What is "running by feel?" I think there are three related features to this approach to training:
1. "Primary experience" is privileged over "secondary experience." What does this mean? It means that when there is a conflict between the immediate experience of running and the reflective experience of thinking about running, the immediate experience is given priority. For example, I might decide after reflecting on my running that what's best for me to do tomorrow is to 8 x 800 at 10k pace. I head to the track and try the first one at 10k pace and struggle to make it. The immediate experience is telling me that this pace is too fast. Instead of clinging to the idea that I have to run 10k pace, I back off and listen to the primary experience of the workout. The reverse is sometimes, also, fortunately true. We can have good days and beat our expectations.
For running by feel, the "problem" of training is always to bring the secondary experience of reflecting about running in line with the primary experience of running. A physiological approach reverses this direction.
2. Running by feel is radically experimental. This is the sense in which running by feel is more scientific than physiological science. Physiology can only deal with the human species as a whole. Training requires a more radically experimental method because each runner is a singular individual. What works best for me, today, most likely won't work best for you--and might not even work well for me tomorrow. The runner must be willing to try new paces, new intervals, and new intensities on a daily basis. In order to measure the effects of this radical, ongoing experimentation, the runner needs an instrument that is as singular as his or her running. This instrument is "feel," and it is built up over time through experience with the multitude of possible sensations that running brings.
Training is an experiment of one and needs an instrument that is adapted to that singularity.
3. Running by feel is comfortable with uncertainty. The great attraction of physiological science is that it pretends to certainty. Everyone has a clearly defined and measurable VO2max. Easy running means keeping your heart rate at exactly 140. Tempo runs should be 20 minutes at 10k pace because that leads to the greatest gains in LT. However, because running is an experiment of one--and that one is constantly changing, sometimes developing, sometimes not--there is no certainty to be found in running, and for this reason any training methodology that pretends to certainty is a bad methodology. Paradoxically, running by feel more precisely measures progress in running because it is vaguer. What does an easy run feel like? How much should a 5k hurt? No one can tell you; it can't be done perfectly. But sometimes, by chance, we capture glimpses of how it feels when it's damn close to being right. We hold onto those glimpses and use them hopefully and uncertainly to guide our training.
Running by feel respects the mystery and risk of running by not demanding that it conform to the demands of certainty.