drachefly wrote:ACtually, Kriestor, the precise definition of simple was invented by Claude Shannon in the mid-20th century, so this isn't exactly old hat.
What was the point of this discussion, again? Whatever it is, though, I don't think how long ago people started using Bayesian inference on a prior determined by information theory is going to affect the outcome.
The point? Drach, I have no idea. IN a world where people say, "Assuming make an a.. of you and me," it's hardly surprising people do not understand the usefulness of Occam's. Or apply it incorrectly, as in the modern version. And you've been here long enough to know I've had this argument more than once, so they've got no hope of convincing me of anything. Making decisions in the face of the unknown is part of my everyday life.
Lilwik, your version of Occam's has to be incorrect, because it does not achieve a decision. Occam's Razor is a decision making process, as are Kepner-Tregoe, and other methodologies. A decision must achieve a goal. Decide what is Safer. What is most profitable. What is least time consuming. And what is true. Fundamentally, all decisions decide what is the best something. Decisions are not colourless, the way you try to twist Occam's. A decision without a goal cannot exist, and so your attempt to remove the goal from Occam's process is fundamentally impossible. There is no general "best" in life. There is the best path, the best view, the best... anything. There is no best "nothing". You prefer something because you have a target goal you are trying to achieve. Occam's Razor tries to guide you to that goal, and thus results in the best, the preferred, the most likely goal. I really don't know how you can hold that Best "void" as a concept in your head, and think Occam's somehow reaches it. The practical use of Occam's is to proceed to an action, so it guides you to the best action to achieve the desired goal.
But I'll use Drachefly's example, again, because you aren't listening to me. For Drachefly, Occam's Razor achieves the most likely curve that fits the data. It is the best curve. It is the preferred curve. It is not the preferred "nothing". It is not the best "nothing". It is not the most likely "nothing". It is a decision about which curve to choose, maybe to use in a Control program for a system, like your Cruise Control in your car. Is that a place where you'd like someone to choose the most accurate and retain responsiveness? All decisions choose the best "something". And here, in this comic, it chooses the most likely "truth" as to what happened.
Doctor Foreman wrote:The problem with this evaluation, Kreistor, is that evaluating likelihood is by definition a statement about truth.
When the goal is a truth, yes. When the goal is the streets you take to get somewhere, it's the best path. When the goal is the fitting of a curve to sampled data, it's the best curve. Truth is correct only in a limited context, and doesn't apply to those other examples. How is a path more true or false? "most likely answer" is what I said, and I think that fits a generalization of Occam's fairly well. Occam's is far broader in application, and so the definitions need to be written far more generally. All decisions can be phrased as a question, so I think "answer" is a general enough term to fit the definition. Sorry, but "truth" is too confining, and restricts Occam's application. It's the correct term for choosing which Speculation is most likely true, but not which curve Drachefly will choose.
Any definition of Occam's Razor which claims it is not a statement of truth but is a statement of likelihood is an internally inconsistent and therefore wrong definition.
No, it isn't. They're trying to write it for generalized decision making, and many decisions are not about "truth", as I have tried to point out with Drachefly's example, and my own of getting out of a burning house. There is no truth to deciding between the front door, window, backdoor, or basement cellar door. That decision has nothing to do with truth, because no path is "false". The evaluation is one of safety and danger. (OCcam's chooses which is the most likely to be safe.) And in Drachefly's curve fit, most likely to be accurate, not true. Drach's curve fit may go into the control program for a system: how is that "true"? And that is what makes writing a description of Occam's Razor so hard. It has to be written general enough that you don't use the word Truth, or you limit its application.
But he's not making any claims about whether or not the explanation is better in any "real-world" sense of being true, false, likely true, or likely false.
Correct, but you missed that he's not modelling "truth". Models are accurate and fast, not "true". His "simpler" will target reduced programming time, reduced processing time, and accuracy of result. No "truth" is involved, is it? And what about his decision making between a model that is fast to program but slow to execute, vs. slow to program and fast to execute? For the human, programming is simpler for the first, but for the second, simpler for the computer. Whose "simple" do we choose? That can change. A Model that runs only once can run slow, so reducing programming time is the better choice. A model that runs constantly should ignore programming time, and promote speed of execution. Every model will be considered "simple" based on its own parameters.
A statement of an explanation's likelihood is a statement about the truth value of the explanation. Occam's Razor does not address an explanation's truth value, and therefore cannot address an explanation's likelihood.
I've already said everything I need to in order to point out the fundamental flaw in this statement. When you choose which way to exit a burning building, you are choosing the safest path. When you pick a curve, the most accurate. When you choose an equation for a model, the fastest, easiest to program, and most accurate. You are confusing "decision making" with "truth finding" and then flipping that back to claim Occam's finds no truth. It doesnt't, in the cases where you're not looking for truth. When you're looking for safety, it provides the most liekly to be safe. But when you're selecting between potentially truthful statements, it provides the most likely to be true.
As or your "truth value" conclusion, each "assumption" in a solution comes with a chance to be true or false. Occam's tells us to reduce the number of assumptions, which fundamentally reduces the chance to be wrong, because the equation for the chance of being correct is the multiplication of each chance to be correct. Let's assume that the chance of being wrong for each assumption is 50%. The chance of being correct with one assumption in the solution is 50%. With 2, it's 25%. With 3, 12.5%. That's just like flipping a coin: if you only winb if all the coins you flip come up heads, you want to reduce the number of coins you flip, right? If you have some source for providing more accurate chances of an assumption being true or false, you can affect those probabilities. But in the vast majority of cases, an additional multiplier on the chance of being wrong is far worse than decreasing the probability of one assumption being correct. Which is more likely to be correct: a solution with two assumptions at 70% probabiltiy of being true, or one assumption at 50%? The one assumption, since 0.7x0.7 = 0.49, or a 49% chance of being correct. This is why Occam's focuses on reducing assumptions, and doesn't bother with evaluating probability of each assumption being correct: the probability of an assumption being correct is often a moot calculation, where the number of assumptions is different. And in the absence of knowledge, you often don't have any probability you can assign to the assumptions in the first place. In that case, you have to look at the achieve=ment Occam's results in as a general rule, and realize the chance reducing assumptions does not improve the chance of correctness is pretty low, since the cases where it wouldn't work out are small, and often would be obvious, anyway.
So, no, you are wrong. Occam's deals with probabilities by reducing the number of multipliers in the probability of a decision being wrong.