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Clarification: I am not seriously asking if a country has a constitution on the level of precision of formal logic. I meant which country exhibits “completeness” more than others, which tends in this direction, but on a realistic level - taking more of a rational approach to law than a rhetorical one. Just the fact that Iceland seems to declare that it is a country rather than assuming that is already huge to me, and I’d love to see other examples of something like that.

I looked at Cuba’s constitution and it began with somewhat gilded rhetoric about the history of this great nation. Iceland’s comes closer to being terse, but it has legal jargon from the beginning.

I am interested if there is a constitution which is more like a logical system founded on axioms, something like this:

  1. There exists an entity, called “The United States of America”.
  2. This entity will referred to as a “country” or a “nation”.
  3. This document recognizes the existence of other “countries”.
  4. The United States of America is an entity capable of “ownership”.
  5. “Ownership” is a property between one thing and another.
  6. Ownership has no inherent meaning; rather, we define “laws” on top of any situation of ownership.
  7. The United States of America is comprised of a set of laws, a set of subjects, and its ownership of certain things.

And so on.

The key point is that you try not to assume the existence of anything, so you have to define every term in terms simpler than it. Iceland does actually nod at this. Article 1 of its constitution flatly states, “Iceland is a republic with a parliamentary government”.

However, this assumes knowledge of what a republic and a parliament is.

Julius Hamilton
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    This looks like a legal question that might be on topic at law.se but I am not sure on that. – Joe W Dec 08 '22 at 22:23
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    @JoeW why would it be off-topic here? The constitution of a nation seems political enough to me. – JJJ Dec 08 '22 at 22:51
  • @JJJ I read the question as talking about laws – Joe W Dec 08 '22 at 22:59
  • Since the distinction between positive and natural law is a basic concept of the philosophy of jurisprudence, definitely law.se. – ccprog Dec 08 '22 at 23:08
  • I seriously doubt that any of them do to that extreme level. – ohwilleke Dec 09 '22 at 00:16
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    I don't think a legal system can work like this, really. Formal logic works very well for mathematics where the things being reasoned about are entirely created by logic from first principles, or in physics where things have a very small number of properties carefully constructed to match rigorously controlled experiments. Law has to deal with much more complicated objects that pre-exist, so it's incredibly difficult to construct truly rigorous formal definitions that correspond to exactly what you intend and nothing else. Let alone fuzzy subjective things like "intent, "consent", etc. – Ben Dec 09 '22 at 01:17
  • And if you're not going to define your entire legal system with this level of rigor, what's the motive to doing it with the constitution? – Ben Dec 09 '22 at 01:21
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    While in general I think that explicitly defining terms used in laws is a good thing, you ultimately need to have some "primitive" set of vocabulary assumed to be already known. – dan04 Dec 09 '22 at 01:31
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    The problem with doing this, is that it gets really annoying real fast. An (in)famous example is Russell and Whitehead's Principia Mathematica which tries to do what you suggest for arithmetic. It famously requires 379 pages until it has laid enough of the groundwork in order to prove that 1+1 = 2. Even more famously, Kurt Gödel proved that any formal system that is powerful enough to describe arithmetic cannot be both complete and consistent, i.e. that there are either true statements that cannot be proven to be true (incomplete) or there are false statement that can be proven to be … – Jörg W Mittag Dec 09 '22 at 03:02
  • … true (inconsistent). Now, I am not a logician, but I would not be surprised to find out that Gödel's Incompleteness Theorems also apply to Laws, i.e. that any axiomatic system that is powerful enough to describe Laws must be either incomplete or inconsistent. (In fact, I am almost sure this is the case since Gödel proved this is true for any system powerful enough to describe arithmetic, and a system powerful enough to describe Laws surely feels like it is also powerful enough to describe arithmetic.) – Jörg W Mittag Dec 09 '22 at 03:05
  • @JörgWMittag: I am not sure that Godel is important here. For once, consistency would be more important than completeness for a set of "legal axioms", as we don't need to cover every possible case. For a mathematical example, group theory is not complete but it didn't prevent anyone to work with groups. Also, the law will never require the full set of integers but a bounded subset of it; I am not sure a system of axioms that consider arithmetics on finite sets cannot be complete and consistent. – Taladris Dec 09 '22 at 04:07
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    @Taladris: You are likely right, as I wrote, I am not a logician. However, the first part of my argument still stands: defining everything axiomatically without "assuming existence of anything" (as the OP specified), is extremely tedious. For example, in their question, the OP forgot to define what "There exists" means, what an "entity" is, what it means for an entity to be "called" something, what it means for an entity to be "referred" as something, what "This" refers to, what a "document" is, what it means to "recognize" something, what "existence" is, what "other" means, etc. – Jörg W Mittag Dec 09 '22 at 04:18
  • @JörgWMittag: the definition of "There exists" and other rules of logic would be pre-axiomatic actually. But I agree with your main points: there are problems in the OP's axioms (2. is not an axiom for example), and even if a logic system and an axiomatic were rigorously written down, it would be impractical (there is a reason why non-logician mathematicians don't write proofs using formal logic) – Taladris Dec 09 '22 at 10:07
  • This question belongs to Law SE. Asking why laws aren't designed such way may be on topic both here and Law SE. – kandi Dec 09 '22 at 11:17
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    This seems a very implausible way of defining a constitution, and I doubt it is possible. But the question of whether any existing national constitution does this (or attempts to do it), is an answerable political question that's on topic. In a world where nations are adopting Bitcoin as currency, who knows what strange notions may take hold next? – Stuart F Dec 09 '22 at 11:30
  • @JörgWMittag That's the completeness part. The other option is to be inconsistent, which means it proves the same thing is both true and false at the same time (Which means it proves everything is true and false, so the whole system is useless). – Alan Dec 11 '22 at 03:38
  • @peters: isn't that "logical system" actually against everything that politics and politician today stand for? Can you explain how politics and politicians would "look like" if that logical system would be put into practice? – virolino Dec 12 '22 at 11:10

