How "Quantity" Disappeared from Philosophies of Measurement: Perspectives from 19th Century Sciences

This dissertation explores how "quantity" was reconceptualized in the context of 19th century experimental sciences. In canonical works of philosophy by Aristotle, Descartes or Kant, "quantity" serves as the link between mathematics and its application in the empirical domain. The conception that "quantities" are composed out of equal, additive units is based on the archetypical geometrical magnitudes and its part-whole structure. Despite the fact that measurement techniques in most experimental sciences involve much more complex conceptual and practical operations than counting units, the old conception of "quantity" continued to play a crucial role in philosophers and scientists' attempt to explain how mathematics is applied well into the 19th century. In the second half of the 19th century, philosophically minded scientists shifted their attention away from defining the generalized "quantity" to reflecting on the methods and foundation of the measurement process. As they incorporated considerations of experimental work into their philosophical thinking, they highlighted the role of measurement operations, instruments, and the underlying hypotheses and laws in constituting the meaning of every quantitative concept. Even length and time—the most elementary quantities known to mankind—are not a priori quantitative, but rest on certain assumptions underlying the measurement process carried over from experience. This shift of attention led to the disappearance of "quantity" with a fixed, generalized definition from philosophical writings concerning measurement from late 19th century onward.