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Deductive reasoning is the process of drawing valid inferences.An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false.
Deduction is a form of reasoning in which a conclusion follows necessarily from the stated premises. A deduction is also the name for the conclusion reached by a deductive reasoning process. A classic example of deductive reasoning is evident in syllogisms like the following:
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 ...
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.
Deductive reasoning offers the strongest support: the premises ensure the conclusion, meaning that it is impossible for the conclusion to be false if all the premises are true. Such an argument is called a valid argument, for example: all men are mortal; Socrates is a man; therefore, Socrates is mortal.
A syllogism (Ancient Greek: συλλογισμός, syllogismos, 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. "Socrates" at the Louvre
Validity of deduction is not affected by the truth of the premise or the truth of the conclusion. The following deduction is perfectly valid: All animals live on Mars. (False) All humans are animals. (True) Therefore, all humans live on Mars. (False) The problem with the argument is that it is not sound.
For the most part this discussion of logic deals only with deductive logic. Abductive reasoning is a form of inference which goes from an observation to a theory which accounts for the observation, ideally seeking to find the simplest and most likely explanation. In abductive reasoning, unlike in deductive reasoning, the premises do not ...