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Free Will

The question as to whether or not free will exists depends on one’s definition of it.  Of the two leading conceptions of free will, the one most intuitively defined cannot exist.

Table of Contents

The Definition of Free Will
The question of whether or not humans have free will is a timeless one in philosophy.  The quest for an answer to this question often suffers from ambiguity and a lack of precision.  I will present here a brief essay that attempts to remove some of this ambiguity and arrive as some definitive answers.

I do not consider free will to be a primitive concept, so the first step in reaching clarity on the subject is to define it.  To this end, let us consider the following terms that I believe are primitive, in that it can be made clear to everyone what is meant by each of them:

  • Agency: A process by which intentions and desires are experienced, beliefs are held, and choices are made.  An entity that exhibits agency is called an agent1.  I will denote agency with a lower case ‘a’.
  • Deterministic: An attribute of a process such that, given any set of inputs to the process, the same set of outputs will always be generated2.  I will indicate that a process x is deterministic by “Dx”.
  • Natural: An attribute of an object, action, process, or another attribute meaning that the thing that has this attribute is part of the natural, observable world3.  I will denote that x is natural by “Nx”.

Note that the concept of an agent here is a rather broad one.  The following discussion would apply just as well if restricted to rational agents, or to human beings specifically.

In addition, let us denote that a process x is free by “Fx”, and in particular, agency is free; i.e., there is free will, by “Fa”.  I know of two possible definitions of free will, as follows:

  • Indeterministic Definition: Fa ≡ ¬Da
    • Note that the symbol ≡ means “is defined as”
  • Supernaturalistic Definition: Fa ≡ ¬Na

The indeterministic definition is fairly straightforward.  All it is saying is that in any particular situation, it is not possible to predict what a particular agent will do at any particular time under any particular set of circumstances.  I consider this a necessary condition for free will in the agent, but not a sufficient condition.  This is because the concept of free will, as most people envision it, seems to involve more than just lack of determinism, meaning more than just randomness.  However, if an agent is completely subject to the laws of nature, it seems like it only has two choices, it can be deterministic or indeterministic as defined above.

If free will contains some element that extends beyond indeterminism, and such an element cannot be obtained naturally, i.e., based on the laws of nature, then free will must entail some sort of supernatural component.  This is the intent of the second definition, which says simply that an agent’s will is free if and only if it exists outside of the natural universe.  Despite its undesirable consequences, I see no choice but to adopt this definition if our goal is to define free will in a way so as to match the concept that most people attach to this phrase.  Note that the assumption that free will cannot exist in a deterministic, completely natural world, amounts to a denial of the doctrine of compatibilism, which is described below.

Determinism and Causality
We must be careful when defining a deterministic process that is not natural.  There could be a supernatural process that is wholly deterministic, but that when observed from the natural world appears indeterministic, because we cannot observe supernatural factors that affect the outcome of the process.  I will be concerned with the latter type of indeterminism; i.e., whether or not a process appears to be deterministic when viewed from the natural world.  Therefore, I will add the following basic axiom:

  • Axiom of Natural Determinism: ∀x:[ Dx ⇒ Nx ].

The inverse of this axiom is not true: a process can be indeterministic and still be natural.

Note that the most common interpretation of quantum mechanics implies that the universe is not completely deterministic4.  This can be represented by the axiom ∃x(¬Dx).  Of course, ∃x(¬Dx) does not imply ¬Da, but this axiom demonstrates that we cannot rule out ¬Da.

Determinism should not be confused with causality.  A particular set of conditions will produce only a single outcome if the applicable process is deterministic.  An indeterministic but causal process can produce one of many outcomes, but the set of possible outcomes, along with their relative probabilities, must be constant in order for the process to be causal.  In a non-causal process, any possible outcome could result.  For example, consider a measurement of the spin of an elementary particle, in which there is a 50:50 chance that the measurement will read spin up or spin down.  The act of measurement causes the result, but the process is not deterministic, because we cannot predict ahead of time which of the two possible outcomes will occur.  I will implicitly assume that the universe is completely causal.

Is the process by which the mind works deterministic?  If the mind has a supernatural component, then it is not.   As mentioned above, ∃x(¬Dx) does not imply a ¬Da, so the mind can still be deterministic despite an indeterministic world.  Those philosophers who assume that the mind is completely natural differ as to whether or not it is completely deterministic.  Roger Penrose supports an indeterministic mind, and indeed, has hypothesized that quantum mechanics is intrinsic to the operation of the mind5.  Compatibilists (see below for more on this term) such as Daniel Dennett believe that the mind is deterministic, or at least that indeterminism is not a necessary feature of the mind6.

Positions on Free Will
To the best of my knowledge, there are four main positions on free will, as follows:

  • Compatibilism: Free will exists, but is deterministic (Fa & Da)
  • Libertarianism7: Free will exists, but is not deterministic (Fa & ¬Da).
  • Supernaturalism: Free will exists and is supernatural (Fa & ¬Na)
  • Denial: Free will does not exist (¬Fa).

The following table demonstrates how each of these positions fares with respect to the two definitions of free will given above.  The logical equations shown are the result of substituting the corresponding definition of free will into the axiom of the theory.

Table 1 – Theories & Definitions of Free Will

Indeterministic Conclusion Supernaturalistic 
Supernaturalistic Conclusion
Compatibilism Fa & Da ¬Da & Da Inconsistent: Denies that free will is indeterministic. ¬Na & Da ⇒
¬Da & Da
Inconsistent with the supernaturalistic definition due to the Axiom of Natural Determinism.
Libertarianism Fa & ¬Da ¬Da & ¬Da Free will is indeterministic by definition. ¬Na & ¬Da ⇒
¬Da & ¬Da
Consistent with a supernaturalistic free will but does not require it.
Supernaturalism Fa & ¬Na ¬Da & ¬Na⇒
¬Da & ¬Da
Requires an indeterministic world due to the Axiom of Natural Determinism. ¬Na & ¬Na Free will is supernaturalistic by definition.
Denial ¬Fa Da Requires that the universe be deterministic. Na Requires that the will is natural.

