I have just finished reading Prof. Hacking’s book, Introduction to Probability and Inductive Logic. An excellent read with much to recommend it. However, I believe there are some serious lacunae and other omissions that are deplorable, even scandalous verging on the negligent:-

1. Extensive use of urn and ball experiments is made in the book but nowhere in the references does it cite that great innovative and creative probabilist who identified urns and balls as the most fundamental building blocks of probability without which there would be no modern day risk and decision analysis. If this had been a student assignment it would have been severely penalised.

2. There is excessive focus on the use of the black ball in the experiments proposed – this is a sphere of esoteric academic interest of little benefit either to the reader or for probabilism as a whole. No reference is made to the social or psychological impact of the use of other coloured balls or even the perceived impact of colour selection on probabilistic experimentation. I opine that there are also important class, religious and gender related issues attached to balls and urns that need to be brought out into the open.

3. There is a very strong inference that the reader should conduct, willy-nilly, ball drawing experiments at home. This is down-right dangerous. There is a sound theoretic basis for believing that balls can cause injury and supported by some recent observational experience. In the case of urns, careless use can be fatal – numerous bodies have been found that have been totally reduced to fine ash in urns. Urns and balls should only be used under the strictest risk free controlled laboratory test conditions.

4. It seems to be implied that urns and balls can be selected on some bizarre random basis. If experiments are undertaken as suggested then the results would be at best quite uncertain and at worst just plain chaotic and as a result totally unreliable. It has been long known that in order to ensure proper repeatable urn-ball experiments that identical balls must used that are entirely consistent with the aesthetics of the urn and carefully matched to its design and physical attributes.

5. Also if, as inferred, urns-and balls are being used so casually there will be the potential for a significant environmental impact particularly if cheap Chinese or Indian substitutes flood the market. Abandoned urns and balls will litter the university campi and countryside with all the consequences that might entail.


I would like to suggest that an international urn-ball standards committee is urgently required to guard and ensure the highest professional standards in urn and ball usage. To develop and market precision engineered ball and urn sets with a certified reliability and conformity that ensures proper controlled use without any of the confusing uncertainty that exists today. That the urns and balls are fully compliant with current health and safety standards. In addition any person using urns and balls must be trained and licensed by the committee. I would also like to suggest that special consideration in urn and ball design needs to be given for the disabled user.

Gavin Lawrence