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Hole-argumentet: ett modernt efterspel till Leibniz kritik av Newton

Hole-argumentet: ett modernt efterspel till Leibniz kritik av Newton I ett tidigare inlägg argumenterade jag för att debatten mellan Newton och Leibniz inte är en historisk kuriositet utan en levande fråga om vilken sorts verklighet fysiken beskriver. Den försiktiga ståndpunkten där var att modern fysik gör en relationell ontologi mer tänkbar, utan att bevisa den. Jag vill här ta ett steg längre och redogöra för ett argument som skärper frågan: det så kallade hole-argumentet. Argumentet har en märklig historia. Einstein formulerade det själv år 1913, under arbetet med den allmänna relativitetsteorin, som ett skäl att förkasta generellt kovarianta fältekvationer. Han trodde att sådana ekvationer gjorde gravitationsfältet otillräckligt bestämt och därmed ledde till en oacceptabel form av underbestämdhet. Denna slutsats försenade hans färdigställande av teorin med omkring två år. I november 1915 kom han fram till att argumentet kunde besvaras och publicerade de färdiga fältekvationer...
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Newton or Leibniz? Modern Physics and Two Concepts of Reality

Newton or Leibniz? Modern Physics and Two Concepts of Reality The old dispute between Newton and Leibniz is often treated as a historical curiosity. It should not be. Modern physics has not left that dispute behind; it has made its central contrast newly vivid. Newton and Leibniz did not merely disagree about technical physics. They disagreed about what sort of reality physics describes. In the Newtonian picture, space and time are fundamental frameworks within which the world exists. In the Leibnizian picture, space and time are not self-subsistent containers but expressions of a deeper relational order. This is not a minor philosophical difference. It is a difference in ontology. Modern physics has not straightforwardly confirmed Leibniz. That would be too simple. But it has made the Newtonian picture of absolute space and absolute time much harder to regard as metaphysically self-evident. Relativity theory abandoned absolute simultaneity and the idea of a universal temporal ...
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Can a Relational Physics Matter Ethically?

Can a Relational Physics Matter Ethically? Modern physics has often been read as a story about matter, law, and measurement. But it may also bear on how we understand moral life, the self, and the possibility of meaning. I have long thought that a relational understanding of physics matters not only for our picture of nature, but also for our picture of ourselves. That claim must still be stated carefully. Physics does not yield morality by deduction, and no symmetry principle can replace ethical judgment. But physics can matter indirectly, by shaping the metaphysical background against which ethical life is understood. If reality is less atomistic than we once believed, then morality and meaning may also have to be thought differently. I take modern physics to invite a relational understanding of reality. Read in light of thinkers such as Ernst Cassirer, Hermann Weyl, and Carlo Rovelli, the older picture of the world as a collection of fully self-subsistent units no longer seems...
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Until very recently, I was not aware that there exists a mathematical literature on revolutions and collective uprisings. That fact alone seemed worth pausing over. At first glance, the idea sounds slightly surprising: one does not instinctively associate revolutions with threshold functions, stochastic transitions, hazard rates, or metastable states. But on closer inspection this is not strange at all. Whenever a system consists of many interacting agents whose behavior depends on what they believe others are doing, the possibility arises that the macroscopic order may change abruptly even when the underlying parameters change only gradually. The text below was generated by AI on the basis of prompts and editorial guidance. It should be read as an exploratory essay in mathematical and conceptual modeling, not as a contribution to political science in the strict disciplinary sense, and not as a predictive statement about any specific country. Revolutions as Stochastic Phase Tr...
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Vad betyder det att tala om ”samma” triangel?

Vad betyder det att tala om ”samma” triangel? En enkel geometrisk iakttagelse kan belysa en mer allmän fråga om objektivitet. Anta att två personer beskriver samma triangel ur olika perspektiv. Beskrivningarna kan då skilja sig åt genom en förskjutning, en rotation eller en spegling. Ändå kan vi säga att det rör sig om samma triangel i geometrisk mening, om skillnaden mellan beskrivningarna motsvarar en kongruenstransformation. Detta kan först låta trivialt. Men just här finns en filosofisk svårighet i koncentrerad form. Det naturliga svaret skulle kunna vara: naturligtvis handlar det om samma triangel, eftersom det hela tiden är ett och samma objekt där ute som de båda personerna ser eller beskriver. Skillnaderna mellan beskrivningarna är då sekundära. Det primära är att ett och samma ting ligger till grund för båda. Det är en begriplig tanke. Men geometrin själv arbetar inte på det sättet. När vi i geometrin säger att två beskrivningar gäller samma triangel, är det inte d...
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When Consciousness Becomes an “Input”

When Consciousness Becomes an “Input” A recent article in Big Think discusses a proposal by cognitive scientist Tom Froese suggesting that consciousness might not merely be the brain’s output but could also act as an input into neural dynamics. The idea is that deliberate conscious effort may introduce increased variability—or entropy—into brain activity. If so, periods of focused awareness would correspond to measurable changes in neural dynamics. The proposal is interesting for a simple reason: it resists the familiar picture in which consciousness is treated as a passive byproduct of physical processes. Instead, it suggests that conscious activity may leave detectable traces in the physical system we call the brain. Yet the conceptual framework of the proposal remains largely unchanged. The brain is still treated as the primary physical system, and the question becomes whether consciousness somehow feeds back into its dynamics. The basic architecture therefore remains two-lev...
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From Beauty to Invariance

From Beauty to Invariance I recently came across the following Facebook post: Source post on Facebook “The Lorentz transformations are a perfect example of Wigner’s ‘unreasonable effectiveness’ thesis. Wigner’s point was that mathematics often: fits nature better than it has any right to predicts phenomena we never intended reveals symmetries we didn’t build in seems ‘unreasonably’ aligned with physical reality Poincaré lived this tension before Wigner articulated it. To Poincaré, the Lorentz group was: too elegant too symmetric too mathematically perfect to be anything but a humanly chosen formalism. Poincaré distrusted the Lorentz transformations precisely because they were too beautiful. He saw elegance as a sign of convention. Einstein saw elegance as a sign of truth. Deep irony here, in that the deeper mathematicians went into GR, the mo...
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