“Hoping for a big tent in which it is understood that disagreement is the price to be paid for exploring important ideas.”
This is conceived as an informal and spontaneous annex to my more extensive blog, Grand Strategy: The View from Oregon.
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Discord Invitation
TODAY IN PHILOSOPHY OF HISTORY
Buckle as the Father of Scientific History
Sunday 24 November 2024 is the 203rd anniversary of the birth of Henry Thomas Buckle (24 November 1821 – 29 May 1862), who was born in London on this date in 1821. Buckle died at only forty years of age in Damascus, Syria.
Buckle is sometimes called the “Father of Scientific History,” and he formulated a method for scientific history that he presented in his History of Civilization in England, a large work left unfinished upon his early death. I take Buckle as a point of departure for considering the scientific status of history.
Quora: https://philosophyofhistory.quora.com/
Discord: https://discord.gg/r3dudQvGxD
Links: https://jnnielsen.carrd.co/
Newsletter: http://eepurl.com/dMh0_-/
Text post: https://geopolicraticus.substack.com/p/buckle-as-the-father-of-scientific
Video: https://youtu.be/nmWClZ3fk6g
Friday 22 November 2024
Grand Strategy Newsletter
The View from Oregon – 316
Permutations of Devolved Industrial Production
…in which I discuss a taxonomy of technologies, the electromechanical era, the replacement thesis, retrograde replacement, gunsmithing, reverse engineering, roundabout production, the ENIAC in your future, and hope for the future in technological complexity…
Substack: https://geopolicraticus.substack.com/p/permutations-of-devolved-industrial
Medium: https://jnnielsen.medium.com/permutations-of-devolved-industrial-production-b43485423a08
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TODAY IN PHILOSOPHY OF HISTORY
The Second World War Begins
On Friday, 01 September 1939, eighty-five years ago today, Germany invaded Poland, transforming a dangerous and ambiguous military and political situation into a “hot” war. It is this date that is most frequently employed for the beginning of the Second World War. What was the nature of the war? What kind of war was it? This deceptive simple question is difficult to answer.
Quora: https://philosophyofhistory.quora.com/
Discord: https://discord.gg/r3dudQvGxD
Links: https://jnnielsen.carrd.co/
Newsletter: http://eepurl.com/dMh0_-/
Video: https://youtu.be/iL46n4AbQdo
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TODAY IN PHILOSOPHY OF HISTORY
Wilhelm Windelband and the Place of History among the Sciences
Saturday 11 May 2024 is the 176th anniversary of the birth of Wilhelm Windelband (11 May 1848 – 22 October 1915), who was born in Potsdam on this date in 1848.
Windelband formulated a distinction between nomothetic sciences and idiographic sciences, placing history in the latter category with its own distinctive methodology. The nomothetic is the lawlike, the regular, and the universal; the idiographic is the individual, the particular, and the unique. But does this distinction hold up as a rudimentary taxonomy of the sciences? Are the sciences one or many?
Quora: https://philosophyofhistory.quora.com/
Discord: https://discord.gg/r3dudQvGxD
Links: https://jnnielsen.carrd.co/
Newsletter: http://eepurl.com/dMh0_-/
Text post: https://geopolicraticus.substack.com/p/wilhelm-windelband-and-the-place
Video: https://youtu.be/nOnELO64kwE
Axes of Formal Thought
There isn’t one, single way of formulating a taxonomy of formal methods, but there are ways that are more or less helpful for how a given individual approaches formal problems. For years I’ve been casting about for such a taxonomy, and I have worked out different ways of doing this.
