sarge@thirdi.UUCP (Sarge Gerbode) (01/01/70)
In article <20194@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: >But a theory may make more assumptions >(even logically stronger ones) than another, and yet have each of its >assumptions play an explanatory role. Ockham's razor enjoins us to >disbelieve the first theory, other things being equal; and I'm still >wondering if there's an argument for it. > I think if one theory has greater explanatory power than another, the two theories don't satisfy the conditions for applying Occam's Razor (How do you spell that, anyhow?). The law (as I understand it -- I hope the same way Occam did) states that of two explanations, each of which fits all the available facts equally well, one should pick the simpler or more modest one. If one of the explanations doesn't explain all the facts as well (lacks equal explanatory power), then Occam's razor doesn't apply. -- "Absolute knowledge means never having to change your mind." Sarge Gerbode Institute for Research in Metapsychology 950 Guinda St. Palo Alto, CA 94301 UUCP: pyramid!thirdi!sarge
kube@cogsci.berkeley.edu (Paul Kube) (08/21/87)
In article <8727@ut-sally.UUCP> turpin@ut-sally.UUCP (Russell Turpin) writes: >Ockham's razor is a demand for parsimony of assumptions. Whether >or not one finds it compelling is a philosophic debate over which >much paper has been dirtied (and bits flipped.) But it is a >philosophic, as opposed to aesthetic, principle. Philosophic it may be, but so far it is just a pronouncement of taste, like Quine's preference for desert landscapes. I was wondering if you had an argument. >In my original >posting, I made it clear that I was talking about two physical >theories which (a) had identical explanatory power and (b) one of >which required logically weaker physical assumptions (laws). No, you did not make this clear. You talked about three cases: A pair of equiexplanatory theories, one of which makes fewer unexplained assumptions than the other; a pair of equiexplanatory theories which make the same assumptions but one; and a pair of equiexplanatory theories which make all the same assumptions. Entailment relations between the assumption sets wasn't mentioned, nor were assumptions equated with `laws'. >In short, the other theory is making physical assumptions that >provide no additional explanatory power. Since belief in physical >laws is justified (in many epistemologies) by reference to their >explanatory power (amongst other things), these extra assumptions >(putative laws) should be rejected. (This, of course, is just a >restatement of a strict version of Ockham's razor.) Now this is an argument, but it's not an argument for Ockham's razor. It's an argument for not believing theories that make assumptions that play no explanatory role. But a theory may make more assumptions (even logically stronger ones) than another, and yet have each of its assumptions play an explanatory role. Ockham's razor enjoins us to disbelieve the first theory, other things being equal; and I'm still wondering if there's an argument for it. --Paul kube@berkeley.edu, ...!ucbvax!kube
eric@snark.UUCP (Eric S. Raymond) (08/22/87)
In article <20194@ucbvax.BERKELEY.EDU>, kube@cogsci.berkeley.edu (Paul Kube) writes: > Ockham's razor enjoins us to > disbelieve the first [simpler] theory, other things being equal; and I'm > still wondering if there's an argument for it. > > --Paul kube@berkeley.edu, ...!ucbvax!kube There is no *formal* argument for Occam's Razor. It's a heuristic, based on experience of what kinds of theory-building practices yield the most predictive and robust theories. The argument for it, like the argument for scientific method itself, is simply that it works. -- Eric S. Raymond UUCP: {{seismo,ihnp4,rutgers}!cbmvax,sdcrdcf!burdvax,vu-vlsi}!snark!eric Post: 22 South Warren Avenue, Malvern, PA 19355 Phone: (215)-296-5718
kube@cogsci.berkeley.edu (Paul Kube) (08/24/87)
In article <100@thirdi.UUCP> sarge@thirdi.UUCP (Sarge Gerbode) writes: >In article <20194@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: > >>But a theory may make more assumptions >>(even logically stronger ones) than another, and yet have each of its >>assumptions play an explanatory role. Ockham's razor enjoins us to >>disbelieve the first theory, other things being equal; and I'm still >>wondering if there's an argument for it. >> > >I think if one theory has greater explanatory power than another, the two >theories don't satisfy the conditions for applying Occam's Razor... That's why I said "other things being equal". I was supposing that the only difference between the two theories was their "size" given some metric on theories. Others have suggested the metric be the number of assumptions that the theory makes; I don't like this much since assumptions seem hard to count but I'll go along with it for sake of argument. It's also unclear how to order theories with respect to "explanatory power"... I've been assuming two theories to have the same explanatory power if they license all the same inferences among observation sentences, but this hasn't played much of a role in the discussion yet. (So if one of two equiexplanatory theories has a logically stronger assumption set than the other, it means the nonobservaton sentences it entails are a superset of the other; they entail the same observation sentences.) >(How do you spell that, anyhow?). My Webster's prefers Ockham, giving Occam as a variant. >The law (as I understand it -- I hope the same way >Occam did) states that of two explanations, each of which fits all the >available facts equally well, one should pick the simpler or more modest >one. Yes, "Don't multiply entities beyond necessity" is the gist of it. And there are reasons for taking this advice: You tend to get theories that are easier to understand, and maybe easier to use in practice (though simplifying one's ontology can make a theory harder to use; cf. Hartry Field's _Science without Numbers_). But some people (maybe Ockham himself) wanted to say that one should always pick the simpler theory *because it's more likely to be true*, and I have been wondering what reasons there are for believing *that*. --Paul kube@berkeley.edu, ...!ucbvax!kube
