Mathematics Is About the World by Robert Knapp

The question of whether and  how mathematics connects with reality is an  important one which has occupied the attention of philosophers intermittently since the time of the pre-Socratics.   In his book Mathematics Is about the World, mathematician Robert Knapp attempts to answer it.

Along the way he makes some good points, particularly in his criticism. He is right that the “official” view of mathematics as an exercise in the formal analysis of undefined objects and  relationships  according to various lists of postulates and having no necessary connection to real things is  both intellectually faulty and operationally dishonest (the latter because mathematicians usually do not really  believe it).  He is right that the answer is not a return to some Pythagorean or Platonic notions of numbers as a higher or determinative sort of reality above the real world.   He is right  that the fact mathematics can be used to understand and predict things and events is not a lucky accident.  The sections on context determining needed, required, or possible precision are interesting as are some of his thoughts on Euclid and Greek mathematics. 

His solution to the main question is to tie mathematics to reality on the basis of objectivist epistemology,   in particular  on Rand’s theory of concepts and their formation. The book goes through a hypothetical development of mathematical ideas in geometry, analysis, algebra and other areas in terms of the integration/measurement omission process of that theory. The work is extensive  and well thought out, but I believe it is a case of someone using the wrong  tool. There are simpler, more thorough and  to the point, and to me better and more convincing ways to establish and describe  the connection between mathematical ideas and reality.  

However, it is surely worthwhile to stimulate people to think about the question and to look at  the standard  answers from the textbooks critically.  To the extent it would do that, the book might  be worth reading whether or not the reader had an interest in objectivist epistemology.  But it is not a book I would recommend to someone wanting to get started thinking about its main topic.

New Book from Peikoff

Discovering Great Plays: As Literature and as Philosophy is a collaboration of  an unusual sort between Leonard Peikoff and Marlene Trollope.  The book is based on transcripts of  lectures he gave in the 1990s, but, as he emphasizes in a preface,  was edited and put together by her with no input from him.   There are eight lectures – one each on Antigone, Othello, Le Cid, Don Carlos, An Enemy of the People, Saint Joan, Monna Vanna, and Cyrano de Bergerac  - from a man who passionately loves the theater and appreciates good writing.  They are well organized, thoughtful, clear, and decisive as to viewpoint. It is easy to tell where he stands  and why. His methods and standards are the usual “official” objectivist ones familiar from Rand’s essays on aesthetics, and many of the results, such as his following her in a gross misreading of Shakespeare , are predictable.  However some of the conclusions and insights are surprising, particularly in the treatment of Antigone. 

All in all it is a book to be read critically and skeptically but also enjoyably. His passion for these plays is infectious and appealing. Also he (and/or she; I don’t know how closely the book follows the transcripts or how much cleaning up and revising she did) is talking seriously about important and interesting subjects worth contemplating.  One can disagree with much  of what he says and still find that something to appreciate.  It surely beats following the news on TV.  

Not Getting to Know You

It is not a trivial activity to learn what another human being is really like. It usually takes time and effort.  The  time and effort can be well spent when selecting friends, lovers, or certainly a husband or wife.  However there are many other times when it is not  necessary or worthwhile  to expend them because something else is fully sufficient.

Suppose you are listening to your local superintendent of schools pitching a bond issue. You know she has said things that were false when she argued for bond issues and other funding in the past.  You  do not know if she was lying, careless, stupid, or simply honestly misinformed  when she did so. You do not know enough about her character and intelligence even to have an opinion,  but you do know  what you need to know to make a decision. You know enough not to accept her new claims and promises without separate verification and guarantees.

Consider an American president who fairly consistently behaves as though he despises the country, its basic principles, and most of the people in it, including you. From following him in the news and reading things he has said or written, you have evidence that leads you to believe those are his actual sentiments.  However  you have never met the man. You realize that  some people you respect who know him  think he is only  misguided and  not ill-intentioned.  You might like to know definitely  what sort of person he is, but for  the important purposes of guessing what he might do,  deciding whether to oppose him politically, or making  plans  to protect yourself, you do not need to know.  It is enough to know his pattern of behavior.  You don’t need to peer into his soul, and you probably wouldn’t want to anyway.

Similar things are true for many of life’s interactions.  There are  no general obligations and often no need or good reason  to analyze and draw definite conclusions about people’s  overall motivations and character.  (Which is good thing, because many times neither are there means for doing so fairly, validly, and rationally.)  It is usually enough to learn  what  you need to know about people to decide or accomplish what you want to and let it go at that. Besides one of the benefits of minding your own business is that it leaves you more time to see  to your own business. 

Going Through Old Files

The split between Nathaniel Branden and Ayn Rand in of 1968 brought the end of the first organized objectivist movement.  The organization offering taped lectures, the book selling company, and other ventures shut down immediately.  He moved to California and started a new career. She continued the magazine and then a newsletter for a  few years, writing  mainly about current events.  

She denounced him in harsh  terms in a notice in the magazine, labeling him as a  scoundrel and a traitor to her and her philosophy. He responded in print, admitting mistakes but disputing several of her accusations and more than hinting that an intimate personal conflict was the main cause of  what had  happened. Years later in books written by Branden and his ex-wife Barbara, it came out that Rand and Branden had had an off and on sexual relationship for over a dozen years and that the split was caused by Rand’s learning about Branden’s concurrent involvement  with an attractive young woman. 

