Determinism and free will

In everyday life, all of us feel that we are free, and only rarely do we question this perception: we have the impression that every action we take and every word we speak originates from our will.

In common sense, free will is the faculty to choose among different options spontaneously and not imposed by external factors.

But are we sure we are truly free?

In the debate on free will, a classic starting point is to consider Newtonian physics and its deterministic framework. According to this perspective, the universe follows rigorous and predictable physical laws: it is like a gigantic mechanical clock, where every event is the consequence of a previous state. During the Enlightenment, from Descartes to Laplace, the idea took hold that, with the right information and adequate mathematical tools, one could in principle predict the entire evolution of the cosmos.

At the base of this perspective lies the combination of initial states and deterministic laws, which produces a single, pre-established evolution of the system: each link derives from the previous one. In Newtonian formalism this translates into ordinary differential equations which, if we knew the initial conditions with absolute precision, would provide the state of the system at every other instant, both in the past and in the future.

From this follows an immediate critique of the possibility of free will: a genuinely free action would seem to have to “break” the causal chain in some way. But the Newtonian picture offers no room for this kind of break: everything is connected in a continuum of causes and effects that leaves no gaps for indeterminacy.

If this still does not make us understand the problem, then we must reflect on the fact that we too, and in particular our brain, are made of the same atoms that make up the rest of the universe. For this reason, in this deterministic view of the world, we can see our brain as a finite-state automaton (an input-output machine), whose output at time t is perfectly determined by the state of the universe at time t-1 (inputs from 1 to N) and by the internal state of our brain at time t-1.

In this scenario, free will seems suffocated: if everything is already determined by natural laws and initial conditions, what space is left for our personal choices?

Laplace’s demon and classical physics

An emblematic icon of this view is “Laplace’s demon”: a hypothetical intelligence capable, at a given instant, of knowing the position and velocity of all particles in the universe, together with the physical laws that govern their evolution. This entity, by virtue of an “infinite” computational power, could reconstruct the entire history of the cosmos, past and future, in a deterministic way.

From this comes a feeling of inevitability: if everything is in principle calculable, then our life, our actions, and even our thoughts would be entirely “written” into natural laws. The very idea of freedom of choice would seem to be reduced to an illusion, because every choice would already be implicit in the previous state and in the laws that connect it to the subsequent state.

The illusion of freedom

Even within this deterministic framework, our subjective experience leads us to perceive ourselves as “free.” Two main factors contribute to this “illusion” (or presumed illusion).

Chaos theory

Classical physics prescribes that everything is calculable, but in practice the precision with which we can measure initial conditions is finite. Deterministic chaos (double pendulum, Lorenz equations, meteorology) makes clear that even in a strictly deterministic scenario, predictability can be limited. Small differences in initial conditions are amplified exponentially, making an exact long-term calculation of the future effectively impossible.

Chaos theory can make the idea of infallible prediction (Laplace-style) very fragile, but it does not introduce an authentic violation of causal chains. The evolution of the system remains perfectly determined by the laws that govern it, even if we are unable to track its evolution.

Therefore, complexity and practical unpredictability do not amount to metaphysical freedom. A planet or a double pendulum appears “chaotic,” but it is still constrained by its equations. However, even in a classically deterministic universe, our experience of unpredictability could be enough to leave us with the impression (or the illusion, if we wish) that we can “decide” among different alternatives.

Time symmetry

Classical physics (and parts of contemporary physics) shows that fundamental laws are time-reversible: the equations do not change if we consider time flowing “forward” or “backward.” In other words, at a purely mathematical level, past and future are not distinguished by the laws. Yet, in everyday life:

We perceive the past as fixed: we know what has been, we have documents, memories…
We perceive the future as open: unknown and unpredictable.

This difference between a “determined” past and an “uncertain” future arises not so much from a structural difference in physical laws, but from an epistemic asymmetry:

We have access to the history of what happened;
We do not have (in general) complete or certain access to what will happen.

Complicating matters is the thermodynamic arrow of time: entropy increases and this creates an irreversible “course” of events. As a consequence, our knowledge of the past is immensely more solid than our knowledge of the future. This ignorance about tomorrow fuels the conviction that we “can act in different ways” to build different futures.

This ignorance, combined with the inability to predict infallibly, would produce the impression of freedom.

In essence, our epistemic limitation creates the sensation that the future is indeterminate, even if the fundamental equations do not really establish an ontological difference between past and future. The illusion therefore derives from our non-omniscient position: not seeing a single obligatory evolution makes us confuse the impossibility of predicting with the possibility of choosing.

