In a "split-brain" the corpus collosum (white matter with billions of cortical neurons) connecting the two brain hemispheres is cut. When subjects are shown words or object that can be seen only by the left eye (which is connected to the right hemisphere), the left hemisphere, which controls speech, can say nothing about what the word or object is.

However, Gazzaniga and LeDoux discovered that if the left hemisphere is asked whether the object or word describes something good or bad, it responds for example to "mom" with "good," and to the word "devil" with "bad."

LeDoux writes...

The left hemisphere had no idea what the stimuli were. No matter how hard we pressed, the patient could not name the stimulus that had been presented to the right hemisphere. Nevertheless the left hemisphere was consistently on the money with the emotional ratings. Somehow the emotional significance of the stimulus had leaked across the brain, even though the identity of the stimulus had not. The patient's conscious emotions as experienced by his left hemisphere were in effect being pushed this way and that by stimuli that he claimed to have never seen...

The left hemisphere, in other words, was making emotional judgments without knowing what was being judged. The left hemisphere knew the emotional outcome, but it did not have access to the processes that lead up to that outcome. As far as the left hemisphere was concerned the emotional processing had taken place outside of its realm of awareness (which is to say had taken place unconsciously).

The Emotional Brain, p. 15

The explanation is simple. Regions of the brain below the cortex, such as the left and right subcortical amygdalae, did not have the neurons between them disconnected.

LeDoux set his goal to figuring out how the brain processes the emotional meaning of stimuli, a goal he pursues to this day.

He offers what he calls a "Simple Idea" that can explain how the brain becomes conscious of emotions.

A Simple Idea

My idea about the nature of conscious emotional experiences, emotional feelings, is incredibly simple. It is that a subjective emotional experience, like the feeling of being afraid, results when we become consciously aware that an emotion system of the brain, like the defense system, is active. In order for this to occur, we need at least two things. We need a defense system and we need to have the capacity to be consciously aware of its activity. The upside of this line of thought is that once we understand consciousness we will also un­derstand subjective emotional experiences. The downside is that in order to understand subjective emotional experiences, we’ve got to figure out consciousness.

To my way of thinking, then, emotional experience is not really a problem about emotion. It is, instead, a problem about how con­scious experiences occur. Because the scientific study of emotions has mostly been about conscious emotional experiences, scientists who study emotions have set things up so that they will not under­stand emotions until they’ve understood the mind-body problem. the problem of how consciousness comes out of brains, arguably the most difficult problem there is and ever was.

The field got this way at the beginning, when William James brought up the business with the bear. He started with a questions about why the sight of a bear makes us run away (the stimulus-response problem in emotion) but ended up with a question about why we feel afraid when we see the bear (the stimulus-to-feeling problem in emotion). Ever since, the study of emotion has been fo­cused on where conscious feelings come from...

By treating emotions as unconscious processes that can sometimes give rise to conscious content, we lift the burden of the mind-body problem from the shoulders of emotion researchers and allow them to get on with the problem of figuring out how the brain does its unconscious emotional business. But we also see how conscious emotional experiences are probably created. They are probably cre­ated the same way that other conscious experiences are — by the es­tablishment of a conscious representation of the workings of underlying processing systems. Although much remains unknown about how conscious representations come about, recent studies have begun to provide important clues.

The Emotional Brain, pp.268-269