Determined to Be Free


Imagine yourself 20 years from now. A brilliant cognitive neuroscientist claims to be able to read your brain and predict your future behavior. She studied with Sam Harris in Los Angeles and then completed her postdoctoral work with Chun Siong Soon and John-Dylan Haynes in Berlin. She knows her stuff and she uses the most advanced technology.

You will be able to press one of five buttons. Before you do so, the neuroscientist will take a scan of your brain, analyse it and predict which button you will choose. She will pay particular attention to the posterior cingulate gyrus and the rostral prefrontal cortex. She is willing to bet you that her prediction will be correct.

If you take the bet, you believe in free will. If you do not, you are a determinist – or in this context a “neuro-determinist.”

Faites vos jeux!

wager blog

Concept of Determinism

Modern determinism was most clearly stated by Pierre-Simon Laplace in 1812. He proposed that an intelligence – whether God or Demon, whether real or hypothetical – could completely predict the future from the present if the intelligence knew all the “forces by which nature is animated” and could measure the exact “situation” of everything in the present universe:

We ought then to regard the present state of the universe as the effect of its anterior state and as the cause of the one which is to follow. Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situation of the beings who compose it – an intelligence sufficiently vast to submit these data to analysis – it would embrace in the same formula the movements of the greatest bodies of the universe and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes (Laplace, 1812/1902, p 4).

Determinism is the basic premise of science, which attempts to discern the causal laws by which the universe operates (Earman, 1986; Hoefer, 2010). Everything is caused by something else. Nothing is a causa sui (cause of itself). The universe contains no freely acting anything or anybody.

Determinism is usually interpreted in terms of what will happen. However, in Laplace’s definition it also casts its net backward: if we know everything about the present then we can tell exactly what happened in the past.

What is not always recognized is that Laplace wrote his definition of determinism in the introduction to his book A Philosophical Essay on Probabilities. Now, probability is what we use when we cannot predict exactly what will happen. A hypothetical vast intelligence might, but we cannot. We estimate the odds rather than predict the outcomes.

If the concept of determinism is taken seriously, then the present is determined by the immediate past, that past is itself determined by what preceded it, and so on. Ultimately, everything must have been decided when the world began, and all our actions determined 13.8 billion years ago at the moment of the Big Bang. In the words of Omar Khayyam:

With earthʹs first clay they did the last man knead,
And there of the last harvest sowed the seed.
And the first morning of creation wrote
What the last dawn of reckoning shall read.
(Fitzgerald translation, 5th Version LXVIII)

Determinism is a powerful working hypothesis but it may not be universally applicable. In the early 20th century, we became aware that atomic and sub-atomic processes are not deterministic (Ismael, 2015). They follow exact rules, but these are expressed in terms of probabilities rather than certainties.

Most biologists consider that at the levels of chemistry and physiology, quantum uncertainty averages out and we are “for all intents and purposes” fully determined. At macroscopic levels, quantum uncertainty therefore plays no significant role in the prediction of the future.

My suggestion, however, is that the universe veers away from strict determinism both at levels of extreme simplicity – quantum uncertainty – and at levels of extreme complexity – conscious choice.

Problem of Chaos

Sometimes, as Edward Lorenz (1996) has shown, fully determined systems are liable to chaos. Chaos occurs “when the present completely determines the future, but the approximate present does not approximately determine the future” (Lorenz, 2005).

The movie below provides an example of a typical deterministic system – billiard balls on a billiard table. If the rules by which the system operates and the positions and velocities of the balls are exactly known, the future of the system can be precisely predicted. The life of a billiard ball goes from collision to collision. Although there are occasional near misses there is no choice.

On the left is the actual system. It is not perfect – the table is frictionless and the balls are inelastic (there is only so much an old man can program) – but it does follow deterministic laws.  On the right is the modeled system. If we initiate movement in the white ball, our prediction fits exactly with what happens.

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Some determined systems, however, are chaotic. In a chaotic system our predictions can be wildly off the mark if our measurement of the initial state of the system is not exact. Chaos is usually considered in terms of complex systems such as the weather: butterflies in Brazil causing tornados in Texas. However, chaos also occurs in very simple systems, even in billiards.

The next example shows the same deterministic system on the left as in the previous movie. On the right is the prediction. This time the measurement of the initial position of the white ball was out by one pixel. The measurement of the velocity vector was exact.

At the very beginning the prediction is approximately correct. After the first few seconds, however, the model shows no relationship whatsoever to the actual.

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Chaos is an inherent part of physical determinism. It is therefore often impossible to measure the state of the world with sufficient accuracy to give any meaningful predictions of what will actually occur. Our model of the future may look nothing like what it will be.

Chaos does not disprove determinism: chaos is completely determined. However it makes it very difficult to prove that determinism underlies everything. That hypothesis would require that we be able to measure the universe with absolute accuracy. That we cannot do.

Limits of Prediction

Even without chaos, complete predictability is impossible. The universe contains neither time nor space enough to map its own future.

Laplace was wrong to claim that even in a classical, non-chaotic universe the future can be unerringly predicted, given sufficient knowledge of the present. (Wolpert, 2008).

turingThe proof is related to Gödel’s Incompleteness Theorem and Turing’s Halting Problem. A Turing machine reads an infinite tape one symbol at a time. According to its internal state at the time of reading, the machine then changes the symbol written on the tape, moves the tape, and changes its state. The Turing machine is a model of a computer. We cannot predict when the machine will stop. We are unable to know if a problem is soluble before it is solved. We cannot predict the entire future before it has already occurred.

