A Positive Trend
Posted by Jerry on August 14, 2007
An Objectivist blogger from the UK–specifically, from Cambridge I think–attended the recent Objectivist conference in Telluride, Colorado, organized by the Ayn Rand Institute. His account of the experience at the conference is very interesting to read. Particularly noteworthy are his notes on a lecture by an Objectivist intellectual that dealt with the area of mathematics. I have little to no knowledge about mathematical issues or the Objectivist perspective on the concept of numbers. My readings in mathematics have been mostly of the abstract philosophical nature–like reading a popular account of the Last Theorem of Fermat and the Incompleteness Theorem of Godel. So, I am really intrigued to learn more about the works of Objectivist intellectuals in the field of mathematics.
Here’s an excerpt from his post:
I was particularly taken with [Pat Corvini's] identification of number as the conceptualisation of a particular relationship between a unit of a particular kind and a group of such units, or a compound entity divisible into such units. For example, “two” is an abstraction standing for the relationship one apple bears to a pair of apples, one dog bears to a pair of dogs, one TV programme bears to a pair of TV programmes, and so on. Likewise, “one half” stands abstractly for the relationship between a stick one metre long and a stick half that length, and a lecture one hour long and one thirty minutes long, etc. Seen in this light, counting numbers and fractions are clearly the same kind of thing.
I was particularly taken with her identification of negative numbers as conceptualising the relationship between a unit of a particular kind, and a group of units of some opposite cancelling kind, such as credits and debits, or units of temperature relative to a chosen zero such as the freezing point of water. For example, “minus seven” conceptualises the kind of relationship that exists between a credit of £1 and a debit of £7, or a rise of one metre relative to sea level and a fall of seven metres. Corvini made a very good point about the laws about combining sign (e.g. a negative number times a negative number being a positive number) being a consequence of this underlying reality which negative numbers conceptualise, and not a primary axiom or arbitrary convention as some mathematicians have argued.
All this is satisfactory to me because it links the various forms of numbers, and it makes them proper concepts with real referents (just like “table” or “green” or “above” or “justice”), not floating abstractions plucked from the void or arbitrary constructs devoid of objective justification.
I also enjoyed Corvini’s observations about the many ways in which the system of numbers mankind has developed satisfy his need for unit-economy. A nice integration with Ayn Rand’s ideas about the “crow epistemology”.
Corvini also had some interesting material on measurement, units and irrational numbers.
Obviously there is a huge amount more to be done here: Corvini never left the realm of very basic school mathematics. She did not cover, for example, “imaginary numbers” (where I think Rand’s treatment of them as concepts of method rather than numbers, later echoed by Dr. Binswanger who treats i as an operator not a number, is essentially correct). [emphasis in original]
Oh, and while reading his post, it was a delight to come across the following as well:
- Objectivism is more acceptable in academia now than it has ever been in history. Literally scores of universities now have courses on the ethics of capitalism or similar topics, where books like Atlas Shrugged or Capitalism: the Unknown Ideal are required reading.
- We have seen the first Objectivist works, such as Tara Smith’s Ayn Rand’s Normative Ethics: the Virtuous Egoist, published by world-leading academic publishers (in this case Cambridge University Press).
- John McCaskey of the Anthem Foundation (which does excellent work sponsoring Objectivist scholarship and the promotion of Objectivism in academia) reported the ground-breaking news that a number of non-Objectivist professors who are world leaders in their fields in philosophy have said that they regard Ayn Rand as basically right in what she said about their field, and others have expressed their pleasant surprise at actually reading what Rand had to say. The field of perception was one I recall being mentioned, and Tara Smith spoke of similar trends in ethics.