Does C minor care about the Pathetique, or evolution about Darwin? Will hard work make one equal to the canvas upon which one paints? Of course not; to ask such questions is nonsensical. Nevertheless, while denying the influence of Beethoven, Darwin, or Picasso on their respective arts would be folly, they merely showed us what was possible from the beginning, had we the ability to bring it forth.

We left off in our discussion on additivity by stating that there is no such thing as a bad idea. While we hold firm to this belief, some ideas have clearly approximated what we believe to be true better than others. For example, Newton's Law of Universal Gravitation has brought us much closer to our current understanding of the truth than the idea that the Earth is flat and supported on the back of a giant turtle. (However, an example of additivity at work is that a large amount of artwork and culture springs from such notions as the world being supported on the back of an animal or a titan, indicating that this seemingly-absurd idea has still contributed something to humanity).

Objectivity formalizes this distinction between ideas. It is the principle that ideas possess inherent nature and worth.

Ideas possess inherent nature in the sense that an immutable and common idea underlies every one of its manifestations within reality. Trees, for example, differ in many properties, such as shape and size, and certainly no two are exactly alike down to the molecular level. However, these varying properties are manifestations of other ideas - there is only one “tree” idea, and it is sufficiently broad to include all trees. Should a new type of tree arise, we may change our definition of what a tree is, but it was then our understanding of the “tree” idea that was incomplete, not the fundamental idea itself. The idea itself transcends time and space, but remains rooted in reality (or rather, reality remains rooted in it); there is no Platonic abstract realm of ideas, but neither is an idea defined only by how it appears to us (that is, in the Aristotelian sense).

Ideas possess inherent worth in that every idea does in fact have a range of applications and new ideas which may spring forth from it, and that the cardinality of this range is not the same for every idea. Thus, some ideas do have greater “worth” than others, in the sense that they result in deeper or more valued advancements. Again, this inherent worth does not vary with our own estimation or understanding of the idea; our understanding may change (and frequently has throughout history), and we may thus apply the idea differently, but the underlying worth - the range of applications - remains the same. Thinking again in mathematical terms, if an idea is represented as a matrix, its worth would be something similar to the cardinality of its image. Our own uses of an idea are akin to specific linear combinations: different combinations yield different results, but all are contained within the original image, which is independent of the specific choice of linear combinations we apply. Note that the cardinality of a set, as the range of other ideas that may result from an idea, may be infinite, but even then, not all infinite sets are of the same size. The natural numbers, for instance, are infinite (ℵ₀) and yet are a subset within the larger set of the real numbers.

While ideas do possess objective nature and worth, neither lie within our ability to accurately assess. This will be discussed in the following section, subjectivity.