Specifically, Lewis is making the case that emotions, rather than reason, lead us toward objective value in the world. In a word, The Abolition of Man concerns orthopathy--"right affections" or "right emotions." (As contrasted, say, with orthodoxy, "right belief.")
These lectures are where Lewis makes the (in)famous claim that the modern world is producing "men without chests." I've heard this line before, that the modern world is full of "men without chests," but upon reading the lectures for myself what I took to be Lewis' meaning was actually not his meaning. So I'd like to set the record straight in this post before moving to his actual argument.
The line "men without chests" is often taken to mean, as I took it to mean, that the modern world is making men timid, cowardly, and, well, "unmanly." And true enough, in the part of the lecture where Lewis describes "men without chests" he is talking about martial courage on the battlefield. But Lewis' point here isn't really about masculinity and bravery.
Lewis' point in these lectures is about emotion and value. One illustration in the lectures involves the emotions of loyalty and bravery in fighting for one's country. Lewis' audience had fought in WWI and WW2, so the example was poignant, personal and powerful. And the point Lewis raises about these emotions is simple: These emotions are responding to a value, namely the good of being loyal to one's country, to the point of self-sacrifice. Loyalty and bravery are virtuous because they converge upon a good. That is the crux of Lewis' argument. You cannot describe emotions as being "right" (like bravery) or "wrong" (like cowardice) without the existence of objective value. So the point about "men without chests" isn't about masculinity. The point is about orthopathy.
Lewis' argument is that emotions like loyalty and courage can only be deemed "right" and "proper" if they are truly aligned with some objective good. That's what makes these emotions virtuous and praiseworthy, that they are properly aligned with a value. But what has happened in the modern world, according to Lewis, is that we have come to doubt and question the linkage between emotion and value. Specifically, we doubt that objective value exists. In such a situation, emotions don't point to anything truthful, good, or beautiful in the world. Lacking this objective locus of affection, emotions become privatized and subjective, and therefore relative. In this world, a world that denies objective value, emotions like courage and loyalty aren't virtuous and good. They are personal sentiments, "emotional opinions" if you will, and might even be pathological. And how could you even tell? Without objective value there's no way to tell if an emotion is a virtue or a vice.
Lewis' real point in the line about "men without chests" isn't that modern men are cowards. His real point is that the modern world denies objective value, which turns emotions like loyalty and courage into subjective fictions and fantasies. The modern world isn't vanishing men, it's vanishing value. Because when value goes, so does courage. Along with all the other virtues we aspire to.
All that to say, to start this series, Lewis' line "men without chests" isn't about masculinity and manly men. What Lewis means by "men without chests" is "people without right affections." In the modern world, people can't be properly called cowards or heroes because the values that make heroes and cowards no longer exist. "Right affection" and virtue requires the existence of objective value. Otherwise, there's just feelings, and no such thing as right feelings or wrong feelings. No virtue, no vice. Just feelings, all alike, cowards and heroes all the same.
