Hard science is science that uses systematic observation, experiments and sometimes mathematics to get knowledge. In hard science, experiments have to be reproducible (if the experiment is done a second time, it will have to produce the same results as the first time). Also, in hard sciences there is usually good agreement as to what is known for sure. This is not true of soft sciences. Also, in hard science there is a world-view or theory which is widely agreed.
Hard science subjects include the natural sciences, which are about the natural world. These include physics, chemistry, biology, geology, astronomy, and botany. Soft science is any of the social sciences, including history, sociology, and political science. Those sciences are soft because something could be done more than once, and produce a very different result each time. Also, there are radical disagreements between various schools of thought. Some aspects of psychology are hard science, especially relating to perception.
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