OK GD people, which book are you reading now?

[Bugsby]

I'm not so sure that works as an analysis of knowledge. For one thing, you need to be more explicit about the premises and the reasoning. Are these premises also beliefs held by the agent? Must the agent also know these premises? Or is it sufficient for the agent to hold these beliefs without having them count as knowledge? Either way is problematic.

Suppose that I need not know the premises. If this is the condition we are working with, then it could be the case that our agent is delusional, and some belief(s) just pops into his head that happens, through mere chance, to be true. Our agent, locked in his cell in the mental ward and completely ignorant of all the goings-on in the world, suddenly forms both the belief that Laura Bush is the First Lady and the belief that Laura Bush is married to G. W. Bush. Based on these premises, our madman concludes that G. W. Bush is President of the U.S. In this case, this belief - that G. W. Bush is President - meets all your conditions for knowledge. The belief is true, it is based on true premises, and it is arrived at by valid reasoning (we can say that our madman, despite his other shortcomings, has a firm grip on standard logic). But we would not say that this madman KNOWS that G. W. Bush is President; the beliefs that led him to that conclusion were nothing more than the illusions of a sick mind.

So say instead that the premises must be known. This leads us to the problem of an infinite regress. Because if the premises must be known, then they must in turn be true beliefs based on true premises and arrived at by valid reasoning. But the premises of this further argument must be known, and so on and so forth. By requiring "known premises" for knowledge, we create for ourself a chain of justifications. The chain either does not end - which is absurd - or it does end, which is impossible given your conditions.