I think you need to add your PrincipleOfParsimony (which is only superficially related to OccamsRazor) to your set of MaterialistPresuppositions.
-- TomKreitzberg
I see your point about the "PrincipleOfParsimony" not being equivalent to OccamsRazor. Please see my comment on that page.
Generally though, I refuse to state as axioms what I regard as elements of rational discourse. OccamsRazor is not an axiom; it's part of the rules of the game. If you don't accept OccamsRazor as one of the ways by which we judge the validity of an argument, regardless of what theory, what philosophy, what axioms we are discussing, then I don't want to talk, with you, period.
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- Then I guess you don't want to talk with me, period. Nevertheless, OccamsRazor has nothing to do with the validity of an argument; add "Lemons taste sour" to any argument you like, and you won't change its validity. -- tk
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- I might want to take you up on that. Let's say I concede your point and let you add "Lemons taste sour" to an argument you are defending. After all, you just did that in the above. But then, if I manage to prove that lemons don't taste sour, you will have to grant that your argument is, as a whole, incorrect. I would only need to assert that, for me, under some circumstances, lemons taste sweet; in lemonade, for instance.
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- There are lots of directions we can take this, most of them for pure entertainment (I'm tempted to write a SummaWay article on "Whether lemons assume sweetness in lemonade"). The point remains, though, that the validity of an argument does not depend on its simplicity. -- tk
It has been also suggested that "deductive logic" be added to the materialist axioms, and I also reject that suggestion, on the grounds that without deductive logic we can't reason about anything. We are willing to grant anyone any axioms they care about, but everybody should play the game under the same rules;
OccamsRazor and deductive logic are (IMNSHO) part of these rules.
-- LaurentBossavit
I can think of four reasons why the PrincipleOfParsimony ought not be considered a "rule of the game" for choosing between two proposed philosophies:
1. The "simplest" explanation is not, per se, the true explanation.
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- That's true, but the PrincipleOfParsimony calls, not for the simplest explanation, but for the simplest explanation that will fit all known facts.
I show you a shoebox, slip a hand inside, remove a red marble, show you the
marble, then put the marble back in the shoebox. I bet you US $100 that one of the following hypotheses is true:
A) The shoebox contains one red marble.
B) The shoebox contains three red marbles and the four of diamonds from a deck of playing cards.
C) The shoebox contains nothing; when you thought I put the marble back in the box, I actually palmed it and put it in my pocket.
Apply the PrincipleOfParsimony and determine which is the true hypothesis.
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- ...and remember that parlor tricks rely on your not knowing all the facts you need to account for. Give me the box, I'll give it a shake, and depending on whether I hear one, two, or many things rattling inside I'll tell you which of the above hypotheses fits the facts best.
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- I've given you above all the facts you need to account for. All three choices account for all the facts. My handing you the box is like my handing you a hyper-dimensional travel capsule that enables you to observe without affecting the Big Bang.
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- OK, fine. I'll choose A, anytime. I wouldn't choose B unless I had the feeling that there was something about the box you hadn't told me; nor choose C unless I had the feeling you did something unexpected. Unless I have a reason to think otherwise, I'm assuming that you (the Universe) are playing a straight game with me, which is pretty much one of the MaterialistPresuppositions. If I've seen a box and a ball, that's all there is, and both are still here afterwards. Unless I have a reason to think otherwise, A is not only the simplest theory but also the most likely to be true.
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- Your last statement is simply false. A is not the "most likely to be true"; none of the theories is more "likely to be true" than the others, or a thousand other theories like them. You're making an assumption about probabilities without any evidence whatsoever (and after all this, to assume that I'm playing straight with you...?). But "I'll choose A, anytime," is good science -- not because it is probably true, but because it is easier to use.
You guys missed something along the way. We reject
C because nature does not play tricks on us (if it did, science would crumble), so we are left with
A and
B. We cannot resolve this one, not even using
OccamsRazor. Both require the same amount of assumptions,
A requires us to assume that we have seen all that there is, and
B requires us to assume that there must be more. In this case, we must resort to
D, make another observation, then pick again. --
KyleJerviss
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- That is not correct. There are fewer assumptions involved in A than B. A assumes that there is no more to the puzzle. B assumes that 1) There is more to the situation; and 2) of the (almost) infinite set of possibilities, the one case 3 red balls, one 4 of diamonds is selected. Strictly speaking, then, option B requires more bits of information to represent than option A, the simplest. -- SunirShah
You're very kind, but I am not nature. I do, sometimes, play tricks. As for nature not playing tricks, I suspect that you are younger than I am. -- tk
2. It often begs the question of what is "simplest".
Attempts to express a philosophy in some minimum number of axioms are misguided. Is it reasonable to assert that a system of 16 axioms is necessarily truer than a system of 17 entirely different axioms? How valid is cardinality as a measure of simplicity?
