From: Thomas Walker Lynch Date: Tue, 25 Aug 2026 10:33:34 +0000 (+0000) Subject: . X-Git-Url: https://git.reasoningtechnology.com/?a=commitdiff_plain;h=72ecc153a5bb2602d85d6a496e033fcd77f19ef7;p=TM-2026 . --- diff --git a/document/book/TM-2026.html b/document/book/TM-2026.html index 7011047..4f4cbc7 100644 --- a/document/book/TM-2026.html +++ b/document/book/TM-2026.html @@ -444,20 +444,19 @@

This perspective, that knowledge comes from the categorization of observations of nature rather than, as Plato taught, from the conceptualization of Forms, is the pillar of the philosophy of Naturalism.

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In modern times the term carries two meanings, that of the biologist who studies nature, and that of the philosophy holding that nothing exists outside nature. This latter meaning is generally taken to deny the Realm of Forms, and with it any abstraction standing outside nature and apart from anything that could be observed. This book takes up the first meaning: observing the machine as a natural phenomenon, writing down what it does in a useful notation, and holding each conclusion answerable to further observation. While doing this we will build a structure, which defines the term abstract concept, and thus integrates Plato’s Realm of Forms. Perhaps in so doing, Plato is pulled into Naturalism, and the two are not distinct. If the argument is successful, many philosophers who have debated them as a dialectic over the centuries would surely be disappointed. - Aristotle is ancestor to the first meaning and only distantly to the second, holding as he did that the first mover is no part of nature; Metaphysics XII.7. The metaphysical doctrine is a nineteenth-century development. +

There are two modern definitions for Naturalism. One definition is that of a philosophy that nothing exists outside of nature. This philosophy is generally taken to deny the existence of any abstraction standing apart from what could be observed, including that of the Realm of Forms. The other definition is that of a study of nature, that of a wildlife biologist. Computational Naturalism holds that a machine is a natural phenomenon and can be observed, and that computation theory is a useful notation for cataloging these observations. However, within the study of Computational Naturalism there arises a metamathematics and layers of abstraction that do the work the Realm of Forms was posited to do. Plato described that realm and never defined it, and Computational Naturalism supplies a definition for at least some of what he described. Thus Computational Naturalism does not debate the question as to which view is correct, but instead holds that they are two aspects of the same thing. + Aristotle is ancestor to the biologist’s meaning and only distantly to the philosophical one, holding as he did that the first mover is no part of nature; Metaphysics XII.7. The metaphysical doctrine is a nineteenth-century development.

- - The dialectic without a specimen + The presumed dialectic -

The pattern of a thesis met by its opposite and settled in a third position is commonly credited to Hegel, and it is not his. Fichte set it out, and Heinrich Moritz Chalybäus fixed the three names upon it in a popular history of 1837, from which it passed into the schoolroom and has stayed there. +

The pattern of a thesis met by its opposite and settled in a third position is commonly credited to Hegel; however, it was Fichte who first articulated it, and it was Heinrich Moritz Chalybäus who fixed the three names upon it in a popular history of 1837. Johann Gottlieb Fichte, Grundlage der gesammten Wissenschaftslehre (Leipzig, 1794), §§1−3. Heinrich Moritz Chalybäus, Historische Entwicklung der speculativen Philosophie von Kant bis Hegel (Dresden, 1837). Hegel’s own term is Aufhebung, in which a position is cancelled, preserved, and raised at once. The three-step formula is not in his vocabulary, and scholars of Hegel are quick to say so. - Wherever it came from, it trains a reader to sort positions into opposed camps and to wait for the resolution to arrive from somewhere above them. The sorting is the easy part and it is habit-forming.

+ The approach is easy to reach for and it is habit-forming. Our courtrooms, legislatures, and debating societies set rules for adversarial contest, and build in the expectation of progress by picking winners.