David Wolpert’s work means that “No matter what laws of physics govern a universe, there are inevitably facts about the universe that its inhabitants cannot learn by experiment or predict with a computation.” (Collins, 2009). The most we can hope for is a “theory of almost everything” (Binder, 2008).

However, even though we cannot prove determinism, we cannot disprove it. It continues to be a reasonable working hypothesis for most situations.

Lack of predictability is a characteristic of free will. A test for free will (Lloyd, 2012) might involve the following criteria: the ability to make decisions, the use of recursive reasoning in making those decisions, the ability to predict the future, and the inability to predict what one will decide. If you are in the process of deciding how to act and if you cannot predict how you will decide, you are in a state of free will.

Quantum Uncertainties

One way out of the problem that quantum uncertainty poses for determinism is to claim that yet-unknown deterministic laws underlie quantum events. Once we discover these laws we will be able to re-cast quantum mechanics so that all events are exactly rather than stochastically determined. The problem with such a “superdeterminism” is that in order to derive the underlying laws governing quantal processes we would have to observe events at subquantal levels. That would require using subquantal measuring devices, and that would run up against Heisenberg’s Uncertainty Principle (Hilgevoord & Uffink, 2006). I think indeterminism is here to stay. The only thing we can be certain about is ultimate uncertainty.

Quantum uncertainty may provide a way for our behavior not to be fully determined by antecedent causes. We would need to imagine some way for unpredictable quantum events to change brain activity. Penrose and Hameroff (2011) have suggested that quantum events in the neuronal microtubules – the Orchestrated Objective Reduction of Quantum States – could underlie our choices of one action over another.

However, making free will depend on quantum uncertainty is unsatisfying in that it reduces free will to chance rather than choice. Random is not the same as free. If we make our decisions on the basis of random quantum events, we are just subject to the tyranny of the atom rather than the will of God.

Even Sam Harris agrees:

Chance occurrences are by definition ones for which I can claim no responsibility. And if certain of my behaviors are truly the result of chance, they should be surprising even to me (Harris, 2012).

However, randomness can still play a role in free choice. We might decide to base our decisions on a random event, such as flipping a coin, so as to be fair to both sides of a question. We might also use a random process to add noise to a decision (like raising the temperature in an annealing process), or to determine how many options to evaluate or for how long (e.g. Dennett, 1978). For Peter Tse (2013) free will is caused by the “criterial selection” of random synaptic activity in cerebral cortex.

Logical Problems

Two contradictory statements can be made in relation to free will and determinism (van Inwagen, 1983, 2008):

(i) Freedom of the will is not possible if the world is completely determined. Free will means that we are sometimes in the position with respect to a contemplated future act that we are able either to perform the act or to do otherwise. If we can indeed do otherwise – if two different futures can equally follow from the same present – then the future is not determined. The claim that we can choose between these two futures is incompatible with the idea that the past and the laws of nature together determine, at every moment, a unique future.

(ii) However, free will cannot act without determinism. If we make a decision, we can only carry it out if our behavior is determined by that decision – if action potentials travel down the nerves to the muscles, if the muscles move the limbs, and if the limbs perform the intended physical acts. Unless the world is deterministic, we cannot exercise our free will.

So we cannot have free will if the universe is completely determined, and free will is meaningless if the universe is not determined. There are two ways out of this conundrum. We can accept that the universe is determined, and conclude that our idea of free will is an illusion. Or we can agree with van Inwagen that free will is true and conclude that the world is not completely determined.

Van Inwagen considers free will to be true because he cannot imagine human life without personal moral responsibility. If there is no free will, everything we do is determined before we have anything to do with it. We need not think; we are never responsible for our actions; any idea of justice is meaningless. All evil will be exculpated by fMRI evidence that the brain was just unable to be good.

A world where people do not believe in free will is not pleasant. Simply suggesting to subjects that there is no free will encourages dishonesty and mischief. The less someone believes in free will, the more likely he or she will cheat if the opportunity presents (Vohs & Schooler, 2008), and the more likely she or he will indulge in anti-social acts if they will not be discovered (Baumeister et al., 2009).

So, even if we are not free, should we act as if we were? This is a strange way to live our lives.

However, we can take positions other that of full determinism in relation to the problem of free will:

fw determ table

Van Inwagen’s position is one of philosophical “libertarianism.” (This is not the same as political libertarianism, which disputes the laws of society rather than the laws of science.)

Most of us believe that we have free will, but we are also convinced that the universe is determined. We are “compatibilists” – determinism is true but so is free will. We do not know how the two co-occur, but somehow they must. In surveys of what we believe, compatibilists are in a clear majority: 75% of normal folk (Nahmias et al, 2005), and 80% of biologists (Graffin & Provine, 2007). Even 60% of philosophers, those that should not support logical contradictions, consider themselves compatibilists (Bourget & Chalmers, 2014). The other 40% are evenly divided between undecided, libertarians and determinists.

Dan Dennett is the most prominent of our present compatibilists. But he is unclear about exactly how free will can exist in a world of causes. Something to do with human knowledge and communication:

Our autonomy does not depend on anything like the miraculous suspension of causation but rather on the integrity of the processes of education and mutual sharing of knowledge. (Dennett, 2003).

