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Gödel Without Tears, slowly, 12

And, at last …. Cue drumroll … ‘The First Incompleteness Theorem, syntactic version’ This is the version of the theorem that Gödel highlights in his epochal 1931 paper, and which people usually have in mind when they talk of ‘the’ … Continue reading → The post Gödel Without Tears, slowly, 12 appeared first on Logic [More]

Gödel Without Tears, slowly, 11

And at last, we get to a proof of ‘The First Incompleteness Theorem, semantic version’, uisng pretty much Gödel’s materials. And given our background work over previous chapters, it is very easy. Grasp the trick in constructing the described Gödel … Continue reading → The post Gödel Without Tears, slowly, 11 appeared first on Logic [More]

Trump’s Strength

In my high school and college track and cross-country days I was accustomed to the usual unflattering comparisons between runners and football players. Runners were often mocked as weak and unmanly, while football was a sport for manly men. When Trump’s followers praise his strength, this reminds me of those days and leads me consider [More]

Famines as Military Weapons: Is Europe in Danger?

 A Dutch girl photographed at the time of the "hongerwinter", the famine that hit The Netherlands in 1945, during WW2.  In the West, we tend to think of famines as events of the remote past that will never return, a view typified by Steven Pinker in his 2011 book "The Better Angels of our Nature." This attitude is often accompanied by sneers at Paul Ehrlich who, in 1968, had predicted extensive worldwide famines that were soon to occur. Even when famines are discussed as a real possibility, they are seen as affecting only those remote countries where hordes of dark-skinned or slant-eyed people already live in near-starvation conditions. We forgot how close in time was an age in which hunger was a fact of life and famines a common occurrence. The last important famine in Europe was in the Netherlands in 1946 -- that was less than a hundred years ago, not in the Middle Ages. Our lack of historical memory is the reason why we see books such as "One Billion Americans" by Matthew Yglesias, where the author happily neglects the problems involved with supplying food and energy to a U.S. population three times larger than it is nowadays. The real problem with assessing the possibility of future famines is that they are often man-made, that is actively created by human actions. Starving an enemy is a time-honored strategy that works beautifully. We have a detailed report of how it was put into practice by the Romans at the time of the Siege of [More]

Gödel Without Tears, slowly, 10

A good time to join the party, if you haven’t yet been following along with this chapter-by-chapter posting of a new version of Gödel Without (Too Many) Tears. Along with revised versions of early chapters (thanks to all those who … Continue reading → The post Gödel Without Tears, slowly, 10 appeared first on Logic [More]

Famines as a Military Weapon: Is Europe in Danger?

 Above, a Dutch girl photographed at the time of the "hongerwinter", the famine that hit The Netherlands in 1945, during WW2. One of the best ways to make wrong predictions consists of extrapolating from a too small set of data. You see that when people speak of the "Pause" in global warming, but it is a very general rule. About famines, in 1968 Paul Erlich predicted extensive worldwide famines that were soon to occur in his book "The Population Bomb" (1968)  That didn't happen and, instead, famines declined worldwide to the point that an optimistic view of the future became prevalent. In 2011, in his book "The Better Angels of our Nature" Steven Pinker argued for the opposite of Ehrlich's predictions, that there will be no more major famines in the world for the foreseeable future.In this post, I argue that both Ehrlich's and Pinker's predictions were affected by the classic mistake of extrapolating from too few data. Ehrlich was influenced by the famines of the 1950s and 1960s, in particular by the Chinese famine of 1959-1961 that killed a number of people estimated in the range of tens of millions. Pinker, instead, was influenced by the lull in famines of the past 30 years or so, that can't be considered as a rule in human history. But can famines return for real? In the West, when we discuss this subject, we tend to think of famines as events of the remote past that will never return. Or, if they will, they will affect only those remote countries [More]