The logical second intentions depend upon the first...

The logical second intentions depend upon the first intentions because the first intentions are the conceptual building blocks of the new knowledge which second intentions link together: but logic studies the second intentions in abstraction from whatever particular first intentions the logical relations depend upon in any given case. Secondary Intelligibles A more careful statement is provided by Avicenna.

Concepts like “horse”, “animal”, “body”, correspond to entities in the real world, entities which can have various properties. In the realm of the mental, concepts too can acquire various properties, properties they acquire simply by virtue of existing and being manipulated by the mind, properties like being a subject, or a predicate, or a genus.

These are the subject matter of logic, and it seems it is only mental manipulation that gives rise to these properties: If we wish to investigate things and gain knowledge of them we must bring them into Conception ( fî t-tasawwur ); thus they necessarily acquire certain states ( ahwâl ) that come to be in Conception: we must therefore consider those states which belong to them in Conception, especially as we seek by thought to arrive at things unknown from those that are known.

Now things can be unknown or known only in relation to a mind; and it is in Conception that they acquire what they do acquire in order that we move from what is known to what is unknown regarding them, without however losing what belongs to them in themselves; we ought, therefore, to have knowledge of these states and of their quantity and quality and of how they may be examined in this new circumstance.

These properties that concepts acquire are secondary intelligibles; here is an exposition of this part of Avicennan doctrine by Râzî: The subject matter of logic is the secondary intelligibles in so far as it is possible to pass by means of them from the known (al-ma‘lûmât) to the unknown (al-majhûlât) not in so far as they are intelligible and possess intellectual existence (an existence) which does not depend on matter at all, or depends on an incorporeal matter)..

The explanation of “secondary intelligibles” is that man Conceives the realities of things ( haqâ'iq al-ashyâ’ ) in the first place, then qualifies some with others either restrictively or predicatively ( hukman taqyîdiyyan aw khabariyyan ).