Evolution and Free Will

Darwin thought that free will was a delusion. Since we are not conscious of the instincts that actually drive our actions, we only think that we freely choose. In fact we do not.

The general delusion about free will obvious – because man has power of action, & he can seldom analyse his motives (originally mostly instinctive, & therefore now great effort of reason to discover them: this is important explanation) he thinks they have none. (from Darwin’s Notebooks, about 1839, edited by Barrett et al., 1987, p 608; these notes are discussed in Wright, 1994, p. 350).

Evolution is often considered as part of a general determinism. Selection occurs according to hard and fast rules. Species that cannot survive to reproduce do not continue. Yet indeterminism rests at the very heart of Darwin’s theory. Evolution depends on two processes: the production of offspring with variable characteristics and the selection of those offspring that survive in a world of limited resources. The variation is largely a result of genetic mutations and these are caused by indeterministic quantum events.

Some people have likened cognitive processing to Darwinian evolution (e.g., Edelman, 1987). In evolution, various species are created and only the most adaptive are selected. In cognition, various possible actions are considered and only the most appropriate are selected.

A major problem is why evolution determined that consciousness and free will occur. Human beings are certainly the most successful of all earth’s species. This would suggest that consciousness and free will are highly adaptive traits that have been selected to facilitate our survival. Evolution is a deterministic process. Yet by selecting out the fittest, evolution has led to consciousness and free will. We have been determined to be free.


Neuroscience entered the philosophical arena in the early 1980s when Benjamin Libet evaluated the relations between volition and the readiness potential (or Bereitschaftspotential) recorded from the scalp. The readiness potential began up to a second before the movement but the subject consciously perceived the time of movement initiation at about 200 ms before the movement. The brain decides unconsciously; awareness follows after.

BSP libet blog

Similar experiments have recorded unit activity in the human frontal cortex beginning about 2 seconds before the act (Fried et al., 2011) and fMRI activation patterns (Soon et al., 2008, 2013) between 4 and 10 seconds prior to the act.

These experiments have led to a theory of volition that has been called “neuro-determinism.” Perhaps a better term might be “Libetarianism.” Our actions are willy-nilly determined by cerebral processes about which we are unaware. We only become conscious of what we are doing just before we do it. We do not control our actions, we just watch them taking place.

The 200 ms between the awareness of response-initiation and its occurrence could make it possible to inhibit or “veto” a response in process. Thus we can be consoled with the idea that even if we don’t have free will, we have “free won’t.” Yet recent experiments have shown that even this might be unconsciously driven (Filevich et al., 2013).

One problem with the neural measurements is that we do not know what they represent. Many different cerebral processes contribute to the readiness potential – estimating time, preparing to respond (or not), monitoring performance, etc. Some of these can be unconscious and can correlate significantly with later acts. Yet such processes do not necessarily cause the act – the mind can always change at the last minute (or millisecond).

In addition, our concept of volition is multidimensional (Roskies 2010). It can refer to the general intentions that one has in regard to a particular situation, the planning of how and when to respond, and the specific initiation of an act. A subject’s voluntary participation in a Bereitschaftspotential experiment involves his or her agreement to do what is asked by the experimenter, the setting up of the necessary timing and motor programs to control the responses, and the final initiation of the act. Any or all of these processes may contribute to the physiological recordings at different times.

Nevertheless, these physiological findings have led many scientists and philosophers to claim that our idea of free will is illusory:

Our sense of being a conscious agent who does things comes at a cost of being technically wrong all the time. The feeling of doing is how it seems, not what it is (Wegener, 2002).

Free will is an illusion. Our wills are simply not of our own making. Thoughts and intentions emerge from background causes of which we are unaware and over which we exert no conscious control. We do not have the freedom we think we have (Harris, 2012)

Farewell to the purpose-driven life. Whatever is in our brain driving our lives from cradle to grave, it is not purposes. But it does produce the powerful illusion of purposes (Rosenberg, 2011).

Eddy Nahmias (2015) has suggested that we call their position “willusionism.”

I submit that this idea is wrong – free will is not an illusion. Now, this is an illusion!

tp cafe wall blog

The argument that a particular experience is illusionary presupposes that other experiences are veridical. Indeed we only know that something is illusory if we can prove by some other experience that reality has been distorted. Despite the illusion of the tilting tiles in Richard Gregory’s café-wall, we can prove with a spirit level that they are actually all horizontal.

tp cafe wall with spirit level blog

So in order to show that a particular experience of volition is illusionary, there would have to be other experiences of volition that are not illusionary and that are demonstrably different form the one considered illusionary.

Those who have proposed that free will is an illusion also point to clear evidence that we often do not know why we behave in a particular way. Psychoanalysis has long shown that we invent plausible but false reasons for how we act. This quotation is from Ernest Jones, one of Freud’s early disciples:

… the large majority of mental processes in a normal person arise from sources unsuspected by him. … No one will admit that he ever deliberately performed an irrational act, and any act that might appear so is immediately justified by distorting the mental processes concerned and providing a false explanation that has a plausible ring of rationality (Jones, 1908).

The psychoanalytic idea of rationalization has been supported by numerous recent psychological studies showing the effects of subliminal stimulation, the extent of our unconscious prejudices, and the vagaries of intuitions. We often are far more certain about things than we should be on the basis of the actual evidence (Burton, 2008).

