*I have never had a feeling politically that did not spring from the sentiments embodied in the Declaration of Independence* — Abraham Lincoln

### Background

“THE PROPOSITION that all men are created equal,” President Abraham Lincoln said was the reason that inspired the American forbears to declare independence four score and seven years earlier. His remarks on the afternoon of Thursday, November 19, 1863 were attending the dedication of the Soldiers’ National Cemetery.^{1}

“Now,” Lincoln said, raising his voice, “**We are engaged in a great civil war, testing**….” Two years later, in his second inaugural address, characterized as the only speech worthy of comparison to his address at Gettysburg, Lincoln famously admitted that the test of slavery was “the cause of the war.” ^{2}

### The Problem

Despite the reasoning Lincoln seemed to communicate so effortlessly throughout his career, one might question a statement released during his first presidential campaign – he had “**nearly mastered the six books of Euclid**,” referring to the ancient mathematician credited with discovering geometry through a collection of books entitled the “Elements,” about elementary geometry and its underlying logic.

With a close reading of the Gettysburg Address in light of Lincoln’s claim, there remains absolutely no doubt that he could and should have a more powerful argument against slavery in America, if he had simply applied the same logic of **Euclidean geometry** that he claimed to have studied in his 1860 autobiography, when he was campaigning to win the presidency in the first place.^{3}

### The Evidence

LINCOLN WROTE A LETTER on April 6, 1859 to decline an invitation for a Boston celebration in honor of Thomas Jefferson’s birthday.

After explaining how prior engagements would keep him from attending, Lincoln wrote about the irony of the celebration being held in the same city that was once headquarters to the Federalists that opposed Jefferson.

Lincoln continued by relating Jefferson’s standards for the nation in terms of the math developed by Euclid, even going so far as to write that “**the principles of Jefferson are the definitions and axioms of a free society**.” ^{4}

### Euclidean Logic

The language of Euclid’s math described by Lincoln refers first to the definition** **of** axioms**, which are preliminary statements accepted as self-evident and always true.

Some examples of Euclid’s axioms include the one that says points are the ends of a line and another that says given any two points such as *A* and *B*, there is one and only one line *AB* that can have *A* and *B* as its endpoints.

Through deductive reasoning, one can prove a given proposition as either true or false through the utility of supporting axioms and supporting propositions already proven to be true in the reasoning process.

As implied above and unlike axioms, **propositions** are statements that first need to be proven as true before they can be of any use. By their very definition, **propositions are subject to proof through testing based on the support of self-evident axioms**.^{5}

### Common Sense

**Why did Lincoln at Gettysburg argue that the statement “all men are created equal” was a proposition being tested if it was instead an axiom postulated in Declaration of Independence as self-evident and thus automatically true?**

One possible explanation is that by speaking to a different level of certainty, Lincoln was able to shift his trajectory from past ideas to present realities.

But his letter about the Boston celebration revealed a capacity for him to have utilized all of Jefferson’s self-evident postulates in the Declaration of Independence in support of his arguments to preserve the Union, while at the same time working to abolish slavery.

Lincoln’s letter ended with him praising the personal qualities of Jefferson, who himself said of Euclid’s logic that “there is scarcely a day in which he will not resort to it for some of the purposes of common life.” ^{6}

**References**

1. “The Heroes of July,” *The New York Times*, November 20, 1863. Drew Gilpin Faust, *This Republic of Suffering: Death and the American Civil War* (New York: Knopf, 2008), 69.

2. Garry Wills, *Lincoln at Gettysburg: The Words That Remade America* (New York: Simon & Schuster, 1993), 189. Roy P. Basler, ed., *The Collected Works of Abraham Lincoln*, 9 vols. (New Brunswick: Rutgers University Press, 1953-1955), 7:23. Ibid., 8:332.

3. Ibid., 4:62.

4. Ibid., 3:374-376.

5. Thomas L. Heath, trans., *The Thirteen Books of Euclid’s* *Elements, Vol. 1: Books 1-2 *(New York: Dover, 1956), 153-155.

6. Barbara B. Oberg, ed., *The Papers of Thomas Jefferson*, 36 vols. (Princeton: Princeton University Press, 2004), 31:126.

IMAGE: Weisstein, Eric W. “Axiom.” From MathWorld—A Wolfram Web Resource. https://mathworld.wolfram.com/Axiom.html

Weisstein, Eric W. “Proposition.” From MathWorld—A Wolfram Web Resource. https://mathworld.wolfram.com/Proposition.html

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