Simanaitis Says

On cars, old, new and future; science & technology; vintage airplanes, computer flight simulation of them; Sherlockiana; our English language; travel; and other stuff


YESTERDAY, WE SAW Englishman George Boole progress gradually from a “petty shopkeeper’s son” to an aspiring mathematician. His The Mathematical Analysis of Logic, 1847, become a core of pure mathematics, of mathematical philosophy, not just mathematical application to worldly matters. Today, Part 2’s tidbits continue from E.T. Bell’s fine Men of Mathematics.

Cross-channel Rivalries. Evolution of mathematical thought accompanied national rivalries among European academics. Boole, having previously taught himself some Latin and Greek and having also learned French, German, and Italian, was prepared for this.

Bell’s description of rivalries is particularly entertaining: “The fact is that British mathematicians have often serenely gone their own way, doing the things that interested them personally as if they were playing cricket for their own amusement only, with a self-satisfied disregard for what others, shouting at the top of their scientific lungs, have assured the world is of supreme importance.” 

In a sense, what came to be known as Boolean Algebra was an example of this independent thinking.

A Philosophy of Mathematics. Bell cites another matter in the first half of the nineteenth century, “which raised a devil of a din in its own day but which is now almost forgotten except by historians of pathological philosophy.”

Sir William Hamilton, 9th Baronet, 1788–1856, Scottish metaphysician.

To mathematicians, the Scottish philosopher Sir William Hamilton is usually referred to as the other Hamilton. (We’re more familiar with the Irish Sir William Hamilton, of quaternion fame here at SimanaitisSays.) Bell also cites Georg Wilhelm Friedrich Hegel, German philosopher considered one of the most important figures in German idealism, and Hermann Lotze, German philosopher and logician. 

Above, Georg Wilhelm Friedrich Hegel, 1770–1831, German philosopher, a fundamental figure in Western philosophy. Portrait by Jakob Schlesinger. Below, Rudolf Hermann Lotze, 1817–1881, German philosopher and logician. He also had a medical degree and was well versed in biology

“Now,” Bell wrote, “if there is anything more obtuse mathematically than a thick-headed Scotch metaphysician it is probably a mathematically thicker-headed German metaphysician. To surpass the ludicrous absurdity of some of the things the Scotch Hamilton said about mathematics we have to turn to what Hegel said about astronomy, or Lotze about non-Euclidian geometry. Any depraved reader who wished to fuddle himself can easily run down all he needs.”

Uh, thanks; l take Bell’s word for it.

Back to Boole. Bell wrote (back in 1937, by the way) that “Boole reduced logic to an extremely easy and simple type of algebra. ‘Reasoning’ upon appropriate material becomes in this algebra a matter of elementary manipulations of formulas far simpler than most of those handled in the second year of school algebra. Thus logic itself was brought under the sway of mathematics.”

George Boole, 1815–1864, English mathematician, philosopher, and logician. Largely self-taught, he is best known for The Laws of Thought, 1854, whence evolved Boolean Algebra.

To paraphrase Bell, one can easily run down all that one wants at Wikipedia’s article on Boolean Algebra. Also, for a taste of Boolean operations, see “GMax, the Schmid LSR—and Set Theory” here at SimanaitisSays  

“The daring originality of Boole’s whole project needs no signpost,” Bell wrote. “It is a landmark in itself.” All that one needs to confirm this is to turn on a digital device. ds

© Dennis Simanaitis,, 2021  


  1. muunyayo
    October 26, 2021

    Reblogged this on muunyayo .

  2. muunyayo
    October 26, 2021

    Great insight!!

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: