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Background
Background
Zeno of Citium
Zeno (c. 495 – c. 430 BC) was born in Citium (in modern day Cyprus). The Stoics thought that the key to happiness was to be logical. Zeno thought that if we are logical, then we would understand what we can change to make things better, but also we would understand those things that we can’t change and therefore not worry about
Chrysippus
Chryssipus (c. 279 – c. 206 BC) was born in Soli, which was in the south of modern day Turkey, but he moved to Athens to become a pupil of the Stoic Cleanthes. Chrysippus made some great advances in logic, that had a direct bearing on the invention of computers 2,000 years later.
Method: A summary of Chrysippus approach to logic (I have simplified it slightly)
Method: A summary of Chrysippus approach to logic (I have simplified it slightly)
He was interested in propositions - which were descriptions of things.
He thought there were two kinds of simple propositions: affirmations (saying things are true) and denials (saying things are NOT true/false)
He also described how we can connect simple propositions together as compound propositions using logical connectives:
p AND q
EITHER p OR q
If p THEN q
BECAUSE p, q
IT IS MORE LIKELY p THAN q
He then showed how we can combine these simple propositions and compound propositions to create arguments:
The method that affirms by affirming:
q because p
If p, then q
The counterexample is p and NOT q
p
∴ q
The method that affirms by denying:
q because not p
If NOT p, then q (Either p or q)
The counterexample is NOT p and NOT q
NOT p
∴ q
The method that denies by denying:
not q because not p
If NOT p, then NOT q (If q then p)
The counterexample is NOT p and q
NOT p
∴ NOT q
The method that denies by affirming:
not q because p
If p, then NOT q (NOT p and q)
The counterexample is p and q
p
∴ NOT q
Task
Task
Write down an example of each kind of method of arguing.
Find counterexamples for other people’s arguments
Improve your own arguments in response to counterexamples.
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