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The motivation for this question is extraordinarily stupid, but it requires just enough thought and specific knowledge of formal logic that I think it still falls within the broad scope of "philosophical logic."

The basic problem is this:

Given a "three wishes" scenario where

  1. The wish granter must grant any wish unless the wish explicitly conflicts with the rules

  2. It is against the rules to wish for additional wishes

  3. It is against the rules to wish for changes to the rules

find a way to acquire infinite wishes, and/or turn your prospective monkey's paw into a universe annihilating bomb (just in case you need to issue an ultimatum to the almighty cosmic being of your choosing.)

My original solution to the problem is this:

Wish 1: I wish for either my second or my third wish to be granted.

Wish 2: I wish for either my third wish to be granted or my first wish not to be granted.

Wish 3: I wish for infinite wishes.

My reasoning being that as neither Wish 1 nor Wish 2 conflict with the rules, both wishes will be granted. Hence either Wish 3 will be granted in order to satisfy Wish 1 and Wish 2 simultaneously, or Wish 3 will not be granted, resulting in a contradiction that leads to Wish 3 being granted anyway (or all of reality being destroyed.) The proof follows

1  | A -> (B || C)     [Wish 1]
2  | B -> (~A || C)    [Wish 2]
3  | A                 [Granted 1]
4  | |__~C             [Hypothesis: suppose that Wish 3 is not granted]
5  | |  B || C         [MP 1,3]
6  | |  B              [DS 5,4]
7  | |  ~A || C        [MP 2,6]
8  | |  ~A             [DS 7,4]
9  | |  X              [X 3,8]
10 | ~~C               [~I 4-9]
11 | C                 [DNE 10]

(Comment: Presumably, the same could be done with only two wishes by way of

Wish 1: I wish for either my second wish to be granted, or my first wish not to be granted.

Wish 2: I wish for infinite wishes.

But this makes use of direct self-reference, which is just... gross.)

Now this is all well and good, but it seems natural to question whether or not my logic actually corresponds to the intended meaning of "wish." In my thesis, I assume that a "wish" is effectively a sort of command which can be interpreted in propositional logic by treating "true" and "false" as "do" and "do not," respectively. I also assume that the wish itself consists of two parts

  1. A label (A, B, and C in the proof)

  2. An instruction (B || C for Wish 1, and ~A || C for Wish 2 in the proof)

so that it makes logical sense to refer to a particular wish within the scope of another wish (of course, this means that Wish 3 should have properly been stated as C -> D, but then D would follow by modus ponens, anyway.)

But what if this isn't how wishes ought to work?

A reasonable-sounding counterargument to my proposed solution might be that a "wish" consists only of its contents, and lacks any kind of identifier that another wish can point to. When I made Wish 1, I began with "I wish," not "Wish 1 is," so by referring to "my first wish" I have effectively attempted to suggest the infinite sentence "I wish for either (I wish for infinite wishes.) to be granted or (I wish for either (I wish for either (I wish for infinite wishes.) or...". In this case neither Wish 1 nor Wish 2 can be granted, because neither one is well-formed (i.e. Wish 1 and Wish 2 are not actually "wishes" to begin with.)

Other counterarguments can be produced with relative ease. In any case, this leaves me in an awkward situation. Given any particular formalization of the problem, I'm confident that I can find a solution (provided that one exists), but I'm not sure how or if the notion of "wish" can be "logicized" in a meaningful way - at least not in a way that everyone can agree on.

Note: This is my first post to philosophy SE, and I don't know what tags to use. If someone knows what the correct tag for whatever pseudoquotational semantic thing I'm doing is, feel free to change the tags accordingly.

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  • I think wishing is a modal context. That is, there is a modal operator W which acts on a proposition p such as Wp means "I wish that p". See Mar 13 at 20:40
  • @DavidGudeman Was there supposed to be a citation after "See"?
    – R. Burton
    Mar 13 at 22:40
  • Sorry, I was going to link to SEP: plato.stanford.edu/entries/logic-modal. As I recall (I read it a year or two back) the article is very detailed on different kinds of modal logics. Mar 14 at 3:03
  • 1
    Voting to close because there are infinite ways to translate from natural language to formal logic, none of which can be objectively the right way.
    – tkruse
    Mar 14 at 15:23
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    Due to the Principle of Explosion, making logic over something illogical results in illogical outcomes. If those are the rules, I would simply ask to get the power of granting wishes to myself, or to change the rules of math so that 3-1 = 3, so, all the time I still have three wishes to ask. Or to have a magic wand, or to become God.
    – RodolfoAP
    Aug 12 at 4:02

1 Answer 1

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How can a wish be granted that references a wish not yet uttered? If it was that easy, you could just

  1. Wish the next wish to be granted
  2. Wish infinite wishes

Not granting the second would invalidate the first supposedly, but supposedly the first does not break rules.

However, it is not possible to grant the first wish before the second is known. It is incomplete. However once the second wish is known, the first wish breaks the rules, because it is the same as the second wish.

That's also obvious if you turn them around:

  1. Wish for infinite wishes - declined, it's against the rules
  2. Wish for the first wish to be granted - oh, ok, now that seems fine. Here you go.

Obviously not. Or else your whole effort was useless, since that's a much easier solution.

Generally speaking, a wish which contains references to other wishes is equivalent to a wish where those references are dereferenced. If in the dereferencing of a wish the wish became one which asks for more wishes, it becomes invalid by the rules.

If logical contradiction was a working trick, you could also do

1: Wish for either true to be false or getting infinite wishes.

So whatever loophole you are trying to invent and exploit, it's probably easy to find a straightforward solution for that loophole instead of jumping through all the hoops of your solution.

Another loophole would be to:

  1. Wish for a horse plus a sword plus a shield plus a wife plus a castle plus ... (Infinite things)

Or

  1. Wish to become able to grant wishes to yourself.

There is no end to the possible loopholes if you allow them in the first place.

If you look for a way to formally analyze the situation, you first need to describe both the universe and the rules of the wishes. This will be difficult for anything but very simple universes. As an example in the Conway game of life, a wish could be to instantly set a number of cells. But your question becomes to broad unless you provide those formalisms first.

Note that there is no single or objective way to translate from natural language to formal logic, so your question is not relevant in philosophy or anywhere else (maybe world building forum could have fun with it if you try to write a fantasy story).

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  • I'm not asking for an objective answer. I'm asking what logical mechanism the respondent thinks is necessary to capture the intuitive idea of how "wishes" work. Discussion of hypotheticals is often riddled with undisclosed assumptions, which makes it difficult to even conceive of an answer that won't violate some "obvious," unspoken law. I am trying to figure out what those laws are in the context.
    – R. Burton
    Mar 14 at 15:33
  • For instance, in your answer, you introduce a notion of time. This was not part of the original problem, but it makes sense, seeing as the wish-maker (presumably mortal) experiences time. In fact, I also made this assumption, since I expect every wish to be of finite length on account of the wish-maker's mortality, so I should consider time to be an inherent part of the wishing process.
    – R. Burton
    Mar 14 at 15:39
  • Then your question seems definitely opinion based and not a good fit for this site. People have different intuition of wishes in different contexts. A Christmas wish is different from a customer wish at a hairdresser or a wish of a cancer patient.
    – tkruse
    Mar 14 at 23:39

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