Logical Possibility and the Laws of Thought

Logical Possibility and Possible Worlds

True propositions are those which are true in the actual world.

False propositions are those which are false in the actual world.

Possibly true propositions are those which are true in at least one possible world.

A possible world is a philosophical concept that allows one to consider what follows from a set of assumptions rather than what is the case.

Logically possible propositions are those that can be asserted without implying a logical contradiction.

Examples:

  • Logically Possible: A major flood will occur in Charleston in the next ten years.
  • Logically Impossible: Em and Dee are taller than each other (a contradiction).

Laws of Thought

  • Law of the Excluded Middle: Everything is or is not.
    Symbolically: (~p ∨ p)
  • Law of Non-Contradiction: Nothing both is and is not.
    Symbolically: ~(p ∧ ~p)
  • Law of Identity: Everything that is, is.
    Symbolically: (p = p)

Identity has to do with unity, and unity is "nothing but consistency, or the recognition of it."

Properties of Identity

  • Reflexive: (q = q) — Everything is identical to itself.
  • Symmetric: p = q if and only if q = p.
  • Transitive: If (p = q) and (q = r), then (p = r).

Active Learning Exercises: Laws of Thought and Relations

Exercise Set 1: Relational Properties

1. The relationship of "liking" is reflexive (A necessarily likes A). True or false?

2. The relationship of A "liking" B is a transitive one (if A likes B, and B likes C, then A necessarily likes C). True or false?

3. The relationship of A "liking" B is a symmetrical one (if A likes B, B necessarily likes A). True or false?

Exercise Set 2: Biological Relations

1. The relationship of A "is biologically related to" B is a transitive one (if A is biologically related to B, and B is biologically related to C, then A necessarily is biologically related to C). True or false?

2. The relationship of A "is biologically related to" B is a symmetrical one (if A is biologically related to B, B necessarily is biologically related to A). True or false?

Submit Your Work