few decades ago. Of course, in his noodly wisdom he planted really old looking dinosaur bones and ruins of civilizations around, just to keep us on our toes. Any test one could perform to determine that, no, the world is older than that can immediately be trounced with the statement that the f.s.m is just messing with you and constructing the phenomena you're examining. Thus, it couldn't be false that he created the world only recently.

There are critics of Popper's demarcation criterion (Kuhn, for instance), but on the whole it's a decent condition to take into consideration.

 

[Moridin]

Carl Sagan pushed the concept further in The Demon-Haunted World: Science as a Candle in the Wind, which is find pretty interesting:

The Dragon in My Garage

Now, what's the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all? If there's no way to disprove my contention, no conceivable experiment that would count against it, what does it mean to say that my dragon exists? Your inability to invalidate my hypothesis is not at all the same thing as proving it true. Claims that cannot be tested, assertions immune to disproof are veridically worthless, whatever value they may have in inspiring us or in exciting our sense of wonder. What I'm asking you to do comes down to believing, in the absence of evidence, on my say-so.

 

[sd01g]

No, science advances by disproving hypothesis.

When one disproves an hypothesis, all one has is a disproved hypothesis. When one empirically verifies a hypothesis, then science advances.

 

[sd01g]

Carl Sagan pushed the concept further in The Demon-Haunted World: Science as a Candle in the Wind, which is find pretty interesting:

The Dragon in My Garage

An imaginary dragon is something--it is an imagination that requires neurological activity. No dragon is just that. No thing. Nothing.

 

[Hurkyl]

For instance, say one was to come up with the theory that they're a brain in a vat, being fed all sensory input by scientists or crazy robots or something, and this theory hypothesized that there was absolutely no way they could interact with the "real world" (because, say, they'd lost their body and were just the brain in that vat). Being that there is absolutely no test they could perform to determine whether or not the theory is true, this sort of reasoning is completely unscientific.

They aren't scientific, but such arguments are still incredibly important.

 

[deimors]

When one disproves an hypothesis, all one has is a disproved hypothesis. When one empirically verifies a hypothesis, then science advances.

Quite the opposite really... when one disproves a hypothesis, one has eliminated one of the various possibilities, thus narrowing down the "truth". When one finds evidence verifying a hypothesis, especially a universally quantified one (such as "all particles exhibit property X"), which are really the only hypotheses anyone's concerned with, there's really no advance. You've shown that the base case hold true (there exists an X such that ...), but you've shown nothing as to whether the hypothesis holds generally.

I know it's not 'scientific' per se, but consider the (classic) hypothesis "all swans are white". All the white swans you may stumble upon will verify this hypothesis, but these really add no validity to the hypothesis. It is only by finding a black (or any other non-white) swan that our knowledge advances, as we can now say "it is not the case that all swans are white" with certainty.

 

[sd01g]

Quite the opposite really... when one disproves a hypothesis, one has eliminated one of the various possibilities, thus narrowing down the "truth". .

What one learns from failed experiments might be usefull in designing a new or different experiment, but the 'advance in science' takes place when the experiment works. My dictionary list 35 different definitions for the word advance, so maybe we will never agree exactly what an advance in science actually is.

 

[Moridin]

What one learns from failed experiments might be usefull in designing a new or different experiment, but the 'advance in science' takes place when the experiment works. My dictionary list 35 different definitions for the word advance, so maybe we will never agree exactly what an advance in science actually is.

When a scientific experiment works, a hypothesis is falsified. Science cannot prove anything, but it can disprove it. Therein lies the answer to how science advances.

 

[Niv]

I think that science advanced when we are able to describe more phenomenons in less entities. When we have a disprove we are take leave of a wrong theory, so we are able to think of new one that will describe the new experiment too, although this theory will probably be disproved too - the new theory will explain the laws and equations of the previous one.
For example theory of relativity is explaining why Newtonian mechanics is a good proximity for c>>v.

 

[wuliheron]

It is part of the philosophy of science, just like deduction, induction and the use of experimental data is.

Contrary to what some people might lead you to believe, there is no single philosophy of science anymore than there is merely a single scientific discipline. Science takes a very pragmatic approach to philosophy, whatever gets results you keep and everything else gets thrown out with the bathwater. However, currently the popular philosophical discipline among the sciences is Contextualism.

 

[sd01g]

Contrary to what some people might lead you to believe, there is no single philosophy of science anymore than there is merely a single scientific discipline. Science takes a very pragmatic approach to philosophy, whatever gets results you keep and everything else gets thrown out with the bathwater. However, currently the popular philosophical discipline among the sciences is Contextualism.

My dictionary lists seven different definitions for the word science. The scientific method is the philosophy for one type of science that requires empirical verification to establish truth. The philosophy of the science of mathematics uses axioms, rational constructs and definitions to determine its truths. Most of the sciences use a combination of the empirical science of the scientific method and the rational science of the mathematical science to attempt to understand and control the REAL world.

 

[Niv]

Contrary to what some people might lead you to believe, there is no single philosophy of science anymore than there is merely a single scientific discipline. Science takes a very pragmatic approach to philosophy, whatever gets results you keep and everything else gets thrown out with the bathwater. However, currently the popular philosophical discipline among the sciences is Contextualism.

I agree with "whatever gets results you keep and everything else gets thrown out with the bathwater".
But I think that is the real philosophy of science just in other words, and it can be well defined.

I think that "whatever gets results you keep" in combination with what we do is another wording to say not to keep what isn't working (because it wrong or just doesn't have any prediction - the Falsifiability) because anything else then working we throw out.
I think that "everything else gets thrown out with the bathwater" is just to take out anything entity that does not help to do the work - which also known I think, as Occam's razor.