Science is a First-Order Discipline: Why Science Needs Philosophy

[Dre89]

I've never understood how Occam's Razor works, seeing how complexity can be defined in multiple ways.

By one view, God can be a simpler explanation than a physical cause, in that He has no form, or any contingent properties, whereas the physical first cause has a form and multiple contingent properties. On the other hand, one can say God is more complex simply because being non-physical makes a proposition automatically more complex.

Also, what makes the simpler explanation more favourable? Surely a more complex explanation with logical premises is better than a simple one with illogical premises. If simplicity is the key, I don't see how one doesn't fall into an infinite regress of simpler and simpler explanations.

 

[rvkevin]

I've never understood how Occam's Razor works, seeing how complexity can be defined in multiple ways.

This is the most standard method for quantifying complexity. However, complexity has little to do with Occham's Razor. Ozzham's Razor has to do with the number of assumptions that one needs to make for a certain hypothesis to work. A hypothesis that requires few new assumptions will be preferable to one that requires a lot of new assumptions.

 

[Dre89]

Well then OR can't address metaphysics then because metaphysics has no default positions.

For example, the idea that the first cause must be a formless eternal being is equally simple/complex as the idea that it could consist of multiple contingent parties with specific forms.

 

[blazedaces]

Bias opinion? You make it sound as if I'm saying it with a negative connotation.

Not many people will contest that a lot of scientists are empiricists or scientisimists, because most people not educated in philosophy and metaphysical propositions think they're not cognitive.

And seriously, that doesn't even matter. Posts like this just slow the debate down.

Do I really have to go and get a source which shows most scientists believe in god? It slows the debate down because I ask for proof about a point?

This whole debate is about convincing this group of people who believe they don't need "philosophy" (that you have yet to explicitly define) that they do... and my point of questioning that this group is at all large slows the debate down?

-blazed

 

[rvkevin]

Well then OR can't address metaphysics then because metaphysics has no default positions.

OK...I didn't even bring up Occham's Razor and it has nothing to do with default positions. Relevance?

For example, the idea that the first cause must be a formless eternal being is equally simple/complex as the idea that it could consist of multiple contingent parties with specific forms.

This is false as explained here.

 

[Theftz22]

A hypothesis needs to be able to state what should happen given a certain phenomena. If you propose a certain hypothesis, you need to be able to state what should happen when you do X so when you conduct the test you can see whether the result is what should have happened if the hypothesis was true. If you can’t do this, then you haven’t sufficiently defined the proposed hypothesis. If you think the definition of empiricism doesn’t allow for definitions, then I guess empiricism is inconsistent with science. This would seem like an unnecessarily narrow definition for empiricism since it would exclude empirical methodologies.

I don't think that deducing the entailments of a hypothesis is a purely definitional process, it isn't decided purely by definition. For example, the hypothesis that god does not exist entails that Jesus was not raised from the dead, but that's not in the definition of god not existing. "God does not exist" simply means that "there is no entity with the predicates of omnipotence, omniscience, omnibenelovence, etc." There is nothing even about Jesus contained in that definition. Rather that definition entails that Jesus was not raised from the dead, since the resurrection of Jesus depends upon the existence of a supernatural entity.

You would then have to go into why Occham’s Razor is a good principle. Is it because when we find the actual explanation for something that it tends to be simpler than we thought? If so, that’s an empirical observation that we are making; this would make the justification for Occham’s Razor empirical in nature and thus be consistent with empiricism. It would be interesting to try to justify Occham’s Razor otherwise; I wouldn’t know where to start.

The justifications I know of Occam's razor are not empirical. Time and lack of competency with regards to Bayesian probability theory permits me to merely copy paste:

When some set of supposed entities has neat logical properties, it turns out, in a great many instances, that the supposed entities can be replaced by purely logical structures composed of entities which have not such neat properties. In that case, in interpreting a body of propositions hitherto believed to be about the supposed entities, we can substitute the logical structures without altering any of the detail of the body of propositions in question.This is an economy, because entities with neat logical properties are always inferred, and if the propositions in which they occur can be interpreted without making this inference, the ground for the inference fails, and our body of propositions is secured against the need of a doubtful step. The principle may be stated in the form: ‘Whenever possible, substitute constructions out of known entities for inferences to unknown entities’

