The place of psychology in science was controversial since the beginning of this branch of knowledge. As we know psychology is very, very diverse. The problem is that within a psychology you have so much paradigms that exlude each other - you can say that behaviourism says opposite things than psychoanalysis. Yet they both have some effiacy in psychotherapy! How's that!? The problem with psychology as science is that it has not even settled the definitions for most basic thing.
Many philosophers of science have exploring this problem. I've got deepen into that topic because I wrote my master thesis on contemporary attempts and empirical verification of jungian psychology. Jungian thought is often (wrongly) considered as unscientific, mystical, occulitc etc. so I had to really investigate his methods and his thoughts on psychology as science. For me it's easier to say that there is no one psychology, but many psychologies, thus many psychologies as sciences. Carl Jung said that psychology is a "mediatory science" and is quite different than other because it investigates a natural phenomena (like other natural sciences) but it uses methods from human sciences. And that is a MUST because there's no Archimedean point regarding observation of mind - whatever we do, we can't exclude our mind from the equation.
Anyway, this subject fascinates me I could go on and on but there's no point :D I prefer a wider definition of science, taken from german understanding of this word - that science is a knowledge gathered in order (Anglo-Saxons has a more strict one). Good post, but I'd argue a little that psychology is "objective" even with statistical and empirical methods. But it definitely is a science!
Wow @saunter, thank you so much for all this info. You are right, one could just go on and on and on... I appreciate very much you taking the time to add these points to this debate.
Happy 2018!
You too - Happy New Year Abi!