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
The wish granter must grant any wish unless the wish explicitly conflicts with the rules
It is against the rules to wish for additional wishes
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
A label (
Cin the proof)
An instruction (
B || Cfor Wish 1, and
~A || Cfor 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.