Alternative Possibilities are one of the key requirements for the freedom component of free will, critically needed for libertarian free will. They allow for what William James called open and ambiguous futures. The old page on Harry Frankfurt's denial of the Principle of Alternate Possibilities (PAP) can be found here. This Possibilities page is now about the philosophical difference between "possibilities" (especially those never realized) and the one realized "actuality."

The existential and ontological status of mere "possibilities" has been debated by philosophers for many centuries. Diodorus Cronus dazzled his contemporaries in the fourth century BCE with sophisticated logical arguments, especially paradoxes, that logically "proved" there could be only one possible future.

Diodorus' Master Argument is a set of propositions designed to show that the actual is the only possible and that some true statements about the future imply that the future is already determined. This follows logically from his observation that if something in the future is not going to happen, it must have been that statements in the past that it would not happen must have been true.

Modern day "actualists" include Daniel Dennett, for whom determinism guarantees that the actual outcome is and always was the only possible outcome. Dennett, as dazzling as Diodorus, cleverly asks "Change the future? From what to what?"

The ancient philosophers debated the distinction between necessity and contingency (between the a priori and the a posteriori). Necessity includes events or concepts that are logically necessary and physically necessary, contingency those that are logically or physically possible. In the middle ages and the enlightenment, necessity was often contrasted with freedom. In modern times it is often contrasted with mere chance.

Causality is often confused with necessity, as if a causal chain requires a deterministic necessity. But we can imagine chains where the linked causes are statistical, and modern quantum physics tells us that all events are only statistically caused, even if for large macroscopic objects the statistical likelihood approaches certainty for all practical purposes. The apparent deterministic nature of physical laws is only an "adequate" determinism.

In modern philosophy, modal theorists like David Lewis discuss counterfactuals that might be true in other "possible worlds." Lewis' work at Princeton may have been inspired by the work of Princeton scientist Hugh Everett III. Everett's interpretation of quantum mechanics replaces the "collapse" of the wave function with a "splitting" of this world into multiple worlds.

According to the Schrödinger equation of motion, the time evolution of the wave function describes a "superposition" of possible quantum states. Standard quantum mechanics says that interaction of the quantum system with other objects causes the system to collapse into one of the possible states, with probability given by the square of the "probability amplitude."

One very important kind of interaction is a measurement by an "observer."

In standard quantum theory, when a measurement is made, the quantum system is "projected" or "collapsed" or "reduced" into a single one of the system's allowed states. If the system was "prepared" in one of these "eigenstates," then the measurement will find it in that state with probability one (that is, with certainty).

However, if the system is prepared in an arbitrary state ψ_a, it can be represented as being in a linear combination of the system's basic eigenstates φ_n.

where

The system ψ_a is said to be in "superposition" of those basic states φ_n. The probability P_n of its being found in a particular state φ_n is