Alternative Possibilities are one of the key

requirements for the freedom component of free will, critically needed for

libertarian free will. The 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 "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.

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

c_{n} = < ψ_{a} | φ_{n} >.

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

P_{n} = < ψ_{a} | φ_{n} >^{2} = c_{n}^{2} .