Inspired by this thread, I was wondering if there is any concept of infinity in legal contexts. For example, if Joe and Bill sign a contract stating, “Joe will mow Bill’s lawn for a payment of aleph-null dollars.”, could such a contract be valid? Would a court rule that Joe may obtain an indefinite garnishment against Bill’s bank account or salary and continuously seize property for the rest of Joe and Bill’s life? If an agreement states, “In exchange for $5, Joe will give to Bill an infinitesimal percentage interest in the profit of Joe’s business”, and Joe’s business makes $40,000 profit, exactly how many $$$ does Bill get? Would an American court rule that the payment shall be one mill, because it is the smallest amount of money that is legally recognized? Would the court order the payment rounded down to zero?
Are there any statutes that purport to specify what happens when a contract mentions an infinite amount of time, an infinite amount of money, or an infinite amount of goods or materials, or a similar infinitesimal? Have their been any cases where the court ruled on such a clause to such an extent that they needed to define what “infinite”, “infinity”, “aleph-null”, “aleph-one” or some other word actually means? Would the court strike any clause that referenced an infinite or infinitesimal amount as totally void, or would it substitute a specific value such as one million or one cent?
I had always thought that “infinity” was my tax liability, according to the contract I never signed.
But as a concept in contract law, the idea that performance (as in, in return for consideration) continues indefinitely, at least until some event occurs or ceases to occur, is quite common.
This isn’t enitrely related, but there’s also a rule against perpetuities. So it would seem that the legal system recognizes the existence of infinite amounts of time, and doesn’t like them.
In relatively primitive conceptions of land law, one owned the land down to the centre of the earth and the airspace above to infinite height. This is why your neighbours can’t build a deck that is engineered to completely overhang your back yard by the mere expedient of not touching any of your dirt.
Of course, these primitive ideas are so hedged about with important exceptions that they have little practical application, so far as the potential infinities are concerned.
You dont own the minerals under your land. You don’t own the moon when it happens to pass over your quarter acre. You can’t prevent planes from flying over, or satellites for that matter. And so on.
All that said, I don’t know of any area of the general law where trouble is taken to distinguish among the various degrees of infinity in the Cantor sense. Perhaps some specific patent, copyright or other intellectual property might touch upon the subject, but they wouldn’t be sufficiently general to address the question I apprehend the OP is asking.
Interesting, and in retrospect it makes sense. Are there any acknowledgements in law (e.g. in statutes, cases, principles) that recognize a concept of an infinite amount of money or an infinite amount of tangible goods or materials? For example, if the Ohio state legislature passed a law providing that, “No person shall possess a firearm in a public park unless they have obtained the permission of a park ranger. Any person violating this section shall be guilty of a felony and shall be punished by incarceration for infinity years and a fine of infinity dollars (or an infinite amount of dollars…)”, it stands to reason that a court might interpret “infinity years” to mean a Life Sentence, but what might it do with “infinity dollars”? Does that represent every dollar the offender possesses and every dollar they will ever obtain for the rest of their life?
I don’t know the law in every jurisdiction* but I doubt there would be any statutes or cases covering contracts involving payment of infinitely large or small amounts for the obvious reason that no one would ever enter into them.
Working from first principles, I think if you did enter into a contract requiring the payment of an infinite sum, the first question would be whether the person who entered into a contract by which they would become obliged to pay such a sum had capacity to make the contract. If they signed as an individual you would have to question whether they were sane. If they purported to sign for a company you would have to question whether they could possibly have authority to do so on behalf of the company.
Assuming however that the court found such a contact valid, then I’m not aware of anything to specifically prevent a court entering judgment for $aleph-null. Personally if I were acting for the plaintiff I would (at least in the alternative) just ask for judgment to be entered for a massive sum, far exceeding the defendant’s assets.
Because the point is that whether the judgment is for $aleph-null, or for such massive sum, the ultimate outcome is going to be the same: the defendant is going to go into liquidation or become bankrupt, and not have to pay anything beyond what they can pay.
As to the contract entitling one party to an infinitesimally small payment, the first question is whether the contract is going to be enforceable at all, given that consideration is generally required. Of course, nominal consideration (of $1 or something) is valid. On that basis perhaps a court would consider there was consideration. In the end it probably doesn’t matter because of the principle of de minimus non curat lex (the law does not concern itself with trifles). Even if there is consideration and a valid contract, anything the court might award is *de minimus *anyway, so the court probably would refuse to enter a pointless judgment.
