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
We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind.
It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour.
We should like Nature to go no further; we should like it to be finite, like our mind; but this is to ignore the greatness and majesty of the Author of things.
For, above all, I hold a notion of possibility and necessity according to which there are some things that are possible, but yet not necessary, and which do not really exist. From this it follows that a reason that always forces a free mind to choose one thing over another (whether that reason derives from the perfection of a thing, as it does in God, or from our imperfection) does not eliminate our freedom.
Every mind has a horizon in respect to its present intellectual capacity but not in respect to its future intellectual capacity.
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.
Indeed in general I hold that there is nothing truer than happiness, and nothing happier and sweeter than truth.