At one time I wrote a series of posts on the Banach-Tarski paradox (which is a paradox in the sense of being counter-intuitive, but not a paradox in the sense of being contradictory; cf. the list of resources, below, under “Wordpress Posts on the Banach-Tarski Paradox”), and in working through these ideas I came up with the following classification of formal thought:
This was obviously built around the motivation of understanding the Banach-Tarski paradox, which involves decomposing a sphere into a finite number of parts, and then reassembling the parts into two spheres. I realized that this was interestingly complementary to what is going on with fractals, in which there is an infinite iteration of a finite operation. Thus the Banach-Tarski paradox and fractals are kitty-corner from each other in the above table, with the other two permutations of these possibilities filled in by primitive recursive arithmetic (PRA), with its finite operations finitely iterated, and the possibility of infinitely iterating infinite operations, which would be infinite fractals.
While this is interesting, and it was the attempt at a taxonomy that pointed out to me the possibility of infinite fractals (I don’t know if anyone else has suggested this possibility), as noted above this taxonomy is highly derivative from my thoughts on the Banach-Tarski Paradox, and I wanted something less bound by a particular problem. Searching for other approaches, I also formulated the following table:
I honestly don’t remember what I was working on when I drew up the above table, though it obviously embodies my ongoing interest in trying to formulate big picture concepts, with the lower right permutation being the widest possible permutation of formal thought, and the other spots in the table indicating other approaches that are more limited in some respect than a formal overview (cf. The Overview Effect in Formal Thought, also linked below in “Studies in Formalism”).
While this table has some interesting features (classical mathematics appears as “method without any unifying conception,” in the upper right of the permutations), this, too, was too limited and unsatisfying, so I eventually formulated a table that lays out as its two axes the ideas that have long held the greatest fascination for me: formal/informal and constructive/non-constructive:
Here the permutations don’t quite sound as interesting as the above two attempts at a taxonomy of formal thought, but further elaboration allowed me to employ these axes in a comprehensive way that allows us to lay out a variety of formal approaches in one table. This more detailed exposition of the immediately above table is the table at the top of this post. Here the x axis is constructivity, from the constructive to the non-constructive, while the y axis is formality, from the formal to the informal.
With this taxonomy I am able to put Platonism, Neo-platonism, mysticism, computer science, dialethism, insolubilia, the ineffable, intuitionism, classical mathematics, and much more all in one table, and showing the various relations of these disciplines to each other. I could, and maybe someday I will, further expand this table in order to place more instances of distinctive approaches to formal thought within the same matrix.
In the same way that this table didn’t sound immediately as interesting as my other attempts at taxonomy, it also didn’t suggest anything new to me, as the Banach-Tarski derived table suggested infinite fractals to me, but it does seem to furnish a more comprehensive and flexible taxonomy than my other attempts.
Tumblr posts on Constructivism:
- P or Not-P
- What is the Relationship between Constructive and Non-Constructive Mathematics?
- A Pop Culture Exposition of Constructivism
- Intuitively Clear Slippery Concepts
- Kantian Non-Constructivism
- Constructivism without Constructivism
- The Vacuous Identity Principle
- Permutations of Infinitistic Methods
- Methodological Differences
- Constructivist Watersheds
- Constructive Moments within Non-Constructive Thought
- The Principle of Vacuous Pragmatism
- Precise Generality
- Addendum on Precise Generality
- The Two Philosophies of Mathematics
- From Gödel to Historiography
- Gödel between Constructivism and Non-Constructivism
- The Natural History of Constructivism
Wordpress posts on constructivism:
- Cosmology: Constructive and Non-Constructive
- Saying, Showing, Constructing
- Arthur C. Clarke’s tertium non datur
- A Non-Constructive World
Wordpress posts on the Banach-Tarski Paradox:
- A Question for Philosophically Inclined Mathematicians
- Fractals and the Banach-Tarski Paradox
- A visceral feeling for epsilon zero
- A Note on Fractals and Banach-Tarski Extraction
Studies in Formalism:
- The Ethos of Formal Thought
- Epistemic Hubris
- Parsimonious Formulations
- Foucault’s Formalism
- Cartesian Formalism
- Doing Justice to Our Intuitions: A 10 Step Method
- The Church-Turing Thesis and the Asymmetry of Intuition
- Unpacking an Einstein Aphorism
- The Overview Effect in Formal Thought
- Einstein on Geometrical intuition
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Types of Scientific Civilization
Further to my brief remarks in Getting to Starships on the classification of spacefaring civilizations, some subset of which would go on to also build starships, It seems likely that the class of spacefaring civilizations must either be contained within or overlap with the class of scientific civilizations. This suggests that, among the class of scientific civilizations, there is a subset of spacefaring civilizations, and among spacefaring civilization, there is a subset of starfaring civilizations. Already, then, we have three kinds of scientific civilization.
