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
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.
Indeed in general I hold that there is nothing truer than happiness, and nothing happier and sweeter than truth.
Now where there are no parts, there neither extension, nor shape, nor divisibility is possible. And these monads are the true atoms of nature and, in a word, the elements of things.
There is no way in which a simple substance could begin in the course of nature, since it cannot be formed by means of compounding.
It is a good thing to proceed in order and to establish propositions. This is the way to gain ground and to progress with certainty.
Indeed every monad must be different from every other. For there are never in nature two beings, which are precisely alike, and in which it is not possible to find some difference which is internal, or based on some intrinsic quality.
I also take it as granted that every created thing, and consequently the created monad also, is subject to change, and indeed that this change is continual in each one.
And there must be simple substances, because there are compounds; for the compound is nothing but a collection or aggregatum of simples.
I hold that the mark of a genuine idea is that its possibility can be proved, either a priori by conceiving its cause or reason, or a posteriori when experience teaches us that it is in fact in nature.
I agree with you that it is important to examine our presuppositions, throughly and once for all, in order to establish something solid. For I hold that it is only when we can prove all that we bring forward that we perfectly understand the thing under consideration. I know that the common herd takes little pleasure in these researches, but I know also that the common herd take little pains thoroughly to understand things.
When a truth is necessary, the reason for it can be found by analysis, that is, by resolving it into simpler ideas and truths until the primary ones are reached. 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.
Thus God alone is the primary Unity, or original simple substance, from which all monads, created and derived, are produced.
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.