Robert Knapp earned his Ph.D. in mathematics from Princeton University in 1972. He has published work on differential geometry and partial differential equations, and, after a year at the Insitute for Advanced Studies in Princeton, taught graduate and undergraduate mathematics at Purdue University. His study and appreciation of abstract mathematics began in high school and his conviction that mathematics, including abstract mathematics, is about the world began then, as well. Although he retired from the profession in the late 1970s, his study of the content, history and application of mathematics continues to this day. In recent years he has presented his unique perspectives on geometry and the number system in a series of lectures at Objectivist Summer Conferences organized by the Ayn Rand Institute. He has lived in the Philadelphia area for almost 30 years.
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mathematics is about the world by Robert E Knapp 
Are you interested in errata? I’m just starting Chapter 5 and have found four so far.
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Yes I am. Thanks!
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OK. Here you go.
Pg 61, second line from top, “…to draw the line indicated line…” should read “…to draw the indicated line…”
Pg 67, end of second paragraph, “…, they point manifestly point in different…” should read “…, they manifestly point in different…”
Pg 78, middle of 1st paragraph, under Euclid and Abstraction, “But, are there a separate Forms for each…” should read “But, are there separate Forms for each…”
and
Pg 261, fifth paragraph, “…are the left setsof the Dedekind cuts…” should read “…are the left sets of the Dedekind cuts…”
BTW, very interesting and thoroughly enlightening. I’m looking forward to diving into the rest.
Cheers
BA Math, MS Operations Research
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Second installment.
Pg 270, 3rd paragraph, 5th sentence “…it is reality; that ties them…” should read “…it is reality that ties them…”
Pg 286, under Cartesian Coordinates, 1st paragraph, last sentence, “…specifications of the x and y axis…” should read “…specifications of the x and y axes…”
Pg 318, 3rd paragraph, third sentence “…view that “there is nothing is in my pocket,” …” should read “…view that “there is nothing in my pocket,” …”
Pg 319, under Functions, 1st paragraph, 2nd sentence “…a means to both the formulation and the solution of problems in physics.” should read “…a means to both formulate and solve physics problems.”
Pg 320, 3rd paragraph, 1st sentence “…relates to mathematical domain:” should read “…relates to mathematical domains.”
Pg. 326, 4th paragraph, 6th sentence “…in the set of point for…” should read “…in the set of points for…”
Pg 392, 3rd paragraph, 2nd sentence “…if one add an angle of…” should read “…if one adds an angle of…”
Pg 412, 5th paragraph, 1st sentence, “…equivalent vector one chooses to subject to these operations.” should read “…equivalent vector one chooses, subject to these operations.”
Pg 488, footnote #16, 1st line, “…is a set if itcan be put…” should read “…is a set if it can be put…”
On a general note, throughout the text are figures wherein colors are mentioned (see Pgs 363, 364, 431, etc.); however, none of these figures have any color. Green and red are missing.
Finally, on Pg 465, the color pink pops up for the first and only time. I suspect, that should read red, instead.
Finished the book, but will need additional readings to absorb all of it.
Cheers
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Thanks!
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From James Franklin: It seems that my book An Aristotelian Realist Philosophy of Mathematics (Palgrave Macmillan, 2014) is roughly along the same lines as what you are saying. Perhaps we should both look into how parallel they are .A review of my book that explains the content well is at http://www.newcriterion.com/articles.cfm/The-sum-of-its-parts-7955
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Great to hear from you! A friend saw a review of your book a few months ago and brought it to my attention. I bought your book in September but have not yet read it. I would certainly be interested in corresponding. The best review of my book is the one by Andrew Layman on Amazon.
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An author who envisaged for certain respects your ideas about Euclid geometry is Hugo Dingler;a german philosopher and mathematician who published two books about this topic;though a neglected figure in the realm of mainstrem philosophy it has also today some followers in Germany.The books are,alas,in german and the most pertinent to your enterprise is:Die Grundlagen der Geometrie.If you do not find a copy in some USA library I may send you,if interested,my personal pdf copy (which can be used for personal study only).
R.L.
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Thank you for the information! I have ordered a reprint on Amazon with a similar name, but it has the word Angewandten before Geometrie. Does this sound like the same book? If not, I would be interested in the PDF.
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No it is not the same book though the author is the same.I posted all the stuff via e.mail
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On page 261, the paragraph beginning, “To express this symbolically”, the word “form” should be “from”.
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On page 387, paragraph beginning, “But”, “…the theory of vector paces provides…”
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Dear Dr. Knapp,
Thank you for your wonderful book!
I have a BS In Math from Stanford and I am an Objectivist, so your book was doubly welcome.
My Kindle edition seems to be the first printing;; how do I update it?
Some years ago, I wrote an unpublished monograph proving that Objectivist Epistemology was incompatible with Logicism, Intuitionism, and Formalism. This implies that someday there will be a fourth Foundation of Mathematics, this time on a Objectivist base. I also showed why Objectivism is not vulnerable to either of Godel’s Incompleteness Theorems!
I’d like to send you a copy, but I need your email address to do so.
Cordially,
Craig Franklin
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Thank you for your comments and interest.
Unfortunately, there does not exist a kindle of the second printing.
My email address is bobeknapp@comcast.net.
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