Gottfried Leibniz (1646-1716) is responsible for a great many constructions and concepts of current interest:
differential calculus and integral calculus, especially the basic notation that we use today;
the product rule of calculus may be called the Leibniz rule or Leibniz law;
differentiation under the integral sign? follows the Leibniz integral rule;
identity of indiscernibles may be called the Leibniz law;
a version of infinitesimals sometimes regarded as a precursor to synthetic differential geometry;
a philosophy involving ‘monads’, simple mind-like substances, from which we get the names of both the monads of category theory and the infinitesimal neighbourhoods of nonstandard analysis, see at monad in nonstandard analysis
also see in Hegel, Science of Logic the section The monad of Leibniz
An instructive starting point distinction made in the contemporary literature … is between three ‘levels of reality’ in Leibniz’s mature metaphysics. At the most basic level, what is real for Leibniz are simple substances which alone have true unity. These are the famously obscure monads. Next, we have the ‘phenomenal level’ that is made up of phenomena bene funda – well founded phenomena – that, due to pre-established harmony, are accurate reflections of the real and actual monadic states. Finally, we have the ideal level which, by contrast, is made up of entia rationis – abstract or fictional things – that include ‘phenomena’ founded upon possible but non-actual monadic states. Crucially, although both the phenomenal and the ideal levels can include things which are infinite, all concepts that depending upon the continuum are only applicable to the ideal realm. Thus, if we were to define time as the real line, $\mathbb{R}$, then this concept of time could only be represented for Leibniz as an entia rationis and thus ideal. Furthermore, phenomenal things for Leibniz can only acquire their status as phenomena bene funda by their grounding upon the actual. They must always be understood as representations or perceptions of the monads of the actual world. (Thébault 19, p. 2)
On infinitesimals:
Mikhail Katz, David Sherry, Leibniz’s Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond, D. Erkenn (2013) 78: 571 (arXiv:1205.0174, doi:10.1007/s10670-012-9370-y)
Karim Thébault, The Problem of Time, (PhilSci Archive)
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