I've encountered some rather complex and confused philosophical arguments lately, and I think they would benefit from a change in notation. To that end, I'm going to employ my own little notation to denote experiences about things as distinct from the things themselves.
In this notation, my experience of seeing a red ball would be written as:
In addition to experiencing the sight (and the other four sensations) of physical objects, I also experience abstractions, like numbers:
and mental sensations:
I also experience correlations between these sensations. I've noticed that a glass dropped on a concrete floor shatters:
e("glass falls to concrete floor")
=> e("glass shatters on concrete floor at time of impact")
or that certain kinds of symbolic manipulations always produce the same results:
e("x = 1 + 1")
=> e("x = 2")
For day-to-day activities, we can dispense with the experience function and simplify our notation, i.e., write e(X) simply as X. Then we can rewrite
e("x = 1 + 1") => e("x = 2")
"x = 1 + 1" => "x = 2"
We might call this process "realizing our notation."
However, we cannot always realize our notation. We have to retain and be explicit in our notation when considering the philosophical nature of experience itself.
Consider solipsism. Solipsism is the idea that things that we have experience of don't really exist. For example, the solipsist may claim that my best friend doesn't actually exist, or that I am just a brain in a vat receiving synthesized experiences (a lá Matrix).
The problem with solipsism is that it has nothing to do with experience. The solipsist implicitly assumes that the existence of X is somehow meaningful as distinct from e(X). However, nothing I will ever be conscious of can ever tell me anything directly about X.
Unfortunately, the same is true for the claims of philosophical realists who say that my experience of my best friend implies the existence of my best friend beyond my experience. To claim that e(X) implies X is just as unsupportable by conscious experience as the claim of the solipsist.
That said, we're all practical realists. This is because we're all comfortable realizing our notation and notationally converting
e("best friend") -> "best friend"
I think this implicit conversion is something we do naturally, and its the reason why solipsism feels so wrong. Still, my point is that this notational conversion is not philosophically valid, even if it is the de facto means of conducting our day-to-day affairs. We get confused when we partially realize our notation and start to confuse X with e(X).
Now, I know you've all been waiting for the zombies, so I'll get right to it. Philosophical zombies look like people, but they don't have experiences like we do (or should that be like I do?). There are a number of arguments that claim that if zombies are possible, then the world must be more than material, and minds are more than machines.
The potential problem I see with this argument is that it refers to the experience functions of others as if they were my own. Of course, I can never actually see the world as someone else does. If you and I both claim to see a red ball, then I must note this as
eme("red ball + eyou('red ball')")
All I know is that I see a red ball and I see you claiming you see one. But the two experience functions do not act in the same space. It's possible that I may have no way to experience the world as you do.
This is very different from claims about my own experiences. For example, not only do I see the moon:
but I experience the experience of seeing the moon:
Though I am not warranted in concluding the separate existence of e("moon") from (2), I really don't care because it has already been asserted through (1).
The same does not hold true for my experience of your claims of seeing a red ball. So,
does not imply
and nor does this latter statement assert itself without my being you instead of me.
From this I conclude that nothing I can be conscious of can raise or lower my confidence that my best friend is not a zombie. All I know is that my friend acts "as if" she is conscious, i.e.,
e("best friend is conscious").
Daniel Dennett has an excellent counter-argument against zombies. Dennett claims that a zombie who acted indistinguishably from a conscious person would in fact have to understand and believe what a conscious person believes. This follows from our definitions of these terms. Dennett's argument is effective because he recognizes that our definition of understanding is actually founded on e("understanding").
Thus, zombies are at least as absurd as solipsism.
A foreseeable objection to this analysis is that there might be things that are true that are not touchable by experience. That is, there could be some Z that is true even if there is no possible e(Z). Unfortunately, this objection fails because there is no true, only e("true"), and so Z cannot be true without e("Z is true").