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Hilary Putnam, philosopher and mathematician
Hilary Putnam, philosopher and mathematician

The Quine–Putnam indispensability argument reasons that we should believe in abstract mathematical objects such as numbers and sets because mathematics is indispensable to science. One of the most important ideas in the philosophy of mathematics, it is credited to W. V. Quine and Hilary Putnam (pictured). The roots of the argument can be traced back to thinkers such as Gottlob Frege and Kurt Gödel, but Quine introduced its key components, including naturalism and confirmational holism. Putnam gave Quine's argument its first detailed formulation, although he later expressed disagreement with some aspects of the argument. Many counterarguments have been raised against the idea. An influential argument by Hartry Field holds that mathematical entities are dispensable to science. Other philosophers, such as Penelope Maddy, have argued that we do not need to believe in all of the entities that are indispensable to science. (Full article...)

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Adult Balkan terrapin
  • ... that hatchling Balkan terrapins are only 3 to 4 centimetres (1.2 to 1.6 in) in length, while adults (example pictured) can grow as long as 25 cm (9.8 in)?
  • ... that Rush Munro's, New Zealand's oldest ice creamery, has used the same recipes since 1926?
  • ... that the mean sea level observed by the Newlyn Tidal Observatory from 1915 to 1921 defined the reference for height measurement in Great Britain?
  • ... that Orchard MRT station had a dome over the station's circular concourse until it was removed in 2008?
  • ... that there are only 4 locations left of Boloco, which once had 22 burrito restaurants throughout the northeastern United States?
  • ... that Jeʹvida is the first feature film in the Skolt Sámi language?
  • ... that the novel Minor Detail is based on a true story of a 1949 gang rape and murder of a young Arab Bedouin-Palestinian girl by Israeli soldiers?
  • ... that people were scammed on New Zealand television by the host of You've Been Scammed?

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On this day

November 20

Nuremberg trial defendants
Nuremberg trial defendants
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Merkel received the Presidential Medal of Freedom from U.S. president Barack Obama in 2011.
Merkel received the Presidential Medal of Freedom from U.S. president Barack Obama in 2011.

Angela Merkel has received awards and honours from national governments, universities, and other non-governmental organisations. Merkel was the chancellor of Germany from 2005 until 2021, a length of tenure only exceeded by that of Helmut Kohl, and was the first female German chancellor. During her chancellorship, she was widely considered the de facto leader of the European Union. Forbes named Merkel the world's second most powerful person in 2012 and the world's most powerful woman fourteen times. Awards and honours received by Merkel include a special issue of the Grand Cross First Class of the Order of Merit of the Federal Republic of Germany, the United States Presidential Medal of Freedom, and twenty-one doctorates honoris causa. (Full list...)

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Statuette of a seated female from the Bactria–Margiana Archaeological Complex

In archaeology, the Bactria–Margiana Archaeological Complex (BMAC), also known as the Oxus Civilization, refers to a Middle Bronze Age civilization of southern Central Asia, existing in its urban phase from circa 2400 to 1950 BC. Most of the BMAC's urban sites are actually located in Margiana (modern Turkmenistan) on the Marghab River delta, and in the Kopet Dag mountains. There are a few later sites in northern Bactria, in what is now southern Uzbekistan, but these are mostly graveyards belonging to the BMAC-related Sapalli culture. A single BMAC site lies in southern Bactria, in the north of modern Afghanistan. Sites found further east, in southwestern Tajikistan, though contemporary with the main BMAC sites in Margiana, are only graveyards, with no urban developments associated with them. This BMAC statuette of a seated female is an example of a "Bactrian princess", dating to between the late 3rd and early 2nd millennium BC. It is made of steatite or chlorite and alabaster, with dimensions of 3+9⁄16 in × 3+11⁄16 in × 1+7⁄8 in (9.0 cm × 9.4 cm × 4.8 cm). The sculpture is now in the collection of the Metropolitan Museum of Art in New York City.

Sculpture credit: unknown; photographed by the Metropolitan Museum of Art

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