In the study of different argumentation or evidence techniques, the distinction between deduction and induction is important. In deduction, it is often (but not exclusively) made a conclusion from the general to the special - from the main premise, a minor premise concludes or deduces the conclusion. Inductive methods often work (but not exclusively) in the opposite direction, with a general rule, generalization, based on a number of specific observations. Where in deduction the conclusion is logically inevitable from the assumptions, in conclusion the conclusion is not logically inescapable, but probably.
Deductive and inductive argumentation techniques are often combined, as in the empirical cycle. Deductie
Deduction is an argumentation or evidence technique. The evidence consists of a reasoning for which the conclusion is logically inevitable from the assumptions (assumptions). An example of a deduction is the application of a general rule to a specific situation: The general rule is: When it's raining, everything gets wet outside. Furthermore, it is known: It rains. The car is outside. The logically inescapable conclusion is: The car gets wet.
Deduction plays a central role in formal sciences (in which empiry does not play a role) such as mathematics and logic. Deduction also plays a role in the other sciences when strict proofing is possible and required.
A deductive inference can be challenged by showing that the conclusion does not logically result from the premisses: the conclusion is not proven (but can happen to be correct). If the conclusion of a deductive reasoning follows logically from the premises but is nevertheless incorrect, at least one of the premisses must be incorrect. Empirical refutation of an inference obtained through deduction leaves the validity of the reasoning untouched, but requires a revision of the premises.
If a non-valid deductive reasoning - there is a logical error in the conclusion of the conclusion - has a certain probability, it may sometimes be considered as or rewritten to a valid inductive reasoning. Induction
Induction is an argumentation or evidence that does not provide a logically inescapable conclusion, but a conclusion that is likely to have a certain probability. It often involves the distraction of a general rule from a limited set of specific cases. This form of induction - the enumerative (or summarizing) induction - looks as follows: For the first case, A applies, in the second case, A applies, for the third case, A is so, so A applies to all the corresponding cases. The conclusion also relates to those cases not mentioned in the assumptions. If the conclusion was solely related to the cases mentioned in the assumptions, there was deduction - the conclusion would be inevitable. An example of an inductive reasoning. The color of individual ducks is viewed in a park. The first duck in the park is brown. The second duck in the park is brown. .... The last observed duck in the park is brown. The conclusion is: All ducks in the park are brown.
This conclusion is perhaps plausible, but not logically inescapable: a white duck may have been overlooked. A conclusion or conclusion obtained through induction has the possibility to be refuted empirically (falsification): whoever catches one white duck in the park shows that the conclusion, although inductively valid, is nonetheless incorrect.
Sometimes the concept of induction is incorrectly narrowed down to the indumeration described above. In addition to this form of induction, other forms also exist, such as the elimination of induction (or induction by elimination): if phenomenon X does not correlate with possible causes A, B, C, D, F, G ..., but with possible cause E, then cause E provides an explanatory ground for X. The analogy reasoning is also an example of an inductive reasoning trend.
Conclusions obtained through induction are often supported by a statistical analysis. For example, in the example given, statistics can make it plausible that the brown ducks observed form a representative sample of the entire duck population. Also see
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