# Dictionary Definition

propensity

### Noun

2 a natural inclination; "he has a proclivity for
exaggeration" [syn: proclivity, leaning]

3 a disposition to behave in a certain way; "the
aptness of iron to rust"; "the propensity of disease to spread"
[syn: aptness]

# User Contributed Dictionary

## English

### Pronunciation

### Noun

- a tendency,
preference, or
attraction
- He has a propensity for lengthy discussions of certain favorite topics.

#### Synonyms

#### Translations

- Finnish: taipumus

# Extensive Definition

The propensity theory of probability is one
interpretation of the concept of probability. Theorists who
adopt this interpretation think of probability as a physical
propensity, or disposition, or tendency of a given type of physical
situation to yield an outcome of a certain kind, or to yield a long
run relative frequency of such an outcome. This kind of objective
probability is sometimes called 'chance'.

Propensities, or chances, are not relative
frequencies, but puported causes of the observed stable relative
frequencies. Propensities are invoked to explain why repeating a
certain kind of experiment will generate a given outcome type at a
persistent rate. A central aspect of this explanation is the
Law
of large numbers. This law, which is a consequence of the
axioms
of probability, says that if (for example) a coin is tossed
repeatedly many times, in such a way that its probability of
landing heads is the same on each toss, and the outcomes are
probabilistically independent, then the relative frequency of heads
will (with high probability) be close to the probability of heads
on each single toss. This law suggests that stable long-run
frequencies are a manifestation of invariant single-case
probabilities. Frequentists are unable to take this approach, since
relative frequencies do not exist for single tosses of a coin, but
only for large ensembles or collectives. Hence, these single-case
probabilities are known as propensities or chances.

In addition to explaining the emergence of stable
relative frequencies, the idea of propensity is motivated by the
desire to make sense of single-case probability attributions in
quantum mechanics, such as the probability of decay of a particular atom at a particular time.

The main challenge facing propensity theories is
to say exactly what propensity means. (And then, of course, to show
that propensity thus defined has the required properties.) At
present, unfortunately, none of the well-recognised accounts of
propensity comes close to meeting this challenge.

The first propensity theory, due to philosopher
Karl
Popper, noted that the outcome of a physical experiment is
produced by a certain set of "generating conditions". When we
repeat an experiment, as the saying goes, we really perform another
experiment with a (more or less) similar set of generating
conditions. To say that a set of generating conditions has
propensity p of producing the outcome E means that those exact
conditions, if repeated indefinitely, would produce an outcome
sequence in which E occurred with limiting relative frequency p.
For Popper then, a deterministic experiment would have propensity 0
or 1 for each outcome, since those generating conditions would have
same outcome on each trial. In other words, non-trivial
propensities (those that differ from 0 and 1) only exist for
genuinely indeterministic experiments.

Popper's propensities, while they are not
relative frequencies, are yet defined in terms of relative
frequency. As a result, they face many of the serious problems that
plague frequency theories. First, propensities cannot be
empirically ascertained, on this account, since the limit of a
sequence is a Tail event,
and is thus independent of its finite initial segments. Seeing a
coin land heads every time for the first million tosses, for
example, tells one nothing about the limiting proportion of heads
on Popper's view. Moreover, the use of relative frequency to define
propensity assumes the existence of stable relative frequencies, so
one cannot then use propensity to explain the existence of stable
relative frequencies, via the Law of large numbers.

A number of other philosophers, including David
Miller and Donald Gillies, have proposed propensity theories
somewhat similar to Popper's, in that propensities are defined in
terms of either long-run or infinitely long-run relative
frequencies.

Other propensity theorists (e.g. Ronald Giere) do
not explicitly define propensities at all, but rather see
propensity as defined by the theoretical role it plays in science.
They argue, for example, that physical magnitudes such as electrical
charge cannot be explicitly defined either, in terms of more
basic things, but only in terms of what they do (such as attracting
and repelling other electrical charges). In a similar way,
propensity is whatever fills the various roles that physical
probability plays in science.

What roles does physical probability play in
science? What are its properties? One central property of chance is
that, when known, it constrains rational belief to take the same
numerical value. David Lewis called this the Principal Principle, a
term that philosophers have mostly adopted. For example, suppose
you are certain that a particular biased coin has propensity 0.32
to land heads every time it is tossed. What is then the correct
price for a gamble that pays $1 if the coin lands heads, and
nothing otherwise? According to the Principal Principle, the fair
price is 32 cents.

[more to come ...]

which is very defined and is one of a kind.

## See also

## References

- The Self and Its Brain: An Argument for Interactionism. Popper, Karl and Eccles, Sir John. 1977, ISBN 0415058988
- The Propensity Interpretation of the Calculus of Probability and of the Quantum Theory. Popper, Karl. In Obeservation and Interpretation. Buttersworth Scientific Publications, Korner & Price (eds.) 1957. pp 65-70.
- The Logic of Scientific Discovery. Popper, Karl. Hutchinson, London. 1959
- Quantum Mechanics without "The Observer". Popper, Karl. In Quantum Theory and Reality. Springer-Verlag, Berlin, Heidelberg, New York. Bunge, M. (ed.). 1967

propensity in German: Propensität

# Synonyms, Antonyms and Related Words

a thing for, affinity, an ear for, an eye
for, animus, aptitude, aptness, bent, bias, capacity for, cast, character, conatus, conduciveness, constitution, delight, diathesis, disposition, eagerness, eccentricity, fancy, fascination, favor, feeling for, felicity, flair, genius for, gift for,
grain, idiosyncrasy, inclination, inclining, individualism, innate
aptitude, kidney,
leaning, liability, liking, make, makeup, mental set, mettle, mind, mind-set, mold, mutual affinity, mutual
attraction, nature,
partiality, penchant, predilection, predisposition, preference, prejudice, probability, proclivity, proneness, readiness, sensitivity to,
set, slant, soft spot, stamp, strain, streak, stripe, susceptibility, sympathy, temper, temperament, tendency, tropism, turn, turn for, turn of mind,
twist, type, warp, weakness, willingness