The fact that at any instant in time uncountable trillions or quadrillions of individual water molecules are either entering or leaving the ocean makes the prospect of measuring the number of water molecules in the Atlantic Ocean absolutely impossible. The same observation applies to the prospect of counting every single grain of sand along the vast Atlantic Ocean shores.
However, neither Thorndike nor Ludlow would ever have argued that the Atlantic Ocean does not exist. Therefore, even at the macro level of ordinary matter (i.e. individual water molecules and grains of sand) the only defensible interpretation of the Thorndike/Ludlow expression is that it presumes the same concept as expressed by Galton. In that regard, there is no question that an unquantifiable phenomenon may indeed exist notwithstanding its defiance of measurement. the, the meaning of the phrase "If it exists, it can be measured; if it can't be measured, it doesn't exist" would be precisely what Galton argued in 1879: that no proposed volume of the ocean at the level of individual water molecules can be considered scientific simply because there are too many variables capable of being accounted for.
In fact, the physical world around us provides equally illustrative examples that refute the absolute interpretation of the Thorndike/Ludlow expression. Every cement structure consists of a finite number...
None of these can be measured accurately yet they all exist.
At the micro level, the absolute interpretation of the Thorndike/Ludlow position is absolutely false, by virtue of the Heisenberg uncertainty principle according to which the mere act of performing a measurement necessarily changes that which is being measured (Feynman, 1995; Hawking, 2002). Quantum uncertainty is understood by physicists to preclude any simultaneous accurate measurement of the relative position of a subatomic particle in space and the relative velocity of its motion. The Thorndike/Ludlow position applied to the quantum world would, therefore, preclude the existence of anything. Ultimately, it would seem that the Thorndike/Ludlow version of Galton's proposition is excessively narrow and all but meaningless without extraneous supposition.
