Just to clarify, solipsism and determinism are philosophical currents easily refutable by someone with the right tools and with a good methodology. They are not logical or rational beliefs, they only appear to be.
The key to differentiating a logical belief from one that is not, is that the second needs illogical tools to support itself. For example, the determinists themselves accept that belief in free will is a necessary "lie." Just as solipsists don't manage their daily lives as if they were the only existing person.
In any case, it is better to follow intuition before drawing extravagant logical conclusions.
RE: Critique of Critique