When1: 1666
When2: 1716
Who: Gottfried Wilhelm von Leibniz [Leibniz, Gottfried Wilhelm von]
What: mathematician/philosopher/inventor
Where: Germany
works\ On the Art of Combination [1666]; Samples of the Numerical Characteristic [1679]; New Method for maximums and minimums [1684]; Discourse of Metaphysics [1686]; Reply to the Thoughts on the System of Pre-established Harmony Contained in the Second Edition of M. Bayle's Critical Dictionary, Article Rorarius [1702]; Explanation of the Binary Arithmetic [1703]; Theodicy [1710]; Principles of Nature and Grace [1714]; Monadology [1714]; On the Combinatorial Arts [1714: infinitesimal calculus, notation, integration, chain rule, variable separation, Leibniz's test]; On the Method of Distinguishing Real from Imaginary Phenomena [1715 to 1716: letter to Clarke]; calculating machine; water pump
Detail: He lived 1646 to 1716. He invented machines for calculating and for pumping water out of mines. In mathematics, he solved differential equations by isolating variables and used infinitesimals in calculus. He invented integration as summation, integration as differentiation inverse, closed-function integration, logarithmic-function and exponential-function differentials [1694], chain rule, and calculus notation. He studied curvature, curve envelopes, and osculating circles. In logic, he wanted to create perfect language {symbolic logic, Leibniz} {systematic philology}, whose grammar and words can state all logical propositions and proofs. He attempted to write deductive philosophy, using formulas in symbol language that he devised, but he did not complete it.
Epistemology
For all x and y, if x and y are identical, then x and y have same properties {Leibniz' law}.
Truths contain predicates in subjects {concept containment}. Necessary truths have a finite series of containments. Contingent truths have an infinite series of containments.
No proposition can be both true and false at once {principle of contradiction, Leibniz}. Nothing happens without adequate reasons or causes {principle of sufficient reason, Leibniz}, though people usually cannot know reason. Reasoning involves contradiction and sufficiency principles. All analytic statements are true. All true statements are analytic.
Identical things have same intrinsic, non-relational properties. If two objects share all intrinsic, non-relational properties, they are identical {identity, indiscernible} {indiscernible, identity} {Leibniz's law, Leibniz}. The identity relationship is symmetrical for thing and properties. However, no two things have same qualities, and things differing in qualities are two separate things.
Perception is clear if understood. Perception is distinct if people can analyze it into concepts.
Awareness that one's perceptions have become more clear and distinct is pleasure. Awareness that one's perceptions have become less clear and distinct is pain.
Clear and distinct statements have two classes. One class is personal experiences, which are clear and intuitively true, because people have immediate experience of their own existence, but are true for one time only. However, opposites of these facts are also possible, so people can know their truth only after they have happened {a posteriori, Leibniz}. Facts of experience are conditional or contingent truths of the finite world. All things are deterministic, so opposites only appear to be possible. People's senses know only space and time, not physical forces or causes.
The other class is eternal truths, self-evident to reason, whose opposites cannot be true or even possible. People can know their truth before events {a priori, Leibniz}. Eternal truths are unconditional, necessary, and about the infinite.
Ethics
God allows free will, because it is good, but this necessarily allows evil.
Physical evil is punishment for sin. Object finiteness and unclear ideas cause moral evil.
Law
Law must have philosophical bases to be consistent and just. Law has natural divisions. Law and reasoning principles can find document meanings.
Metaphysics
Objects must be finite, because something created them. Finite world had to have evil, but it has as much good as possible because God formed it. The created world has the most variety from simplest causes and laws. What exists is the largest possible set of compatible things. Because existence is good, this makes world have the most possible reality and be the best it can be. God chose the best deterministic mechanical laws. However, laws can be different and so are not absolute truths, only facts {contingent truth, Leibniz}. There are infinitely many possible worlds.
Only finite matter and spiritual force units {monad, Leibniz} exist. Existing things are monad collections.
Ideal things are continuous and so have no monads.
An infinite number of monads differ in intrinsic properties.
Monads form a hierarchy based on their forces, not motions. Highest monad is God, which is pure activity and has all forces. Next highest are souls and minds, possess good memory and perception, and are most active. Soul is will's purpose and is body's central monad. Lowest monads are matter. Monads reflect universe as whole, allowing them to seem to occupy space. Monads perceive other monads more distinctly or less distinctly {universal expression}.
Number of forces is infinite. Forces or energies are active and immaterial. Material properties, such as filling space or being impenetrable, are force consequences. Motions are force consequences. Time and space result from combined force actions. Forces are independent of other forces, but are forms of whole world's essence {world-force}. Forces try to clearly represent world-force, by infinitely small steps.
Monads have unconscious perceptions {minute perception}. Monads continually seek improvement, which perceives more clearly and distinctly. Unconsciously, monads continually perceive entire universe {apperception, monad} but are conscious of only small regions.
Monad wills directly cause actions. Monad beliefs direct will, but not deterministically.
Monads never affect each other, but they appear to do so, because their perceptual states correspond {preestablished harmony}. God synchronizes the pre-established harmony, which is deterministic. In determined worlds, subjects must contain all the infinite number of qualities, actions, and predicates that statements can assert and so must be immortal and unchangeable. Therefore, all statements about reality contain predicate in subject and are analytic. To God, all experience is analytic, but people cannot know all predicates or facts. For God, objects are necessary, and their properties are in object essence.
Only God is necessary. All else is contingent.
God exists, as proved by ontological argument, cosmological argument, argument from eternal truths, and argument from design.
Mind
All ideas are always unconsciously present in soul, which is the central body monad and represents whole universe. Mind can bring ideas to consciousness. Perceptions contain universal concepts and truths.
Social Sciences>Philosophy>History>Invention
6-Philosophy-History-Invention
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0224