Logic and Philosophy of Time Themes from Prior Per Hasle, Patrick Blackburn, and Peter Øhrstrøm (Eds.) Logic and Ph ilo so ph y of Logic and Philosophy of Time A.N. Prior (1914-69) in the course of the 1950s and 1960s founded a new and revolutionary paradigm in philosophy and logic. Its most central feature is the preoccupation with time and the development of the logic of time. However, this was inseparably interwoven with fundamental questions about human freedom, ethics, and existence. This remarkable integration of themes also embodies an original and in fact revolutionary conception of logic. The book series, Logic and Philosophy of Time, is dedicated to a deep investigation and also the further development of Prior's paradigm. The series includes: 1 Logic and Philosophy of Time: Themes from Prior Series editors Per Hasle, Patrick Blackburn & Peter Øhrstrøm

P Q ∀i(Pi→Qi) i P i p i q p P Q ∀i(Pi→Qi) i P i p i x y x y X Y x = 1 1 − x = 0 x X X x X 1−x Y X Y xy X Y x(1−y) xy = yx X Y Y X X Y X Y Y X 19 P Q P Q a −→ b a b a b −→ ∀x(fx→gx) fx ∀x(fx→gx) x F G x x x P Q P Q P Q P Q P Q p p i P i P i Qi i P Q i P i Qi ∀i(Pi→Qi) P Q −∃i(Pi − Qi) x X 1− x x = 1 X x = 0 xy = 0 X Y X Y X Y X Y X Y X Y X Y X Y X X

p (p∨q) ∼∼p (p∧∼∼p) a b R aRb bRa p (p∨q)

∨ ∨ ∨ ⊃ aRb a b R a b aRb R a b ∨

Fp p Pp p Hp P p Gp F p Hp p Gp p p⊃PFp Pp⊃!Pp p⊃PFp !PFp p Fp !(p⊃q)⊃(!p⊃!q) !Fp l l l l l l l p q p q (p∧∼q∧Pq) ∨ P (p∧∼q∧Pq) ∨ F (p∧∼q∧Pq)

p t T (t, p) p t P F Pp Fp p Pp p Fp p H ¬P¬ G ¬F¬ ! ♦ ¬!¬ Pp → !Pp p p (p ⇒Diod q ∧ ♦p) → ♦q q p p q ¬r ∧ ¬Fr ∧ ♦r r r ⇒Diod

internal processes action persistence impingements reaction resilience external processes (activity) stasis/stability dissolution/ destruction

This book is the first volume in the series, Logic and Philosophy of Time. Its various contributions take their inspiration from A.N. Prior's paradigm for the study of time, hence the subtitle "Themes from Prior". The volume contains important research on historical as well as modern systematic challenges related to Prior's work and thought.