PHL 3305 Lecture 22

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2019-10-30

Name	Major Premise		Minor Premise		Conclusion
1^ST FIGURE: middle term (B) is subject of major and predicate of minor
`B: A rb A r A`	every B is A	AaB	every C is B	BaC	∴ every C is A	AaC
`C: E l A r E nt`	no B is A	AeB	every C is B	BaC	∴ no C is A	AeC
`D: A r I I`	every B is A	AaB	some C is B	BiC	∴ some C is A	AiC
`F: E r I O`	no B is A	AeB	some C is B	BiC	∴ some C is not A	AoC
2^ND FIGURE: middle term (M) is predicate of both
`C: A m ES tr ES`	every N is M	MaN	no X is M	MeX	∴ no X is N	NeX
`C: ES A r E`	no N is M	MeN	every X is M	MaX	∴ no X is N	NeX
`F: ES t I n O`	no N is M	MeN	some X is M	MiX	∴ some X is not N	NoX
`B: A r OC O`	every N is M	MaN	some X is not M	MoX	∴ some X is not N	NoX
3^RD FIGURE: middle term (S) is subject of both
`D: A r AP t I`	every S is P	PaS	every S is R	RaS	∴ some R is P	PiR
`F: E l AP t O n`	no S is P	PeS	every S is R	RaS	∴ some R is not P	PoR
`D: IS A m IS`	some S is P	PiS	every S is R	RaS	∴ some R is P	PiR
`D: A t IS I`	every S is P	PaS	some S is R	RiS	∴ some R is P	PiR
`B: OC A rd O`	some S is not P	PoS	every S is R	RaS	∴ some R is not P	PoR
`F: E r IS O n`	no S is P	PeS	some S is R	RiS	∴ some R is not P	PoR

Relating 2nd and 3rd Figure syllogisms to the 1st Figure

Each vowel in the name corresponds to the kind of proposition in major premise, minor premise, and conclusion.
First letter of name corresponds to the first figure syllogism to which it reduces.
Additional letters after each premise shows how to reduce to first figure syllogism:
- S - Simple conversion: Switch terms in the premise; keep same quantity.
  No A is B. → No B is A.
  
  Some A is B. → Some B is A.
- P - Accidental conversion: Switch terms in the premise; switch to lesser quantity.
  Every A is B. → Some B is A.
- M - Mutation: swap major and minor premises.
- C - Contradiction: assume the opposite conclusion, and show that it results in a contradiction ("it can't not be the case")