Yes, Occam's Razor taken with no other limiting principle leads directly to metaphysical solipsism.
It is undoubtable that the conception of the universe that I hold in my mind is less complex than the real universe, if the real universe exists. Therefore, if I want to take the simplest explanation for all the phenomena that I observe, it is simplest ontologically to suppose that there is nothing at all beyond what I directly observe: my own sensory perceptions at the present moment, and my thoughts.
Even to suppose that these have a pattern, much less to ask what that pattern might be, requires adding extra ontological assumptions: We must introduce a category of things such as "laws of physics" or "patterns" and then we can fill it in to explain what I see. Granting this for a moment, the solipsist loses no ground in his argument by declaring: They have a pattern simply because I imagine that they do.
It is natural to point out that solipsism lacks the explanatory power of other theories: After all, solipsism can't explain why you observe X and not Y. However, this is not fair to the solipsist, as the attack assumes a priori that there is something to explain.
As an analogy, suppose we ask an atheist some question in Christian theology, e.g. the mode of Christ's presence in Communion. The atheist cannot explain how Christ is present in the bread and the wine, but a Lutheran, an Anglican, and a Catholic can. Does that mean atheism has less explanatory power than any of these Christian sects? Obviously, that would be unfair. The atheist denies that there is anything there that needs explanation; there's no need to explain how Christ can be present in the communion elements because he isn't present in them.
Likewise, the solipsist has no responsibility to explain phenomena whose existence he denies. For example, you might accuse solipsism of lacking predictive power about future events, but the solipsist does not accept the premise that there are future events to predict.
Let me go into a bit more detail on the application of Occam's razor:
If it is necessary to answer questions of the form "why is X true instead of Y?" then every worldview must face a brick wall at the end of the chain, i.e.
Why is X1 true?
X1 is true because X2 is true.
Why is X2 true?
X2 is true because X3 is true.
Etc.
Obviously, if we don't want to get caught in a loop, we cannot answer every demand for an explanation. (Note: of course each step Xk might be a complex statement containing many claims, in which case X(k+1) should explain all of those claims.) Let's say we stop at n, i.e. "Because Xn is true" and that's the step we leave unexplained. All the Xk for k<n are explained in terms of Xn, so that forms the basis of our whole explanatory system. All things are explained in terms of Xn. Xn is the set of all brute facts.
Occam's razor suggests two or three non-equivalent ways to evaluate a given chain of explanations. Firstly, we ought to have the simplest possible Xn to explain our X1. Secondly, we would ideally have n as small as possible. Thirdly, we would like to have some handle on what Xn actually is and the chain of logic from there to X1 (though I'm not sure that this properly falls under the umbrella of "Occam's razor", it definitely seems desirable; more on this topic at the bottom).
With this in mind, let's evaluate some possible worldviews might be:
- Deterministic Naturalism: Xn is the set of physical laws plus the initial state of the universe. n might be quite large. The physical laws might be quite complex, or quite simple, we can't really tell. Modern physics suggest something rather complicated.
- Nondeterministic naturalism: Similar to deterministic Naturalism, we must include in Xn the laws of physics and the universe's initial state. However, in light of random processes, we must also include the outcome of every random event as something "unexplained"; if A or B happens randomly, and B is the one that actually happened, we must add to Xn that B happened, since there was no reason for it. Thus Xn includes not just the initial state and the physical laws, but a track of the universe's history up til now.
- Religious monotheism (inc. Christianity, Judaism, and Islam): All things are made by a single God. Xn is the statement defining God, n may be quite large. Most monotheists believe in some notion of divine simplicity, that is, God is not made of parts, and therefore we have hope that Xn is a relatively simple proposition. The cost of this is the complete impossibility of actually knowing Xn renders that simplicity pretty much a moot point in terms of explanatory power. Basically, even if we have Xn, we're missing X(n-1) because we don't have any idea how or why God does most or all of the things that he does. (And for the record, religious monotheists are OK with this, obviously an omniscient, omnipotent God may have reasons and methods that we can't even possibly know anything about.)
- Philosophical monotheism (e.g. Platonism or Daoism): this is similar to monotheism, but "God" is an impersonal first principle which is fundamentally unknowable. These worldviews usually take as an article of faith that Xn is actually reducible to a single principle, e.g. see Dao De Jing chapter 42, which declares that everything originates from the Dao. This suffers the same problems as monotheism (see above) with more hope of Xn being a single postulate but at the cost of eliminating any hope that we can begin to know what Xn is.