In David Hume and Scientific Civilization and The Relevance of Philosophy of Science to Scientific Civilization I considered scientific civilization as a genera in the classification of civilizations, which suggests the question of the various species of scientific civilization, and of the alternative genera of civilizations. Today I will only consider the former question, i.e, if science is a genera for the classification of civilizations, what are the species that fall within this genera? In other words, what are the types of scientific civilization? As we have seen above, we can already name at least three kinds of scientific civilization, but ideally we would like to go deeper, and formulate a taxonomy based on more fundamental principles.
At present I will not attempt a systematic answer to the question of the kinds of scientific civilizations, which would require a full taxonomy of civilization (something I am working on, but which is not yet fully formulated), but I will only sketch some interesting aspects of the question of the types of scientific civilization.
Where would we expect to find the fundamental principles of scientific civilizations? In science itself. Distinct types of science would yield distinct types of scientific civilization. Can we recognize distinct types of science? There is a passage from Eugene Wigner that I have quoted many times, which suggests that there may be distinct types of science:
“…someone came to me and expressed his bewilderment with the fact that we make a rather narrow selection when choosing the data on which we test our theories. “How do we know that, if we made a theory which focuses its attention on phenomena we disregard and disregards some of the phenomena now commanding our attention, that we could not build another theory which has little in common with the present one but which, nevertheless, explains just as many phenomena as the present theory?” It has to be admitted that we have no definite evidence that there is no such theory.” (Eugene Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”)
This suggests a number of sciences based upon the selection of empirical evidence. There might also be distinct forms of science based upon the theoretical frameworks employed in the epistemic organization of empirical knowledge. And at the most fundamental level, there may be distinct forms of mathematics at the basis even of formalized, mathematicized sciences.
Bertrand Russell imagined a counter-factual form of mathematics in an amusing passage:
“If one could imagine intelligent beings living on the sun, where everything is gaseous, they would presumably have no concept of number, any more than of ‘things.’ They might have mathematics, but the most elementary branch would be topology. Some solar Einstein might invent arithmetic, and imagine a world to which it would be applicable, but the subject would be considered too difficult for schoolboys.” (Bertrand Russell, “Reply to Criticisms,” in The Philosophy of Bertrand Russell, New York: Harper & Row, 1963, p. 697)
We need not have recourse to the unlikelihood of beings on the sun in order to imagine a different mathematics. What if a civilization’s mathematics began with projective geometry instead of the Euclidean plane geometry of ancient Greece, and, again, what if the method of organizing this body of geometrical knowledge were not axiomatic, as with Euclid, but, say, natural deduction? Given that the architectonic of mathematics is the framework for natural science, if we began with a different mathematics, would be end up with different physical sciences? How different exactly would the mathematics be, and how different the physical sciences?
It is unlikely, I think, that the final mathematics and science would be all that different, but the formulations would likely be quite different. This, however, is a difficult matter that requires further thought. Our knowledge of the sciences is far from final, far from finished. Also, the order in which the sciences are developed and come to maturity could be very different in different civilizations. Scientific civilizations of a radically different genealogy than that of terrestrial civilization would be shaped by a radically different history. In so far as civilization has not an essence but a history (as Ortega y Gasset said of humanity), scientific civilizations with different histories could still be radically different civilizations, even if each individual science converges on a universal form.
