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He envisaged the reduction of the elements of meaning (“monads”²⁵³) to elementary, calculable symbols and their logical relations. And this insight:

I have found an astonishing thing, which is, that we can represent all sorts of truths and consequences by Numbers … [T]here are certain primitive Terms which can be posited if not absolutely, at least relatively to us, and then all the results of reasoning can be determined in numerical fashion, and even with respect to those forms of reasoning in which the given data do not suffice for an absolute answer to the question, we could still determine mathematically the degree of probability.

Followed by this utopian flourish: “ … and where there are disputes among persons, we can simply say, Let us calculate, without further ado, in order to see who is right.”²⁵⁴

“Let us calculate” has been revived as a slogan in the era of computer-mediated meaning. Today, we calculate incessantly, though the monads of our calculation involve peculiar transpositions between quantity from other meaning functions, transpositions which are one of the subjects of this grammar.

For all his prescience about the trajectory of modernity, Leibniz also found himself caught in some practical and intellectual dead-ends. One was to apply his prodigious scientific and mathematical capabilities to the problem of draining the water from the Duke of Hanover’s silver and lead mines. Six years of calculation and design of windmill-powered pumps came to nothing.²⁵⁵

Then, consuming him for another six years at the end of Leibniz’s life there was the debilitating dispute with Isaac Newton about which of them had been the inventor of the calculus, a huge breakthrough in the technology of calculability. Newton claimed that Leibniz had plagiarized his idea. The consensus judgment of peers was that indeed he had, though scholars now believe that each invented the calculus independently because their systems of notation were so different.²⁵⁶ Long after he died, Leibniz’s system came to be the preferred one. In Newton’s old school, Cambridge University, Charles Babbage^§MS1.3.2a became one of Leibniz’s strongest advocates.²⁵⁷

Meanwhile, Newton, though a great physicist and mathematician, wandered into his own dead ends of calculation. When Cambridge University economist John Maynard Keynes^§AS2.4a received a tip that a trove of Newton papers was to come up for sale at Sotheby’s London auction house in 1936, he was there to purchase them. In his lifetime, Newton had written about two million words that are pivotal achievements of the Western scientific canon, but the auction brought to light another seven million words.²⁵⁸

“Newton was not only the first of the age of reason,” said Keynes after he started to read them, and the full scope of Newton’s calculations became clear to him. “He was the last of the magicians.” Most of what he had purchased at the auction was “wholly devoid of scientific value.”²⁵⁹

The world had long known about Newton’s mathematics, physics, and optics,^§MS1.3.1c but not his chemical and metaphysical calculations. The chemical calculations are today dismissed as “alchemy.” The metaphysical ones attempted to calculate the time of the realization of prophesies made in the Bible’s most obscure books, Daniel and Revelation.²⁶⁰ “Of the Vision of the Four Beasts; … Of the ten Kingdoms represented by the ten horns of the Fourth Beast; … Of the power of the eleventh horn of Daniel’s fourth Beast, to change times and laws; … Of the Prophecy of the Seventy Weeks” – these are some of the chapter heads, in one of the few of his religious manuscripts to be published. This was Newton at work, calculating “The design of God.”²⁶¹

Calculation had frustratingly reached its limits in Leibniz’s mine pumps and Newton’s prophetic revelations. Calculation alone is not enough. It needs a schema for what is calculable and worth calculating, or what we call ontology.^§MS3.1 It is not enough that the quantities add up. The calculations are no more than transpositions from other meanings into quantities and back again to humanly sensible meanings. The calculations themselves mean not much, unless they can make broader kinds of sense, multimodal sense, ontological sense.

So now to our era of ubiquitous calculation. Three centuries after Newton, here is the editor-in-chief of Wired magazine, Chris Anderson, forecasting the latest version of “Let us calculate”:

Out with every theory of human behavior, from linguistics to sociology. Forget taxonomy, ontology, and psychology … This is a world where massive amounts of data and applied mathematics replace every other tool that might be brought to bear … With enough data, the numbers speak for themselves.²⁶²

No, we would say. Though the calculations of the computers connected to our fingers and minds are fast and helpful, we need ontologies to make sense of them. If computers work for us today, the calculation part of their work is trivial. But what they are calculating may be profound, because any such meanings are made by transposition, where the inputs and outputs make more than just mathematical sense.

Today, the fundamental source of the practicality of calculated meanings lies in one aspect of calculation, and that is the by now exhaustive, universal, and dynamic but relatively stable scheme of alphanumeric naming.^§MS3.4b The names are ordered into ontologies, supporting the lookupability of instances, concepts, qualities, and a whole host of other things. Modernity has created for itself a vast theory of everything, and this book is a theory of these theories. Only after this can we calculate, and with meaning.

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²⁵² Maria Rosa Antognazza, 2009, Leibniz: An Intellectual Biography, Cambridge, UK: Cambridge University Press, pp. 433–36.

²⁵³ Gottfried Wilhelm Leibniz, 1898, The Monadology and Other Philosophical Writings, translated by R. Latta, Oxford, UK: Oxford University Press.

²⁵⁴ Gottfried Wilhelm Leibniz, 1951, Leibniz: Selections, translated by P.P. Weiner, New York, NY: Charles Scribner’s Sons, pp. 50–51.

²⁵⁵ Maria Rosa Antognazza, 2009, Leibniz: An Intellectual Biography, Cambridge, UK: Cambridge University Press, pp. 210–12; 227–30.

²⁵⁶ Ibid., pp. 486–88, 495–97; Richard S. Westfall, 1980, Never at Rest: A Biography of Isaac Newton, Cambridge, UK: Cambridge University Press, pp. 698ff.

²⁵⁷ James Essinger, 2014, Ada’s Algorithm: How Lord Byron’s Daughter, Ada Lovelace, Launched the Digital Age, Brooklyn, NY: Melville House, pp. 106–7.

²⁵⁸ Sarah Dry, 2014, The Newton Papers: The Strange and True Odyssey of Isaac Newton’s Manuscripts, Oxford, UK: Oxford University Press.

²⁵⁹ Ibid., pp. 158–59; Daniel Kuehn, 2013, “Keynes, Newton and the Royal Society: The Events of 1942 and 1943,” Notes and Records of the Royal Society of London 67(1):25–36.

²⁶⁰ Iliffe Robert, 2017, Priest of Nature: The Religious Worlds of Isaac Newton, Oxford, UK: Oxford University Press, pp. 219ff.; James E. Force and Richard H. Popkin, 1990, Essays on the Context, Nature, and Influence of Isaac Newton’s Theology, Dordrecht, NL: Kluwer.

²⁶¹ Isaac Newton, 1733 [1922], Sir Isaac Newton’s Daniel and the Apocalypse, with an Introductory Study of the Nature and Cause of Unbelief, of Miracles and Prophecy, edited and translated by W. Whitla, London, UK: John Murray, pp. xvi, 306.

²⁶² Chris Anderson, 2008, “The End of Theory: The Data Deluge Makes the Scientific Method Obsolete,” Wired, 16 July.

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Cope, Bill, and Mary Kalantzis. 2020. Making Sense: Reference, Agency and Structure in a Grammar of Multimodal Meaning. Cambridge UK: Cambridge University Press, pp. 169-172. https://doi.org/10.1017/9781316459645

Gottfried Leibniz: “Let us Calculate” §MS1.3.2d