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Empirical reasoning is the sort of reasoning we associate with the hard sciences. People try to discover truth through observation and quantification. They come up with a hypothesis and then they observe and count what happens to confirm or disconfirm that hypothesis. This is, perhaps the strongest type of reasoning in that it (ideally) rests upon tangible and quantifiable evidence. If I test, for example, the boiling point of water at various elevations, I will get real world results that can prove the relationship between these variables.
The major risk here is in thinking that everything can be answered in an empirical way. In the social sciences in particular, empiricists tend to think that they can reduce everything to numbers. They tend to think that anything that they cannot quantify cannot be the legitimate object of study. This can cause them to miss out on things that are very important simply because they cannot be easily quantified and measured.
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