Concordant or consensual connection between the two contrasting themes of a counterpoint is essential to an understanding of its impact on the mind. A counterpoint is not simply two distinct themes set together. There must be intrinsic relationship between them. Grasping this relationship can lead us into deep neurological and philosophic waters.

Neurologically, the receptors in our brain can in certain circumstances image the same object in opposing ways. The painting of the Mona Lisa is an example.
Try putting a card on a print with the edge down her nose to split her face into two halves. If we 'see' the painting by viewing the left side of her face, where she is unsmiling, the brain receives one image. If we now change to the right side, where she has the gentlest of smiles (the cat who has licked the cream in one description) the brain will record a counter image. Flipping from one version to the other, the brain instinctively seeks a resolution of the two counter-images, and this intriguing feature may be the source of much of the painting's 'mystery'. For practical demonstrations of the opposing ways the brain can see 'reality', go to internet references to 'Necker's Cube' and especially to 'Mark Newbold's Animated Cube'.

Philosophically, a counterpoint is formed when it is appreciated that a thing - an entity or concept - is mirror-imaged as both 'being' and 'not being'. In our thought-world, an entity can be said to 'be' (to exist) when we have it in the forefront of our mind. But what can said of it when we do not have it in mind? It cannot cease to 'be' simply because we do not happen to be thinking about it. It must have another form of existence, which we can label as 'not being'. In other words, when we think about an entity, it becomes a
shape we recognise as part of our consciousness - eternal to us - but which, when we are not thinking about it, is still 'eternal' but is now an entity-shaped 'hole' in our thought world, an opposite or a diametric. The function of a counterpoint is to show that these two existences can be brought together in the mind simultaneously to generate a unity, a concept Stanley clearly appreciated.

Here is Professor Mary Warnock explaining the implications of the notion in her Introduction to the English edition of Sartre's The Psychology of Imagination:

.........he [Sartre] insists that man's freedom to act in the world is a function of his ability to perceive things not only as they are, but as they are not. If a man could not, first, describe a present given situation both as it is and as it is not; and if he could not, secondly and consequentially, envisage a situation as possibly being otherwise than how it is, then he would have no power to intervene in the world and change it........One must have the power of imagining a thing as well as perceiving it;  that is, of imagining it otherwise. For the power to see things in different ways, and to form images about a so far none-existent future, is identical with the power of imagination.