Formality and non-alethic conditions

Perhaps the problem with

"Give these flowers to your wife!"

is that it is a clumsy thing to say.

But Stenius, and others -- incl. Grice -- have done well in considering and analysing

satisfaction-conditions.

We tend to assume, with Grice, that the prospects of a FORMAL semantics (for why is he mentioning 'formality' as a criterion for central meaning if he is not having the construction of a formal system -- like the ones Quine avoided -- in mind?) are best understood in terms of strict alethic conditions.

But in "Method in philosophical psychology" Grice DOES prove that '... believes...' can be defined in terms of '... wants...' -- so he must have thought that a satisfaction-condition for an order is just as basic as a truth-condition for a 'declaration'.

Behead the king of France!

it may be argued that the above presupposes that there is a king of France. Here, the asymmetry with the indicative is otiose:

Don't behead the king of France!

sounds neater (recall that Grice found the existential presupposition as a case of ENTAILMENT in the affirmative, "The king of France is bald", and a case of implicature in the case of the negative, "the king of France ain't bald").

And so on.

So, the task for the semanticist is not as hard. It is to define satisfaction-conditions (akin to truth-conditions) for imperatives such as

any imperative you wish.

S is P
Let S be P.

--- Grice uses alpha and beta.

Fido is shaggy
The alpha is beta.

Jones's dog -- rahter than Smith's cat -- is hairy-coated, i.e. shaggy.

Let Jones's dog be shaggy.

----

The only way to introduce all operators as per WoW:VI is to have the ascription of a property (or class) to an individual

Fa

a has property F

in the indicative.

In the imperative

!Fa

let a have property F.

------

Nothing so mysterious about this.

So, the semantics for System G should proceed neutrally as regards the mode-indicator.

The interpretation and assignment (or correlation) of satisfaction-values proceed in a neutral way.

It is not that we look at the universe of discourse:

Does a have property F?
If it does, then "Fa" is true.
If it doesn't, then "Fa" is false.

Since we are dealing with satisfaction-conditions we proceed in a different manner. We wonder about the satisfactions that would turn

!Fa

a fulfilled command.

i.e.

Fa.

The door is closed.
Close the door!

-----

It may be argued that 'a' is otiose in "Fa". We need variables, since, as Quine shows,

the "a" in "Fa"

can be turned into a predicate. (x pegasizes).



Now, the most basic order in this respect is

!(x)Fx

Make every x _F_.

In general, it is best to restrict our attention to the Square of Opposition for canonical subject-predicate formulae, involving at least TWO predicates, F and G, or alpha and beta.

A (x)Ax --> Bx
E negation
I (Ex)Ax & Bx
O negation

So, we have the imperatival versions:

!(x)(Ax ) Bx)

----- Post the letters!

----

(or burn them)


!(Ex)(Ax & Bx)

---- POST _some_ letters
----------------- provided you don't burn them.

Or something.