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There is an older story, of blind men and an elephant. One takes hold of the trunk and reports a snake, one the ear and reports a fan, one the leg and reports a pillar. It is usually told against them, as a lesson about partial views. It can be told the other way. Every report was accurate, every man had hold of something real, and what was wanting was not better observation but the recognition that the reports were of one animal. Plato and Aristotle have been handled as an opposed pair for a long while, and this chapter follows what came of that. It is a survey and it is selected, the question put to each man being whether he went and looked at something.

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There is an ancient story from India telling of blind men and an elephant. One takes hold of the trunk and reports a snake, one the ear and reports a fan, one the leg and reports a pillar. So then, if these men had a debate, who would the judge pick as the winner? Or should we accept mutually contradictory points of view as being indicative of a deeper truth? Not one synthesized, but one discovered.

After the Athenian Academy declined, the transmission of Greek thought fractured. Western Europe retained fragments of Aristotle’s logic while the corpus migrated east, carried by Syriac Christians to eighth-century Arabic-speaking scholars who rendered Aristotle, Euclid, and Galen into Arabic. The problem those scholars faced was fitting philosophical demonstration to Islamic faith. Hunayn ibn Ishaq (809−873) and his circle drove the translation movement under Abbasid patronage. The arriving texts contained Aristotle layered with late-antique commentary and Neoplatonic adaptations circulating under his name, notably the Theology of Aristotle (an adaptation of Plotinus). See “Greek Sources in Arabic and Islamic Philosophy,” Stanford Encyclopedia of Philosophy. @@ -473,11 +472,11 @@ René Descartes, Meditationes de Prima Philosophia (Paris, 1641), Meditations III and V. The position is called rationalism. Descartes held the body to be a machine and animals to be machines entire, while reserving the mind from mechanism; the line he drew there was erased a century later by Julien Offray de La Mettrie, L’Homme Machine (Leyden, 1747). John Locke (1632−1704) answered him by saying there are no innate ideas, the mind begins empty, and everything in it arrives through sensation and through reflection upon what sensation delivers. Yet Locke declined to include mathematics, which he conceded comes from the agreement among our own ideas. John Locke, An Essay Concerning Human Understanding (London, 1690), Book I against innate ideas, Book II on the two sources, and Book IV chap. 4 on mathematical certainty. The position is called empiricism. - This is the pattern to watch through the whole period. Knowledge is made to begin in the world, and mathematics is made the exception. Every man who takes the outward road arrives at the same door and declines to open it, and the reason is always to hand: he can point at what a mathematician does and see no apparatus.

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George Berkeley (1685−1753) attempted what is attempted here, which is to dissolve the opposition rather than to settle it. He held that perception is reality itself and not a report about some further thing standing behind it, so that the world as it is met and the world as it is are the one world, with nothing left for them to disagree about. Asked what becomes of the furniture in a room when nobody is in it, he answered that God perceives it. +

George Berkeley (1685−1753) attempted to dissolve the dialectic by proposing that perception is reality itself and not a report about some further thing standing behind it. Thus, the world as it is sensed, and the world as it is perceived, are one and the same. When asked what becomes of the furniture in a room when nobody is in it, he answered that God perceives it. George Berkeley, A Treatise Concerning the Principles of Human Knowledge (Dublin, 1710), §§3 and 6 for the doctrine, §§28−33 and §146 for the argument reaching God, and §48 for the objects that persist unperceived by any man. Put again, and more accessibly, in Three Dialogues between Hylas and Philonous (London, 1713). - The unification held. The price was an entity outside the system, brought in to keep a truth available when no instance of it was to be had. A reader is entitled to ask what this book pays for the same purchase, and to hold the question open until it is answered.

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Thomas Hobbes (1588−1679) opened the Leviathan by asking why the heart is not a spring and the nerves so many strings, and made geometry a science of bodies and of the motions that generate them. Thomas Hobbes, Leviathan (London, 1651), Introduction; De Corpore (London, 1655), Part II. The fuller statement of man as machine is Julien Offray de La Mettrie, L’Homme Machine (Leyden, 1747).