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"You changed my life. I am going to study, practice, and remember your information." Bill Funchion, Adjunct Instructor of English, Waubonsee Community College, commenting on Abraham Lincoln and the Structure of and the revolutionary nature of the six elements of a proposition.

Lincoln scholar and author Brian Dirck in March 13, 2012, The Civil War Monitor:

"Hirsch and Van Haften are an attorney and a mathematical engineer, respectively. They know their business, and there is much to like and to learn from their expertise. No previous scholars have so systematically and minutely examined and laid bare the considerable influence of geometry and the law on Lincoln’s thinking. They make a convincing case. Reading their side-by-side, sometimes almost sentence-by-sentence juxtaposition of, for example, Lincoln’s 1860 Cooper’s Union Address with Euclid’s “elements of a proposition,” and the influence of the latter upon the former is unmistakable.

"Kudos, then, to Hirsch and Van Haften for their creativity, their insight and their ability to reveal heretofore hidden substrata in Lincoln’s writing, speaking and thinking. They have made a valuable contribution to Lincoln scholarship."


Review is in Volume 84, Number 5 of Mathematics Magazine, December, 2011, page 397. Mathematics Magazine is a publication of the Mathematical Association of America. It has more than 20,000 members:

" 'Lincoln transformed geometry into speech.' So hold this book's authors, who demonstrate how Lincoln's self-proclaimed independent study of books I-VI of Euclid formed the basis for the structure of his oratory. The authors map the six elements of a proposition (p. 29) as given in Euclid to components of a legal argument, dissect notable speeches and letters by Lincoln into those elements, and include in full text a dozen annotated speeches and letters." Reprinted with permission.


The January 2012 edition of Structure:

The review concludes:

"I believe that engineering is more intentional than rational, since it routinely involves selecting a way forward from among multiple options when there is no one 'right' answer. Even so, I see parallels between the Euclidean elements of a proposition and what William Addis calls a design procedure ('The Nature of Theory and Design,' May 2009). For the enunciation, exposition, and specification, the client requirements, applicable codes and standards, and time and cost constraints constitute the given, and the completed project is what is being sought. The construction is the engineer’s artful development of a suitable model, and the proof is the deterministic analysis showing that the structure will provide adequate strength and serviceability (justification). The conclusion is what is conveyed in the contract documents (description)." 


Burlington, Iowa, The Hawk Eye, October 11, 2011 
reprinted with permission
Copyright 2011, by The Hawk Eye, all rights reserved
This article was also reprinted in The Hellenic Voice

Book looks at Lincoln speech structure

Authors to discuss Lincoln's use of Euclid's 'Elements' at Burlington Public Library.


"And the war came," is a widely celebrated phrase President Abraham Lincoln made during his second inaugural address during the midst of the Civil War.

But two scholars argue the phrase, while brilliant, owes a debt not to Lincoln but to the structure of his speeches.

David Hirsch, formerly of Burlington, and Dan Van Haften of Batavia, Ill., contend Lincoln tapped into the wisdom hidden in Euclid's "Elements" - that every geometric proof has six elements to form a proposition.

The men share their theory in "Abraham Lincoln and the Structure of Reason."

Hirsch and Van Haften demarcate Lincoln's speeches and letters beginning in 1853, when his words took on the new structure. The speeches, notably the Gettysburg Address and the Cooper Union Address, have six elements that shape a convincing argument for the public that would have read his speeches in newspapers across the country.

The six elements they discovered, which have been mentioned in texts on Greek mathematician Euclid that were popular in Lincoln's time , are:

* enunciation, or stating a given and a sought;

* exposition, or further explanation of the given using indisputable facts;

* specification, or further explanation of the sought;

* construction, or additional statements of fact to build up to the proof;

* the proof, which is stating the argument for the sought; and

* conclusion, which demonstrates the proof.

"In general, Lincoln doesn't get enough credit. As famous as he is, as revered as he is, people don't fully appreciate his intellectual power and how good a lawyer he was and how developed his mind was," said Hirsch, who now lives and practices law in Des Moines. "On the other hand, occasionally, he's given too much credit."

Hirsch pointed to the restraint Lincoln used in the "And the war came" phrase.

"That took no brilliance whatsoever. As beautiful as that phrase is, as beautifully as it was set up, remember this is up toward the top (of the speech). He's just stating indisputable facts."

He compared the words in Lincoln's speeches to leaves. When on a tree, they have structure, but they don't after they fall to the ground.

Hirsch and Van Haften will talk about their book and autograph copies of it at 7 p.m. today at the Burlington Public Library.

Hirsch became hooked on Lincoln when he wrote a paper about how well the president would have adapted to modern technology and modern law. He and Van Haften set about to write a book about the president's time as a lawyer, staying away from his political life that had been written about before.

