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Deductive Logic

by George William Joseph Stock, M.A.

Part 3: Chapter 25

Additional Information
  • Year Published: 1888
  • Language: English
  • Country of Origin: England
  • Source: Stock, G. W. J. (1888). Deductive Logic. Oxford, England; Pembroke College.
  • Readability:
    • Flesch–Kincaid Level: 11.0
  • Word Count: 1,003
  • Genre: Informational
  • Keywords: math, math history
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PART III.—OF INFERENCES

CHAPTER XXV.

The Disjunctive Syllogism regarded as an Immediate Inference.

770. If no stress be laid on the transition from disjunctive hypothesis to fact, the disjunctive syllogism will run with the same facility as its predecessor into the moulds of immediate inference.

771.
  Denial of Antecedent.       Subalternation.

  Either A is B or C is D,       Every case of A not being B
                                 is a case of C being D.
  .'. A not being B, C is D.     .'. Some case of A not being B
                                 is a case of C being D.
772.
  Denial of Consequent.      Conversion by Contraposition
                                    + Subalternation.

  Either A is B or C is D.       All cases of A not being B
                                 are cases of C being D.
  .'. C not being D, A is B      .'. All cases of C not being D are
                                 cases of A being B.
                                 .'. Some case of C not being D is
                                 a case of A being B.
773. Similarly the two invalid types of disjunctive syllogism will be found to coincide with fallacies of immediate inference.

774.
  Affirmation of Antecedent.   Contraposition without
                                      Conversion.

  Either A is B or C is D.         All cases of A not being B are
                                   cases of C being D.
  .'. A being B, C is not D        .'. All cases of A being B are
                                   cases of C not being D.
775. The affirmation of the antecedent thus comes under the formula—

All not-A is B, .’. All A is not-B,

a form of inference which cannot hold except where A and B are known to be incompatible. Who, for instance, would assent to this?—

All non-boating men play cricket. .’. All boating men are non-cricketers.

776.

  Affirmation of Consequent. Simple Conversion of A.

  Either A is B or C is D.          All cases of A not being B are
                                    cases of C being D.
  .'.C being D, A is not B.         .'. All cases of C being D are
                                    cases of A not being B.
777. We may however argue in this way—

                                     Conversion of A per accidens.
  Either A is B or C is D.           All cases of A not being B
                                     are cases of C being D.
  .'. C being D, A is sometimes B.   .'. Some cases of C being D are
                                     cases of A not being B.
The men who pass this examination must have either talent or industry.
.’. Granting that they are industrious, they may be without talent.