myers@tybalt.caltech.edu (Bob Myers) (08/25/87)
In article <20271@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: >cf. Hartry Field's _Science without Numbers_). But some people >(maybe Ockham himself) wanted to say that one should always pick the >simpler theory *because it's more likely to be true*, and I have >been wondering what reasons there are for believing *that*. Are we still talking about scientific theories? What does it mean to say that a scientific theory is more likely to be true? Do you mean more likely to fit observation, over a wider range of phenomena? That's the only possible explanation I can see. As I've said, I think it is a mistake to use the word "true" with respect to science. It has too many absolute connotations that science just doesn't deal with. ------------------------------------------------------------------------------- Bob Myers myers@tybalt.caltech.edu {rutgers,amdahl}!cit-vax!tybalt.caltech.edu!myers
sarge@thirdi.UUCP (Sarge Gerbode) (08/25/87)
In article <20271@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: >I've been assuming two theories to >have the same explanatory power if they license all the same >inferences among observation sentences, but this hasn't played much of >a role in the discussion yet. (So if one of two equiexplanatory >theories has a logically stronger assumption set than the other, it >means the nonobservation sentences it entails are a superset of the >other; they entail the same observation sentences.) Very interesting concept of explanation. But would the "nonobservation sentences" (by which I assume you mean statements about unobserved or unobservable entities) necessary have to be the same between two theories of unequal explanatory power? Seems to me that different explanations often make different assertions about non-observed entities. For instance, Jung talks about Archetypes and Freud about Ego, Id, and Superego. One could imagine these theories explain the same observable phenomena but allege the existence of *different* non obwervables; one is not merely a superset of the other. In this case, you might have a problem deciding which has greater explanatory power, a problem which wouldn't exist if one was a superset of the other. You'd have to make some type of judgment about the number of non-observed entities alleged and the modesty of asserting the existence of these non-observed entities. For instance it is *slightly* more modest to say that the "Id" causes various psychological effects than to say that Men From Mars cause them. >My Webster's prefers Ockham, giving Occam as a variant. OK, but "Occam" is simpler :-). >But some people >(maybe Ockham himself) wanted to say that one should always pick the >simpler theory *because it's more likely to be true*, and I have >been wondering what reasons there are for believing *that*. Well, when a theory is fundamentally flawed (such as the Ptolemaic system), it tends to get very complex when one tries to shoehorn it into existing observations. The history of science, as Kuhn points out, is that of gradually expanding complexity of a given paradigm, followed by a new paradigm that is simpler and fits the same facts (or most of them). In this case, simplicity is a sign of truth. Whether that's because the universe actually *is* simple or whether we just get along better with simpler theories is something we probably will never know. It's probably safer to believe the latter. More modest, anyway. -- "Absolute knowledge means never having to change your mind." Sarge Gerbode Institute for Research in Metapsychology 950 Guinda St. Palo Alto, CA 94301 UUCP: pyramid!thirdi!sarge
kube@cogsci.berkeley.edu (Paul Kube) (08/26/87)
References: In article <132@snark.UUCP> eric@snark.UUCP (Eric S. Raymond) writes: >There is no *formal* argument for Occam's Razor. It's a heuristic, based on >experience of what kinds of theory-building practices yield the most predictive >and robust theories. The argument for it, like the argument for scientific >method itself, is simply that it works. If by `formal' you mean `deductive', I'd guess you're certainly right. Ockham's razor isn't a truth of logic. If you mean `rigorous', I don't see what its being a heuristic has to do with it. It's certainly possible to give a rigorous justification for a heuristic. I'd believe a strong inductive argument for Ockham's razor along the lines you sketch, but I'm not optimistic about there being one. For one thing, the clearest sorts of violation of the razor--where a theory is complexified *without any change in observational consequences*--exactly preserve predictiveness and robustness. For another, I'd bet that application of the razor without regard to observational consequences does at