But must all mature science converge onto the same laws of nature, with the
definitive formulation of laws being a mathematical expression? Suppose
that this is true, and that all mature sciences converge upon the same
laws of nature: still, other approaches to mathematics might lead to
very different formulations of these truths of science.
It may be that all science is ultimately one, but as soon as we have formulated this idea we realize that it is a distinct thesis that must be defended on its own merits, and cannot simply be assumed. And today the idea that all science converges upon one truth sounds like a very distant echo of Platonism that the modern world could scarcely accept.
These, then, are some of fundamental ways in which science and scientific civilizations might differ among particular instances, the core and fundamental principles of science, and they are not yet settled. We require a much more sophisticated philosophy of science before we would be prepared to give an adequate answer to these problems that ultimately concern the origins of destiny of scientific civilization.
Addendum on the Ecological Conception of Nature
A few days ago in The Ecological Conception of Nature I recounted what I saw as the stages in the development of the conception of nature in Western thought from Plato to the present day. In other words, I provided a genetic account of the concept of nature, roughly based on historical periodization. But what has historical periodization have to do with our conception of nature?
The relationship between historical periodization and theoretical division of subject matter tend to coincide because thought develops over time, and upon reaching certain stages of development settles upon a particular paradigm, but the correspondence is not perfect. Some ideas go on to a long career, outlasting the phase of thought that produced them, while other ideas lapse, and become defunct. There is, then, a tension between time and taxonomy. Biology experiences this tension also, where it appears as the species problem.
Here I would like to digress to consider a parallel case. Some time ago on my other blog I wrote a critique of what is sometimes called the generational warfare model. Advocates of this conception gave a genetic account of the development of warfare in terms of first generation warfare, second generation warfare, and so forth.
After I wrote this, a reader wrote back to me to let me know that the generational conception of war had been superseded by the gradient conception of war, so instead of speaking of first generational warfare, it was now the thing to do to speak of first gradient warfare. I then wrote a post on the gradient conception of war and then what I called gradient superiority.
Most of the conceptual distinctions of the earlier idea were retained, but the terminology was adjusted to reflect that fact that gradients of war don’t perfectly track historical generations of war, even though historical generations of war were clearly the inspiration for both the generational conception and the gradient conception.
Something very similar could be said of the conceptions of nature that I recounted genetically as the result of the succession of stages of human thought from Plato to the present day. I could say that my generational ecological model does not perfectly track historical generations of thought, so that the generational ecological model needs to be superseded by a gradient ecological model. Well, sort of, but not exactly.
Some stages of human thought have given birth to perennial conceptions that long outlive the stage of intellectual development from which they sprang. Some stages of human thought, on the other hand, have little to contribute to subsequent ages, and their conceptions disappear as soon as their representatives are in the grave.
To be quite bold, I will say that there will always be Platonists among us, and therefore always a Platonic conception of nature, but while there will always be romantics, there wasn’t much in the way of content in the romantic worship of wild nature, although what there was was carried forward and eventually informed our ideas of wildness and wilderness today. These ideas – i.e., contemporary conceptions of wildness and wilderness – will have more of a history, I think. Romanticism will live on in paintings and novels and attitudes, but it didn’t contribute much to the world’s stock of ideas.
And does the world improve on its stock of ideas over time? Some thinkers – and not a few, but a substantial number – hold that there is no conceptual progress over time. Kuhn’s interpretation of the history of science has been pressed into service to defend this position, but I don’t think for a moment that Kuhn himself would have defended absolute non-novelty in human thought. I addressed the issue of non-novelty in a geopolitical context in my post Gödel’s Lesson for Geopolitics, but I have yet to formulate a completely general defense of conceptual novelty, though I hope to get to this at some point.
Can time (in the form of historical periodization) provide an adequate taxonomy of ideas? In some cases yes, in other cases no. It might be worthwhile to inquire if there are historical circumstances that influence when a period produces an enduring taxonomy and when it does not. That is an effort I will save for another time.