Ways to preserve the concept of Free Will

From what we have said so far, there are two main constraints that prevent us from being free:

The definition of free will as the possibility of choosing among multiple options freely, incompatible with a strongly deterministic universe.
The apparently deterministic structure of the universe in which we live.

To challenge the absence of free will, we must therefore try to modify or prove the inaccuracy of at least one of the previous concepts.

Modifying the definition of free will: compatibilism

Many philosophers have proposed compatibilist positions. According to these authors, the notion of “free will” should not be confused with the “metaphysical possibility of violating physical laws”; rather, it is tied to the agent’s capacity to act in accordance with their desires, motivations, and reflections without external coercion.

In compatibilism, the concept of choice does not imply that you could have chosen otherwise in an absolute sense (indeterministic freedom). Instead, choice is seen as the result of your preferences and reasons at a given moment. You are free as long as:

The action reflects what you truly want to do.
There is no external coercion or interference.

If you had desired or wanted something different, then you would have acted differently, but your desires are the result of causes that precede them.

For example, imagine a person who decides to drink a glass of water:

The desire to drink is determined (they are thirsty, the body requires hydration, etc.).
The person drinks without being forced or threatened.
Even though the desire and the action are determined by previous causes (thirst, biology), the action is considered free because it arises from their will.

This means that, unless you are forced in your actions by other individuals or external causes, you can still be held responsible for your actions even though they are the product of the deterministic evolution of reality, because your desires are aligned with that deterministic evolution, since you yourself are part of this reality.

Loopholes in strong determinism

a. Quantum mechanics

The advent of quantum physics revolutionized the idea of a completely determined universe in the classical sense. At the heart of this revolution is the wave function Ψ, a mathematical tool that describes probabilistically the state of a subatomic system (for example, an electron).

Ψ contains all possible information about the system: if an electron is in an atom, its wave function describes all “probable” positions in which you might find it.

Illustrating the behavior of the wave function is the Schrödinger equation, which provides information about the possible energies of the system.

What does it mean that the wave function “collapses”?

Before measurement the electron is not at a single defined point, but in a superposition of possible states.
During measurement: the wave function “collapses,” that is, it “selects” one of the possible outcomes. Suddenly, one obtains a specific value (for example, the exact position or the energy level of the electron).
After measurement the wave function updates and reflects that the electron is now “fixed” in that observed condition.

This collapse is apparently indeterministic: we cannot know a priori which of the possible outcomes will be selected, but only the probability with which each will occur.

There are different possible interpretations of this phenomenon:

Copenhagen interpretation: posits an indeterministic collapse, thus denying a rigid classical determinism.
Many-Worlds: keeps the Schrödinger equation as the only universal law (therefore deterministic), but claims that every measurement outcome is realized in a different branch of the universe. Here “total” determinism exists, but at the cost of postulating infinitely many parallel worlds.

This plurality of interpretations shows that quantum physics did not abolish determinism all at once, but made it more complex, introducing scenarios in which evolution may or may not be deterministic depending on the interpretation adopted.

And above all, even if quantum indeterminacy were real, it does not automatically restore genuine freedom or moral responsibility. Random events, by themselves, do not guarantee a self-determining will: if we “roll a quantum die” to decide, we are not really “choosing freely.”

b. General relativity and singularities

Einstein’s general relativity is in fact a classical and deterministic theory in its basic equations.

However, relativity theory allows for the existence of singularities, that is, points or regions of spacetime in which physical quantities (such as energy density or spacetime curvature) become infinite, and Einstein’s equations cease to be defined.

Singularities can arise in specific solutions of Einstein’s equations, as in the case of black holes or the Big Bang.

There are two types of singularities:

Hidden singularities (black hole singularities): they lie inside an event horizon, which prevents such singularities from directly influencing the outside.
Naked singularities: singularities that are not hidden by an event horizon, allowing them to have effects on the external universe. These singularities could threaten determinism, since they would entail unpredictable phenomena.

General relativity therefore does not guarantee determinism in the strict sense. To preserve a deterministic view of the universe, the following additional hypotheses are needed:

Topological regularity hypothesis: it is assumed that spacetime has no naked singularities and is globally well-defined.
Validity of cosmic censorship: if all singularities are hidden inside event horizons, determinism is safe outside those regions.

However, such assumptions are widely accepted by physicists, so this would not seem to save the notion of free will.

Conclusions

The most plausible hypothesis is that free will in the metaphysical sense does not exist. This, however, does not make the assumption of responsibility superfluous: although our intentions are part of the causal chain that made us what we are, it remains sensible to attribute to individuals responsibility for actions that reflect their will and their desires.

If I had desired or wanted something different, then I would have acted differently, but my desires are the result of causes that precede them.

Angelo Antona, 9 AUGUST 2025