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This question is based on the following considerations:

  1. There's some Philomena Cunk video out there where she interviews an economist or politician or something, about the 2008 financial catastrophe (IIRC). The interviewee says something about how the economy was too complicated to be reasonable/justified, and this lack of justification was reflected in the ethical problem of the catastrophe. (I know Diane Morgan is a comedian, but this video is one of those joking/serious blurred-lines cases.)

  2. The commodity/credit distinction in economics. The SEP article on the philosophy of money and finance says of credit:

According to the main rival theory [to the intermediary commodity theory], coins and notes are merely tokens of something more abstract: money is a social construction rather than a physical commodity. The abstract entity in question is a credit relationship; that is, a promise from someone to grant (or repay) a favor (product or service) to the holder of the token (Macleod 1889, Innes 1914, Ingham 2004). In order to function as money, two further features are crucial: that (i) the promise is sufficiently credible, that is, the issuer is “creditworthy”; and (ii) the credit is transferable, that is, also others will accept it as payment for trade.

  1. Keisler's book on the infinitesimal calculus mentions its use in economics. The preface to the first edition in part reads:

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  1. Improving the efficiency of calculus education then includes improving the preconditions of creditworthiness in societies thus educated.

  2. (Non-strict inference) So Abraham Robinson, H. Keisler, et. al., merit some credit for improving the efficiency of calculus education in our world.

  3. (Conclusion) Combining an infinite number of infinitesimal monetary values initially equals some finite value. But then combining infinitely many sums of infinitely many infinitesimals can equal an infinite value. So the improvers of calculus education might merit an infinite credit reward for their efforts.

I appreciate that this argument is not very "rigorous" (yet). It also depends on the idea that prospective improvements in economics-related education could (should!) translate into contemporary credit lines. And maybe Robinson, Keisler, et. al. haven't achieved the goal, so to speak (if calculus is still too difficult to learn to justify extending infinite credit to such individuals as have only accomplished just so much, but not enough, for such a justification to obtain). But is it possible for anyone to be justifiably given an infinite credit line, along these lines? I'm imagining that the economic-moral value of education improvement would represent a "promising line of work" in both senses of "promising" (i.e. also the sense of credit as involving some sort of "credible promise").

Default objection: even if there is a way to combine infinitesimal values to get infinite ones, that will never happen in an effectively finitary economy. We could imagine an indefinite or open credit line, in this connection, but not a properly infinite one. I should grant this, more or less, for the time being, although my lack of certainty in this context is sufficient to make me wonder if the ability to make infinitary promises itself bypasses the problem of this objection? (An infinitary promise being, that is, a promise to aim for infinity in some way, or the making a priori of infinitely many promises, etc., which things seem possible to me, even here on Earth rather than in some storehouse of a treasury of merit in Heaven...)

Inflationary objection: would extending an infinite credit line to someone make all money worthless via some kind of ultra-inflation? I don't know that this was always thought necessary, since in past times no one (or hardly anyone) would say, in Christendom specifically that is, that the infinite credit of Christ, and His ownership of all things, made everything worthless. But perhaps that was an oversight on the part of the metaphorists, there, that they overlooked the economic implications, modulo inflation, of their proposal (but then perhaps they were debit-minded rather than credit-minded, after all; the SEP article seems to indicate so, no less!).


Caveat: just found out that there's an EconomicsSE. Will transfer this to there if enough people here recommend doing so!

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  • Since in practice all financial transactions are finitistic and discrete, the exact context of the claim that the calculus based on infinitesimals is used in that domain requires closer scrutiny than a "trust me".
    – Dave
    Commented Dec 7, 2023 at 17:39
  • @Dave I found the passage I was thinking of, and have added it to the body of the question. It is a brief remark, evocative but not necessarily very (or at all) informative, but I trust that Keisler was not simply making the claim up. OTOH I have never taken an economics class so I can't say from direct experience that I know what he's talking about... Commented Dec 7, 2023 at 19:16
  • So you are proposing a royalty to people who improve education? Maybe more people will go in to the field then. In general the same amount of value is more compelling sooner rather than later. So a stream of pennies extending in to the future could be purchased for a finite sum.
    – Scott Rowe
    Commented Dec 7, 2023 at 20:43
  • @ScottRowe at least if people help improve education with respect to economics, although eventually I would hope to broaden the scope of such a credit allowance. I guess that's what's done to some extent with credit cards already, so again, I must emphasize that I know very little about economics (most of what I know is either experiential, from my own financial life, or from Rawls' A Theory of Justice). Commented Dec 7, 2023 at 21:13
  • @Dave, I tried to address your concern in my answer. Commented Dec 18, 2023 at 13:26

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This is partly a response to some of the questions posed by the OP, and partly a response to some of the comments below the original question.

Yeneng Sun has a 50-page chapter explaining applications of nonstandard analysis in Mathematical Economics, in

Nonstandard analysis for the working mathematician. Second edition. Edited by Peter A. Loeb and Manfred P. H. Wolff. Springer, Dordrecht, 2015. xv+481 pp. ISBN: 978-94-017-7326-3; 978-94-017-7327-0

The point here is not modeling "indefinite largeness via open credit lines" but rather to provide mathematical models for the large market phenomenon. Here the technical term would be "unlimited" rather than "infinite" number. Obviously, any mathematical modeling will involve certain idealisations, but the point of such models is that they capture qualitative as well as quantitative large-scale behavior. This point is even clearer in axiomatic approaches to nonstandard analysis, where the unlimited numbers are elements in N (rather than any extension thereof). See a possible introduction.

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