Michael Gazzaniga’s studies of split-brain patients showed how the left hemisphere can invent totally inaccurate explanations for our actions. He suggests that the left-hemisphere language-system tries to make sense of our experience but that sometimes the story it comes up with is false:

It is the left hemisphere that engages in the human tendency to find order in chaos, that tries to fit everything into a story and put it into a context … even when it is sometimes detrimental to performance (Gazzaniga, 2011).

So perhaps we are always wrong? I think not. Just like the argument from illusion, the argument from rationalization only works if we are sometimes right. We have to know the real explanation in order to show that our rationalization is false.

Nature of Free Will

Only a small part of what we do is under conscious or controlled processing. Most of what we do occurs automatically. We are therefore often mistaken about why we acted in a particular way. We are not aware of causes outside of ourselves or hidden from conscious scrutiny, and we may invent reasons that are unrelated to what actually occurred, so that we can make sense of ourselves and our actions.

Nevertheless, we sometimes come to a decision about how to act by deliberately weighing the future consequences of several possible actions and choosing the most appropriate. We bring to bear on the problem all that we have so far learned about what things entail. For really important decisions, we often consult with others. We seek advice about what to do, ask our friends how they would decide in our position, and present scenarios for their comments. Freedom is inherently social. As mentioned above in relations to Dan Dennett’s compatibilism, free will has something to do with human knowledge and communication.

The future does not determine the present. That is not the way time flows. But the imagined future can determine the present. Once a feedback loop is created, time and causality become complicated. In causal circles, cause and effect can be simultaneous rather than sequential. Once we conceive of consequences, the future becomes part of the present and we can base our actions on how the future will (or should) be.

imagined future blog

These ideas of the “imagined future” are similar to the concept of episodic simulation proposed by Dan Schachter and his colleagues (Schachter, 2012; Szpunar et al., 2014) and the thoughts behind Carl Hoefer’s Freedom from the inside out (2002).

Such future-directed thought can have a top-down effect on the present. In particular, acts of free will can form a “self” – a set of predispositions to act in a characteristic way, sometimes automatically and sometimes deliberately (Kane, 2011, 2014).

Every undetermined self-forming choice is the initiation of a novel pathway into the future, whose justification lies in that future and is not fully explained by the past.” (Kane, 2011)

In a way the exercise of free will is like setting a legal precedent. Past decisions can then contribute to present choices.

Return to the Scenario

And so we return to the hypothetical wager from the beginning of this post. Should we bet that our actions cannot be predicted? Will it be possible 20 years from now for a brilliant neuroscientist to predict our actions before they occur?

In the experiments of Eddy Nahmias and colleagues (2014), subjects were asked about just such a scenario: a future neuroscientist reads the brain activity of a person called Jill and predicts what Jill will do. More than 80% of subjects accepted that this will be possible, but still claimed that Jill has free will if she is acting according to her own reasons. They believe that “the brain scanner is simply detecting how free will works in the brain” (Nahmias, 2015).

The astute among you may wonder whether during the scan you could fervently and honestly intend to press the red button. But then, once you have made your bet, on second thought you might wilfully decide to press one of the other buttons. After all, even at the last millisecond you can change your mind. You do not usually do this. That is why the brain scanner can often predict your behavior. But you always can change your mind.

I would take the bet.


I have considered physical determinism and pointed out its limitations in quantum uncertainty, chaos and incomputability. I have shown that complete determinism is in logical conflict with free will. I have reviewed some of the evidence that suggests that our unconscious brain determines what we might falsely believe to be our free choices. And I have refused to accept that evidence, arguing that we are still free whenever we base our actions on an evaluation of their consequences.

Determinism rules but only within limits. At the level of the atom there is quantum uncertainty. At the level of the brain there is conscious choice.

In our brains, most of what happens follows the laws of determinism, with the past causing the present and the present causing the future. Most of what we do is unconscious. Yet some acts are deliberately chosen after a conscious evaluation of what will happen. These are as much determined by the imagined future as by the actual past. As such they are both determined and free.

Note: This posting was derived from a talk given at the Rotman Research Institute Annual Conference. A pdf of the slides and the notes for the talk is available for download.


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Baumeister, R. F., Masicampo, E. J., & DeWall, C. N. (2009). Prosocial benefits of feeling free: Disbelief in free will increases aggression and reduces helpfulness. Personality and Social Psychology Bulletin, 35, 260-268.

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Collins, G. P. (2009). Within any possible universe, no intellect can ever know it all. Scientific American, March, 2009,

Dennett, D. C. (1978). Brainstorms: Philosophical essays on mind and psychology. Montgomery, VT: Bradford Books. (Chapter 15. On giving libertarians what they say they want. pp. 286-299).

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Fried, I., Mukamel, R., & Kreiman, G. (2011). Internally generated preactivation of single neurons in human medial frontal cortex predicts volition. Neuron, 69, 548–562.

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Hoffstaedter, F., Grefkes, C., Zilles, K., & Eickhoff, S. B. (2013). The “What” and “When” of self-initiated movements. Cerebral Cortex, 23, 520-530.

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Kane, R. (2014). Acting ‘of one’s own free will: Modern reflections on an ancient philosophical problem. Proceedings of the Aristotelian Society, 114, 35-55.