- Solipsism: Xn is simply the existence of my own thoughts. n=1.
So as far as n being small is concerned, obviously solipsism wins by a country mile.
Complexity of Xn: Of the two forms of naturalism, it seems like that deterministic Naturalism is simpler because then Xn doesn't need to track the history of the universe. But it's possible that a "non-deterministic physical laws + universe's history" is simpler than the simplest deterministic explanation. But, in any case, the total complexity of the universe and its physical laws seems certain to be greater than the complexity of my own thoughts. I do not even understand all the mathematical background required for quantum mechanics, and I am a mathematician! So it appears that the physical laws themselves are quite complex, and we must add to that some (probably many) statements about the initial state of the universe. It is certain at the very least that naturalism's Xn must posit the existence of more things than solipsism, as solipsism proposes only "my mind" while naturalism proposes "all the raw material of the universe (including whatever my mind is made of)". So solipsism is better than naturalism in terms of Xn's complexity.
Compared with naturalism, both forms of monotheism have the advantage that their Xn postulates (as a brute fact) the existence of only one thing. Comparing religious monotheism with solipsism, however, it is plain that God's mind ought to be in some sense "greater" and almost certainly more complex than mine, so religious monotheism's Xn is of greater complexity than that of solipsism.
Philosophical monotheism's Xn on the other hand, resists measures of complexity. It is assumed to be simple. So these worldviews may beat solipsism on the count of complexity of Xn. However, if we even speak about the Dao, the concept we have in our mind is not the true Dao, so such statements cannot be asserted with confidence. Perhaps "complexity" isn't a concept that is actually applicable to the Dao.
So, as regards complexity of Xn, philosophical monotheism might be superior to solipsism, but more likely the two are just non-comparable. Both of them beat all the other worldviews handily.
Knowability of the explanation: Here, solipsism is the clear victor again, as the entire chain of reasoning is one singular step, which is very easy to grasp, and Xn by definition contains nothing that I don't already know. The other worldviews all hang on a theoretical possibilty of following the chain of reasoning from Xn down to X1. But without the possibility of actually doing this in real life, it seems like a moot point. (Philosophical monotheism might deny even the theoretical possibility of following the chain of logic.)
As an example, suppose we ask each worldview: "why did my friend get cancer?" We all might trace this back to some proximate cause, but no one can actually follow the logic back to first principles. To say "God works in mysterious ways. We can't know why he does what he does, but we can know that he has good reasons for what he does" is no different (as an explanation) from "the universe is too complex to actually trace from the big bang until now what caused your friend to get cancer, but we can be sure that there is a chain of cause-and-effect all the way back to the beginning." Both "explanations", while categorically quite different, hinge on the same idea: theoretically, an explanation from first principles exists, but we don't have access to it, so we can't know what it is.
Thus, we can see that all worldviews except solipsism rest on the claim that "an explanation exists, but I don't know what it is". While not actually a brute fact, in terms of explanatory power, such assertions aren't much different. However, for the solipsist, all the conceivable explanations are known a fortiori and we never encounter that issue. Nothing that is unexplained is in the category of things that require explanation.
Conclusion: In terms of Occam's razor, solipsism is clearly favored over other worldviews. The reasoning used to get here applies whether we understand "simpler" in ontological or in syntactic terms. Even considering explanatory power as a factor, solipsism still comes out on top. Indeed, this is solipsism's trump card as it never needs to resort to the cop-out "an explanation exists" when none is demonstrated. Unlike all other worldviews, solipsism can actually exhibit every explanation that it claims exists.
Postscript: I have not addressed polytheistic worldviews, as I do not feel confident that I can accurately present them. It is my impression that Hinduism is actually philosophically monotheistic, i.e. all the gods are emenations (in some sense) from the fundamental divine principle Brahman. I may be mistaken about that understanding, however. In any case, I don't think polytheism of any form would fare much differently from the other non-solipsistic worldviews I assessed.
I think that the best way to refute solipsism is to resort to innate knowledge and intuition. One might also use a variant of Pascal's wager: even if solipsism is correct, there is no benefit offered from believing in it. On the other hand, if it is wrong, it seems that believing in it would be detrimental. However, this suffers the same weaknesses as the classical version of Pascal's wager.
In any case, it is clear to me that Occam's razor as the guiding principle will point inevitably towards solipsism unless it is limited by other principles or taken with the context of some strong assumptions. I would interpret this as a reductio ad absurdum argument why a worldview must be evaluated on more sophisticated grounds than simply Occam's razor and explanatory power.
