What is The Principle of Parsimony? (Ockham's Razor)
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- Опубліковано 5 вер 2024
- An explanation of several varieties of Ockham's razor, as well as a number of questions it raises about elegance vs parsimony, qualitative and quantitative parsimony, and more.
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I would define simplicity is the least number of premises with each premise being an atomic sentence that can not be broken down further into other sentences.
Thank you! I believe it would be of interest for everyone to continue this series on decision principles by analyzing Hanlon's razor, the one that says "Never attribute to malice that which is adequately explained by stupidity."
Today's science is complex, but has better explanatory power. Ockham's razor only applies to theories that have equal explanatory power. Explanatory power is the 'benefit' provided by theory. Since this benefit is equal in this case, we would want to minimize costs. Anything that reduces costs - reduced complexity, reduced observations needed, reduced axioms, - is preferable.
Preferable in utility , but not compelling concerning the truth of the explanation?
@@tdsdave the truth explanation power is equal between the competing theories.
@@InventiveHarvest
A theory tends to involve a narrative , the explanation, as a poor example Newtons description of gravity as a force, whilst Einsteins description of it as an effect of the curvature of space-time , the truth of a fundamental physical description of gravity might be neither of these ( certainly not Newton's) . If these two theories were at the stage where the data available to validate them were consistent with the predictions of both, your metric would choose Newtons,( Relativity is counter-intuitive at times and has notably more complex math, at least to me ) but Newtons explanation is at least further from truth in actuality.
I'd make a distinction between the truth of the explanation from it's ability to produce accurate, "true", results, it's explanatory power. I see your use case scenario for parsimony as being an example of under determination I think. I don't think parsimony can tell us about the truth of the explanation, you might agree on this?.
I think your choice is simply pragmatic on utility, you get the same results for the less work, but it's not informing you if the explanation you chose is necessarily on the path to the actual "truth" of the matter, is necessarily the "best explanation( of two or more) given the data"
Any how probably overly long hot air, All the best.
@@tdsdave There are a number of criteria we might use to evaluate theories. We can give different weights to the criteria. These include explanatory power, parsimony, falsifiability,, consistency with other knowledge, etc. Certainly explanatory power is a more highly weighted criteria than parsimony. But in cases where the difference between the criteria for competing theories cannot be measured, we have to rely on parsimony, or other pragmatic criteria.
In the situation you described, both Newton's theory and Einsteins theory would both have an equal chance of being the truth. If you had to pick one of these theories, which one would you pick and why?
@@InventiveHarvest
I feel you are wondering off topic a little into theories that we would not need to invoke parsimony for, the question on the table is how is parsimony useful if at all in determining which is the best theory.
Explanatory power , we've defined this to be identical in our examples, they both give identical results to the same question, if the results of one were at odds with nature then we'd reject it in favour of the other, if the other was consistent with nature , no matter how much more complicated it was. ( which is really what happened with Newton vs Relativity, e.g. orbit of Mercury, and is normal "progress" in science).
If a theory were unfalsifiable it would not be scientific imo.
The last of your criteria , consistency with other knowledge, have you an example in mind that would make a meaningful distinction between two theories with identical explanatory power, I can't think of one.
"In the situation you described, both Newton's theory and Einsteins theory would both have an equal chance of being the truth."
Again I would highlight the distinction between the narrative and the results derived from that narrative. The results in our examples were identical , the narratives radically different. I'd see no reason to conclude either narrative is the truth, or best explanation.
"If you had to pick one of these theories, which one would you pick and why?"
I pragmatically make us of the one with the most utility , if there were such a meaningful distinction between them. But I would not adopt the narrative associated with it as being the case, there would appear to be no justification for doing that . In QM we have several interpretations , narratives, that all attempt to explain in some manner the nature of Quantum behavior , but none have been show to be the actual case , but the math of QM does not care and produces accurate results regardless. Favouring one interpretation over another is above my paygrade , though some brighter people do , though as far as I know it is still an open question if any are the actual explanation. To me this is similar to this case to our conundrum, use the math , but don't buy into the narrative. I think this is underdetermination
"In the philosophy of science, underdetermination or the underdetermination of theory by data (sometimes abbreviated UTD) is the idea that evidence available to us at a given time may be insufficient to determine what beliefs we should hold in response to it"
Cheers for the conversation , have a good one. Sorry I'm so long winded.
I would define simplicity as the least number of axioms and rules of inference you need to adopt in order to prove your statement. (In First Order Logic.)
I would interpret the razor in that sense, that it prefers the skeptical theory that suspense judgment on most topics since this decreases the number of possible sources of error.
This doesn’t imply that the universe itself is simple, which is the reason why it is not that surprising that scientific theories become more complex.
I think the argument with the fewest unjustified assumptions is the one that is most likely. Any alternative to this believe involves a principle of explosion.
I come from a computing and statistics background on this. I would suggest a definition of "simplicity" of a theory to be this: Complexity is the number of possible universes that could be accurately explained by a theory if you tweak its non-fundamental propositions to fit that particular universe. all theories have fundamental propositions that cannot be changed without changing the complexity of the theory. Furthermore, all theories have non-fundamental propositions that you can tweak to change the predictions of a theory, but not its complexity. For example, if my theory of four humours doesn't line up with medical results, i could change my theory to have a different "correct" ratio of blood to mucus. maybe I up it from 2:1 to 3:1 or something. However, if I add a 5th humour, now I've increased the complexity of my theory because there are more ratios between 5 things than 4. I have more stuff to tweak.
Key issues with this idea: How do we determine what is fundamental and what isn't? Also, how can we compare the "number of possible universes that could be accurately explained" when for any theory involving natural numbers, it's likely to be infinite for both theories?