least as much harm as good; I'd offhand expect complexification to work just as well. But I'm prepared to be convinced by a careful study of the history of science that shows otherwise. I'd also believe an argument that goes along the folowing lines, but I'm not optimistic about it being extendable in the appropriate ways. Maybe you can suggest something: As I've characterized it, Ockham's razor is a claim about the relative likelihoods of the truth of theories, viz. that the simpler of two is more likely to be true. So suppose there are two theories, T1 and T2, and let W1 and W2 be the sets of possible worlds in which they are respectively true. Suppose T1 and T2 have all the same observational consequences; then W1 and W2 are both subsets of the set of possible worlds that, for all we can tell by observation, the actual world is in. The question is: Is the actual world in W1 or W2?, and we want to maximize the likelihood of making the right guess. Well, the rational thing seems to be to pick the bigger of W1 and W2 (and so the least restrictive, i.e. simplest, of T1 and T2). But it seems to me that for lots of cases we care about, W1 and W2 are going to have the same cardinality; and a natural measure will assign them both the same measure; and then I don't know how to say one is more likely than the other. --Paul kube@berkeley.edu, ...!ucbvax!kube
eric@snark.UUCP (08/27/87)
In the following, OR = Occam's Razor. In article <20297@ucbvax.BERKELEY.EDU>, kube@cogsci.berkeley.edu (Paul Kube) writes: > [quotes my claim that OR is just a heuristic, not formally demonstrable] > > I'd also believe an argument that goes along the folowing lines, but > I'm not optimistic about it being extendable in the appropriate ways. > > [Argument that says we should trust weaker theories because they describe > larger subsets of the set of all possible universes, so our universe is > more likely to be in the set] That's a really interesting way to think about the problem which hadn't occurred to me at all. It's no kind of 'demonstration' of OR but it seems to translate our intuitive notion of 'theory strength' into terms that may make it easier to think about. > But it seems to me that for lots of cases we care about, [the truth sets > of the theories being compared] are going to have the same cardinality; and a > natural measure will assign them both the same measure; and then I > don't know how to say one is more likely than the other. Well, then...don't. There are situations like this in the real world where scientists work with several predictively-equivalent but distinct formalisms. I understand, for example, that there are three distinct formalism, very different in style, in which you can do quantum mechanics. One of them is called S-matrix theory, I think the second one is based on systematic use of Feynman diagrams, and the I think the third involves trying to solve the time-dependent Schrodinger equations by analytic means. I may have those three flavors wrong (physicists be gentle with me, I am merely a defrocked mathematician) but I hope this makes the point. Nobody says that you *have* to choose one out of a bunch of predictively-equivalent theories and swear allegiance to it... > --Paul kube@berkeley.edu, ...!ucbvax!kube -- Eric S. Raymond UUCP: {{seismo,ihnp4,rutgers}!cbmvax,sdcrdcf!burdvax,vu-vlsi}!snark!eric Post: 22 South Warren Avenue, Malvern, PA 19355 Phone: (215)-296-5718
sarge@thirdi.UUCP (08/27/87)
In article <20297@ucbvax.BERKELEY.EDU> kube@cogsci.berkeley.edu.UUCP (Paul Kube) writes: >As I've characterized it, Ockham's >razor is a claim about the relative likelihoods of the truth of >theories, viz. that the simpler of two is more likely to be true. So >suppose there are two theories, T1 and T2, and let W1 and W2 be the >sets of possible worlds in which they are respectively true. Suppose >T1 and T2 have all the same observational consequences; then W1 and W2 >are both subsets of the set of possible worlds that, for all we can >tell by observation, the actual world is in. The question is: Is the >actual world in W1 or W2?, and we want to maximize the likelihood of >making the right guess. Well, the rational thing seems to be to pick >the bigger of W1 and W2 (and so the least restrictive, i.e. simplest, >of T1 and T2). But it seems to me that for lots of cases we care >about, W1 and W2 are going to have the same cardinality; and a >natural measure will assign them both the same measure; and then I >don't know how to say one is more likely than the other. Very interesting idea -- but it seems to me that you are talking about *another* criterion for desirability in scientific theories, namely: scope. Of two theories, we will pick the one that has the broadest potential applicability (something that explains *all* trees, not just grapefruit trees, for instance -- the biggest W1 or W2, as you say). And this makes sense, for the reason you give. But is it really necessarily the *simpler* theory that has the wider scope? That doesn't seem to be necessarily true. It seems that sometimes to generate a wider W1 or W2 of applicability, one might have to add complexities to the theory. It *might* be the case, but if so, an example or an argument to demonstrate this would help. I may have missed the boat totally on what you are trying to say. -- "Absolute knowledge means never having to change your mind." Sarge Gerbode Institute for Research in Metapsychology 950 Guinda St. Palo Alto, CA 94301 UUCP: pyramid!thirdi!sarge