Our knowledge is both co-extensive with being, and opposed to it. Our knowledge is co-extensive inasmuch as we speak of “all” and “nothing”; “is” and “is not”; “possible” and “impossible”. There can be nothing outside of thought. At the same time, thought is opposed to being, because the first principle of our knowledge contains “not” and “impossible”, although being does not contain “not” and “impossible”. In other words “impossible” proves both the infinity of human thought, and its opposition to being.
If our knowledge were in no way opposed to being, it would contain all being simply, totally, and with no admixture of non- being: the “not” and “impossible”.
Just Thomism 
viator said,
March 6, 2006 at 11:06 am
CDK on the relation of knowledge to being:
Resume of lecture notes of Methodologie Generale given by M. Charles De Koninck. 1938-39:
I. Knowledge in general, which consists in becoming another as other. That is a definition of objectivity which at the same time manifests what subjectivity is. A being which is purely and simply subject is incapable of going out from itself, is closed to all that which is exterior to it as it is closed for itself. It does not know itself, for if it did it would know itself as other (in the cognitive sense). Other means simply object.
II. Intellectual knowledge. This is necessary to understand if we are to know what science is. This knowledge extends to all things absolutely. No need for demonstration; merely a little dialectics to cause the fact to be observed. The soul is in a certain manner all things. The sensitive soul of the animals is in a sense all sensibles, but in the case of the intellectual soul, it is a question of all things in a completely rigorous sense. “Nam unaquaequae intellectualis substantia est quodammodo omnia, in quantum totius entis comprehensiva est suo intellectui” III CG 112.
How do we know all things? It is impossible to pose the question without at the same time knowing all things. How could the question arise unless you knew all things? The reply is implied in the question. One cannot know that he does not know all without knowing all. To the question: what is the extent of our intelligence, the reply, in all frankness, is that we know all, and this without exception. What exception can be imagined? The exception is again among the things which are. All things, that is, all which is not nothing, all which is not impossible. Hence we arrive at the paradox that it is impossible to know nothing sans knowing everything, or rather that it is impossible to know that one knows nothing without knowing everything. This is a paradoxical idea: one can know all and know nothing in a certain manner. This manifests the nature of our intelligence, for although it extends to all things, yet considered in itself it is in potency. All this is implied in the principle of contradiction, which is, that a thing cannot be and not be at the same time and in the same respect, and since this principle is first, without which nothing else can be known, it is impossible that we know something without knowing everything, since everything is implied in this principle. The principle applies to everything which is possible.
Therefore, there is an absolute co-extensivity between being and non-being, being and the impossible, that is, that non-being is absolutely outside being. Being is not opposed to non-being in a certain respect, but it is entirely opposed to it, the impossible is excluded absolutely from being. As this opposition between being and non-being is absolute, and absolutely universal, we have an opposition of contradiction. [end of p. 1]