Without explicitly using the evidence procedure, the Occam factor argument can be summarized as follows (see [MacKay 1991, Berger e t al. 1992, Loredo 1990, Jeffreys 1939, Gull 1989a, Garrett 1991D. Consider a parameter space C. Define a "model", or a "theorist", as a mapping from any c E C to a target function from X to Y. (This is essentially the same as what is called a "method" in [Wolpert 1990] or an "interpreter" in [Pearl 1978].) As an example, i fX is the real numbers, R, as is Y, and i fC is the set of possible quintuples of real numbers, the 4th order polynomial series
using those five parameters is a model: the model is the mapping {PO, PIo P2, P3, P4} -7L~o Pi xi. (Note that this example could be easily modified so that either X and/or Y is not infinite.) Another example of a model, which uses the same C but in a nonlinear manner, is the following 5th order series of Legendre polynomials: {PO, PI , P2, P3, P4} -7 L~o Li(Pi x). Note that the
image space of C (i.e., the set of functions from X to Y which are expressible with some c E C)differs for the two models. Together, a particular model and a particular set of parameter values define a particular target function. Accordingly, I will often write (m, c) as shorthand for the function given by parameter c and model m.

Now consider two models, ml and m2, with associated parameter spaces CI and~. For simplicity, assume that both CI and are subsets of the same Euclidean vector space and have the same dimension. Assume further that CI C C2. (For example, CI might be the interior of one hypercube in R n, and C2 the interior of a larger hypercube, properly surrounding CI.) Let c i refer to
elements of C1> and similarly for c2. Our event space consists of triples (data, model, parameter value from the parameter space associated with that model). So for example P(data =L, model =m1> C2 parameter value =c2) is undefined.

Now in general, the posterior for a model, P(mj I L), equals peL I mil x P(mi) / peL). In turn, PeL I mil = Idci peL I mi, Ci) x P(ci I mil. Examine two particular models, ml and m2. Since we have no way of choosing between the two models, by the "principle of indifference" [Loredo 1990], we
might wish to take P(ml ) =P(m2). Using this gives

P(m!1 L) / P(m2 I L) =peL I ml ) / PeL 1m2)
=IdcI peL I ml , CI) x P( c i I ml ) / Idc2 PeL 1m2, c21 x P(c21 m2).

This is the so-called "Baye s factor" for model ml over model m2. Dividing it by the ratio of maximum likelihood values, (maXc I[P(L I ml , cI)]} / (maxC2
[P(L 1m2, c21]), we get the so-called "Occam factor" [Loredo 1990]

To see why this might have something to do with Occam' s razor, for simplicity assume that the ratio {IdcI PeL I ml , cI)} / (fdc2 PeL 1m2, c2)} can be well approximated by the ratio maxc i[P(L I ml , cI)]} / {maxC2
[peL 1m2, C2)]}. (This might be reasonable, for example, if
PeL I mi, Ci) is peaked a s a function of ci, for both i =1 and i =2.) Also assume the "uninformative"5 fonn for P(Ci I mi), namely a unifonn density: P(Ci I mi) = 1/ [fc. dCi 1] '" [V(q) rl. These conditions giveP(mllL)P(mZ'L)V(Cz) x maxci[PeL I mb CI)]=V(CI) x maxCZ [PeL , mz, cZ)]

Dividing the right-hand side by the ratio of maximum likelihoods, we see that the Occam factor for model 1 over model 2 is simply the (inverse) of the ratio of volumes of the associated parameter spaces. To clarify the discussion, assume that in addition to P(ci I mi) = 1 / [fc. dCi 1], we also have 1f dCI [PeL I ml , cI)] =JdcZ [PeL I mZ, cZ)] (whether or not the ratio of those integrals equals the ratio of the respective maximum likelihoods). Under this assumption, the ratio of P(ml I L) to P(mz I L) is jus t the ratio of volumes of the parameter spaces. So everything else being equal, the "bias" favoring ml ove r mz is given by (the reciprocal of) the ratio of the volume of CI
to the volume of Cz. Models with a large a priori range of possible parameter values are penalized. This is the basis for the conventional "Occam factor" argument for why Occam' s razor must hold a priori ([MacKay 1991, Jeffreys 1939, Berger 1992, Loredo 1990, Ou11l988, Oarrett 1991]), for the case
where CI and Cz have the same dimension but different volumes.

I'm sure that the formatting on that got horribly botched. Anyway, it is possible to give empirical support to Occam's Razor, but that presupposes, rather than proves, the reliability of our cognitive faculties, since any empirical investigations as to the success of the principle presuppose that our cognitive faculties are giving us reliable data. So you could give empirical support to Occam's Razor, but only after you establish the reliability of our cognitive faculties. And so any argument from Occam's Razor to the reliability of our cognitive faculties will have to rely on an a priori justification of the razor or else taking it as properly basic, otherwise you have circularity.

