On the Branching Tree
In our
study of time, we compare four leading theories: Presentism, Eternalism,
Growing Block Theory, and Branching Tree Theory. We aim to show in a future
post that a metaphysics of time anchored in the work of Thomas Aquinas is
superior. The last of the four in our survey is the Branching Tree Theory
(BTT).
In Favor
of the Branching Tree. Over 50 years ago, Arthur Prior[1] developed
tensed logic, which today has become an essential tool in the Belief-Desire-Intention
(BDI) framework in AI systems.[2]
Tensed logic uses operators that form propositions from propositions. The past
operator, P, stands for “it was the case that”. The future operator, F, stands
for “it will be that”. Prior reasons that future contingents lack a determined
truth value until resolved. Their truth is retrospective. In the development of
his thinking Prior concludes that time can be described as a trunk with
branches. Something that is possible is not true on every branch. Agents decide
which branch to take.
In How
Life Works,[3]
science writer Philip Ball provides a scientific complement to the Branching
Tree theory. Bringing attention to Third-Way evolutionists such as Denis
Noble, Michael Levin, and James Shapiro, he argues that living systems are
adaptive agents who match their behavior to a changing environment. Life exhibits
agency and purpose. Living systems make decisions and manipulate environments
to achieve goals. They possesses causal power as a result of causal emergence. Life’s
properties cannot be derived from its parts.
Against
the Branching Tree. Consider two objections: whether a trunk with
branches is the best way to describe possible worlds, and whether ontological
emergence has explanatory power. And a third: if humans have free will, where
does this agency come from, and what can it accomplish?
Possible
Worlds. David Lewis[4]
considers possible worlds, but his possible worlds have fixed timelines. He distinguishes
between external time (the timeline) and personal time. A time traveler
returning instantly to the time of his grandfather would not age a day. He
considers the paradox of whether it is possible for a time traveler to kill his
own grandfather. According to Lewis, although this is logically possible, this
is not possible in the actual world because the timeline is already fixed—you
exist. For Lewis, possible worlds are fixed manifolds (akin to the B-series). A
time traveler can logically travel along his static B-series timeline. There
may be some other possible world in which a time traveler kills his
grandfather, but it is not this one.
Unlike the
independent conceptual worlds of Lewis, the Many-Worlds Interpretation (MWI) of
quantum mechanics uses a branching tree description associated with each quantum
event. Rather than wavefunction collapse associated with a measurement, MWI advocates
believe the universe branches into multiple realities without wavefunction collapse.
MWI has many critics, including quantum physicists, but the metaphysical issue
is one of identity. If I exist in multiple possible worlds and all of them are
real, which world holds the real me?
Ontological
Emergence.[5] A better
explanation for ontological emergence is agency. Emergent properties from pairs
of participants produce results that cannot be explained by the individual
contributors.[6]
Life is better explained by an external agent operating on earthly materials to
produce the combined (emergent) properties of life (Gen. 2:7).
Purpose. Prior worried about whether man lives in a predetermined world or if man has free will. Consistent with free will, BTT successfully describes the decision-making processes of intelligent agents. However, although choices are possible along the tree, these actions are limited by the headlights of the agents. Unless the larger world has meaning, and endows agents with purpose, agents’ actions will not be meaningful. BTT is another incomplete theory. It does not explain the origin of time (or life) nor the purpose nor reach of human agency within time.
Image credit: M. Watters
[1] David
Jakobsen, Peter Øhrstrøm, and Per Hasle, “In Celebration of Past, Present and
Future,” in Logic and Philosophy of Time: Themes from Prior, Volume 1,
ed. Per Hasle, Patrick Blackburn, and Peter Øhrstrøm, 2nd ed. (Aalborg,
Denmark: Aalborg University Press, 2018), 9–28.
[2] Anand S.
Rao and Michael P. Georgeff, “Decision Procedures for BDI Logics,” Journal
of Logic and Computation 8, no. 3 (June 1998): 293–343, https://doi.org/10.1093/logcom/8.3.293.
[3] Philip
Ball, How Life Works: A User’s Guide to the New Biology (Chicago:
University of Chicago Press, 2023).
[4] David
Lewis, “The Paradoxes of Time Travel,” American Philosophical Quarterly
13, no. 2 (April 1976): 145–152.
[5] Epistemic
emergence pertains to material properties that surprises investigators,
given the known properties of the constituents. The properties of water
are a mystery given only hydrogen and oxygen gases. Deeper knowledge of
chemistry provides the knowledge that explains this repeatable, emergent
behavior. Ontological emergence describes properties that cannot be
predicted from the sum of the parts. Life and consciousness are common
examples, but this begs the question. Non-life examples of ontological
emergence, such as gravity, invariably yield to reductionist explanations. Although
some like cosmologist Erik Verlinde describe gravity as an emergent force, atom
interferometers sense gravity gradients. Individual atoms are subject to the
universal law of gravity. The properties are intrinsic (L. Badurina, O.
Buchmueller, J. Ellis, M. Lewicki, C. McCabe, and V. Vaskonen, “Prospective
Sensitivities of Atom Interferometers to Gravitational Waves and Ultralight
Dark Matter,” Philosophical Transactions of the Royal Society A 380
(2021): 20210060, https://doi.org/10.1098/rsta.2021.0060).
[6] A river
emerges on land because water has the capacity to flow and land has disposition
of erodibility. Each needs the other. A sand-castle on the beach, or the
letters HELP dug into trenches combine sand (and water) with human agency.
Human agency leaves an informational signature that the beach sand could not
originate on its own. The beach sand has degrees of freedom (capacity) that
enable human agency. Not only does life have an informational signature in its
DNA, but its actions show intention.
