Mental reality

When it comes to the mental world, it is an age-old controversy whether there is objective reality. For one thing, everything that deserves to be called a mental object exists only in my or your mind. Can there be concepts which are independent of observers? Can a sentence mean anything to nobody? Speaking introspectively, we seem to be able to render all mental ``things'' subjective.

However, this is not necessarily the case. For example, consider a mathematical expression $1+1=2$. This equation is a mental object. To establish this equation, one must already have the concepts 1, 2, +, and =. Almost everyone claims that she/he understands this equation. Would one argue that these concepts are also subjective, in the sense that my 1 is not equal to your 1? At least for mathematical realists (and it seems to me that most of us are educated as realists), there must be some mental objects, such as well-defined mathematical expressions, that deserve to be called ``reality.'' These are the ``objective'' mental ``things'' -- at least it appears so.

In fact, any serious mind-related science should be able to accommodate logic and mathematics. Better yet, a good mind-oriented science should either explain why logic and mathematics are the way they are; or offer alternatives, say, an alternative Pythagoras theorem in Euclidean geometry.

Let us now make our first attempt to unify physical reality and mental ``things.'' For this purpose, it is worthwhile to notice that at the present time the prevailing scientific view of mental phenomena is physicalist. This includes various schools of reductionism, materialism, functionalism, and emergentism. According to these views, mental ``things'' are nothing but movements of physical objects, so the objectivity of mental ``things'' can be guaranteed by the objectivity of physics. Let us, for this moment, take quantum theory as the ultimate theory of physics. Now a mathematical wave function such as Equation 2.1 must literally point to physical properties. And according to our working hypothesis, it must be taken as a part of mental reality (because it is well-established mathematics). If this is correct, we have a unified explanation of logico-mathematical mental objects and seemingly subjective mental objects (e.g. qualia).

But this naive physicalist approach cannot work. This is because the physical properties pointed out by the wave function are physically not well-defined, therefore not objective. In fact, a quantum mechanical account of mental reality will render the complementary quantities (technically speaking, conjugate observables) totally in limbo. For the sake of argument, let us assume that an abstract object as Equation 2.1 refers to (called it the particle picture) is a classical picture of particle movement (and indeed quantum mechanics needs it, for measured results are classical mechanical objects^2.10). If the particle picture is to be asserted in my mind, a complementary object of Equation 2.1 (i.e. a wave picture which uses momenta as basis) cannot be asserted.

Interestingly enough, even mathematical expressions that look well defined are not necessarily qualified to be called mental ``reality.'' A notable example is Russell's Paradox of Naive Set Theory. In Naive Set Theory, a primary relation is member-of (denoted by $\in$). A set is then a mathematical object associated with a member statement which determines whether or not an entity is a member of the set. Now consider the following set:

$$A \equiv \{ x \vert x \notin x\}.$$ (2.2)

Clearly, $A$ is not the empty set ($\emptyset$), for at least one entity $\emptyset \notin \emptyset$, thus $\emptyset \in A$ according to the member statement. The paradox manifests itself when we consider whether

$$A \in A?$$

Now suppose it is the case (i.e. $A \in A$), we conclude that $A$ is a member of the set $A$, so $A$ must have fulfilled the member statement. Consequently, $A \notin A$. Ad absurdum. Therefore $A \notin A$. But if it is the case, according to the member statement, $A$ must be a member of $A$, therefore $A \in A$. Again, ad absurdum. $A \in A$ turns out to be an undecidable statement.

There are several approaches that allow us to get away with this paradox, notably the Axiomatic Set Theory [21], according to which a ``thing'' as $A$ is simply not a set. This leads to the question: is $A$ qualified as an adequate object of discussion in the sense that a concept associated with Equation 2.2 exists? Or it is just something conjured by a naughty mathematician? Even in clear-cut mathematics, the objectivity may be subject to question. In a sense, quantum mechanics asserts at the same time ``classical mechanics $\in$ quantum mechanics'' and ``classical mechanics $\notin$ quantum mechanics.'' We therefore have a similar self-referring situation as in Equation 2.2.

In everyday life, there are many mental ``things'' that are difficult to clear up, no matter if they are conjured subjectivity or universal objectivity. An example is qualia. Qualiae are introspectible and seemingly monadic properties of sense-data, the raw feelings. They are ``something that it is like.'' A raw feeling like ``redness'' is a concept built around a set of sensorial data. My sensorial data are never the same as yours. Consequently ``my redness'' can never be ``your redness,'' strictly speaking.

Indeed, this question of private qualia has a deeper philosophical root. For one thing, for a purist physicalist we have nothing but our sensorial data. Our concepts -- let them be mathematical or whatsoever -- are based on our eidetic experiences. These experiences, however, can not float around without physical substrate. In other words, we need memory of these data for later perusal. Consequently, a concept such as ``redness'' must be seen as a constant comparison between experience and a reconstructed environment based on memory of the past perception of ``redness.'' This is also the case for mathematical concepts such as $\pi$ or 1. The question is how these ``things'' are memorized. For one thing, memory is never the real thing, it is a representation of the real thing (if there is anything real). Thus we have reduced the problem down to representation. This process is illustrated in Figure 2.1. (More details in next section.)

Figure 2.1: A spiral view of mental reality (cf. Bohm [1]).