Some comments are in order.  The first regards compatibilism.  The central compatibilist thesis is that free will is consistent with a fully natural, deterministic universe.  But as mentioned above, I believe that complete determinism is at odds with the common perception of what free will is.  I would challenge compatibilitist to come up with a viable definition of free will based on unambiguous primitives that is consistent with their thesis.  I believe that compatibilists confuse free will with lack of fatalism, and what they really want to express is that a non-fatalist attitude is consistent with a deterministic world8.  I will discuss fatalism and its relationship to free will below.

The essence of philosophical libertarianism is that free will means exactly that the mind is indeterministic.  This may well be so, but I also believe, as mentioned above, that indeterminism is insufficient for the concept that is normally associated with free will.  It does not seem that a computer with the ability to roll dice and act on the result could be said to have a will.  It is for the same reason that the indeterministic definition of free will seems to me to be inadaquate.  Note also that if the human mind could be demonstrated empirically to be fully deterministic, libertarianism would be refuted.

Supernaturalism is by definition consistent with the supernaturalistic definition of free will.  Indeed, I believe that when most people believe in free will, they believe also in a supernatural component of the will, e.g., an immortal soul.  However, the claim that there is anything supernatural that can affect the natural world has numerous philosophical problems, as discussed in my essay on Naturalism & Theology.

For the reasons just described, I do not believe that either the libertarian or supernatural theory of free will is viable.  Compabitilism is also highly suspect, and could only be made viable by a definition of free will based on more primitive concepts that is consistent with the compatibilist axiom Fa & Da.  Because I know of no such definition, I do not consider compabilism to be viable either.  This leaves only one conclusion, that the Denial view is the correct one: free will, as normally conceived by most people, does not exist.  I will next consider the consequences of this conclusion.

Lack of Free Will vs. Fatalism
As mentioned above, it has been observed that many people confuse free will with fatalism.  However, the questions of whether the mind is indeterministic, supernaturalistic, or free in some sense are questions about the mind as a process.  Fatalism, on the other hand, I see as a normative belief, in particular, the belief that the consequences of our actions do not matter; they have no moral significance9.

The inference from lack of free will to fatalism is often made, but it is an invalid one.  Assume, for example, that your mind is wholly deterministic.  It is processing the information written here (and perhaps other information) about fatalism.  Despite being not free, it will make a decision as to whether or not fatalism is true.  That decision will influence future decisions.  If your mind chooses not to adopt fatalism, then its decisions will be different than if it did.  The knowledge that your mind is not free does not imply it will adopt the position of fatalism.

Indeed, an agent will be better off if it does not adopt fatalism.  Any agent is normally making decisions driven by the desire to raise some level of well-being, either that of itself or others10.  An agent that believes that its decisions cannot influence its level of well-being will execute algorithms whose results are indeed independent of the agent’s well-being.  Thus, an agent that does not adopt the doctrine of fatalism will tend to make decisions to raise its own level of well-being, and thus will be better off.

In conclusion, despite our instincts to the contrary, it appears that by a sufficiently strong definition of free will, our minds are not free.  They may or may not have an indeterministic component, but a lack of determinism is insufficient to qualify as a will.  The fact that our minds are not free does not imply that we should adopt a fatalistic attitude.  We are still morally responsible for the choices that we make.  Even with the knowledge that our minds are not free, we should proceed with business as usual.

End Notes

  1. For a more detailed discussion of agents, see my essay on Ethics.  The term “agent” here is slightly narrower than the term as it is used in that essay, corresponding to those agents that are not “unconscious” in the terminology used there.  I use the single term “agent” here for simplicity.
  2. For a discussion of determinism in physics, see my essay on Quantum Theory.
  3. For a more detailed discussion of naturalism, see my essay on Naturalism & Theology.
  4. The most widely accepted interpretation of quantum theory is the Copenhagen Interpretation, which if adopted, implies that there are some fundamentally indeterministic processes in nature.  The only fully deterministic mainstream interpretation of which I am aware is the Bohm interpretation, but it has many even more undesirable consequences, such as nonlocality and causal paradoxes when combined with relativity theory.  The many-worlds interpretation is also deterministic, but from the standpoint of a single observer is indeterministic, because that observer cannot predict in which of the many worlds he will end up.
  5. Penrose, Roger, The Emporer’s New Mind, Oxford University Press, Oxford, GB (1989).
  6. Dennett, Danial, Elbow Room: The Varieties of Free Will Worth Wanting, The MIT Press, Cambridge, MA (1984).
  7. The term used here is philosophical libertarianism, not to be confused with political libertarianism, which is discussed in my essay on that subject.
  8. The potential confusion between fatalism and determinism was first suggested to me in Harris, Sam, The Moral Landscape, Free Press, New York, NY (2010), pg.105.  Harris in turn references Dennett, Daniel, Freedom Evolves, Penguin Books, New York, NY (2003).
  9. There are certainly other definitions to which the world “fatalist” is applied.  For example, a condemned prisoner may have a fatalistic attitude in that he believes that his fate can only result in one outcome.  However, this definition concerns factors that affect one’s choices that originate from outside the mind, whereas the type of fatalism which I am discussing here involves only the processes that occur within the mind.
  10. At least this is an assumption about agents and rational choice.  For more on this, see my essay on Naturalism in Ethics.

November, 2013


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