Cambridge change

A Cambridge change is a philosophical concept of change according to which an entity x has changed if and only if there is some predicate F that is true (not true) of x at a time t1 but not true (true) of x at some later time t2.

The term Cambridge change was coined by Peter Geach in the late 1960s, in reference to Russell and McTaggart, philosophers active at Cambridge University.

Suppose that at t1, person A is 180 cm tall and person B is 175 cm tall, while at time t2 A is still 180 cm tall but B has grown to be 185 cm tall. Since the predicate `is taller than B' is true of A at t1 but not true of A at t2, A has changed according to the Cambridge change definition of "change"---he has gone from being taller than B to not being taller than B.

Intuitively, however, it is only person B, and not person A, who has changed: B has grown by 10 cm, but A's height has stayed the same. This problem with Cambridge changes is usually thought to call for a distinction between intrinsic and extrinsic, or natural and non-natural, properties. Given such a distinction, it is possible to define "real" change by requiring that the respective predicates express intrinsic properties, like being 175 cm tall, rather than an extrinsic property, like being taller than B.

But this assumes that there "really" are strictly unary (non-relational) properties that, as such, are thus intrinsic. Namely, a property is intrinsic if and only if it is actually (really, analytically, fundamentally, necessarily, ontologically) unary.

But imagine that all "meter sticks" as of time "t2" have contracted at a rate such that B's height at time "t2" would be measured as having increased by 10 cm. Imagine further that A's height has actually (really) shrunk so that it would be measured with a respectively shrinking meter stick as remaining constant from time "t1" to time "t2".

Intuitively, B's height will have remained the same whereas A's height and all ways of measuring height will have changed. Really, it is A's height and all ways of measuring height that will have changed. The problem with the notion of "Cambridge change" is its failure to acknowledge that B's or anything else's height is relational (relative to ways of measuring height). "Height" is thus not unary and thus is extrinsic, not intrinsic.

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