Scientific Treatises

Overview

About two hundred pages, the scientific and mathematical writings of Blaise Pascal, composed between 1647 and 1665 and gathered under this heading in the Great Books set. They include Pascal’s account of the experiments on the vacuum and his preface on the authority of the ancients in science.

They also include the treatises on the equilibrium of liquids and the weight of the mass of the air, which established hydrostatics, the essay on the geometrical spirit and the art of persuasion, the treatise on the arithmetical triangle with its use of mathematical induction, and the 1654 correspondence with Fermat that founded the theory of probability.

What happens

The vacuum experiments. Pascal recounts his experiments on the vacuum, directly testing whether a genuine vacuum could exist against the prevailing Aristotelian consensus that nature abhors one, gathering empirical evidence through careful experimental design.

The preface on ancient authority. Pascal’s accompanying preface on the authority of the ancients in science argues explicitly that genuine scientific progress requires testing inherited authority against actual experiment rather than simply deferring to received tradition.

Establishing hydrostatics. The treatises on the equilibrium of liquids and the weight of the mass of the air establish hydrostatics as a systematic mathematical science, giving what became known as Pascal’s law its rigorous theoretical foundation.

The geometrical spirit and persuasion. The essay on the geometrical spirit and the art of persuasion addresses how mathematical reasoning’s own rigor might inform methods of argument and persuasion more broadly, connecting Pascal’s scientific and rhetorical concerns.

The arithmetical triangle and mathematical induction. The treatise on the arithmetical triangle develops this mathematical structure with systematic use of mathematical induction, giving this proof technique one of its earliest rigorous articulations.

Correspondence with Fermat on probability. The 1654 correspondence with Fermat, working out how to fairly divide stakes in an interrupted game of chance, founds the mathematical theory of probability, a genuinely novel framework for reasoning about uncertainty.

How to read it

Read Pascal’s vacuum experiments and his preface on ancient authority together as a coordinated challenge to inherited scientific tradition; the experiments provide the empirical evidence while the preface supplies the explicit methodological argument for why such testing matters.

Pay close attention to how the treatises on liquid equilibrium and air pressure establish hydrostatics as genuine mathematical science; Pascal’s law emerges here with systematic rigor that shaped subsequent physics and engineering well beyond his own seventeenth-century context.

Notice how the correspondence with Fermat, prompted by a practical gambling question about dividing interrupted stakes, founds an entirely new mathematical framework for reasoning about uncertainty, one of intellectual history’s most productive examples of practical problems generating theoretical breakthrough.

Consider the treatise on the arithmetical triangle’s systematic use of mathematical induction as a foundational contribution to mathematical method whose influence considerably outlasted the specific triangle it was originally developed to analyze.

Read these treatises alongside Pascal’s own Pensées to see how the rigorous experimental and mathematical mind evident throughout this scientific collection relates to the more explicitly religious and philosophical concerns he would pursue in his later, unfinished apologetic work.

Questions it raises

• Does Pascal’s explicit argument in the preface on ancient authority, that scientific progress requires testing tradition against experiment, represent a genuinely novel methodological position for his period, or does it primarily formalize an approach already implicit in earlier natural philosophy?
• How did the practical origin of probability theory, in a gambling question about dividing interrupted stakes, shape the mathematical framework Pascal and Fermat developed? Does this origin reveal something about how abstract mathematical theory often emerges from concrete practical problems?
• What does Pascal’s systematic use of mathematical induction in the arithmetical triangle treatise suggest about the relationship between his mathematical and scientific work more broadly? Does this proof technique connect to his experimental methodology in the vacuum studies?
• How do the hydrostatics treatises’ mathematical rigor compare to the more empirical, experimental approach of the vacuum studies? Does Pascal’s scientific work reveal a consistent methodology, or does it draw on genuinely different modes of reasoning depending on the problem at hand?
• Given that these treatises span roughly two decades of Pascal’s relatively short life, what does this range suggest about the breadth of his scientific and mathematical interests before his later turn toward more explicitly religious and philosophical writing?
• What does the essay on the geometrical spirit and the art of persuasion suggest about Pascal’s own understanding of the relationship between mathematical rigor and effective argument? Does this connection between scientific and rhetorical method anticipate his later apologetic writing?