Life of Leibniz

1. Biographical.  Born July 1, 1646.  Lutheran family.  Father: Notary, Vice Chairman of philosophy, professor of moral philosophy.  Married three times (1st wife gave him two children and died, 2nd died childless).  Father’s third wife was orphaned at 11, brought up by a law professor, had two children: Leibniz and a sister. 

Leibniz was an eager student.  Complaints he read things beyond his age.  Complaints settled by letting him into father’s library at 8.  Read Latin classics and Fathers.  At 15, entered U. of Leipzig.  Bachelor’s dissertation on individuation.  He eventually specialized in law.  Master’s degree at 17, dissertation on legal questions like whether people asleep are “present” and whether bees are wild, claiming we need philosophy to settle things.  Mother died soon.  Intrigues over doctoral degree, given that it led to faculty appointments.  At 20, got doctorate in law (U. of Altdorf) on “difficult cases”.  Thought law always had answers, though sometimes the answers required philosophy.  Declined academic post, thinking that reform of sciences could best be done outside of university. 

• Leibniz never married.  A later biographer ascribed an illegitimate child to him, but Leibniz’s whereabouts do not match the likely whereabouts of the conception.
• Worked all his life in the service of various German noblemen, on all kinds of political, genealogical and other projects.  At the time, the Holy Roman Empire was ruled by an Emperor, who was elected by a number of Electors (eight, then nine).  Eventually L ended up living in Hanover.  Most of his life, L served under the Dukes of Hanover, who during his tenure became Electors.  He wasn’t too happy to do this: He would rather have been a paid member of the French Royal Society, but when he was interested in this, the feeling was that there were too many foreigners there.
• And eventually the Elector of Hanover became King George I of England.  L in his lifetime rose in the service from Librarian and Councilor, to Privy Councilor and eventually even to a Privy Councilor to the Emperor of the Holy Roman Empire.  He was a commoner, though on occasion he styled himself as von Leibniz or de Leibniz.  When he was appointed as Imperial Privy Counselor, he wrote a draft of the document appointing him, and called himself “von Leibniz” there.  But the “von” was removed throughout.

2. Chemistry.  Very early, became member of alchemical society.  Later claimed this was based on a spoof letter.  He might have lied about that, though.

3. Political contributions.  Various projects:

• Earliest political work was in trying to get a German nobleman elected as King of Poland.  In working for the campaign, L used a method he would use over and over: Writing a pamphlet, supposedly by a Polish nobleman, including arguments.
• The Egyptian project.
• Making a case for a ninth elector, especially a Protestant.
• The genealogical work.  This was his official occupation, his excuse.  He eventually put out a handful of volumes taking the history up to the early 11th century.  Lots of complaints from his Elector over how slowly the work was going and how much L was working on other projects.

4. Other contributions.

• Family services like arranging education.  E.g., for a nobleman’s 17-year-old son he arranged a course of education that would busy him from 6 am to 10 pm (with some breaks).  It didn’t work since the young man didn’t want to study.
• Mechanical calculator that could add, subtract, multiply and divide.  This made people sit up and take notice of him.
• Correspondence, often through noble intermediaries, with the most famous people of his time, like Arnauld.
• Around 1672, he visited Spinoza and had long conversations with him.
• Mining project.  In the Harz mountains.  Hoped his improvements to mining operations would generate lots of money for himself, his Duke and for a proposed German scientific society.  He designed new pumps that ran on windpower for draining the mines.  This solved the problem of inadequate drainage in the season in which the waterpower-based pumps failed.  Much time and money went into this.  The Bureau of Mines didn’t like him, since he wasn’t a specialist.  Moreover, he forgot to check how much wind there was.  Whoops.  He came up with an alternate design that could run on less wind, but people weren’t that interested by then in his stuff, it looks like.
• Poetry for all occasions.  Satires of kings, such as Louis le Grand. 

5. Mathematics:

• Invented calculus.  So did Newton.  L’s notation prevailed.  Big fight over priority.  Eventually, L was accused of stealing N’s ideas, and L reciprocated the accusation.  The evidence against L was that N had sent him some letters around the time L was doing his research on calculus.  But, (1) a crucial letter actually reached him a number of months later than N thought, and (2) N’s letters did not describe methods, except in anagram form, but only results. 
• L’s calculus involved the notion of an infinitesimal.  An infinitesimal was to be thought of as something smaller than every positive number but bigger than zero.  Once you had infinitesimals like dx, you could do things like define the derivative of a function: f’(x)=(f(x+dx)-f(x))/dx.  You could also add them up, and when you added up infinitely many of them, you got something finite: integration.  What kinds of things are infinitesimals?  People have criticized them as incoherent ideas.  “Ghosts of vanished quantities.”  L did not claim that they were real, but rather he claimed that they were idealizations: numbers you could take as small as you wished.  People were somewhat dubious about a calculus based on infinitesimals until the 19th century when people figured out how to do calculus with the notion of a limit, and do so rigorously.  Finally, in the middle of 20th century, Robinson figured out how to make sense of infinitesimals.
• L could solve all kinds of problems that were not solvable before.  He could arithmetically calculate the area of a circle.  He could find the equation of the curve describing a hanging string.  He found that the brachistochrone is a cycloid. 
• He tried to set geometry on a new grounding based on the notion of similarity.  We’ll see that this is relevant to some of his work on the nature of space.  E.g., he described a circle as ABC ɤ ABY. 
• Designed a logical calculus for symbolic logic.  Represent concepts with numbers, composite concepts with products of numbers.
• Simultaneous linear equations and determinants.

6. Physics

• A theory of gravitation generating elliptical orbits by means of a rising vortex.
• Optics: principle of least action.  Leading to final causes in physics, something he thought was quite important.  Snell’s law. 

7. Church

• Lutheran.  Worked for reunion of churches. 
• On the one hand, he argued that the Council of Trent could be accepted almost entirely by Protestants.
• On the other hand, he argued that Catholic theology should not hold Protestants to be formal heretics.  (Explain.)
• Leibniz was asked more than once by people to convert to Catholicism.  At one point he was even offered the post of Vatican Librarian, but would have been expected to convert.  If he did, he’d probably’ve been made a cardinal.  He said he wasn’t happy with things like the Galileo affair, though he said that were he born Catholic, he’d’ve stayed Catholic.