more from this thinker | more from this text
Full Idea
Philo (of Megara) says that a valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood,' as for instance the syllogism 'If it is day, I converse,' when in fact it is day and I am conversing.
Gist of Idea
A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood'
Source
Sextus Empiricus (Outlines of Pyrrhonism [c.180], II.110)
Book Ref
Sextus Empiricus: 'Outlines of Pyrrhonism', ed/tr. Bury,R.G. [Prometheus 1990], p.132
A Reaction
Russell endorses this, and Rumfitt quotes it as the classic case of denying that there is any modal aspect (such as 'logical necessity') involved in logical consequence. He labels it 'material or Philonian consequence'.
12196 | A valid hypothetical syllogism is 'that which does not begin with a truth and end with a falsehood' [Sext.Empiricus] |
14106 | Implication cannot be defined [Russell] |
14108 | It would be circular to use 'if' and 'then' to define material implication [Russell] |
9520 | The paradoxes of material implication are P |- Q → P, and ¬P |- P → Q [Lemmon] |
6879 | 'Material implication' is defined as 'not(p and not-q)', but seems to imply a connection between p and q [Mautner] |
6878 | A person who 'infers' draws the conclusion, but a person who 'implies' leaves it to the audience [Mautner] |
10689 | A step is a 'material consequence' if we need contents as well as form [Beall/Restall] |