A.A. Hodge:

Refute the objection drawn from such passages as 1 Tim. ii. 4. “Who will (thelei) all men to be saved and to come unto the knowledge of the truth.”

The word (thelei) has two senses–(a) to be inclined to, to desire; (b) to purpose, to will. In such connections as the above it is evident that it can not mean that God purposes the salvation of all, because (a) all are not saved, and none of God’s purposes fail, and (b) because it is affirmed that he wills all to “come to the knowledge of the truth” in the same sense that he wills all to be saved–yet he has left the vast majority of men to be born and to live and to die, irrespective of their own agency, in heathenish darkness.

Such passages simply assert the essential benevolence of God. He takes no pleasure in the death of the wicked. He does take great pleasure in the salvation of men. Yet as a matter of fact, in perfect consistent with his benevolence, for reasons sufficient, though not revealed to us, he has provided no redemption for lost angels, and no efficacious grace for the non-elect among mankind. These passages simply assert that, if it were not for these reasons, it would be agreeable to his benevolent nature that all men should be saved.

A.A. Hodge, Outlines of Theology (London: Thomas Nelson & Sons, 1879), 227.

[Note: A.A Hodge is not as forceful as C Hodge was on this point, but his view is clear enough.]