Understanding simple equations like 'two plus two equals four' has an inner certainty not subject to doubt, distinct from belief—it operates at a level of necessity beyond mere conviction.

The 'meaning crisis' in contemporary culture stems partly from materialism's denial that consciousness has substantial reality, combined with eliminativism about intelligible/mathematical reality—leaving no basis for understanding ourselves in terms adequate to self-consciousness.

Consciousness appears to have an intrinsic relationship to intelligible reality (mathematics) and possibly to other non-material realities (truth, beauty, morality); if human consciousness has a structure that enables understanding of these realities, then human realization (self-understanding) must be thought fundamentally through this relationship.

Many people struggle with a deep alienation and sense that they are not loved and have no connection to a transcendent whole. Something deep in the nature of things does not have their back, undermining their sense of meaning and worth.

Forgiveness is the overcoming of apparent opposition—discovering in a relationship and in the other a beauty and unity that abides even through suffering, division, difficulty, or hardness of life.

The sophists showed that any position is partial and insufficient, but then concluded there is no truth at all. This is a fallacy. Rather, the partiality of perspectives shows that truth is discovered through the movement between and above opposites, not that truth does not exist.