The version of Occam's Razor quoted above seems to support solipsism, the view that only one's conscious experience exists, over a view which also admits the reality of the external world. After all, solipsism is committed to fewer entities than the latter view, which also countenances the existence of stars, atoms, and rollercoasters.
I'll interpret the quote that explicates Occam's Razor as holding that the following is a priori: if we have two theories, X and Y, and Y says that fewer kinds of things exist than X does, then Y is more likely to be true, on some given some body of evidence, than X. This principle does indeed indicate that we should take solipsism to be more likely to be true than realism about the external world. The problem is that the principle isn't quite right.
As it stands, the above principle says that the theory on which nothing exists is more likely to be true than any other theory, given our current evidence. No matter what you take our current evidence to be, even if you restrict our evidence to conscious experience, the theory on which nothing exists is almost certainly false. For if there were nothing, there would be no conscious experience. So, given our evidence, the theory on which nothing exists is less likely to be true than either solipsism or realism about the external world, contradicting the above version of Occam's Razor.
This is why Occam's Razor often has a clause specifying that all other theoretical virtues, aside from ontological parsimony, must be equal in order for Y to be more likely than X. By "theoretical virtues" I just mean whatever features theories can have that increase their likelihood of being true, such as explanatory power. If we were to add such a clause to the version of Occam's Razor I formulated above, it should no longer be obvious whether it supports solipsism over realism about the external world. The reason is that if realism explains more of our evidence than solipsism or explains the evidence better, this new principle will say that realism may be more likely to be true despite its positing more kinds of entities.
I leave it up to you to determine whether realism about the external world in fact has more theoretical virtues like explanatory power than solipsism does.
The version of Occam's Razor
The version of Occam's Razor quoted above seems to support solipsism, the view that only one's conscious experience exists, over a view which also admits the reality of the external world. After all, solipsism is committed to fewer entities than the latter view, which also countenances the existence of stars, atoms, and rollercoasters.
I'll interpret the quote that explicates Occam's Razor as holding that the following is a priori: if we have two theories, X and Y, and Y says that fewer kinds of things exist than X does, then Y is more likely to be true, on some given some body of evidence, than X. This principle does indeed indicate that we should take solipsism to be more likely to be true than realism about the external world. The problem is that the principle isn't quite right.
As it stands, the above principle says that the theory on which nothing exists is more likely to be true than any other theory, given our current evidence. No matter what you take our current evidence to be, even if you restrict our evidence to conscious experience, the theory on which nothing exists is almost certainly false. For if there were nothing, there would be no conscious experience. So, given our evidence, the theory on which nothing exists is less likely to be true than either solipsism or realism about the external world, contradicting the above version of Occam's Razor.
This is why Occam's Razor often has a clause specifying that all other theoretical virtues, aside from ontological parsimony, must be equal in order for Y to be more likely than X. By "theoretical virtues" I just mean whatever features theories can have that increase their likelihood of being true, such as explanatory power. If we were to add such a clause to the version of Occam's Razor I formulated above, it should no longer be obvious whether it supports solipsism over realism about the external world. The reason is that if realism explains more of our evidence than solipsism or explains the evidence better, this new principle will say that realism may be more likely to be true despite its positing more kinds of entities.
I leave it up to you to determine whether realism about the external world in fact has more theoretical virtues like explanatory power than solipsism does.