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.
never married. A later biographer ascribed an illegitimate child to
him, but Leibniz’s whereabouts do not match the likely whereabouts of the
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
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:
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,
a case for a ninth elector, especially a Protestant.
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
4. Other contributions.
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.
calculator that could add, subtract, multiply and divide. This made
people sit up and take notice of him.
often through noble intermediaries, with the most famous people of his
time, like Arnauld.
1672, he visited Spinoza and had long conversations with him.
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.
for all occasions. Satires of kings, such as Louis le Grand.
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.
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.
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.
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.
a logical calculus for symbolic logic. Represent concepts with
numbers, composite concepts with products of numbers.
linear equations and determinants.
theory of gravitation generating elliptical orbits by means of a rising
principle of least action. Leading to final causes in physics,
something he thought was quite important. Snell’s law.
Worked for reunion of churches.
the one hand, he argued that the Council of Trent could be accepted almost
entirely by Protestants.
the other hand, he argued that Catholic theology should not hold
Protestants to be formal heretics. (Explain.)
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.