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Axioms aren't really how constitutions work.

The main purpose of constitutions is to define what the government can and can't do; it gives rules for how government works.

Now the US constitution does contain lines like

All legislative Powers herein granted shall be vested in a Congress of the United States, which shall consist of a Senate and House of Representatives.

Which, I suppose could be framed in a more mathematical way:

Axiom: There exists a Senate and a House of Representatives

Defn: The set {Senate, House} is termed "Congress"

Axiom: There exist Legislative Powers.

Axiom: If x is a Legislative power then x is vested in Congress

Axiom: The Power to lay taxes is a Legislative Power

Theorem: Congress has the power to lay taxes.

and so on. Just as Euclid uses terms like "length" without definition, we use terms like "Power" without further definition.

There are many styles of constitution writing, from the legalistic Indian Constitution, to the form of the US constitution (that owes much to Enlightenment notions of Government) to the Bombastic, to the terse.

Of the Terse style, Indonesia seems to have gone down the path of something like axiomatic statements of existence:

Indonesia is a Unitary State in the form of a Republic.

Sovereignty is in the hands of the people and is implemented according to this Constitution.

Indonesia is a law-based state.

[...] The People’s Consultative Assembly consists of the members of The House of Representatives and the members of The Council of Representatives of The Regions elected through general elections, and regulated further by law.

However "completeness" isn't a function of constitutions. There is no need to define "Senate" or "State", only to say what they can or can't do.

James K
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  • And where is the good place to define those terms? I will not even start the discussion about "no need"... – virolino Dec 12 '22 at 11:23
  • The ether. The culture. The courts.... If Euclid is allowed to say "A line is breadthless length" then we can say "Congress shall be composed of a Senate and a House of Representatives". – James K Dec 12 '22 at 11:47
  • True, until we understand that a "breadthless length" will not have decision / ruling power over the lives and deaths of millions. A line is abstract in itself, a way for us to understand / explain the world around us. A Congress / Senate / whatever is something created by people - and therefore should have a more concrete definition. – virolino Dec 12 '22 at 11:52
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    "The ether. The culture. The courts**" - that is the ultimate statement. The constitution tells the courts how to judge, and the courts define what the constitution should tell. And that's how we have the dictatorship of the courts. Are the courts the new Gods? – virolino Dec 12 '22 at 11:55
  • @virolino The point of the Constitution is to define what these terms mean. You do not need to attach a dictionary to define each and every single word. For example, in U.S. Constitutional Law, we look to documentation by the authors of a particular section to understand their intent. At all stages, the debates on the wording and grammar were very specific. – hszmv Dec 12 '22 at 18:52
  • @hszmv: "The point of the Constitution is to define what these terms mean." - I agree, although it does not always happen. "You do not need to attach a dictionary to define each and every single word." - I also agree. – virolino Dec 13 '22 at 06:41
  • Wonderful answer, thank you! So nice to see the tip-off about Indonesia. In case you wish to expand your answer with more detail and references, I would love that. It would be nice to get the line / section numbers of quotes, for example the US one. Thank you – Julius Hamilton Dec 19 '22 at 12:03
  • The us quote is from article 1, it is right after the preamble to the constitution. The Indonesian constitution is so short that it probably fits on a couple of sides of A4, The quotes section is again near the top. – James K Dec 19 '22 at 12:07