This must actually mean that we are unconscious of the non-intuitive immediate ground. The knowledge itself is neither believed nor thought, as such, and it is not explicitly present to us as the table or chair is perceptually. This is ultimately an appeal to intuition, but in present time it is only an appeal to memory. Demonstration is merely a showing of the obvious. Where the obvious is no longer present or escapes the nature of our perceptions, then other considerations come into play.
Deduction is a showing of the unobvious, but still importantly a showing.
Deduction cannot logically prove the propositions in questions any more than the demonstration of an intuitive ground can. But the cognitive force of each is the same. The first questions about non-intuitive immediate knowledge would be how it comes to be consciously known, having been unconsciously known, and then how we know that it is what we think it is. Nelson's theory in this respect is not satisfactory. But since Nelson did think that this occurs through Socratic Method, it is possible to ignore the intuitionistic aspects of his theory and just see Socratic Method, as described above, using the logic of falsification.