Euclidian logic, being created equal, slavery, natural law and self-evident truths

1:00  The institution of slavery still exists in the US

A Structured Proof: Historians and scholars, such as Donnie Dottei in his Ashbrook thesis, argue that Jefferson structured the entire document like a Euclidean proof.  It follows a six-point logical sequence: stating the proposition (enunciation), outlining the premises (exposition), applying them to the case of the colonies (specification), building the argument (construction), demonstrating the necessity of independence (demonstration), and concluding with the final assertion (conclusion). 

10:00  Declaration of Independence

12:00  Equality

13:00  Equality of opportunity

14:00  Monarchy

15:00  Natural rights and natural law

16:00  Logos

17:00  Noahide laws

18:00  Liberty

Noahide laws

19:00  Freedom of belief

20:00  Consent

21:00  Pursuit of happiness should be pursuit of justice.

22:00  Duty to change the political system if it is destructive.

28:00  Syllogisms

30:00  Is it possible to express the Declaration of Independence as a formula or formulae?

It is possible to express key parts of the US Declaration of Independence (particularly its famous preamble and overall argumentative structure) as logical formulae, syllogisms, or even a simplified mathematical inequality. The document itself is not a mathematical proof or equation in the algebraic sense, but its reasoning closely mirrors Euclidean geometry (which Thomas Jefferson studied) and Enlightenment logic: it begins with self-evident axioms (premises treated as obvious truths) and deduces a conclusion through a chain of reasoning. The Core Preamble as a Logical ChainThe most famous section can be broken down into a series of connected propositions (often analyzed as a syllogism or chain of implications):We hold these truths to be self-evident,

• that all men are created equal,
• that they are endowed by their Creator with certain unalienable Rights,
• that among these are Life, Liberty and the pursuit of Happiness,
• that to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,
• that whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.

This can be formalized in propositional logic (using symbols where → means "implies," ∧ means "and," and premises build toward a conclusion):Let:

• E: All men are created equal.
• R: They are endowed with unalienable rights (Life, Liberty, Pursuit of Happiness).
• G: Governments are instituted to secure these rights, deriving powers from the consent of the governed.
• D: A government becomes destructive of these ends.
• Rev: The people have the right to alter or abolish it and institute new government.

Then:
(E ∧ R) → G
G ∧ D → RevOr, as a single chained implication (reflecting the long sentence's structure):
E ∧ R ∧ G ∧ D → RevThis treats the "self-evident truths" as axioms (starting points accepted without further proof, akin to geometric axioms like "things equal to the same thing are equal to each other"). The right to revolution follows deductively. Overall Structure as a SyllogismScholars often describe the entire Declaration as a deductive argument in syllogistic form (major premise + minor premise → conclusion):

• Major Premise (philosophical axiom): When any form of government becomes destructive of the ends of securing unalienable rights, it is the right (and duty) of the people to alter or abolish it.
• Minor Premise (empirical claim): The government of Great Britain (King George III) has become destructive of these ends, as evidenced by the long train of abuses and usurpations listed in the document.
• Conclusion: Therefore, the American colonies have the right (and duty) to declare independence and institute new government.

This mirrors classical logic: if the premises are true, the conclusion necessarily follows.A Mathematical Analogy (Moral Calculus)One legal scholar has playfully formalized the Declaration's underlying "moral calculus" as a simple inequality: If L < (F + E), then R Where:

• L = Law (or the existing legal order),
• F = Freedom,
• E = Equality,
• R = Revolution (justified when law insufficiently protects freedom and equality).

This captures the idea that when the current system fails to deliver on natural rights, replacement is warranted. It is not a literal equation from the text but a concise symbolic summary of its logic. Limitations

• The full document (introduction, grievances list, denunciation, and formal declaration) cannot be reduced to a single compact formula without losing its rhetorical power, historical context, and evidentiary details (the "long train of abuses" serves as empirical support for the minor premise).
• It blends natural law philosophy, legal indictment, and political rhetoric rather than pure mathematics.
• Formalizations in predicate logic (with quantifiers like ∀ for "all" or ∃ for "exists") are possible but more complex and less illuminating than the propositional/syllogistic versions above—for example, ∀x (Human(x) → HasRights(x)), but this quickly becomes cumbersome for the entire text.

In short, while the Declaration is not itself a mathematical formula, its axiomatic structure, deductive reasoning, and self-evident premises make it highly amenable to expression as logical formulae or a proof-like argument. Jefferson and the founders drew on Euclidean-style reasoning, where self-evident truths lead inescapably to conclusions. This logical clarity helped make the document persuasive to "a candid world."