You have already used quantity and studied it. You have counted what was on the table as a child. You have trusted a clock, a scale, a graph. Modern schooling often wants to begin there: as if number were the first language of knowledge, and words were unnecessary or at least not fundamental. That is understandable. Measurements can refute a theory but not by themselves alone; a measured quantity cannot, by itself, say what was counted or whether the count was of the same kind of thing twice.
The limitation of purely quantitative reasoning is the one this course makes clear how to overcome. A number that cannot be named cannot be spoken about. A measurement that cannot be stated cannot be checked. The trivium is not aimed at delaying or superseding mathematics. We consider the trivium at length because it lays the truest and most general foundations for all reasoning and therefore for quantitative and mathematical reasoning too. The trivium teaches and exercises students in precisely how something universal like quantity can enter the mind at all.
The quadrivium is the study of quantity and the application of quantity to real things. Classically there are four arts here. Arithmetic treats numbers, multitudes measured by one, that is, discrete quantity. Geometry treats magnitude, the continuous, the line and the figure. Music treats quantity as it is found in sound, a consideration of discrete quantity. Astronomy treats quantity as it is found in the moving heavens, a treatment of continuous quantity.
Studium Institute will provide an exposition of the quadrivium here, just as we have done of the trivium. It will use the same pedagogical pattern as this one has. It will start from modern expectations about number and measure, that they are the first properties of what is real.
Interactive courses in aspects of the arts of the quadrivium are already available on Studium Institute.
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