On the indeterminacy of the meter

Abstract

In the International System of Units (SI), ‘meter’ is defined in terms of seconds and the speed of light, and ‘second’ is defined in terms of properties of cesium 133 atoms. I show that one consequence of these definitions is that: if there is a minimal length (e.g., Planck length), then the chances that ‘meter’ is completely determinate are only 1 in 21,413,747. Moreover, we have good reason to believe that there is a minimal length. Thus, it is highly probable that ‘meter’ is indeterminate. If the meter is indeterminate, then any unit in the SI system that is defined in terms of the meter is indeterminate as well. This problem affects most of the familiar derived units in SI. As such, it is highly likely that indeterminacy pervades the SI system. The indeterminacy of the meter is compared and contrasted with emerging literature on indeterminacy in measurement locutions (as in Eran Tal’s recent argument that measurement units are vague in certain ways). Moreover, the indeterminacy of the meter has ramifications for the metaphysics of measurement (e.g., problems for widespread assumptions about the nature of conventionality, as in Theodore Sider’s Writing the Book of the World) and the semantics of measurement locutions (e.g., undermining the received view that measurement phrases are absolutely precise as in Christopher Kennedy’s and Louise McNally’s semantics for gradable adjectives). Finally, it is shown how to redefine ‘meter’ and ‘second’ to completely avoid the indeterminacy.