The Structure of Aristotelian Logic by Miller James Wilkinson

Author:Miller, James Wilkinson
Language: eng
Format: epub
ISBN: 978-1-317-37542-5
Publisher: Taylor & Francis (CAM)

44. The Sorites with Three Premises: Valid Moods.

3.51 a0Ea1′ and a1Ea2′ and a2Ea3 implies a0Ea3

[3.11]

a0Ea1′ and a1Ea2′ implies a0Ea2′

(1)

[3.11]

a0Ea2′ and a2Ea′3 implies a0Ea3

(2)

[(1);(2)]

theorem

3.52 a0Ea′1 and a1Ea′2 and a0Ea3 implies a0Ia′3

[3.51;2.44]

3.53 a0Ea1 and a1Ea′2 and a2Ea3 implies a′0Ia′3

[3.14;3.13]

3.54 a0Ia1 and a1Ea′2 and a2Ea3 implies a0Ia′3

[3.13]

3.55 a0Ea1 and a1Ia2 and a2Ea3 implies a′0Ia′3

[3.13]

From these valid moods (3.51–3.55) all the other valid moods of the sorites with three premises may be derived immediately by substitution.

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