Deductive Reasoning

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[edit] Definition

Deductive Reasoning (as opposed to Inductive Reasoning) is the process of reasoning from general principles to other general principles or specific examples. For example, a reasoner, knowing that all crows are black (a general fact about crows) can conclude that my pet crow (a specific example) is black. Similarly, the same reasoner, knowing that crows are birds, can conclude that some birds are black (another general principle regarding birds).

Much of the study of formal logic has involved mechanistic or algorithmic methods both for the representation of these general principles and for methods of making inferences from these principles that are guaranteed to be correct. When properly performed, deductive logic is sound, which is to say that if the premises of the argument are true, the conclusion is guaranteed to be true (or alternatively, if the conclusion is false, at least one of the premises must have been false; if my pet is white, then either I am mistaken in thinking it to be a crow, or not all crows are white).

It should be noted that deductive reasoning can never generate "new" truths, therefore all genuine experimentation or empirical research will of necessity involve elements of inductive reasoning.

[edit] Types of Deductive Logic

Logicians have identitified many systems of logic that differ both in the kind of general statements they can represent and the type of inferences they permit. For example, Aristotle's Organon laid out the basis for a system of reasoning based upon syllogisms. An example of a syllogism is as follows:

  1. All cats are mammals
  2. No mammals are insects
  3. Therefore, no cats are insects.

In syllogistic deduction, there are a few relationships between concepts that are permitted ("All X are Y, No X are Y, Some X are Y, Some X are not-Y"), and a set of acceptable ways in which statements are permitted to be inferred (the above example is of the Camenes form). It can be easily seen that the Camenes syllogism is sound, even in cases such as the following:

  1. All zorfs are sneeches
  2. No sneeches are wibdicks
  3. Therefore, no zorfs are wibdicks.


However, there are obvious truths that cannot be expressed or proven within syllogistic logic. For example, it is obvious that if

Some cat is feared by every mouse

that

Every mouse fears at least one cat

However, the formal structure of syllogistic logic prevents statements of this sort from being represented and inferred within this system. Logicians have therefore developed other systems with greater expressive power. Examples of these systems include propositional logic, predicate logic, term logic, and modal logic.

It might be hoped that there would be a perfect logical system that would be capable of expressing and proving anything even remotely true. Unfortunately, Kurt Gödel proved in the early 1930s that such a system was not possible. Some advocates of the paranormal have seized on this result (without justification) as an excuse to reject logic altogether as a path to knowledge.

[edit] Fallacies of Deductive Logic

An unsound argument is sometimes called a fallacy, which strictly speaking merely means an argument where the truth of the conclusions is not guaranteed by the truth of the premises. Logicians distinguish between "formal" fallacies, arguments that superficially resemble valid deductive reasoning but that commit an easily recognizable logical error, and "informal" fallacies that do not appear to be valid arguments but that rely on other aspects of human cognition for their plausibility.

It should be noted that just because an argument is fallacious does not necessarily invalidate the truth of its conclusion (to believe otherwise is to commit the Fallacist's Fallacy). In particular, inductive reasoning, such as from empirical experiments, is always fallacious in the strong sense defined here, and thus most of modern science is fallacious in this limited sense.


[edit] Formal Fallacies (examples)

Examples of formal fallacies include


[edit] Informal Fallacies (examples)

Examples of informal fallacies include

[edit] Related Topics

See also various individual fallacies indexed in that page.

[edit] References

[edit] Comments

For all contributors:

  • Try to keep the "Definition" as straight and encyclopaedic in style as possible. Use the "Discussion" section for editorialising
  • Use the references section for footnotes to books and other sources
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