Contents

  • 1.1 Background
  • 1.2 Why Study Logic
  • 1.3 Sentences, Truth-Values, and Arguments
  • 1.4 Deductive Validity and Soundness
  • 1.5 Inductive Arguments
  • 1.6 Logical Consistency, Truth, Falsity, and Equivalence
  • 1.7 Special Cases of Validity

Notes

truth preservation.

argument. An argument is a set of sentences one of which (the conclusion) is taken to be supported by the remaining sentences (the premises).

deductively valid. An argument is deductively valid if and only if it is not possible for the premises to be true and the conclusion false.

deductively invalid. An argument is deductively invalid if and only if it is not deductively valid.

deductively sound. An argument is deductively sound if and only if it is deductively valid and all its premises are true.

deductively unsound. An argument is deductively unsound if and only if it is not deductively sound.

inductive strength. An argument has inductive strength to the extent that the conclusion is probable given the premises.

logically consistent. A set of sentences is logically consistent if and only if it is possible for all the members of that set to be true.

logically inconsistent. A set of sentences is logically inconsistent if and only if it is not logically consistent.

logically equivalent. The members of a pair of sentences are logically equivalent if and only if it is not possible for one of the sentences to be true while the other sentence is false.

logically false. A sentence is logically false if and only if it is not possible for the sentence to be true.

logically indeterminate. A sentence is logically indeterminate if and only if it is neither logically true nor logically false.

logically true. A sentence is logically true if and only if it is not possible for the sentence to be false.