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Deductive reasoning is the psychological process of drawing deductive inferences.An inference is a set of premises together with a conclusion. This psychological process starts from the premises and reasons to a conclusion based on and supported by these premises.
Examples include most fields of science and aspects of personal knowledge. The terms originate from the analytic methods found in Organon , a collection of works by Aristotle . Prior analytics ( a priori ) is about deductive logic , which comes from definitions and first principles.
The implication flows in only one direction, as in the syllogism used in the discussion on deduction. Therefore, it is never correct to say that a scientific principle or hypothesis/theory has been "proven" in the rigorous sense of proof used in deductive systems. A classic example of this is the study of gravitation.
Deductive inference is monotonic: if a conclusion is reached on the basis of a certain set of premises, then that conclusion still holds if more premises are added. By contrast, everyday reasoning is mostly non-monotonic because it involves risk: we jump to conclusions from deductively insufficient premises.
Non-deductive reasoning is an important form of logical reasoning besides deductive reasoning. It happens in the form of inferences drawn from premises to reach and support a conclusion, just like its deductive counterpart. The hallmark of non-deductive reasoning is that this support is fallible.
The reasoning in a deduction is by definition cogent. Such reasoning itself, or the chain of intermediates representing it, has also been called an argument, more fully a deductive argument. In many cases, an argument can be known to be valid by means of a deduction of its conclusion from its premises but non-deductive methods such as Venn ...
For example, the argument, "All young girls wear skirts; Julie is a young girl; therefore, Julie wears skirts" is valid logically, but is not sound because the first premise isn't true. The syllogism is a form of deductive reasoning in which two statements reach a logical conclusion. With this reasoning, one statement could be "Every A is B ...
For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic (as well as the semantics of many other non-classical logics ), in the sense that if the premises are true (under ...