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Libet, B., Gleason, C. A., Wright, E. W., & Pearl, D. K. (1983). Time of conscious intention to act in relation to onset of cerebral activity (readiness-potential). The unconscious initiation of a freely voluntary act. Brain, 106, 623–642.

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Lloyd, S. (2012). A Turing test for free will. Philosophical Transactions of the Royal Society, A 28, 3597-3610.

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Nahmias, E., Morris, S., Nadelhoffer, T, & Turner, J. (2005). Surveying freedom: Folk Intuitions about free will and moral responsibility. Philosophical Psychology, 18, 561–584.

Nahmias, E., Shepard, J., & Reuter, S. (2014.) It’s OK if ‘my brain made me do it’: People’s intuitions about free will and neuroscientific prediction. Cognition, 133, 502–516.

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Newcomb’s Problem

The concepts of determinism and freedom are nicely illustrated in a philosophical problem originally invented by William Newcomb, a California physicist. The philosopher Robert Nozick published an analysis of the problem in 1969, and since then it has been widely discussed (Nozick, 1969; Gardner, 1973, 1974, 2001; Drescher, 2005, Chapters 5 and 6; Mark in Malaysia, 2009, summarizes the issues on his webpage).

The basic problem is to decide how to act in the following situation. There are two boxes. The first contains $1000. You can see inside this box: the money is certainly there. The second contains either $1,000,000 or nothing. You cannot see inside this box. You can choose (i) to take both boxes or (ii) to refuse the first box and just take the second. A superior being predicts how you will choose and, before you do so, places in the second box either $1,000,000 if it predicts that you will refuse the first box, or nothing if it predicts that you will take both. The choice must be deliberate: it cannot be made on the basis of some random event such as a coin toss. How do you choose – one box or two?


Perhaps you need more information about the superior being who is predicting your choice? If you are a theist, the being can be likened to an omniscient God, who knows everything that will happen. The problem is then related to the concepts of predestination and free will. Christian believers have long sought to reconcile these two contradictory ideas. The one-box solution to problem suggests that you should renounce what you have for certain in the world to obtain the more valuable eternal salvation that can only be known by faith. Horne (1983) presents some other religious parallels.

If you are a scientist, the problem can be posed in an experimental context. Many other people have already tried the problem and the prediction of how they would choose was always correct. You should therefore infer that the prediction of your choice will also be correct.

If you are a neurophysiologist, the prediction can be made on the basis of a sophisticated brain scan that can tell which way you will choose before you make your choice (e.g. Bode et al., 2011, Haynes, 2011; Soon et al., 2011).

One box or two?

As Nozick remarked

To almost everyone it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly. (p. 117).

Nozick, himself, believed that one should take both boxes (p. 135). He believed in the freedom of the individual and became famous for his 1974 book defending political libertarianism, Anarchy, State and Utopia. According to Gardner (1973), Newcomb argued for just taking the second box.

When Martin Gardner reviewed the problem for Scientific American (1974), readers of the journal who wrote in were 89:37 (approximately 3:2) in favor of just taking one box. In a review of what philosophers believe, Bourget and Chalmers (2014) found that of philosophers divided in the opposite way with 292 choosing two boxes to 198 only one. There were only low-level correlations with other beliefs: theists were more likely to choose one box, and those with a physical view of the mind more likely to choose two. Bar-Hillel and Margalit (1972) urge their reader to choose only the one box, and “join the millionaire’s club.” Schlesinger (1974) states that two boxes should be chosen, because voluntary choices are inherently unpredictable. Myself, I am a definite two-boxer.

Payoff Matrices and Decision Theory

payoff matricesOne approach to making a decision is to evaluate a payoff matrix. For the Newcomb problem the matrix is shown in the upper section of the figure on the right. Since we do not know what the future holds we have to consider the relative probabilities of what might happen. From the payoff matrix we can then assess the expected “utility” of a decision: how valuable the result is to the decider given the probabilities of each outcome.

One way to assess the expected utility (middle section) is to estimate the accuracy of the superior being’s predictions For example we may guess that the superior being predicts our decision correctly 90% of the time. The expected utility of a decision is calculated by summing the payoffs for that decision with each payoff weighted by the probability of that outcome (lower section of the figure). One box is the better choice unless the chance of the superior being making a correct prediction becomes less than 50.05%. If the superior being acts by chance it might be worthwhile to take two boxes. We might also consider the possibility that the being is playing a joke or trying to outwit us, in which cases the prediction will be less than 50%

The expected utility is affected by other factors in addition to the relative probabilities of the possible outcomes. For example a decider may be “risk-averse,” preferring to have the certainty of the $1000 rather than risk the possibility (however low its probability) that there will be nothing in the second box: a bird in the hand is worth two in the bush. This can be factored into the assessment by applying a personal “utility function” that weights how valuable the decider considers each of the possible outcomes.

However, instead of being based on the predictions of the superior being, the payoff matrix can be set up according to the state of the world at the time of the decision (lower section of the illustration). In this case the first box contains $1000 and there is either $1000000 or $0 in the second box. The superior being has made a prediction and now it is up to you to decide. You do not know the probability of the second box being empty. The illustration uses a probability more likely to put money in that box. However, whatever this probability you always get $1000 more by choosing to take both boxes.

However, as Nozick points out, both these approaches do not really assess the relative utilities of the two decisions because the actions and the outcomes are not independent. In the basic statement of the problem the outcomes are necessarily correlated to the actions: your decision to take one box or two determines whether there is a million dollars in the second box or not.

