Underrated: Bernard Bolzano

The little-known Bolzano formed remarkably modern conceptions of logical truth and probability

Peter Simons

The Bohemian polymath Bernard Bolzano (1781–1848) is not so much underrated as unrated. A few historians of mathematics and philosophy aside, he is virtually unknown. Yet in the opinion of a handful of fans, he is not just a good philosopher, but a great one, in my view the finest of the 19th century. So how come he is so little known, and why should he be more highly valued?

Bolzano’s enduring obscurity is due firstly to politics. A professor of religion in Prague from his early twenties, he had the misfortune to be a prominent political and religious liberal during the Napoleonic era and its reactionary aftermath, when the Austrian establishment under Metternich was deeply averse to such dangerous ideas. Bolzano was dismissed in 1820 and forbidden to teach, publish, or practise his vocation as a priest. The major works produced during his enforced leave were published obscurely in Bavaria. After his death, his manuscripts languished untouched for a generation. A critical edition, which will eventually run to over 130 volumes, was not begun until 1969.

Another reason for Bolzano’s obscurity is the extent and style of his work. Freed from university and ecclesiastical duties and cared for by a wealthy admirer, he had the leisure to write. The resulting somewhat dry treatises, on the philosophy of religion and on logic, run to four volumes apiece. Even Bolzano saw the need to abridge them, but never got around to it, not least because he suffered from poor health throughout his life.

What was in those works that merit a revision of reputation? Firstly, Bolzano was not just a philosopher. He was also a talented mathematician, remembered in the names of some theorems. Listed for the chair of mathematics at Prague, he was offered and accepted the chair of religion, considering he could thereby do more good. In his early works on geometry and analysis he was one of the first to stress the need to liberate the foundations of mathematics from extraneous ideas such as motion and time. His posthumously published Paradoxes of the Infinite, dealing with the infinite in mathematics and physics, influenced Georg Cantor, the inventor of set theory and transfinite arithmetic.

Bolzano brought mathematical rigour to his philosophy. He argued the assumptions and inferences justifying particular views should be set out logically and expressed clearly. Realising that traditional logic was not up to this, Bolzano set about single-handedly refashioning and extending logic, defining the concepts required. His principal tool was a conception of abstract propositions and ideas as existing in themselves, independently of thought. Using these, Bolzano created, in his Theory of Science, the first modern semantic treatment of logic: that is, one based on the truth of propositions. Along the way, he formulated astonishingly modern conceptions of logical truth, valid inference, probability and more.

In his ethics and philosophy of religion, Bolzano was a utilitarian, though his grand name for the principle of utility is The Supreme Moral Law. He expressed the utilitarian principle with a clarity unsurpassed until the 20th century: “Always choose from all the actions that are possible for you the one which, all consequences considered, most advances the welfare of the whole, in whatever parts.” Thus his argument for Catholicism is that believing it is the best way to improve the world. While critical of most arguments for the existence of God, he does offer a cosmological argument of his own to the effect that if there is anything, there must be an unconditioned thing—God. The argument fails, but very subtly. Even the point of logic for Bolzano is ethical. Knowledge that is clearly and logically argued for in books is conducive to the general good.

In his practical ethics, Bolzano was egalitarian, ecumenical and anti-racist. His Edifying Sermons, delivered weekly to the students of Prague University, were hugely popular, contributing to his official downfall. In the year of his death, Bolzano welcomed the liberal revolution, but cautioned against the use of violence. His utopia Of the Best State recommends a republic with democratically elected representatives, subject however to potential veto by a council of enlightened elders, not, perhaps, unlike himself. In the interest of equality, Bolzano advocates drastic limitations on private property and inheritance, which lend his vision a disturbingly authoritarian communistic note.

Bolzano’s chief philosophical adversary—his “rubbing post”, as he called him—was Kant. While Bolzano admired and respected the German giant, he considered him terribly wrong in many ways. By contrast, Bolzano thought Hegel so absurdly wrong as to be not worth discussing.

Bolzano was the most accomplished logician between Leibniz and Frege. Where Bolzano scores is in his breadth: few areas of philosophy are left untouched by his clarity. While unlikely ever to be a widely popular thinker, and far from infallible, Bolzano deserves to be much better known and appreciated.

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