In 1958 Arthur Prior received a letter from Saul Kripke in which the latter expounded
an idea Prior found congenial, as it suggested one way to give substance to some of
his re fl ections on time and modality. The idea was that in order to capture the idea
of indeterminism, one should represent the courses of events which are possible
from a given moment on as branches of a tree (see Ploug and Øhrstrøm 2011 ). Prior
( 1967 , p. 126) sketched a model for tense logic along these lines:
[…] a line without beginning or end which may break up into branches as it moves from left to
right (i.e. from past to future), though not the other way; so that from any point on it there is only
one route to the left (into the past) but possibly a number of alternative routes to the right.
Shortly after , the tree model was formulated in a more rigorous way by Richmond
Thomason ( 1970 ), and since then it has constantly aroused the interest of people
working in philosophy and logic, as well as other areas such as computer science
and physics. 1
This volume discusses the philosophical implications of the tree model. Over the
past few years, the model has been widely employed to deal with issues concerning
the semantics of temporal discourse. The thought which has motivated its adoption
is the Kripke-Prior thought that the most plausible way to make sense of indeterminism
is to conceive of future possibilities as branches that depart from a common
trunk, constituted by the past and the present. However, the thought still needs to be
further articulated and defended, and several important questions, both semantic
and metaphysical, remain unanswered. The volume is intended to be a 360° re fl ection
on the tree model. The contributions it gathers concern the model and its alternatives,
both from a semantic and from a metaphysical point of view.
One of the questions that are still open is how actuality can be understood and
formally represented in a branching framework. This question, which concerns the
conceivability of the actual future as a Thin Red Line (to borrow a term coined in
Belnap and Green 1994 ), is addressed primarily by Andrea Borghini and Giuliano
Torrengo, Manuel García-Carpintero, and Andrea Iacona. Another question is
whether the tree model is really the best way, or even a coherent way, to make sense
of indeterminism. This question is addressed particularly by E. J. Lowe and Sven
Rosenkranz. Further questions may be raised about the relation between the idea of
branching and other notions or views: Craig Bourne and Emily Caddick Bourne
focus on fi ctional representation, Fabrice Correia on presentist reductions of eternalist
discourse, Ned Markosian on presentism and the truth-maker problem, and
Storrs McCall on rational agency.
The idea of a volume with this title comes from a meeting on Language and
Temporality held in L’Aquila, Italy, in September 2009. On that occasion, some of
the contributors had the opportunity to discuss, among other things, the materials of
their papers. The remaining contributors joined the project at a later stage. A shared
feeling that emerged at the meeting, and that grew stronger as other works were
added to the initial papers, is that an extensive discussion on the tree model as such
would be welcome in many respects. We hope that this volume can help to raise the
level of the debate on branching and the open future. Its main purpose is to show
that there is still plenty of room for discussion on these issues.
