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View Diary: Books That Changed My Life--Which book was so far over your head you almost didn’t come up? (254 comments)

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  •  Principia Mathematica (18+ / 0-)

    by A.N. Whitehead and B. Russell. Ouch: memories of lost nights, renting of hair, emotional confusion bubble up unbidden just thinking about this work.

    Today I couldn't exactly tell you how I managed to stumble onto this work; the last math class I ever attended was as a senior in high school. But my love and fascination with math has burdened me for as long as I can remember.  

    PM, however, introduced me to axioms, symbolic logic, and inference rules that--as it turns out--lead me to Godel's theorems and the ever-so-slightly turning of my world sideways. In short, I was introduced to the idea that any system based on axioms (even those based on simple algorithms) cannot be proven absolutely. In essence, an observation can be "true" but unprovable as such; and such a system cannot demonstrate its own consistency.

    The three volumes of PM sought to lay out all mathematical foundations, at least for the natural numbers and systems. The work opens by explaining its goals.

    The mathematical logic which occupies Part I of the present work has been constructed under the guidance of three different purposes. In the first place, it aims at effecting the greatest possible analysis of the ideas with which it deals and of the processes by which it conducts demonstrations, and at diminishing to the utmost the number of the undefined ideas and undemonstrated propositions (called respectively primitive ideas and primitive propositions) from which it starts. In the second place, it is framed with a view to the perfectly precise expression, in its symbols, of mathematical propositions : to secure such expression, and to secure it in the simplest and most convenient notation possible, is the chief motive in the choice of topics.  In the third place, the system is specially framed to solve the paradoxes which, in recent years, have troubled students of symbolic logic and the theory of aggregates ; it is believed that the theory of types, as set forth in what follows, leads both to the avoidance of contradictions, and to the detection of the precise fallacy which has given rise to them.

    From these confusing and dense volumes, it was a short journey to the study of logic and from there to philosophy, which has been a life-long endeavor for me. But one which has, for the most part, been a solitary one. Most cherished of the discoveries along the way is another, slimmer volume entitled Tractatus by Ludwig Wittgenstein.

    Books that challenge me, truly challenge me, are some of those most remembered and appreciated. Thanks for the topic and the introduction, Diana--as usual, beautifully done.

    •  There was a copy of PM (7+ / 0-)

      in my university's undergraduate library. It hadn't been checked out in about thirty years.

      (and I went to an "Ivy")

      The thing about quotes on the internet is you cannot confirm their validity. ~Abraham Lincoln

      by raboof on Fri Mar 01, 2013 at 06:08:10 AM PST

      [ Parent ]

    •  Wonderful comment, P Carey! (5+ / 0-)
      Recommended by:
      koosah, Aunt Pat, Brecht, RiveroftheWest, dewtx

      "Intellectual rigor" of the kind you've described is a mind-bending experience.  You're lucky to have the disciplined nature that permits you to undertake and follow through with such a project.  Congratulations on reading PM and Tractatus!

      In my father's library there was a memoir--a contemporary one--written by a man who lived in New York. Too poor to afford college but possessed of an eager, questing mind, he resolved to get his own college education by reading.  He read on public transportation going to and from his job in New York City.  He read during his lunch break and in the evenings. No subject was excluded from his quest for knowledge.

      I remember a line from this book:  "When I read Lancelot Hogben's Mathematics for the Million, I knew the great hour of my life had struck."

      It has always pleased me to think of that dear man being dazzled by mathematics.  It seems that you've had this experience too.  

      Thanks for coming by--good to see you, as always!

      "Religion is what keeps the poor from murdering the rich."--Napoleon

      by Diana in NoVa on Fri Mar 01, 2013 at 06:10:26 AM PST

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