Logic
(Logic really deserves its own lecture.)
Defined in Webster's 1828 dictionary as:
The art of thinking and reasoning justly.
Logic is the art of using reason well in our inquiries after truth, and the communication of it to others. --Watts.
Logic may be defined, the science or history of the human mind, as it
traces the progress of our knowledge from our first conceptions through
their different combinations, and the numerous deductions that result
from comparing them with one another. --Encyc.
Correct reasoning implies correct thinking and legitimate inferences
from premises, which are principles assumed or admitted to be just.
Logic then includes the art of thinking, as well as the art of
reasoning. --W.
The purpose of logic is to direct the intellectual powers in the
investigation of truth, and in the communication of it to others. --Hodge.
How we can develope our reasoning abilities
- Learn to follow a line of logic
- read Shakespeare, Tolstoy, C.S. Lewis, Euclid
- write down the steps of logic found a you read
- Play a musical instrument
- Don't close your eyes to the obvious
- The solution is usually obvious -- after it is explained to you
- Strategy games
- to practice concentration and logical thinking
- Not all games are good practice: count the number of options you have!
Euclidean Geometry IS Logic
Euclid sets the standard for mathematical logic. Plato wrote "Let no
one ignorant of geometry enter" on the door of his Academy, probably
because he wanted his students to be able to think logically.
Small set of self-evident axioms. Everything else logically derived from them.
2 column proof: State each logical step in column 1, give a
reference (to an axiom or previously proved theorem) to justify the
step in column 2.
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