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A hypercomputational approach to the agent causation theory of free will

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2006
Mersin, Serhan
Hypercomputation, which is the general concept embracing all machinery capable of carrying out more tasks than Turing Machines and beyond the Turing Limit, has implications for various fields including mathematics, physics, computer science and philosophy. Regarding its philosophical aspects, it is necessary to reveal the position of hypercomputation relative to the classical computational theory of mind in order to clarify and broaden the scope of hypercomputation so that it encompasses some phenomena which are regarded as problematic because of their property of being uncomputable. This thesis points to a relation between hypercomputation and the agent-causation theory of free will by exploring that theory's alleged infinite-regress feature, which has been regarded by some authors as problematic and used against the agent causation theory. In order to cope with this problem, we propose a certain hypercomputer, viz. the reverse Zeus machine. The reverse Zeus machine can help to understand the infinite-regress aspect of agent causation better than accelerating Turing machines (or ordinary Zeus machines). Accelerating Turing machines are abstract machines which perform temporal patterning in an accelerating manner by executing each step in half the time required for the previous step. This allows them to compute infinitely many operations in finite time. Although reverse Zeus machines have the same working principle as accelerating Turing machines, we show that agent causation can be represented by reverse Zeus machines better than by the classical Zeus machines.