Reading

Pre-reading quiz.

Brief History of Logic

300-400 BC: A fascinating time.

Greeks. Wanted ways to know when something had to be true. Sophists and smooth talkers. Persuasive. When it had to be true as a consequence of the things we already take to be true. Forms of argumentation.

Heraclitus “Everything is in motion”, “you cannot step into the same stream twice.”

Parmenides “Everything is constant, unchanging, eternal”

Plato gives us, in the allegory of the cave, the fusion of these two ideas.

The things we see are echos, shadows of the platonic ideal.

Euclid’s geometry.

From basic principles, we can deduce more complicated facts. These are the things that follow from others, analytically.

whereas synthetics are the things we induce from experience.

Aristotle’s logic. Part-whole logic.

Lots more, fascinating story. How we get from Aristotle, through the scholastics, through the renaissance and 16th and 17th century mathematics.

Boolean logic, algebraization. Propositional.

Stop off with Boolean logic. George Boole. American.

The logic of propositions. Sentences.

Determine the values of complicated expressions based on the values of smaller expressions.

We can determine the meaning of the whole with the values of the immediately smaller sub-pieces.

Implication.

Difficult and frustrating at times, for students. B/c the way we use implication here isn’t the way you would normally use it.

“Show me a man with a tattoo, and I’ll show you a man with an interesting past.” —Jack London

Truth tables.

  | A  | B  | B => A | A => (B => A) |
  | tt | tt | tt     | tt            |
  | ff | tt | ff     | tt            |
  | tt | ff | tt     | tt            |
  | ff | ff | tt     | tt            |

    NOT     !

    AND     &
    OR      v

    IMPLIES =>

    EQUIV   ==
    XOR     ><

  • Validity

  • Falsifaibility

  • Satisfiability

  • Unsatisfiable

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