Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm von Leibnizwas a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton. Leibniz's notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation. He became one of the most prolific inventors in the field of mechanical calculators. While...
NationalityGerman
ProfessionPhilosopher
Date of Birth1 July 1646
CityLeipzig, Germany
CountryGermany
And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples.
But in simple substances the influence of one monad over another is ideal only.
The monad, of which we shall speak here, is nothing but a simple substance which enters into compounds; simple, that is to say, without parts.
Every substance is as a world apart, independent of everything else except God.
Every present state of a simple substance is the natural consequence of its preceding state, in such a way that its present is big with its future.
And as every state of a simple substance is a natural consequence of its preceding state, so that the present state of it is big with the future.
Finally there are simple ideas of which no definition can be given; there are also axioms or postulates, or in a word primary principles, which cannot be proved and have no need of proof.
It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God, in regulating the rest from the beginning of things, should have regard to itself.
I maintain also that substances, whether material or immaterial, cannot be conceived in their bare essence without any activity, activity being of the essence of substance in general.
It follows from what we have just said, that the natural changes of monads come from an internal principle, since an external cause would be unable to influence their inner being.
There are also two kinds of truths: truth of reasoning and truths of fact. Truths of reasoning are necessary and their opposite is impossible; those of fact are contingent and their opposite is possible.
The ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.
It is this way that in mathematics speculative theorems and practical canons are reduced by analysis to definitions, axioms and postulates.
This is why the ultimate reason of things must lie in a necessary substance, in which the differentiation of the changes only exists eminently as in their source; and this is what we call God.