 I had not thought about any of this for a good while, but a few days ago I came across some articles about the split while going  through some old files.  I was struck again, even allowing for uncertainty about the full details and for plenty of exaggeration and special pleading all around, by how strange,  sad and discrediting to almost all concerned the entire business was. That was nothing new. What was new for me was noticing how truly strangely the public part of the separation was managed, considering they were both supposed to be reasonable and mature adults.

Most reasonable and mature adults would have handled it with something like a statement from her announcing that due to various personal and professional disagreements they had ended their association and a notice from him that he was closing his business to pursue other opportunities across the country. At most  the person in her position might have added a disclaimer that she no longer considered him as any sort of spokesman for her. That would have better served the interests of both parties and also been honest and sufficiently informative. What happened instead was something more like an angry breakup between two overwrought teenagers and itself sad and discrediting all around.

Odd Business

There have been some odd goings on among so-called official objectivists for a long time, going back to some of the condemnations and repudiations of former friends and colleagues by Ayn Rand herself during the 1960’s and 1970’s. Leaving the business with the Brandens aside, there were a number of cases where she turned on people harshly and wrote them out of the objectivist movement for offending her in some way. One can of course note that she was scarcely the first creative person to behave in an imperious way toward members of her entourage or the first artist to display what used to be called an artistic temperament. Still it all seemed disproportionate, overly bitter, inconsistent with her philosophy, and surprisingly frequent - happening often enough to become something of an ongoing joke among people who paid attention to what was happening.

After Any Rand’s death, Leonard Peikoff as her heir became the custodian of her legacy. Even early on there was much in his behavior to call to mind Nietzsche’s comment that the first generation of adherents proves nothing against a philosophy. In particular one can recall his deciding to ride David Kelley- a man who, judged by his writings, is as reasonable and thoughtful a person as you could expect to find just about anywhere – out of town on a rail for violating his parole by consorting with known libertarians.

Peikoff has claimed that objectivism is a fully integrated, closed and consistent system defined by Rand’s writings and not open to corrections of or deviations from the conclusions of those writings. (I don’t know if this extends so far as to saying that if, for example, a person likes Antigone better than Cyrano de Bergerac, he’s off the reservation as far as objectivism goes, but it sounds like it. It also sounds more like a hierophant protecting holy writ than like actual philosophy.) Peikoff wrote that the realm of possible honest error in philosophy is small, and that people, the very young and slow witted excepted, who fail to agree with objectivism mainly do so through bad motives. Aside for the fact that this claim is obviously false , it has a couple of implications that probably would bother most objectivists. It is hard to claim simultaneously that Ayn Rand was a great creative philosophical genius and also that her conclusions are so obvious that only kids, dummies, and bad people would not reach them. Second the notion leads to the conclusion that Aristotle, John Locke, Plato, Isaac Newton, Thomas Jefferson, George Washington, Albert Einstein, and all the other serious people who thought about some of the same questions without reaching the conclusions of objectivism were bad guys, a claim that might be a bit embarrassing to defend. Peikoff also is mainly responsible for the efforts to maintain the fiction that Rand did not undergo a process of development in which her ideas and viewpoints evolved and changed and the accompanying assertion that her thoughts, attitudes, and pronouncements were fully consistent over time. This has included publishing editions of her letters and journals so bowdlerized that some people who have seen the originals deem the published books to be misleading and almost useless for scholars.

All of this stuff came back into the news recently with the controversy over a book a man named David Harriman wrote about induction in physics. In the book the author proposes and works from a theory of induction that he credits to Peikoff. (Peikoff wrote the introduction to the book, and Harriman gives him credit for developing the philosophical ideas behind it and reviewing the manuscript line by line.) The book cites examples and illustrations from the history of science. A historian of science named John McCaskey questioned the accuracy of some of the illustrations – things such as whether Galileo had a firm notion of the idea of friction or whether Newton explicitly understood acceleration as a vector quantity. He also credited the author with good work and good intentions and praised the book as generally a step in the right direction. Well, this all rubbed Peikoff the wrong way, and he launched ballistic big time. McCaskey was on the board of the Ayn Rand Institute, the 501(c3) that Peikoff had created to represent and promulgate objectivism. Peikoff issued an ultimatum to the Institute that either McCaskey goes or he goes. McCaskey resigned from the board but did not retract his comments which he continued to claim were valid. Of course, for the purpose of considering this fiasco, it doesn’t matter a bit if he was right or wrong about what Galileo knew about friction. It matters that Peikoff would allow no criticism, no matter how mild or well intended, and that, instead of laughing him out of the room, the foundation caved in to his demands. The whole incident reeks just a little too much for comfort of theologians squashing heresy or Marxists rooting out deviationism. It provides a really sad insight into the thinking of Peikoff and those around him. It suggests that productive work from objectivist thinkers will more likely be coming from members of the open school of thought than from those bound by orthodoxy and its enforcers. It gives people good reason to remember that Nietzsche was right about that first generation of adherents. Lastly, it gives those on the outside of the controversies a spectacle worthy of a belly laugh, a rueful one maybe, but still a belly laugh.