The situation
Imagine an Ass (Donkey!), who has two stacks of hay, which are equally distant from him, and he has to choose either stack. While the reasons for the choosing of one stack over the other are exactly the same (such as distance to the stack, size, shape, type of hay etc.) What will the ass do?
Let me elicit two options:

The ass will make a decision

The ass will starve
Let me also elicit some assumptions

This is not a real situation (P), or

This is a real situation (Q), and

This is an issue of rational deliberation (R), or,

This is an issue of arbitrary decision making (S)
So, we can say, of this situation, ((P v Q) & (R v S)) & (P–>¬(R v S)) v (Q –>(R v S))
Not quite sure what you mean here. You need another set of brackets. (Advice: use round, square and if necessary curly brackets to make it easier to distinguish them).
At the moment your statement is of the form, “A & B v C”, and I don’t know whether you mean (A & [B v C]) or ([A & B] v C). They are very different statements, as a truth table will show.
Whenever (A & [B v C]) is true, ([A & B] v C) is true but not vice versa. The second proposition is also true when (¬A & B & C) and (¬A & ¬B & C) So the former says something a bit stronger. Call the first one {1} and the second {2} for future reference.
Besides that, in your first conjunct, (P v Q) & (R v S), you seem to be saying that the situation could be both real and unreal, and the decision could be both rational and arbitrary, because P v Q is consistent with P & Q. Instead I think you mean:
(P ¬Q) & (R ¬S)
In the second conjunct (although I’m not sure if it’s the first disjunct, so I mean “the middle bit”, B), you seem to be saying that if the situation isn’t real then the decision is neither rational nor arbitrary. I disagree somewhat with this, especially as you don’t make it clear what you mean by “real”, whether you mean actual or possible. It seems to me that if the example isn’t actual, then it could be possible. And if it were possible then either R or S would be true, which is what you said in the first conjunct. And if you meant by real, “possible”, then I don’t see why in the impossible worlds where the situation is actualized, the decision cannot be rational or arbitrary. Once we are in an impossible world, anything goes anyway. So if you really meant {2} by your formula then you are committed to Q, that the situation is real. Simply take A and B as premises in an argument, and do a modus tollens on B and you get Q from A. So I’m assuming now that you meant {1}. But even then there is a problem with this formula. Since A and B entail Q, you may as well be saying something like:
(R v S) & (Q v C)
And when I look at C, it seems to be saying something trivial in context with the rest of the proposition, so that the whole proposition reduces to just:
R v S.
It’s just a big mess basically. I think what you want to be saying is something like this:
(P ¬Q) & (P > ¬[R v S]) & (Q > [R v S])
That is: The situation is either real or not real, and if it is not real then the decision is neither rational nor arbitrary, and if it is real then the decision is either rational or arbitrary. You can’t say in the first conjunct that (R ¬S) or (R v S) without later entailing that the situation has to be real, because you say that when the situation isn’t real, neither R nor S.
If you wanted to say what I think it is you want to say, then there is still the issue of what you mean by “real”. I think it’s obvious that the situation is logically possible, but perhaps it is not psychologically possible for an ass as we know them, although it seems to me to be biologically possible. Or perhaps you meant “rationally possible”? That seems to me to be the best candidate here. But then there will be some indeterministic worlds where a nonrational ass arbitrarily decides to act, or not act, unless we are committed to the necessity of asses being rational (to some extent). So I think your “If it’s not real then the decision isn’t rational or arbitrary” line is probably false, depending on how you define the ass and “real” etcetera.
Wait, it turns out that what I said you should be saying was badly formed, missing out the biconditional at the start. I eant:
(P ¬Q) & (P > ¬[R v S]) & (Q > [R v S])
But actually I meant:
(P ¬Q) & (P > ¬[R v S]) & (Q > [R ¬S])
Or in other words:
(P ¬Q) & (P > [¬R & ¬S]) & (Q > [R ¬S])
And it doesn’t matter much about having a statement of the form:
A & B & C
…because there’s really only one interpretation of that even if it should technically be written A & (B & C) or (A & B) & C.
OK this website is fucking shit basically, and won’t let me write biconditionals. For some reason you can’t write “” in a row, because, as mentioned, it is fucking shit. So whenever it appears that there is something like (R S) or (R ¬S) you have to imagine a biconditional there.
< WTF
Okay,
Let me recode what you are saying here.
Q1. Is the interpretation of the formalisation {1} or {2}?
A1. It’s {2}
Q2. What do I mean by a ‘real’ situation? Your suggestion – real refers to a modal claim concerning the possibility of the Ass situation obtaining; or an truthbearing claim about whether it is actual or not to our state of affairs (relative world to ours)
A2. I wasn’t concerned with modality here, but I see your point. Indeed, if a claim is assertoric, it must be, by a condition of experience, or in Kantian terms ‘condition of possibility’ it must fit under certain experiential desiderata; POSSIBILITY is one of them. (You just made a transcendental argument…very good)
A2 Corollorary: If a claim is actual, it is possible (as a base condition for the realisation of the actual). So you refer to some Ersatz world or some possible absurd world where the Buridan’s ass situation obtains, but it is a rational or arbitrary situation; given that all sorts of crazy things can happen in the world.
I think there are two very simple points here.
1. Your objections to {1} are entirely correct. I didn’t mean {1}, but {2}. {1} is a bizarre formulation indeed.
2. {2} raises some wider thoughts about modality and truth conditions. While prima facie I don’t see a profound problem, I need to think harder about the role of truth between possible worlds.
3. What do I mean when I say ‘Buridan’s Ass is a real situation’? Umm, I’m just using the intuitive word for ‘real’. So, I guess that would mean, the statement is assertoric is all I have to say really; I could go further but I don’t know if either its’ important or how far I can analyse it. I could say for example:
i. It is a claim about a manifold/unity/particular (quantity)
ii. It is a necessary/contingent/possible claim (modality)
iii. It is a disjunctive/negative/or conjunctive claim (relation?)
iv. (quality)
I’m surprised I even understood this… well, I didn’t really, and that is the whole point1
Michael
Formula {2} is the one that’s completely fucked.
If it really is {2} then your formula is of the form (X v Y). But X basically says:
¬P, Q, (R v S)
And Y says:
¬(Q & ¬R & ¬S)
And when you put them back together as the disjunction, X v Y you still just have:
¬(Q & ¬R & ¬S)
That is what your formula says. That it’s just not the case that the following three claims all hold: the situation is real, the decision isn’t rational and it isn’t arbitrary. Which is the same as saying:
Q > (R v S)
And that is so trivial as to not be worth saying. What is it you really mean to say?
Nothing particularly profound. The Ass is a problem I’m trying to define. Question then becomes, how do we obtain R and S. That’s where the interesting stuff comes.
M