A physical source chosen because the guarantee is about the world rather than the numbers.
Chance
Outcomes not fixed by what preceded them - or by ignorance of what did, which are very different claims.
- Theme
- Cause, time and change
- Tradition
- Cross-tradition
- Term
- τύχη · tuchē
- Term fixed
- c. 330 BC
In plain terms
Two quite different things are called chance.
The first is ignorance. A coin toss is unpredictable because nobody can measure the force, spin and air well enough - but the physics is ordinary, and a sufficiently precise machine tosses heads every time. That kind of chance is a fact about us.
The second is a claim about the world: that some events are not fixed by anything prior, so that even complete knowledge of the present would leave the outcome open. Radioactive decay is the standard candidate.
The practical difficulty is that the two are indistinguishable from outside. A sequence produced by genuine indeterminism and one produced by a process too complex to track look identical, and no test on the output can tell you which you have.
As a philosopher would put it
The standard distinction is between epistemic probability, which measures a degree of belief or ignorance, and objective chance, a feature of the world independent of anyone's knowledge. Classical statistical mechanics uses the first: the underlying dynamics is deterministic and probability tracks what we cannot specify.
Quantum mechanics is where objective chance is at stake, and the interpretations divide precisely here.
On the propensity interpretation, chance is a disposition of a set-up to produce outcomes with certain frequencies. Lewis's Principal Principle connects the two notions by requiring that a rational agent's credence match the known chance, which is the standard bridge between them.
Defining randomness has proved harder than expected. A sequence is not random in virtue of looking disordered; Kolmogorov's definition makes it a matter of incompressibility - a sequence is random if no description of it is shorter than the sequence itself - which is elegant and, for any particular sequence, uncomputable.
Where you meet it
Premium Bonds were introduced in Britain in 1956, and the prize draw needed numbers nobody could predict or influence. ERNIE, the Electronic Random Number Indicator Equipment, ran its first draw in June 1957.
The original machine generated numbers from the thermal noise in neon tubes - a physical process, deliberately chosen so that the output would not be the product of an algorithm anyone could reconstruct. Later versions used transistor noise, and the fifth generation, from 2019, uses quantum optical effects.
Every draw is independently checked by the Government Actuary's Department, which runs statistical tests on the output and will not certify a draw that fails them.
The arrangement is instructive because it takes the philosophical distinction seriously in hardware. A pseudorandom algorithm would produce a sequence passing every statistical test and determined entirely by its seed. The machine is built around a physical source precisely because the state's guarantee is about the world rather than about the appearance of the numbers.
What is actually disputed
Whether objective chance exists.
If the world is deterministic, then all probability is epistemic and chance is a name for ignorance - which is Laplace's position and Einstein's. If quantum indeterminism is real, then some events have objective probabilities and the world is not fixed by its past.
The interpretations of quantum mechanics divide on this and are empirically equivalent, so the question is currently not settled by evidence.
A second problem is what an objective chance could be. A single-case probability - the chance that this atom decays in the next hour - is not a frequency, since there is only one case, and it is not a degree of belief, since it is supposed to be a fact. Propensity accounts posit a disposition and are criticised as naming the phenomenon rather than explaining it. Humean accounts derive chances from the overall pattern of events, which makes the chance depend on the future it is supposed to govern.
Commonly confused with
- Ignorance c. 450 BC A coin toss is unpredictable because of what we cannot measure. Whether anything is unpredictable in principle is a different claim entirely.
- the absence of a cause Aristotle's chance events have causes; what they lack is a purpose or a regular connection, which is a narrower claim than modern indeterminism.
Defined against
- Determinism The pair is exhaustive: either every event is fixed by what precedes it or some are not, and no third option has been made to work
Philosophers
- Aristotle Chance distinguished from spontaneity and from purpose
- Lucretius The swerve, introduced to make freedom possible
- Baruch Spinoza The denial that anything is contingent
- David Hume Probability grounded in habit rather than in the world
Works
- Metaphysics The classical analysis
- On the Nature of Things The atomist swerve
- Ethics The denial of chance
- A Treatise of Human Nature Probability naturalised
- The Logic of Scientific Discovery Propensity, and the interpretation of probability
Schools
- Peripatetic school (Aristotelianism) Where chance is distinguished from purpose
- Atomism Where the swerve is introduced
- Spinozism Where chance is denied
- British Empiricism Where probability becomes epistemic
- Vienna Circle Where the interpretation of probability is formalised
Related concepts
Determinism 1677 · Causation c. 330 BC · Chance c. 330 BC · Fate c. 250 BC · Moral luck 1976
Aristotle distinguishes tuchē, chance in matters of deliberate action, from automaton, spontaneity in nature generally; the modern distinction between epistemic and objective chance is a different cut across the same territory.