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Category: Ideas/philosophy

What do Gödel’s incompleteness theorems truly mean?

What do Gödel’s incompleteness theorems truly mean?

Natalie Wolchover writes: In 1931, by turning logic on itself, Kurt Gödel proved a pair of theorems that transformed the landscape of knowledge and truth. These “incompleteness theorems” established that no formal system of mathematics — no finite set of rules, or axioms, from which everything is supposed to follow — can ever be complete. There will always be true mathematical statements that don’t logically follow from those axioms. I spent the early weeks of the Covid pandemic learning how…

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Mexistentialism embraces uncertainty

Mexistentialism embraces uncertainty

Carlos Alberto Sánchez writes: I recently spent an evening trying to convince my father not to go back to Michoacán. I told him it wasn’t a good time. He reminded me that he’s been a naturalised US citizen since the George H W Bush administration. I reported what I’ve seen on the news: people with decades of US residency, with Green Cards and outstanding civic engagement, are being deported, and the rationale seems to have something to do with previous acts of criminality, like…

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When we turned time into a line we reimagined past and future

When we turned time into a line we reimagined past and future

Emily Thomas writes: ‘It’s natural,’ says the Stanford Encyclopedia of Philosophy, ‘to think that time can be represented by a line.’ We imagine the past stretching in a line behind us, the future stretching in an unseen line ahead. We ride an ever-moving arrow – the present. However, this picture of time is not natural. Its roots stretch only to the 18th century, yet this notion has now entrenched itself so deeply in Western thought that it’s difficult to imagine…

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The next scientific revolution won’t come from scientists

The next scientific revolution won’t come from scientists

Steve Fuller writes: The most influential work on the nature of science for at least the past fifty years has been The Structure of Scientific Revolutions, first published in 1962 by a young physicist-turned-historian, Thomas Kuhn. Although influential, the book has also been widely misunderstood. It is quite common to think—certainly based on the title—that Kuhn was providing a formula for producing scientific revolutions. On the contrary, he was arguing that revolutions only happen once scientists confront insurmountable obstacles in…

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Wikipedia operates in good faith — unlike its critics

Wikipedia operates in good faith — unlike its critics

Renée DiResta writes: Late last month, Elon Musk launched Grokipedia, an AI-generated encyclopedia with 855,279 articles, no human editors, and no way for users to request improvements beyond a suggestion box addressed to its eponymous chatbot author. The tech entrepreneur is eager, he has said, to “purge out the propaganda” that he argues afflicts Wikipedia, the venerable user-generated reference source. But some Grokipedia articles are near replicas of Wikipedia entries. Other articles in the new source seem conspicuously sanitized: The…

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We see the world suffused with causality

We see the world suffused with causality

Mariel Goddu writes: Causal understanding is the cognitive capacity that enables you to think about how things affect and influence each other. It is your concept of making, doing, generating and producing – of causing – that allows you to grasp how the Moon causes the tides, how a virus makes you sick, why tariffs change international trade, the social consequences of a faux pas, and the way each event in a story leads to what happens next. Causal understanding is the foundation of all thoughts why, how, because, and what if….

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How humanity moved from eternal to finite time

How humanity moved from eternal to finite time

Thomas Moynihan writes: Do you recall the first time you knew you would die? It’s a milestone, realising your time is limited. That things happened before you, and will happen afterward, in your absence. As we grow up, the understanding of death comes in stages, but it culminates in acknowledgment of one’s own – unavoidable yet unpredictable – mortality. Sometime between the ages of six and 10, children become aware that their time is inescapably bounded. Roughly the same might be said…

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The art of outlasting: What we can learn from time-proof Japanese businesses

The art of outlasting: What we can learn from time-proof Japanese businesses

Eric Markowitz writes: Picture yourself on a train hurtling toward Nara Prefecture, hours away from the neon-lit frenzy of Tokyo. The urban sprawl gives way to quieter vistas, the journey itself a pilgrimage of sorts. By the time you arrive in Ikaruga, at Hōryū-ji — widely considered one of the world’s oldest wooden temples — the modern world feels like a distant memory. The temple, originally commissioned by Prince Shōtoku in the 7th century, stands as a living testament to…

