Leibniz's Binary Algebra and its Role in the Expression and Classification of Numbers
The work
| Authors | Mattia Brancato |
|---|---|
| Editors | |
| Type | article |
| Year | 2021 |
| Citekey | brancato2021leibnizs |
Where it appeared
| Published in | Philosophia Scientiae |
|---|---|
| Publisher | Éditions Kimé |
| Volume | 25 |
| Issue | 2 |
| Pages | 71--94 |
Identifiers
| DOI | 10.4000/philosophiascientiae.3045 |
|---|---|
| OpenAlex | W3182728725 |
Access
| Landing page | https://doi.org/10.4000/philosophiascientiae.3045 |
|---|---|
| Free full text | https://journals.openedition.org/philosophiascientiae/pdf/3045 |
Abstract
Leibniz's binary numeral system is generally studied for its arithmetical relevance, but the analysis of several unpublished manuscripts shows that from the very beginning Leibniz also envisaged a new form of algebra in the context of dyadics based on the idea that its letters can only express numbers that are either 1 or 0. In this paper, I shall present the most notable results of this binary algebra: the determination of the algorithm for the expansion of squares and the development of the positional notation used to express any possible number. These achievements explain the priority of dyadics over any other numeral system in Leibniz's mind and his impressive work on the classification of numbers which was facilitated by tools and notions which were only accessible to him at that time.
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How it got here
| How it got here | agent via unpaywall |
|---|---|
| Added | 2026-08-05 00:00 UTC |
| Approved by | a person 2026-08-18 09:48 UTC |
Cite it as
@article{brancato2021leibnizs,
title = {Leibniz's Binary Algebra and its Role in the Expression and Classification of Numbers},
author = {Mattia Brancato},
year = {2021},
journal = {Philosophia Scientiae},
publisher = {Éditions Kimé},
volume = {25},
number = {2},
pages = {71--94},
doi = {10.4000/philosophiascientiae.3045},
}
This record lives at https://refs.drheap.org/brancato2021leibnizs/ and will keep doing so.