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 classical mechanical laws is only an
"adequate" determinism, true for macroscopic objects which are large enough, massive enough, to contain so many elementary particles that the
indeterministic quantum effects of individual average out.
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, in each of which everything is
completely determined!
The Ontological Status of Alternative Possibilities
Whereas
Actualities are
physical events involving
material bodies,
possibilities normally have no material content. They are
immaterial, like our thoughts and ideas. In particular, they are
predictions about the future in a universe with multiple possible futures.
Actualists (from Diodorus to Dennett) are
determinists who believe that the only possible future is the one future that will actually happen.
Quantum Mechanics and Alternative Possibilities
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 those 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
cn = < ψa | φn >.
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
Pn = < ψa | φn >2 = cn2.
These probabilities and their information content are ontologically similar to our thoughts and ideas —
immaterial predictions about future
material events. The astonishing mathematical accuracy of these predictions about the future might appear to put them in the same category as logical statements and mathematical proofs.
But this is not so. Physical theories are only tested
statistically, by comparison to the outcomes of large numbers of identical experiments. Scientific theories are not "proven" true or false, neither mathematically nor logically by reasoned arguments. Information philosophy goes "beyond logic and language" to solve
great problems in philosophy and physics.