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Gottfried Leibniz - Philosophy, Learning and EthicsGottfried Leibniz - Philosophy, Learning and Ethics


Gottfried Leibniz (1646-1716)


German philosopher (pictured right) and mathematician who invented:

  • calculus (independently of its other inventor Isaac Newton).
  • the binary number system (used in computer programming).
  • kinetic energy (relating to speed).
  • the idea of the European Union.


What did he say about learning and ethics?

 Gottfried Leibniz - Philosophy, Learning and Ethics

1. Rely on reasoning and the facts

You find out the truth of something by:


a) checking it with the facts

(as used in science)

For example, to prove my friend is thin, you observe her to see if she is thin.

 Gottfried Leibniz - Philosophy, Learning and Ethics

b) reasoning

i.e. seeing if something contradicts itself (as used in mathematics)

For example, the two statements below are both false, because the second part of each statement contradicts the first:

  •  2+2=5.
  • a bachelor has a wife.

These are now called analytic statements.


c) Leibniz’s “law of non-contradiction” 

This said that something is true, if it can’t be contradicted.

(e.g. all bachelors are male, or 2+2=4).

 Gottfried Leibniz - Philosophy, Learning and Ethics

d) “compossibilities”

These are possibilities that don’t contradict each other.

(e.g. flowers are beautiful, and I like flowers).


2. The “principle of sufficient reason”

For everything that is true, there must be a reason (i.e. fact or reasoning, see point 1) for its truth.

This reason must be explained clearly, concisely, and comprehensively by appropriate speech, writing and symbols.Gottfried Leibniz - Philosophy, Learning and Ethics

Leibniz’s symbols for calculus were much clearer than Isaac Newton's (pictured right) and are the ones used in mathematics today.


3. God is loving and perfect

God created the “best of all possible worlds”, an idea savagely attacked by Voltaire (pictured right below), in his book, Candide.

The world has evil, Leibniz believed, because God gives us a free will to choose between good and evil.

A world without evil just isn’t possible.Gottfried Leibniz - Philosophy, Learning and Ethics


4. The “principle of continuity”

“Nature never makes leaps”, he said,

In other words, everything:

  • happens in an orderly way.
  • evolves from one state to another (so that “its present is pregnant with its future”).


5. Everything is different

Every substance and person is different.

If two things are identical, they are the same substance (the “Identity of Indiscernibles”).


6. Mind and bodyGottfried Leibniz - Philosophy, Learning and Ethics

The mind is made of “nomads” that are:

  • eternal.
  • separate from the body (which consists of physical atoms).

So he disagreed with  René Descartes' (pictured right) idea of the mind and body interacting.


7. Put theory into practice

Theory must be used for some practical purpose.

So he designed lots of useful things including a submarine and steam engine.

 Gottfried Leibniz - Philosophy, Learning and Ethics

8. Learn from others

Learning depends on:


a) people sharing their knowledge

(particularly unwritten knowledge, which is more important than books).

So he strongly supported the formation of national scientific societies like Britain’s Royal Society.


b) observation

Learn from everything around you including the small and trivial.

“Even in the games of children there are things to interest the greatest mathematician”, he said.

 Gottfried Leibniz - Philosophy, Learning and Ethics

c) openness to other cultures

Leibniz learned greatly from Chinese mathematics, and their ethics, particularly from Confucius (pictured right).


Key quote on success

Deeds make people.


Key quote on decision making

There are two kinds of truths: truths of reasoning and truths of fact.


Key quote on God and religion

If there were no best among all possible worlds, God would not have created one.


Key quote on creativity

Nothing is more important than to see the sources of invention which are, in my opinion, more interesting than the inventions themselves.

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