1. Your brain is nothing but a mass of tissue and chemicals, electrical impulses and action potentials. Every though, emotion, and behavior has, at its root, a biological basis.
2. As with regards to evidence, so lets start off with what a science is, before I attempt to prove psychology as one.
According to Stanovich, there are three features that define science;
1) the use of systematic empiricism,
2) the production of public knowledge;
and 3) the examination of solvable problems.
Modern psychology is scientific in practice in that it applies all three of these; it uses the scientific method to obtain data, which is then used to find
solutions to problems, which are then published in public psychological journals.
Here's an example of a famous experiment
http://en.wikipedia.org/wiki/Milgram_experiment
In this experiment, Stanley Milgram set out to discover what humans would do when put in a situation where their own morality conflicted with the will of an authority figure (in this case, administering electrical shocks to a subject who was clearly suffering). One participant, the teacher, asked the other subject, the learner, to answer a series of questions. When the learner got a question wrong, they were given an electric shock, starting relatively low at 45 volts and increasing to a maximum of 450. He discovered that approximately 65% of subjects would administer shocks at the experimenters urging up to the 450 volt level.
Dr. Milgram later modified the variables to see if situational factors affected the results; and indeed, if the "teacher" administering the shocks had more direct contact with the "learner", or if the experimenter had less of a presence (eg telling the teacher to continue via intercom, instead of being physically in the room), then the percentage of subjects who would administer shocks up to 450 volts diminished.
Now, lets compare this to the three criterion mentioned;
1) In this experiment, Dr. Milgram had control over the variables involved. This was not Freudian analysis or introspection where it relied solely on self reporting or the subjects own feedback; the subjects were exposed to a phenomena (in this case, the test and subsequent electric shocks) and their responses were recorded into data, which was then computed into meaningful values. Variables in the experiment were kept constant and controlled, and the experiment has been repeated several times with almost identical results.
2) The results obtained form Milgram's experiment were calculated and presented in a published paper. The experiment has been repeated many times based in this publication, and a meta-analysis of these combined values shows consistent results across the board.
3) The Milgram experiment vastly increased our knowledge of the factors which influence obedience. In this case, Milgram wanted to know how Nazi officials in charge of the mass extermination in concentration camps could have carried out their orders without so little resistance. The experiment was devised in part to answer the question, "Could it be that Eichmann and his million accomplices in the Holocaust were just following orders?"
The teachers were debriefed and sent home. As for the learner, they were never actually shocked! All the learner's responses and cries of pain were pre-recorded into a tape recorder, and played back to ensure that every subject received the exact same mix of right and wrong answers, as well as the same protests. The researchers urgings were also pre-decided, though not pre-recorded, as the researcher was in the room with the subject.
To conclude then, psychology’s methods of research follow the same principles and are therefore just as legitimate as those of any other branch of science.