An Ill-Posed Problem?

Newcomb’s problem might be explained by processes that we do not usually consider part of the real world. We could postulate “retrocausality:” the presence of the million dollars in the second box at a time after the decision somehow causes the decision, or my decision somehow causes the prediction that preceded it. However, this is not the world we understand. Causes precede their effects, not vice versa.

We could postulate “time travel:” the predictor may have travelled ahead to the time after the decision and therefore knows what it was (or will be). Again, the world we understand does not allow this possibility.

If we deny these imaginary processes, the problem then resolves to that of free will and determinism. Its insolubility may derive from the fact that these two assumptions are mutually contradictory. If I accept full determinism, I have no choice in the matter. My decision was determined when the world began.

With Earth’s first Clay They did the Last Man knead,
And there of the Last Harvest sow’d the Seed:
And the first Morning of Creation wrote
What the Last Dawn of Reckoning shall read.

(Rubaiyat of Omar Khayyam, translated by
Edward Fitzgerald, 1889, verse LXXIII)

I must therefore “choose” one box or two according to a sequence of cause and effect that is playing itself out according to rules I cannot alter. The future can be known to any intelligence that measures the current state of the universe and knows all the laws determining how it proceeds. The superior being can therefore predict my choice.

Why then do I spend time thinking about what would be the best thing for me to do? Should I not just act by instinct? Choose one box or two by intuition rather than by reason. Thinking about the problem is just a waste of time. Its only purpose may be to buttress my illusion that I am free to choose.

Free will assumes that the future is not fixed. We can act to change the course of events. No intelligence can predict with certainty what I shall do. Many of my actions can be predicted. Clearly, I am often a creature of habit. But not always. Between the prediction of how I shall choose and the moment of my actual choice, I can sometimes change my mind.


Bar-Hillel, M. & Margalit, A. (1972). Newcomb’s paradox revisited. British Journal of Philosophy of Science, 23, 295-304.

Bode, S., He, A. H., Soon, C. S., Trampel, R., Turner, R., & Haynes, J.-D. (2011). Tracking the unconscious generation of free decisions using ultra-high field fMRI. PLoS ONE 6(6): e21612.

Bourget, D., & Chalmers, D. J. (2014). What do philosophers believe? Philosophical Studies, 170, 465–500. The data from this study are available on the PhilPapers website. No correlations are listed for Newcomb’s problem. However one can obtain correlations with other variables by checking their listings (e.g. theism, physicalism).

Drescher, G. L. (2006). Good and real: Demystifying paradoxes from physics to ethics. Cambridge, Mass: MIT Press.

Gardner, M. (2001).The colossal book of mathematics: Classic puzzles, paradoxes, and problems. New York: Norton. Chapter 44 Newcomb’s paradox (pp 580-591). Based on original articles in Scientific American July 1973 (Free will revisited with a mind-bending prediction paradox by William Newcomb) and March 1974 (Reflections on Newcomb’s problem: a prediction and free will problem).

Haynes, J.D. (2011). Decoding and predicting intentions. Annals of the New York Academy of Sciences, 1224, 9-21.

Horne, J. R. (1983). Newcomb’s problem as a theistic problem. International Journal for Philosophy of Religion, 14, 217-223.

Nozick, R. (1969). Newcomb’s problem and two principles of choice. In N. Rescher(Ed.) Essays in Honor of Carl G. Hempel (pp. 114-146). Dordrecht: D. Reidel.

Nozick, R. (1974). Anarchy, state, and utopia. New York: Basic Books.

Schlesinger, G. (1974). The unpredictability of free choices. British Journal for the Philosophy of Science, 25, 209-221.

Soon, C. S., He, A. H., Bode, S., & Haynes, J.D. (2013). Predicting free choices for abstract intentions. Proceedings of the National Academy of Sciences USA, 110, 6217-6222.


Here I stand

The Diet of Worms was an assembly of the lords of the Holy Roman Empire called together by Emperor Charles V in 1521. One of the duties of the Diet was to consider whether the writings of Martin Luther were heretical. The Diet marked the point-of-no-return for the Protestant Reformation. Luther’s ringing statement “Here I stand” reclaimed the spiritual freedom of the individual. Henceforth each person could choose to interpret scripture and to commune with God without the necessary intervention of the church. However, Luther’s actual concept of freedom was far more complicated than this.

luther 1520Martin Luther was an Augustinian monk who studied, taught and preached at the University of Wittenberg in Saxony, one of the states of the Holy Roman Empire. The engraving on the right by Lucas Cranach the Elder shows Luther in his monk’s attire. Cranach was the court painter for the Elector of Saxony. He knew Luther well and made several portraits of him. This engraving was used as a frontispiece for several of Luther’s early books. The Latin beneath the portrait states that Luther’s depiction of his thinking was eternal but Cranach’s portrait of his features only transient. At the bottom is a device used by Cranach as his signature – a winged serpent with a crown upon his head and a ruby ring in his mouth.

