Negative conclusion from affirmative premises

Negative conclusion from affirmative premises

Negative conclusion from affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing a valid categorical syllogism.

Statements in syllogisms can be identified as the following forms:

  • a: All A is B. (affirmative)
  • e: No A is B. (negative)
  • i: Some A is B. (affirmative)
  • o: Some A is not B. (negative)

The rule states that a syllogism in which both premises are of form a or i (affirmative) cannot reach a conclusion of form e or o (negative). Exactly one of the premises must be negative to construct a valid syllogism with a negative conclusion. (A syllogism with two negative premises commits the related fallacy of exclusive premises.)

Example (invalid aae form):

Premise: All colonels are officers.
Premise: All officers are soldiers.
Conclusion: Therefore, no colonels are soldiers.

The aao-4 form is perhaps more subtle as it follows many of the rules governing valid syllogisms, except it reaches a negative conclusion from affirmative premises.

Invalid aao-4 form:

All A is B.
All B is C.
Therefore, some C is not A.

This is valid only if A is a proper subset of B and/or B is a proper subset of C. However, this argument reaches a faulty conclusion if A, B, and C are equivalent.[1][2] In the case that A = B = C, the conclusion of the following simple aaa-1 syllogism would contradict the aao-4 argument above:

All B is A.
All C is B.
Therefore, all C is A.

See also

References

  1. ^ Alfred Sidgwick (1901). The use of words in reasoning. A. & C. Black. pp. 297–300. http://books.google.com/books?id=eScnAQAAIAAJ&pg=PA297. 
  2. ^ Fred Richman (July 26, 2003). Equivalence of syllogisms. Florida Atlantic University. p. 16. http://www.math.fau.edu/richman/docs/syllog-4.pdf. 
v · d · eFormal fallacies
Masked man fallacy · Circular reasoning
In propositional logic
In quantificational logic
Syllogistic fallacy
Other types of formal fallacy · List of fallacies

Wikimedia Foundation. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Affirmative conclusion from a negative premise — is a logical fallacy that is committed when a categorical syllogism has a positive conclusion, but one or two negative premises. For example:: No fish are dogs, and no dogs can fly, therefore all fish can fly. This could be illustrated… …   Wikipedia

  • List of fallacies — For specific popular misconceptions, see List of common misconceptions. A fallacy is incorrect argumentation in logic and rhetoric resulting in a lack of validity, or more generally, a lack of soundness. Contents 1 Formal fallacies 1.1… …   Wikipedia

  • Syllogism — A syllogism (Greek: συλλογισμός – syllogismos – conclusion, inference ) is a kind of logical argument in which one proposition (the conclusion) is inferred from two or more others (the premises) of a certain form. In antiquity, there were… …   Wikipedia

  • Fallacy — In logic and rhetoric, a fallacy is usually incorrect argumentation in reasoning resulting in a misconception or presumption. By accident or design, fallacies may exploit emotional triggers in the listener or interlocutor (appeal to emotion), or… …   Wikipedia

  • Deductive fallacy — A deductive fallacy is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion.[1] Thus, a deductive fallacy is a fallacy where deduction goes wrong, and is no longer a… …   Wikipedia

  • Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… …   Wikipedia

  • Begging the question — Bust of Aristotle, whose Prior Analytics contained an early discussion of this fallacy. Begging the question (or petitio principii, assuming the initial point ) is a type of logical fallacy in which the proposition to be proven is assumed… …   Wikipedia

  • Outline of logic — The following outline is provided as an overview of and topical guide to logic: Logic – formal science of using reason, considered a branch of both philosophy and mathematics. Logic investigates and classifies the structure of statements and… …   Wikipedia

  • Denying the antecedent — Denying the antecedent, sometimes also called inverse error, is a formal fallacy, committed by reasoning in the form: If P, then Q. Not P. Therefore, not Q. Arguments of this form are invalid. Informally, this means that arguments of this form do …   Wikipedia

  • Masked man fallacy — The masked man fallacy is a fallacy of formal logic in which substitution of identical designators[clarification needed] in a true statement can lead to a false one. One form of the fallacy may be summarized as follows: Premise 1: I know who X is …   Wikipedia

Share the article and excerpts

Direct link
… Do a right-click on the link above
and select “Copy Link”