My ponderings on reductionism have led me to think that reductionism is mostly correct, and partially a confusion.
Reductionists think that there is an objective reality, which is a mathematical structure. We have subjective impressions (qualia) which give a sense of this objective reality. Consider, for instance, a table. I can see the table from various angles; I can touch it; and so forth. Each of these subjective impressions gives me partial information about the table. The table itself, on the other hand, is something that I will never experience. The appearance of the table is not the table; the table is not an experience.
The table is a mathematical structure. But if I think of the table’s mathematical structure, that thought once again is not the table. A thought of a mathematical structure is not the mathematical structure itself.
To solidify this conclusion, think of the number two. You may have spoken the word “two” in your mind; you may have imagined two dots next to each other; you may have visualized the printed character “2;” you may have thought something more abstract. All of these are thoughts of two; but none of them are two.
What is two itself? This depends on whether or not we think that two objectively exists. In the first case, where two objectively exists, two is beyond all appearances of two, in the same way that the table is beyond all appearances of the table. Two is not an experience. We can, so to speak, see two from different angles (the word, the two dots, etc.), but we cannot see the whole of two.
In the second case, if two does not objectively exist, then it is only a formality of our language, a concept with no tidy correspondence to reality. It is a confusion to ask what two is, in the same way that it is a confusion to ask what a hipster is, or what rudeness is.
Under reductionism, some set of mathematical structures has an objective existence. These structures are something that we will never experience, just as in the first case we never experience two.
So under reductionism, there is an objective reality of mathematical structure, and we have subjective experiences which are themselves unreal. Through these experiences we can know everything that there is to know about the objective reality; but we can never experience the objective reality itself.
That said, we can imagine a mind which was able to think a thought that contained all possible knowledge of reality. We cannot ourselves see a table from every angle simultaneously; but it is possible to imagine a mind which can see three-dimensional objects in an instant, in the same way that we can see two-dimensional objects in an instant. Similarly, we cannot ourselves think of the whole mathematical structure of a table in an instant; it is too large and complex. But we can imagine a mind which can do this.
So we can imagine a mind which can think everything at once, and perceive the entire structure of reality in an instant. Let us refer to this instantaneous perception of the whole of reality as the “final appearance.” Our metaphysics will give us a sense of what the final appearance would look like. For instance, under reductionism, the final appearance would be a thought of a vast and complicated mathematical structure.
Our concept of the final appearance is an inference based on all of the knowledge we have. We arrive at our concept of a table by looking at it, touching it, thinking about it, etc. By synthesizing these different experiences we conceptualize the “final appearance of the table,” which is our idea of what the table is. And we construct our idea of the final appearance of reality in the same way.
But reductionists throw out some of the information in constructing their final appearance. To see how, empty your mind of all thoughts and look at your hand. Here we have an appearance of a hand, which is just as valid as the appearance which is a thought of the hand’s mathematical structure.
Why should the final appearance of the hand be an appearance of a mathematical structure, and omit the purely qualitative visual impression of the hand? Why do we want to say that the mathematical structure has reality, while the visual impression does not?
Why do we want to say that the objective reality is a mathematical structure? We gain our concept of objective reality by aggregating appearances; but our appearances are not only appearances of mathematical structure, but also entirely different appearances. Why do we throw out the non-mathematical appearances in constructing our picture of reality, in constructing our final appearance?
If reductionism means simply that mathematical structure is everywhere, then reductionism is perfectly correct. But if reductionism means that mathematical structure is the only real thing, then I see no reason to believe that it is correct.