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I agree. Till now, all science theories comes from experiments that provide an evidence
This is not the only aspect that science is based on. In order to gather evidence, you first need a theory, observations, and a hypothesis. Evidence is only one of the components that make up science.
I do agree that science is an evidence based progress, because for all the progress that have been done in world history, there had been a path to follow. Since investigations about a theory or a hypotesis to experiment to prove that a claim is true or discover new things.
Psychology can be classified under science. This is a study that is not solely based on evidence but what people believe, the way they behave and how they feel. This is subjective and cannot always have concrete evidence as emotional and metal factors play a role.
No theory is accepted without evidence as it acts as a support to the theory and hence, it justifies the statement that it is an evidence based process.