How do you know if a conclusion is valid?

You can probably never be entirely sure, but if you know about the subject, and use correct methods, you improve your chances of reaching a correct conclusion. For important conclusions, you may want to have your reasoning checked by other people.

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List all the assumptions and use logic decuctive reasoning to see if it is valid. Deductive reasoning is a fixed set of rules how certain conclusions can follow from assumpions. Wikipedia example:

1. All men are mortal
2. Socrates is a man
3. Therefore, Socrates is mortal