As far as I can tell, you are objecting to my assertion that I know that I'm replying to this thread (my premise 2), and this is what I point to with my premise 1, that any objection to me knowing that I know that I'm replying to this thread can be reduced to an objection to me knowing that I'm replying to this thread. But the opening post presents my first order knowledge as a given, and your initial objection was that I need justification for my second order knowledge. This justification is provided by my argument and assuming JTB, as we are, this adds up to the case that if I know that I'm replying to this thread, then I can know that I know that I'm replying to this thread.
Ah, see this is where I think we get confused. My objection, initially, was against your justification for your first order
knowledge as a given. But I can see how my explanation of my understanding of the closure principle can suggest an attack against your second order knowledge.
As my understanding of the closure principle is, it does not matter whether it is first or second order knowledge. The closure principle will challenge any
form of justification if you hold to the JTB theory of knowledge.
Your initial proposition was that you are posting on this thread. I think we at least agree on that much. :bigsmile:
You were taking for granted that you had JTB for your first order of knowledge - JTB about you posting on this thread. If that is taken for granted, then there is no disputing your second order knowledge - it follows logically, in the way you presented it.
So my challenge was against your having any knowledge at all, but was directed at what you took for granted - your first order knowledge. I was challenging the justification for your first order knowledge, but as I said, the Closure Principle applies to any form of knowledge which adheres to the JTB theory.
I have problems with the JTB theory - between the Closure Principle and the Gettier problem, it doesn't seem like it works.
I liked the way you were going with it though - you seemed like you were working towards Nozick's notion of knowledge, which uses some pretty heavy modal logic. I really like Nozick's conditions for knowledge:
S knows that X IFF:
1.) S believes X
2.) X is true
3.) If it were the case that X was not true, S would not believe that X, and
4.) If if were the case that X, S would believe that X.
As you can see, Nozick uses a counterfactual claim and poses the idea of possible worlds where X would or would not be true, and whether or not S would still believe if X were or were not true.
I thought you might have been leaning towards this theory, but I couldn't tell. Could we agree on this?