How we change what others think, feel, believe and do
Deductive reasoning, or deduction, starts with a general case and deduces specific instances.
Deduction starts with an assumed hypothesis or theory, which is why it has been called 'hypothetico-deduction'. This assumption may be well-accepted or it may be rather more shaky -- nevertheless, for the argument it is not questioned.
Deduction is used by scientists who take a general scientific law and apply it to a certain case, as they assume that the law is true. Deduction can also be used to test an induction by applying it elsewhere, although in this case the initial theory is assumed to be true only temporarily.
Deductive reasoning assumes that the basic law from which you are arguing is applicable in all cases. This can let you take a rule and apply it perhaps where it was not really meant to be applied.
Scientists will prove a general law for a particular case and then do many deductive experiments (and often get PhDs in the process) to demonstrate that the law holds true in many different circumstances.
In set theory, a deduction is a subset of the rule that is taken as the start point. If the rule is true and deduction is a true subset (not a conjunction) then the deduction is almost certainly true.
Using deductive reasoning usually is a credible and 'safe' form of reasoning, but is based on the assumed truth of the rule or law on which it is founded.
Validity and soundness
Deductive conclusions can be valid or invalid. Valid arguments obey the initial rule. For validity, the truth or falsehood of the initial rule is not considered. Thus valid conclusions need not be true, and invalid conclusions may not be false.
When a conclusion is both valid and true, it is considered to be sound. When it is valid, but untrue, then it is considered to be unsound.
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