Logic and empiricism.

A cup is a unit of measurement, but when cooking I have a container that is ~1 cup. I use this container to measure for most recipes. I also have found that some recipes require "a cup" of something, but the recipe may call for packed, heaping, sifted, or some other requirement. Also, sometimes "a cup" is slightly more or less to achieve the desired taste. Units of measurement are relative to the people measuring. An excellent example is the cubit. A cubit is a unit of measurement described as the length of the forearm, elbow to end of middle finger. This measurement holds great possibility of variability. A meter is defined as the distance light can travel in a vacuum in 1/299792458 of a second. Previously it was defined by a prototype bar that was marked at what would be considered a meter. The meter itself has become more exact, but a meter still holds a level of uncertainty. All units of measure are variable on some level, that is why all technical drawings and plans are plus or minus some acceptable level of variability. The exact amount of water in a cup is variable to some extremely minor degree. Even evaporation must be considered. Empiricism would state that it is nearly impossible for 1 cup of water measured to be the exact same as the next cup of water measured, thus your logical statement that 1 cup of water is the same as another 1 cup of water is not empirically correct. But, given this new information the logical statement would change and thus may prove to be empirical. I present this because empirically logic is not always fact. Logic is a tool to be used in empirical research, but logic itself is not necessarily empirical. There is no conflict between the two unless one assumes that logic itself is always empirical.