Free Will, Determinism and Turing’s Halting Problem


Home / Free Will, Determinism and Turing’s Halting Problem
The Enemy of the Predictive Turing Machine by Mike DeHaan

The enemy of the predictive Turing Machine. Image by Mike DeHaan.

Lloyd: Apply the Halting Problem to Free Will versus Determinism

Lloyd applies similar reasoning to any attempt to demonstrate human determinism.

Suppose that the human mind actually follows deterministic processes, which may be no more complex than Turing Machines. Further, suppose that a person were able to predict someone else’s every decision. Lloyd discusses it as if a person were to predict her own decisions, but perhaps it does not matter who makes the prediction, or whether it is a computer. That capability to predict human decisions resembles the predictive TM which could not solve the Halting Problem.

Let’s suppose that a person could predict her own decisions, because her mind/brain is deterministic and she has that talent. She would have the feeling, or impression, that her mind was deterministic because her final decision always agreed with her predictions.

Then her ability to predict decisions is also a deterministic process; that is characteristic of her mind and brain.

In his brief article, Lloyd merely refers to Turing’s mathematical proof that predictions must fail sometimes.

Let’s go a bit further, and try to apply Turing’s “enemy” logic to construct the case that topples a person’s ability to predict decisions.

Once she settles on a prediction, she then could deliberately change her mind. Furthermore, she could apply a rule such as “change my mind for every third decision.”

Even if she were predicting someone else’s deterministic decisions, or if it were a computer predicting a person’s choices, the same enemy logic can apply. Once the prediction is known, a person can choose to do the opposite.

Therefore a person can always make decisions that disagree with some predictions, and feel that she has free will.

A Halting Problem, but Not for Turing, image by ell brown

A halting problem, but not for Turing. Image by ell brown

Lloyd’s Guarantee of Experiencing Free Will

Of course, if people truly have free will, then it would be impossible to predict every decision someone would make. Therefore the experimental results would be the same as for people behaving as deterministic Turing Machines; sometimes the prediction will be wrong and sometimes the decision changes at the last moment.

Therefore Lloyd concludes that most humans experience life as though we have free will. It is difficult to conceive of an experiment to disprove that feeling, and Turing provided a mathematical proof in the Halting Problem.


Lloyd, Seth. A Turing test for free will. (2013). MIT. Accessed October 29, 2013.

MIT MechE. Seth Lloyd at MITAccessed October 29, 2013.

Hoefer, Carl. Causal Determinism. (2010). The Stanford Encyclopedia of Philosophy: section 6: Determinism and Human Action. Accessed October 29, 2013.

Leave a Comment