Luther had published his Ninety-Five Theses on the Power and Efficacy of Indulgences in 1517. Indulgences were sold by the Roman Catholic Church as a means for the sinful to decrease their time in purgatory. Though they might have begun as a means to relieve the sinner, they had rapidly become simply a way for the church to raise money. Whether or not the theses had actually been nailed to the door of the Castle Church of Wittenburg is unknown, but they were quickly printed and made available throughout the Holy Roman Empire:

holy roman empire

In 1518, Luther was arraigned in Augsburg before Cardinal Cajetan, the papal ambassador to the Holy Roman Empire. Cajetan insisted that Luther’s views were heretical in that they questioned the authority of the pope. He asked Frederick the Wise, Elector of Saxony, to arrest Luther and send him to Rome. Frederick refused to do so since Luther had not been formally tried and convicted of heresy.

In 1519 Luther debated on the 95 theses with Johann Maier von Eck in Leipzig. Luther insisted on the freedom of the individual to decide what was right on the basis of the scriptures and conscience, whereas von Eck insisted on the need for obedience to God’s church. Their debate had no resolution.

Over the next year, Luther published several books highly critical of the Roman Catholic Church (Mullett, 1985, Chapter 5). His Address to the German Nobility proposed that the German states should become independent of Roman control and not send Rome its annual payments. The Babylonian Captivity of the Church was a vituperative attack on the papacy, likening it to the power of Babylon and the Antichrist described in Revelations.

A third book The Freedom of a Christian was addressed to Pope Leo and was more conciliatory. The essence of its message was that

A Christian is a perfectly free lord of all, subject to none.
A Christian is a perfectly dutiful servant of all, subject to all.

Christians were granted freedom from sin through the grace of Christ. Nevertheless, they must then act not for themselves but for the benefit of others. Freedom comes with duty.

However, the book was also adamantly opposed to many tenets of Roman Catholicism. Luther proclaimed that salvation comes through faith rather than by works, and that each Christian can be his or her own priest: “Christ has made it possible for us, provided we believe in him, to be not only his brethren, co-heirs, and fellow-kings, but also his fellow-priests.”

In the summer of 1520, Pope Leo X issued the bull Exsurge Domine (Arise Lord), which listed the heretical ideas proposed in Luther’s writings. The pope requested that Luther come to Rome and recant; failure to do so would result in his excommunication. The pope arranged for the burning of Luther’s books in Rome. In Wittenberg, a defiant Luther publicly burned his copy of the papal bull.

The pope assigned Cardinal Girolamo Aleander the task of bringing Luther to trial. His task was facilitated by the coronation of the new Emperor Charles V in November, 1520. Anxious to display his faith, Charles agreed to bring Luther before the Diet of Worms in the spring of 1521. Frederick the Wise of Saxony insisted that Luther be guaranteed safe conduct to and from Worms.

Luther appeared before the Diet on April 17. Since Cardinal Aleander did not allow himself to be in the same room as a confirmed heretic, the examination of Luther was conducted by von Eck, who had previously debated Luther in Leipzig. The following woodcut by an anonymous artist (from a Freiburg History webpage) was used to illustrate one of the early reports of the Diet. In the background is Charles V surrounded by six electors (Frederick of Saxony, Joachim of Brandenburg, Ludwig of Rhine, and the Archbishops of Mainz, Trier and Cologne). The seventh elector (from Bohemia) was not present. In the foreground Luther stands on the right and von Eck on the left. In the center are Luther’s books.

luther worms

Luther was not allowed to present any of the ideas in his books. Rather he was simply asked to acknowledge and recant his authorship. Luther acknowledged that some of his writings had perhaps been too polemical (“more severe than befits my religion or my profession”), but claimed that the criticisms they voiced were nevertheless correct. He asked to have time to consider his response, and this was granted. The next afternoon, he appeared again before the Diet. Von Eck requested that he not make inappropriate comments, but simply state whether or not he would “revoke and retract your books and the errors contained in them” (Atkinson, 1971)

The final words of Martin Luther were variously reported (Deutsche Reichstagsakten, pp. 555-559; Atkinson, 1971; Whitford, 2011; Linder 2010, webpage The Trial of Martin Luther). Luther spoke in both Latin and German. He refused to recant the opinions expressed in his books since no scriptural evidence had been produced to prove them wrong:

Unless I am convinced by the testimony of the Scriptures or by clear reason (for I do not trust either in the pope or in councils alone, since it is well known that they have often erred and contradicted themselves), I am bound by the Scriptures I have quoted and my conscience is captive to the Word of God. I cannot and will not recant anything, since it is neither safe nor right to go against conscience. May God help me. Amen. (Brecht, 1985).

Nisi con victus fuero testimoniis scripturarum aut ratione evidenti, nam neque papae neque concilio solis credo cum constet eos errasse saepius et sibi ipsis contradixisse, vinctus sum scripturis a me adductis, et capta conscientia in verbis Dei, revocare neque possum neque volo, cum contra conscientiam agere neque tutum neque integrum. Gott helfe mir. Amen. (Reichtagsakten, p. 555)

Some reports include the statements “Here I stand. I can do no other.” (Hier stehe ich. Ich kann nicht anders) before “May God help me.” These words were certainly in the mind of Luther. Whether or not they were actually spoken is unknown. Most experts think not.

junker jorgA few days later, Luther left Worms to journey back to Wittenberg. Afraid that the safe conduct granted by Charles V might be revoked, Frederick the Wise arranged a sham kidnapping of Luther, who was spirited away to the castle at Wartburg. There Luther remained incognito. He grew a beard, and was known as Junker Jörg (Squire George). The woodcut on the right (again by Lucas Cranach) shows Luther with this new identity. The verse below the portrait states that “though so often sought and persecuted by Rome, I, Luther, still live by Jesus Christ in undeniable hope. As long as I have this, farewell perfidious Rome!”


