Category Archives: Philosophy

Poznań: Random Structures and Algorithms 2013

   Michal Karonski (left) who built Poland’s probabilistic combinatorics group at Poznań, and a sculpture honoring the Polish mathematicians who first broke the Enigma machine (right, with David Conlon, picture taken by Jacob Fox). I am visiting now Poznań for the 16th … Continue reading

Posted in Combinatorics, Conferences, Open problems, Philosophy, Probability | Tagged , | Leave a comment

Why is Mathematics Possible: Tim Gowers’s Take on the Matter

In a previous post I mentioned the question of why is mathematics possible. Among the interesting comments to the post, here is a comment by Tim Gowers: “Maybe the following would be a way of rephrasing your question. We know … Continue reading

Posted in Open discussion, Philosophy, What is Mathematics | Tagged , , , | 23 Comments

Why is mathematics possible?

Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory.  As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading

Posted in Computer Science and Optimization, Number theory, Open discussion, Philosophy, Updates, What is Mathematics | 15 Comments

The Privacy Paradox of Rann Smorodinsky

   The following paradox was raised by Rann Smorodinsky: Rann Smorodinsky’s Privacy Paradox Suppose that you have the following one-time scenario. You want to buy a sandwich where the options are a roast beef sandwich or an avocado sandwich. Choosing … Continue reading

Posted in Games, Philosophy, Rationality | Tagged , , | 17 Comments

The 1789 Declaration of the Rights of Man

Today (April 27, 2012) it is precisely 213 years 7 months, and 29 days to the completion of the declaration of the rights of man, which makes it a perfect occasion to celebrate this remarkable human creation. Here is a … Continue reading

Posted in Law, Philosophy | Tagged | 4 Comments

A Paradoxical Self-Referential Statement

A small discussion in a meeting about two decades ago. Lior: Some people in the department think that they are wiser than what they really are John: I am really wiser than what I think I am. John’s statement is paradoxical … Continue reading

Posted in Philosophy | Tagged , | 1 Comment

Itamar Pitowsky: Probability in Physics, Where does it Come From?

I came across a videotaped lecture by Itamar Pitowsky given at PITP some years ago on the question of probability in physics that we discussed in two earlier posts on randomness in nature (I, II). There are links below to … Continue reading

Posted in Obituary, Philosophy, Physics, Probability | Tagged , , , | 1 Comment

Randomness in Nature II

In a previous post we presented a MO question by Liza about randomness:  What is the explanation of the apparent randomness of high-level phenomena in nature? 1. Is it accepted that these phenomena are not really random, meaning that given enough … Continue reading

Posted in Philosophy, Physics, Probability | Tagged , , , | 15 Comments

Some Philosophy of Science

The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentieth-century philosophers of science who later proposed alternative approaches. It will be convenient to start with … Continue reading

Posted in Philosophy, Probability | 14 Comments


What is the correct picture of our world? Are noise and errors part of the essence of matters, and the beautiful perfect patterns we see around us, as well as the notions of information and computation, are just derived concepts … Continue reading

Posted in Philosophy | 7 Comments