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The notion of indivisibles and atoms arose in ancient Greece. The continuum—that is, the collection of points in a straight line segment, appeared to have paradoxical properties, arising from the ‘indivisibles’ that remain after a process of division has been carried out throughout the continuum. In the seventeenth century, Italian mathematicians were using new methods involving the notion of indivisibles, and the paradoxes of the continuum appeared in a new context. This cast doubt on the validity of the methods and the reliability of mathematical knowledge which had been regarded as es...

Mind over matter: the contradictions of George Berkeley He did not believe in the existence of the material world. But the 17th-century philosopher’s arguments are less radical than they seem Portrait by John Smybert, 1727. GL Archive / Alamy Stock Photo George Berkeley is one of the greatest philosophers of the early modern era. Along with John Locke and David Hume, he was a founder of Empiricism, which championed the role of experience and observation in the acquisition of knowledge. He influenced Kant and John Stewart Mill, and even pre-empted elements of Wittgenstein. His book The Prin...

  There exists a photograph of this writer standing before a giant “71” mounted outside the Botanic Gardens in Belfast. I am very small. But even if I were larger, the towering red digits would suggest totalitarian confidence of a Riefenstahlian stripe. That wasn’t quite how it was. I had been brought to the now largely forgotten exposition celebrating – or commemorating, or perhaps merely acknowledging – the 50th anniversary of Northern Ireland. I remember having a nice time. I also remember not really understanding what it was all about. It is difficult to mark the...

Abstract The notion of indivisibles and atoms arose in ancient Greece. The continuum—that is, the collection of points in a straight line segment, appeared to have paradoxical properties, arising from the ‘indivisibles’ that remain after a process of division has been carried out throughout the continuum. In the seventeenth century, Italian mathematicians were using new methods involving the notion of indivisibles, and the paradoxes of the continuum appeared in a new context. This cast doubt on the validity of the methods and the reliability of mathematical knowledge which had been rega...

What is philosophy about?   What is the true nature of reality? The meaning of life? How should one live? I read a collection of essays (The Power of Ideas) by philosopher Isaiah Berlin (1909-97). He does not answer such questions. Rather, explores how we are to think about them. Berlin posits four categories of questions. One is a straight factual (empirical) question. Who killed JFK? That can be answered, exactly and certainly, from observation and evidence (conspiracy theories notwithstanding). Two: Why did Oswald kill JFK? Also a factual question, it cannot be answered with similar ex...