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The intersection of
computational theory and the
philosophy of science is
explored, where I focus on the
implications of the physical
Church-Turing thesis (PCTT) and
the halting problem
which affects
predictability of physical
systems. The core argument
examined posits that if the PCTT
holds, there are physical
processes whose outcomes cannot
be predicted due to the
uncomputability of the halting
problem.The inability to predict
certain computational processes,
as claimed in the core argument,
would make it impossible to
consistently forecast or
evaluate physical events,
undermining the principles of
empirical knowledge and the
validity of scientific models.
I critically analyze this core
argument, which is based on
three key suppositions:
physicalism, the PCTT, and the
uncomputability of the halting
problem. It is shown through a
counter-argument that these
suppositions cannot hold
simultaneously. We can
demonstrate that when taking
into account physical
constraints and the
meaningfulness of computations,
the unpredictability posited by
the core argument can be shown
to be flawed and the claim of
uncomputable physical decisions
does not hold under closer
empirical scrutiny.
Nevertheless, it is also
possible to show that a bounded,
empirically constrained version
of the core argument still
holds, preserving some of the
unpredictability under specific
physical limitations. This
offers a refined understanding
of the limits of computability
and prediction in physical
systems.
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