Yes and no. In a way, all lifting is subjective. You can do, for example, 4x8 bench press every week at 190lbs, and progress when you hit 8 reps on that last set, which is certainly an objective way of deciding when you are ready to move on, but deciding that 4 sets is the right amount instead of 3 or 6 or 12 is fairly subjective itself.
Different routines are going to workout for different people, and there will always be a degree of objectivity vs subjectivity in the workout. I wouldn't advocate my approach to anyone that it doesn't work for. I pretty much enter a workout with a goal in mind of how many sets I want to hit per body part. As I approach the end of the workout I listen to my body and determine if I've done enough or if I need more.
How do I know if I'm progressing? I measure my body parts, weigh myself on a scale, and look in the mirror. Since this is the body building forum, that would probably be the most important part. Beyond that, I do a test workout every 3-6 weeks. For example, I'll hit the flat bench for 3x8 and the beginning of the workout. Hopefully I can lift more than the last time I did this test.
Again, this is what I've adopted after years of working out. I find lifting for the burn has yielded more results (and fewer injuries) than chasing a log book. FWIW, as a running coach, I only use half this approach. I give the runners a workout and a time goal, but I prefer them to either leave the watch at home, or run a route that they don't know the distance of. Chasing numbers, I believe, leads to a lot of over-training.....and to follow up on Lonnie's post, I don't mean over-training in terms of volume per week, but rather in terms of lifting loads that can injure you, or with bad form.