Funny how you should say that it’s a good use of philosophy considering that it is flawed. We could use Baye’s theorem to break the tie if the alternative hypotheses have a way to “break the illusion.” For example, it is possible if you’re in the matrix to then escape it. This means that it is an inferior hypothesis from an empirical standpoint. I should also note that this does not make it knowable, since simply being the best hypothesis doesn’t mean that we have enough confidence in it to call it knowledge. However, this would not apply to hypotheses in which you are locked into the world, but then again, I don’t consider any definition of reality that concludes that we are not real to be that meaningful.

Firstly just because it is possible to escape such an illusory reality would not render it improbable. Rather, you would have to establish that it is likely that we would escape the illusion if we could, so that the argument would be something like this:

1. If we were in the matrix, then we would have escaped.
2. We have not escaped.
3. Therefore we are not in the matrix.

2 is empirically verifiable but 1 is not. Finally, my definition of reality is again, "the objective, external world as it actually is independent of how we perceive it to be". I consider that to be a pretty meaningful definition of reality, as to be real implies a lack of certain properties such as not being illusory, which these scenarios are. This definition does not entail that we are not real, rather I exist in every possible skeptical scenario, as Descartes pointed out. Now of course our bodies could be illusory on this definition, but what I as a property dualist would call my mental properties are real on this definition.

 

[rvkevin]

For example, the hypothesis that god does not exist entails that Jesus was not raised from the dead, but that's not in the definition of god not existing. "God does not exist" simply means that "there is no entity with the predicates of omnipotence, omniscience, omnibenelovence, etc." There is nothing even about Jesus contained in that definition. Rather that definition entails that Jesus was not raised from the dead, since the resurrection of Jesus depends upon the existence of a supernatural entity.

I disagree. Proving an omnimax god does not exist does not disprove that Jesus rose from the dead. It is fairly easy to propose that a benevolent omniscient god that although was not omnipotent was able to raise Jesus from the dead. Or you could propose that an omnipotent, but not benevolent, god tricked a large portion of the population into believing a falsehood by raising Jesus from the dead. Then there’s the advanced extraterrestrials with their technology that is indistinguishable from magic. None of these posit the omnimax god and these provide instances in which Jesus was raised. The only way to avoid this is to say that God and Jesus are one, as many Christians do, which means that disproving God would entail that Jesus, as defined as being part of the trinity, would not exist, which is a definitional implication. You have to be very careful with definitions here because you can’t define god as being omnimax, and then use the same term to refer to any supernatural entity and you need to state whether you think the contradiction is with Jesus rising from the dead either naturally or supernaturally. Naturally, if you disprove god, broadly defined as a supernatural entity, this would mean that Jesus could not be supernaturally raised because that hypothesis predicts the existence of gods, and the absence of them falsifies that hypothesis.

I'm sure that the formatting on that got horribly botched. Anyway, it is possible to give empirical support to Occam's Razor, but that presupposes, rather than proves, the reliability of our cognitive faculties, since any empirical investigations as to the success of the principle presuppose that our cognitive faculties are giving us reliable data. So you could give empirical support to Occam's Razor, but only after you establish the reliability of our cognitive faculties. And so any argument from Occam's Razor to the reliability of our cognitive faculties will have to rely on an a priori justification of the razor or else taking it as properly basic, otherwise you have circularity.

Do you understand the method Wolpert used for this analysis? Although it is hard to tell since some of the mathematical notation has been lost, it appears as though he is using Baye’s theorem. The next question is why does this theorem works? On what basis can we be confident in its results? It’s actually quite amazing how simple it is. There are some basic definitions like what a probability is, but the key part is that we are able to describe the same observation two different ways and they are both empirically correct. I didn’t propose Occam’s razor in the first place so I fail to see how I would feel the slightest need to use it to justify the reliability of our cognitive faculties. However, your insistence to disregard the empirical when evaluating the reliability of our mental faculties troubles me. How else do you evaluate them, by using our mental faculties? Seems circular to me.

Firstly just because it is possible to escape such an illusory reality would not render it improbable. Rather, you would have to establish that it is likely that we would escape the illusion if we could, so that the argument would be something like this:

1. If we were in the matrix, then we would have escaped.
2. We have not escaped.
3. Therefore we are not in the matrix.

I didn’t say it would make it improbable, I said it would make it an inferior hypothesis. This would mean that the external world hypothesis would then be preferable, or more probable, to the matrix hypothesis. I didn’t assign any probabilities to these hypotheses, I simply said P(external world) > P(matrix). I thought I made this clear when I said that this wouldn’t allow us to call it knowledge, since we wouldn’t know how likely it is to be true. We would just know that it is the best hypothesis when compared to the competing hypotheses. Also, I too would reject premise one.