I wonder if you could get the contract nullified on the basis that an infinite sum is, by definition, impossible to pay, and thus the beneficiary of the contract entered into it with the full knowledge that the contract was impossible to meet.
Something I remember from a mate of mine who set up a holding company, and bought a self company. Memory a bit hazy here but… The company establishment included a definition of perpetuity that was based upon the UK monarch and all her descendants, with the contract being valid for as long as at least one descendant remained alive. I think the monarch was Queen Victoria, so there are already a massive number of descendants. It was clearly in the mind of the drafter that until the sun went cold this was going to be as close to forever as possible. Although not actually infinite time, as that enters into cosmological issues. At the time it was remarked that this definition was done this way to specifically avoid any mention of “forever”
Not quite forever, forever. The rule is a life currently in being (or in gestation) plus 21 years. So, if you specificy all of the descendants of Queen Victoria, you can be pretty sure that one is in infancy or gestation right now and will live 90 to 100 (perhaps more) years + the additional 21. So 130 years, maybe at the outside. A long time, but not infinity.
I can’t think of any examples of the infinite in American law. An infinite punishment (either in years of incarceration or amount of fine) would pretty quickly be struck down as “cruel and unusual.” Capital punishment is one thing, but even really really really bad people get, say, multiple life sentences run consecutively, not infinite ones.
Going short and naked on various investments (call options, equities, commodities…) can technically have unlimited loss potential, but the amount at any time would be definite.
How could an infinite sentence be “cruel and unusual” when (if my memory serves) US courts occasionally impose sentences that are many times longer than the human lifespan?
Immortal entities such as trusts and corporations are created by the law, so that would have to count as recognizing a type of infinity - an entity with an infinite life span.
Also, the phrase “in perpetuity” is often used in legal document which convey rights in real estate such as easements. I suspect that it also shows up in other types of documents as well.
Even max consec prison terms have some finite limit, however unlikely the felon will ever reach that point. An infinite sentence does not. I know of no state which permits infinite sentences.
Caution: I am neither a lawyer nor a Brit, but I understand that, in British Law, there is the reverse of infinity. The term “time immemorial” means back to 1066.
The U.S. must be one of those primitive societies because you do own the minerals ‘to the center of the earth’ under your land here and it isn’t just hypothetical either. Very deep drilling technologies are allowing people to cash in on petroleum, natural gas, and minerals miles under their land today and it is theirs and no one else’s all the way down. More precisely, the mineral rights owner owns them. Those are usually bundled together with surface rights but can be unbundled and sold separately. My family’s depends on this fact because our land that is being drilled today was bought long before such drilling technology existed yet it is still all ours.
Time Immemorial is set at 6 July 1189 (the date of the accession of Richard I in English law.
There’s an unusual New Zealand case involving a contract of infinite duration. In 1927 the Gore District Council sold all its power generation and transmission assets to the local power company in return for the supply of electricity to the council for 1 penny per unit “for all time hereafter.” In 1995 the power company sought to terminate the contract by giving 15 months notice, arguing the contract could be neded by giving reasonable notice or alternatively that due to inflation and the like the contract had become frustrated.
The Council successfully argued that the contract did not contain any implied term allowing for termination and the contract was not frustrated just because the power company was losing a lot of money on the arrangement. Unfortunately I can’t find a copy of the decision online but here’s the cite - Gore District Council v Power Co Ltd [1996] 1 NZLR 58. And here’s a brief description of the case (warning pdf).
So in New Zealand at least, a contract that is clearly expressed as being binding forever is likely to be upheld.
Also, in West Virginia, we are seeing similar cases. In the late 1800s many landowners signed leases to oil and gas companies with a royalty paid on each barrel of oil, and a flat rate of usually $5 per year for natural gas. The lease renewed every year so long as minerals were produced or the company made a modest (for the time) "delay rental."The rationale was at the time, natural gas was worthless and oil was the money maker.
Fast forward to 2012, and fracking, we still have landowners with no more oil in the ground (mostly all gone) but still getting a handsome $5 per year when their land is producing millions in natural gas. Some companies are voluntarily renegotiating, but we are starting to see circuit judges buying onto the frustration of purposes and unconscionability arguments.