What is Logic? Logical Inference?
Psychologism: logic = laws of human thought.
Gottlob Frege argued: Logic is normative, not merely descriptive.
Logic makes explicit what is implicit.
What does 'implicit information' mean?
What does 'information' mean?
Logically valid inference -- impossible for the premises to be true while the conclusion is false.
What does impossible mean here?
This is gold.
This is element 59.
This is water
This is H20.
Marie has been decapitated.
Marie is dead.
Distinguish: logical possibility & physical possibility.
Imaginable possibility?
There is a 1000-sided figure.
What about:
John is a bachelor.
John is unmarried.
Mary is an optham.
Mary is an MD.
Ludwig Wittgenstein, Tractatus Logico-Philosophicus .
Atomic propositions: either true or false. Logically independent.
Each assignment of truth-values to all atomic sentences is a possible world, a point in logical space.
| A | B |
| T | T |
| T | F |
| F | T |
| F | F |
Truth-functional proposition: a proposition whose truth-value (in any world) is a function of the truth-values of certain atomic propositions in that world.
An argument is logically valid if and only if the conclusion is true in every world in which all the premises are true.
This is a straightforward mathematical question.
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