I wanted to devise some rules for myself, then formulate those rules using formal symbolic logic, and one of the rules that I have set for myself is : "Do not say what is unnecessary", in other words : Do not give much information!.
I wrote it down in a formal way to see what implications that statement may have, thus :
For all x, if it is not the case that you ought to tell x, then you ought not tell x" , in Deontic terms :
(∀x)(~OTx → O~Tx)
One of the inferences from that statement is (reverse squiggles) :
(∀x)(P~Tx → ~PTx) , which reads : for all x, if it permissible not to tell x, then it is not permissible to tell x.
That is interesting, let us assume something (let us call it 'a' through instantiation) is permissible to tell a : PTa
What follows from this (using modus tollens) is ~P~Ta (it is not permissible not to tell a).
Which is equivalent to O~~Ta, hence : OTa , You ought to tell a.
I am not sure I quite understand this inference result, my assumption that something is permissible to tell leads directly to the conclusion that I ought to tell it, based on my first rule.
How is that?
(nevertheless, I think it is an interesting, albeit twisted, result).
Note: The reason I think it is a twisted result, is that although I accept the premise (You ought not tell what is unnecessary), I find it difficult to accept that I ought to tell everything that is permissible to tell.
For example : it is permissible to say "cockroach" , but should I say "cockroach" to every stranger I meet?
So, I have the inclination to think that my first premise (rule) must be, somehow, false (i.e : needs some corrections).
Thank you
Symbolic Proof
- (∀x)(~OTx → O~Tx) {my premise, which I think I agree with}
- ∴ (∀x)(P~Tx → ~PTx) {from 1, reverse squiggle}
- ∴ (P~Ta → ~PTa) {from 2, instantiate a}
- asm : PTa {assume a is permissible to tell}
- ∴ ~P~Ta {from 3 and 4, modus tollens}
- ∴ O~~Ta {from 5, reverse squiggle}
- ∴ OTa {from 6, remove doube not, conclusion : Ought to tell a !}