Interesting approach. I agree with the challenges you have to this formulation. When dealing in possible universes, it is likely that the number is often if not always infinite. And the issue of something being fundamental to a theory gets into all sorts of issues of underdetermination and paradigm shift: i.e. when does something count as a background belief and when does it count as a part of the theory. Newtonian mechanics was arguably fundamental to a lot of theories that were left by the wayside when the paradigm shifted away from it, but many of them would not consider it fundamental since it was the background paradigm they were operating in.
Could you do a video explaining the backwards law by Alan Watts? Thanks.
There's also the matter of the ceteris paribus prerequisite being fulfilled, or possibly being mistaken that it has been; so I wonder how often the principle is really applicable. Certainly it's suspect to try to compare very different theories about the same phenomena for their relative simplicity. You would also have to take into account assumptions or speculations made by the theory. The theory could overly simplify and be too reductionist, perhaps try to torture concepts into variables so that math can be employed, but then the ceteris paribus prerequisite would likely be violated.
I think that parsimony is just the epistemic analogue of efficiency. It's a matter of how much you get out for how much you put in. In the latter case, you more you commit to a strategy, the more exposed to risk you are, so if you can get more good out of your strategy while committing less to it, the lower your risk relative to reward, so the more likely you are to accomplish more good than bad. In the former case, what you are committing is belief, and the more you believe, the more exposed you are to the risk of being wrong, of having false beliefs, so if you can get a lot of truth out of a theory without having to really believe much, you lower your epistemic risk to reward ratio, and the more likely you are to believe more truths than falsehoods. And that just is what epistemic probability is: how likely your beliefs are to be true rather than false. Which is why I say that probability is the epistemic analogue of prudence.
As for how to quantify simplicity/complexity and "amount of belief" in the analogy above, just as we can measure efficiency in action in terms of energy, which can be precisely quantified, so too I think we can measure parsimony in terms of information, which can also be precisely quantified -- bits are as exact as joules, if not more so. We can think of beliefs and theories as abstract programs that model whatever it is that they are about, just like we can think of strategies, intentions, plans of action, like abstract machines for doing whatever they're about, and just as a machine that can take very little energy (including the energy the machine itself is made of) and do a lot with it is efficient, a program that can take very little information (including the information the program itself is made of) and accurately model a lot from it is very parsimonious.
This take on the principle of parsimony seems to favour an antirealist attitude toward science (against which I have nothing, but I want to point it out). And it's a decent one at that- as in it's motivated unlike most takes in this regard. However, I do think it can be criticized. Namely, in saying that the principle of parsimony derives from our interest in maximizing explanatory power while minimizing the effort to applying a theory, you invoke the notion of effort. To investigate effort, as that is a physical quality, one must look to the world, so to say. That is, effort is subject to scientific inquiry. Then the question becomes: how do our theories identify effort and how do we know they are optimal? Because if a theory that explains effort relies on effort put into it for epistemic virtue, I'm unsure what can be made of it, but some incredulity seems highly appropriate, if not a full on suspension of judgement.
Regarding information, I think Kolmogorov complexity is relevant. Plausibly the most sophisticated attempt at quantifying simplicity. My issue with any such attempt is, it seems that it is context sensitive. To illustrate, take 3 sentences we shall call a, b and c that respective to their language are simple. Arguably, creating longer sentences using logical connectives should make more complex expressions. Now, you can make another language with sentences p, q and r such that each sentence translates to the first language as a long (complex) expression with a, b, c as atomic, and a, b, c translates to the second language as a long expression with p, q, r as atomic (possible and trivial using DNF, but it would pain me to write it out here). So, our complexity evaluation seems to judge equivalent sentences across languages with very different complexities.
@@fountainovaphilosopher8112 Can you elaborate on how this favors antirealism? I definitely don't intend for it to.
As for the stuff about effort, I didn't mean that parsimony is getting more truth out for less effort in, but that it's analogous to efficiency in the ordinary sense of getting more done with less effort. The analogue of effort on the epistemic side there, the thing that more parsimonious theories requires less of, is commitment to the truth of things, in the sense that completely suspending all judgement and answering "I dunno" to every question is zero of such commitment, while confidently giving a definite answer to every question is a maximal amount of such commitment.
This is analogous to the effort, or energy, or resources, put into a practical endeavor, in that the more you put into such an endeavor, the more you stand to lose if the endeavor fails -- you have put a lot on the line, trying to get more out, but if that doesn't work then you've failed big time. You could avoid any losses by just not putting any effort/energy/resources into anything, but then you would also forsake any possible reward.
Similarly, if you just suspended all judgement about everything forever, you could avoid ever being wrong about anything, but at the loss of ever being right about anything either. So it's worthwhile to at least tentatively believe some things, but if you have to believe a lot, take a whole complex lot of stuff (a large volume of information) to be true, then you're exposing yourself to more risk of being wrong, so if you can get a lot of explanatory power from fewer assumptions, that's epistemically putting less on the line, risking less, being less likely to turn out wrong, and thus more probably right, than an equally powerful explanation that requires you to commit to a lot of belief in order for it to work.
'...the simpler idea is better....' I inquire, better for what? You have three hypotheses, each one clearly more complicated than the previous one. To which one do you want to devote the time and energy necessary to analyze and falsify? Also, think about what that principle would be that is the opposite of Ocham's Razor. If you think Ockham's Razor per se explains something, I would think that you don't understand what it means. It's Ockham's Razor not Ockham's Answer.
Rocky Gerung bring me here
Simpler theories make the brain spend less ressources for their computation for the same result. That's why we favor them.
That is also why we are lazy xxx procrastinators !
why is benefit equal in this case?
The benefit is the explanatory power of the theory. Ockham's razor compares theories with equal explanatory power.