Further, consider hypotheses B and C from above. Which hypothesis is simpler? Why?
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- Point (already) granted. In a lot of cases, however, it's obvious which theory is simplest. In a spirit of fairness, I'll cite two examples, one of a complex theory that turned out to be better than the simple one; Darwin's theory of evolution vs. creationism, and Wigener's theory of continental drift vs. the former "statist" geologic orthodoxy.
3. It is subjective, rather than objective.
The reason we apply the PrincipleOfParsimony is not because of the objective nature of the situation, but because we as subjects investigating that nature have small brains which work better on simpler problems than on more complex problems. Those problems which aren't amenable to simple explanations generally aren't yet solved.
4. No one follows it anyway.
The simplest philosophy, in terms of expression (and, for that matter, in terms of numbers of axioms), is solipsism. But no one older than 19 or younger than 16 is a solipsist (well, maybe babies are; I don't remember). Therefore, practically everyone uses something other than the PrincipleOfParsimony to choose their philosophy.
-- TomKreitzberg
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- LB: I beg to differ - solipsism, like theism, is an extra axiom that does little to account for any observable facts. OK, so the world only exists because I think it exists and is all a product of my imagination; but then the subject of study becomes my imagination, and the question becomes, why do the things I'm imagining behave in certain ways and not others ? That's why most of us let go of solipsism sooner or later.
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- TK: First, I think, you need to construct the concept of "why," a concept I don't think needs to be granted by solipsism. I don't know why most of us aren't solipsists; I'm not one because I don't find it a satisfactory explanation of my experiences, even though, as a logical system, it is the only complete explanation of my experiences that I know.
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- LB: Complete it might be, but it certainly isn't an "explanation"; not in the everyday usage of that term. When I ask a theory to explain something, it had better come up with something more convincing than "just because". IOW, a good theory not only fits observed fact but is also falsifiable, i.e. it fits only the set of observed fact it is constructed to explain, not all possible sets of observed fact.
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- TK: When you demand that a theory be "more convincing than 'just because'," you're injecting a subjective element into your philosophy -- it has to be more convincing to you. I don't think this is a bad thing -- I implied above that I demand a theory to be a "satisfactory explanation" -- but I do think we need to recognize that science itself is not a purely objective act.
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- LB: Well, I beg to differ (again !) - if "just because" is convincing enough to somebody, they'd have to be either a child or a fool. A theory should be, objectively, a satisfactory explanation. One such objective criterion is falsifiability : a theory that accounts for everything indiscriminately is not a good theory.
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- TK: I guess my claim is that "objectively satisfactory" is an oxymoron. [Okay. It's an ExtremeOxymoron until proved otherwise]
Even simpler than solipsism is nihilism. Nihilism has one axiom: "Nuh uh." No matter the question, the answer is "nuh uh." You say this leads to self-contradictions? Nuh uh.
Simpler solutions are only more probable than more complex solutions as there are fewer simpler solutions than complex solutions. Remember, probability does not exclude possibility, and possibility does not imply probability. -- SunirShah
Why do we talk about explanation instead of talking about prediction? What is the use of explaining things we cannot or need not predict? --NikitaBelenki
A few reasons. First, it's fun. Second, sometimes by poking around for an explanation, you find a way to make good predictions. Or you find a sub-field that is amenable to prediction. Or you find an explanation for why predictions are impossible; that's learning something, too. Or you come up with something completely different. Searching for explanations is one of the main drivers that leads us to new and unexpected insight. If you demand a known payoff before searching for explanations, you'll quash a lot of fruitful searching. --BenKovitz
OK, we've enjoyed the search and ended up with some explanations, each of them seems not to contradict the facts we have. Why would we throw away any of them? -nb
Relevance Of Occams Razor