# Alternative Possibilities [Alternative Possibilities](https://www.informationphilosopher.com/freedom/alternative_possibilities.html) are one of the key [requirements](https://www.informationphilosopher.com/freedom/requirements.html) for the freedom component of free will, critically needed for [libertarian](https://www.informationphilosopher.com/freedom/libertarianism.html) free will. They allow for what [William James](https://www.informationphilosopher.com/solutions/philosophers/james/) called open and ambiguous futures. The old page on [Harry Frankfurt](https://www.informationphilosopher.com/solutions/philosophers/frankfurt/)'s denial of the _Principle of Alternate Possibilities_ (PAP) can be found [here](https://www.informationphilosopher.com/freedom/alternative_possibilities.html). 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](https://www.informationphilosopher.com/solutions/philosophers/diodorus/) 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](https://www.informationphilosopher.com/afterwords/glossary/#Master_Argument) is a set of propositions designed to show that the [actual](https://www.informationphilosopher.com/afterwords/glossary/#Actualism) 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](https://www.informationphilosopher.com/solutions/philosophers/dennett/), for whom [determinism](https://www.informationphilosopher.com/freedom/determinism.html) 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](https://www.informationphilosopher.com/freedom/necessity.html) 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](https://www.informationphilosopher.com/freedom/). In modern times it is often contrasted with mere [chance](https://www.informationphilosopher.com/freedom/chance.html). [Causality](https://www.informationphilosopher.com/freedom/causality.html) is often confused with [necessity](https://www.informationphilosopher.com/freedom/necessity.html), 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](https://www.informationphilosopher.com/freedom/adequate_determinism.html). In modern philosophy, modal theorists like [David Lewis](https://www.informationphilosopher.com/knowledge/philosophers/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](https://www.informationphilosopher.com/solutions/scientists/everett/). Everett's [interpretation](https://www.informationphilosopher.com/introduction/physics/interpretation/) of quantum mechanics replaces the ["collapse" of the wave function](https://www.informationphilosopher.com/solutions/experiments/wave-function_collapse/) with a "splitting" of this world into multiple worlds, in each of which everything is [completely determined!](https://www.informationphilosopher.com/freedom/determinism.html) According to the [Schrödinger](https://www.informationphilosopher.com/solutions/scientists/schrodinger/) 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](https://www.informationphilosopher.com/freedom/probability.html) given by the square of the "probability amplitude." One very important kind of interaction is a [measurement](https://www.informationphilosopher.com/problems/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](https://www.informationphilosopher.com/freedom/certainty.html)). However, if the system is prepared in an arbitrary state ψa, it can be represented as being in a linear combination of the system's basic eigenstates φn. ψa = Σ cn | n >. where cn = < ψa | φn >. The system ψa is said to be in "superposition" of those basic states φn. The probability Pn of its being found in a particular state φn is Pn = < ψa | φn >2 = cn2 .