The results of Luther’s examination before the Reichstag was published as the Edict of Worms in May 1821. Luther was denounced as an “obstinate, schismatic heretic.” He was to be apprehended and punished. Those favoring or supporting him would be guilty of treason against the empire and would forfeit all their goods. All of Luther’s books were to be burned.

Luther found the seclusion in Wartburg a relief from the disputations and polemics of the preceding years. He considered it his Patmos – the island where legend has it that St. John wrote Revelations. During his retreat in Wartburg, Luther translated the New Testament into German. In March 1822 he returned to Wittenberg. Frederick the Wise had negotiated with Charles V that the Edict of Worms did not apply to him. The young emperor did not wish to alienate one of the most powerful princes of his empire. Luther resumed his teaching and his writing.

One of his works on his return was a reply to the book On Free Will (De Libero Arbitrio), published in 1524 by Desiderius Erasmus, the humanist scholar. Erasmus was actually reacting to Luther’s earlier scriptural interpretations that man had no free will. The papal bull Exsurge Domine had listed this claim as one of Luther’s heresies. Luther had replied in an Assertion of all Articles: “free will is really a fiction and a label without reality because it is in no man’s power to plan any evil or good … everything takes place by absolute necessity” (Winter, pp. 44-45). All that mattered to Luther was salvation through the grace of God. Erasmus recognized the grace of God but insisted that we could accept or reject this salvation. Furthermore we could choose to do either good or evil. Why would the scriptures exhort us to follow God’s commandments, if there were no choice between obedience and disobedience?

In 1525 Luther denounced the ideas of Erasmus in his book On the Bondage of the Will (De Servo Arbitrio). Since God is omniscient and omnipotent,

all things which we do, although they may appear to us to be done mutably and contingently, and even may be done thus contingently by us, are yet, in reality, done necessarily and immutably, with respect to the will of God. (p. 27)

Luther proposed that the purpose of the commandments is simply to demonstrate that man cannot obey them without the grace of God.

man, by the words of the law, is admonished and taught what he ought to do, not what he can do …  he is brought to know his sin, but not to believe that he has any strength in himself. Wherefore, friend Erasmus, as often as you throw in my teeth the Words of the law, so often I throw in yours that of Paul, “By the law is the knowledge of sin,”(Romans 3:20) — not of the power of the will. (pp. 111-112)

Luther interpreted the words of Paul as irrefutable truth. He had replaced the authority of the Church with the authority of the scriptures. There is no reason to accept either. Both represent incomplete attempts to understand how we should act.

These ideas bring into question Luther’s statements at the Diet of Worms. According to our understanding, we exercise free will when we choose to act in one way when we could have acted otherwise (van Inwagen, 1983). Typically this requires “deliberation” – we imagine the outcomes of our possible acts, and evaluate these against our principles of what is good or right.

One of the great paradoxes of Judeo-Christian thought is how free will is possible when God knows everything that will happen. In our modern and more agnostic times, this paradox has been transformed. Now we wonder whether free will is possible when science proposes that everything is determined. Most consider that free will and determinism are compatible but it remains unclear how this can be so.

Much of what we do occurs without thinking. We often respond instinctually or reflexively. Sometimes we do things for reasons of which we are unaware. After the act we invent rationalizations for our behavior. Nevertheless, we remain convinced that some of our actions are truly deliberate. We choose to do them because we have thought carefully about the consequences. Various options are freely available to us. We select what we think is best. We try to do the right thing.

Luther had deliberated overnight whether to recant. In the end he decided not to. Yet he believed that this decision was not his. He was merely acting out God’s preordained will. He could do no other.

Luther had constructed his personal system of values from his interpretation of the scriptures. This set of values had determined his decision. He attributed his ideas about what he should do to God. He did not say so for fear he might be wrong. For he had conceived these ideals, and he chose to follow them. He could have done otherwise.


Atkinson, J. (1971). The trial of Luther. London: Batsford.

Bayerische Akademie der Wissenschaften. (1962). Deutsche Reichstagsakten: Jüngere Reihe. Göttingen: Vandenhoeck & Ruprecht. Volume 2. An earlier version (1896) is available online.

Brecht, M. (1981, translated by Schaff, J. L., 1985). Martin Luther. His road to reformation. 1483-1521. Minneapolis: Fortress Press.

Luther, M. (1520, translated by W. A. Lambert & H. J. Grimm, 1999). The freedom of a Christian. From J. J. Pelikan, H. C. Oswald & H. T. Lehmann, Eds.). Luther’s works, Volume 31 Philadelphia: Fortress Press.

Luther, M. (1525, translated by Cole, H. 1823). De servo arbitrio. “On the enslaved will” or the bondage of the will. Grand Rapids, MI: Christian Classics Ethereal Library

Mullett, M. A. (2004). Martin Luther. London: Routledge (Taylor and Francis).

van Inwagen, P. (1983). An Essay on Free Will. Oxford: Oxford University Press.

Whitford, D. M. (2011). Luther: a guide for the perplexed. London: T & T Clark.

Winter, E. F. (1961). Discourse on free will. New York: Ungar. This is an annotated translation of Erasmus, D. (1524). De Libero Arbitrio, and Luther, M. (1525) De Servo Arbitrio.