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Without chaos theory social science will never understand the world

Without chaos theory social science will never understand the world

Brian Klaas writes: On 30 October 1926, Henry and Mabel Stimson stepped off a steam train in Kyoto, Japan and set in motion an unbroken chain of events that, two decades later, led to the deaths of 140,000 people in a city more than 300 km away. The American couple began their short holiday in Japan’s former imperial capital by walking from the railway yard to their room at the nearby Miyako Hotel. It was autumn. The maples had turned…

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‘Metaphysical experiments’ probe our hidden assumptions about reality

‘Metaphysical experiments’ probe our hidden assumptions about reality

Amanda Gefter writes: Metaphysics is the branch of philosophy that deals in the deep scaffolding of the world: the nature of space, time, causation and existence, the foundations of reality itself. It’s generally considered untestable, since metaphysical assumptions underlie all our efforts to conduct tests and interpret results. Those assumptions usually go unspoken. Most of the time, that’s fine. Intuitions we have about the way the world works rarely conflict with our everyday experience. At speeds far slower than the…

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The new math of how large-scale order emerges

The new math of how large-scale order emerges

Philip Ball writes: A few centuries ago, the swirling polychromatic chaos of Jupiter’s atmosphere spawned the immense vortex that we call the Great Red Spot. From the frantic firing of billions of neurons in your brain comes your unique and coherent experience of reading these words. As pedestrians each try to weave their path on a crowded sidewalk, they begin to follow one another, forming streams that no one ordained or consciously chose. The world is full of such emergent…

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Reimagining balance

Reimagining balance

Joel Kaye writes: Between approximately 1250 and 1375, a manifestly new sense of what balance is, and can be, emerged. When projected onto the workings of the world, this new sense transformed the ways the workings of both nature and society could be seen, comprehended and explained. The result was a momentous break with the intellectual past, opening up striking new vistas of imaginative and speculative possibility. The group of medieval scholars whose speculations most clearly reflected this new modelling…

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Bernard Stiegler’s philosophy on how technology shapes our world

Bernard Stiegler’s philosophy on how technology shapes our world

Bryan Norton writes: By the start of the 1970s, a growing number of philosophers and political theorists began calling into question the immediacy of our lived experience. The world around us was no longer seen by these thinkers as something that was simply given, as it had been for phenomenologists such as Immanuel Kant and Edmund Husserl. The world instead presented itself as a built environment composed of things such as roads, power plants and houses, all made possible by…

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Ancient Greek antilogic is the craft of suspending judgment

Ancient Greek antilogic is the craft of suspending judgment

Robin Reames writes: In Syracuse, 2,500 years ago, there was a famous teacher of rhetoric named Corax. This new discipline was in high demand: mastery of persuasive speaking, it was hoped, led to fame and wealth. As the story goes, Corax’s most talented student was Tisias. Corax agreed to teach Tisias with the understanding that the student would pay when he won his first court case. Tisias advanced so rapidly through his lessons that Corax wanted Tisias to hand over…

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What chaos theory has to teach us about human events

What chaos theory has to teach us about human events

Brian Klaas writes: The 21st century has been defined by unexpected shocks—major upheavals that have upended the world many of us have known and made our lives feel like the playthings of chaos. Every few years comes a black swan–style event: September 11, the financial crisis, the Arab Spring, Brexit, the election of Donald Trump, the coronavirus pandemic, wars in Ukraine and Gaza. Even daily life can feel like a roll of the dice: With regularity, some Americans go to…

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How mathematics built the modern world

How mathematics built the modern world

Bo Malmberg and Hannes Malmberg write: In school, you might have heard that the Industrial Revolution was preceded by the Scientific Revolution, when Newton uncovered the mechanical laws underlying motion and Galileo learned the true shape of the cosmos. Armed with this newfound knowledge and the scientific method, the inventors of the Industrial Revolution created machines – from watches to steam engines – that would change everything. But was science really the key? Most of the significant inventions of the…

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