But Van Haften decided to look into speeches Lincoln made during his debates with Stephen Douglas during their bid for U.S. Senate. Hirsch was worried that they would be wading into political territory, until Van Haften found a reference to Euclid in those speeches.

While the fact Lincoln studied Euclid was no secret, no one viewed the president's scholarship as anything more than mental exercises. Van Haften, a retired software engineer who studied mathematics, went back and retraced Lincoln's steps and made the discovery.

"David said to me, 'Well, Dan, you go and study the first six books of Euclid and learn what it means to demonstrate.' And I kind of got excited about that, because I thought, 'I get to do what Abraham Lincoln did.' I mean, a number of people get to be lawyers ... there's a few people that get to be president; but I don't think anyone has ever done this before," Van Haften said.

He said whoever ultimately came up with the six elements of a proposition deserves credit, as Euclid mostly compiled known geometry in about 300 BCE.

Throughout history, few people have used the style to make their arguments, but Van Haften said those who have are no slouches.

The easiest text to demarcate using the six elements is the United States' founding document written by Thomas Jefferson, the Declaration of Independence. His other noted work, the Virginia Statute for Religious Freedom, also used the style.

Before him, there was Isaac Newton, who used the six elements in his proofs for "The Principia: Mathematical Principles of Natural Philosophy."

Since Lincoln, though, the only other person aside from the authors to use the elements has been President Barack Obama.

The pair are writing another book - due out in the spring - on 34 of Obama's speeches, beginning with the speech he gave in January in Arizona after U.S. Rep. Gabrielle Giffords was shot.

Their goal, however, is to show anyone can craft arguments using Euclid's logic and reasoning.

"Almost any literate person can become an Abraham Lincoln. We show how," they say in the introduction to the 440-page book.

This appears in the April 2011 Newsletter "Old Baldy" of the Civil War Round Table of Philadelphia. It has a great write-up of David Hirsch's National Archives II presentation:

"We have often heard about Lincoln teaching himself Euclidean geometry and have wondered how it helped him. The next presenter David Hirsch in his presentation, " 'And the War Came:' The Geography of Language" explained how Lincoln's in-depth study of geometry gave him his verbal structure. Hirsch is a lawyer in Des Moines, Iowa and a former columnist for the ABA Journal. He co-authored Abraham Lincoln and the Structure of Reason with his friend since the first grade Dan Van Haften. Van Haften is a retired engineer from Alcatel-Lucent. After a trip to Springfield, they started some research to discover what Hirsch called "a secret in plain sight." It is their conclusion that Lincoln embedded the ancient structure of geometric proof into his speeches after 1853. During the presentation Hirsch demarcated the Second Inaugural and the Gettysburg Address into the six elements of a proposition [enunciation, exposition, specification, construction, proof and conclusion]. Additional speeches are reviewed in their book. It was very interesting how easily the speeches broke down into the format of a proof. Just when you thought there was nothing new to learn about Lincoln. The content it occurred after Lincoln's Congressional Term
when he went back to Springfield to reinvent himself to be a better presenter. It aided him greatly in his law practice. Lincoln viewed the survival of the nation as a legal contract."

The online bookstore for the Abraham Lincoln Presidential Library & Museum in Springfield, Illinois, describes the book: "David Hirsch and Dan Van Haften delve into the logic, reason, and cognitive tools that fueled Lincoln's political and intellectual genius."

February 2011, The Iowa Lawyer, by Mark McCormick, former Iowa Supreme Court Justice and attorney at Belin McCormick:
    Abraham Lincoln and the Structure of Reason is “a fascinating study of the structure of Lincoln’s speeches and writings.”
    “They [Hirsch and Van Haften] found a remarkable conformity between the structure of Lincoln’s communications and Euclid’s elements of a proposition.”
    “The book contains much more than an analysis of Lincoln’s speeches and writings. The authors devote considerable attention to Lincoln’s career as a lawyer prior to his election to the presidency. We learn a good deal about Lincoln’s practice of law, including the handling of trials and appeals.
    “We also learn a good deal about Lincoln’s experience in politics. This background sets the context for Lincoln’s interest in Euclid and development of a discipline and consistent rational structure in his speeches and writings. The authors draw impressive parallels between the practice of law in Lincoln’s day and today. For example, the authors contend that ‘A trial itself is a Euclidian proposition.’”
    “The Hirsch-Van Haften book is an impressive contribution to Lincoln scholarship. It helps us understand how Lincoln developed and applied his magnificent analytical and persuasive talents in his most famous speeches and writings.”

Illinois Attorney Steven N. Peskind: "I have read many Lincoln books and think this [Abraham Lincoln and the Structure of Reason] is a great addition to the scholarship."
_____________________________________________________ reviews of Abraham Lincoln and the Structure of Reason.