Thirdness, the Mediating Element - a Middle Way
His categories may be the foundation of much of Pierce' thought, but more transformative is his example of how to think. So much philosophy seems to be about a search for universals that have some kind of ultimate truth value, when our concerns should be more about the processes of thinking and knowing over dualistic or even monistic metaphisics.
It isn't that any one metaphysic is right or wrong, or that philosophy can definitively answer questions about ultimate ground of being. If we take seriously his insistence on the importance of categories, the way forward becomes clear. It is a middle way, a mediating thirdness that is an openning to all sorts of multiplicities. But, before going into thirdness, let's look at the smaller numbers.
You would think the One is first, but how about zero? It took a while for people and even mathematitions to notice zero and its importance. Categoritcally, it is the empty set with no category. Should we say that every other category, individually or together, can only exist in relationship to non-existence, nothingness? When we don't forget about the importance of the cypher, it reveals itself in the bootstrapping of possibility into existence.
Not forgetting about zero, but starting again from one, firstness. We have a pure sort of existence, one that Pierce largely connects to phenominology, with the experiencial. You must read Pierce closely and notice that the firstness of a sign and in analysis of signs in semiotics isn't the same thing as the category. The categories are a critical tool of thought to work on signs, and the firstness of a sign is closely tied to the experience, first of the immediate experiences, but also the immediate experience of thinking with signs. Already in firstness, the presence of a thirdness is present. This discussion of firstness, is itself a thirdness mediating between the firstness of firstness and its secondness. A firstness, at least in signs if not taughtologically, is that which can be first with respect to secondness, thirdness and by extension, all multiplicities beyond.
Secondness is factuality, it is an actual relationship, it is true or false. Quantum physics doesn't get started in his lifetime, but I think his categories could be very helpful in resolving the paradoxes and understanding what the discoveries of physics are really telling us about existence. What quantum physics is saying, is that facts, secondnesses, are not strictly locallized in spacetime. Things that we can measure, get a signal on (firstnesses, qualities) obey certain laws (thirdnesses), that include non-local facts (relationships). The facts are actual signals, whether they are recorded in a digital memory, or responded to by a living entity. Actually, they are facts regardless of any thirdness potentially making judgements and responding intelligently, but they are not independent of their firstness. Qualities (firstness), can produce facts (secondnesses) that are lawfully (thirdness) connected and non-local. There is a technical definition of non-local, but simply put, experiments can show it would take faster than light comunication to observe certain corelations in experimental results. It is as if complimentary expressions of the identical object are spread accross spacetime, so there is no communication because there is no between, only pure firstness.
In physics, every potential quantum entity is in its firstness, one of a small family of patterns represented in the standard model (law, thirdness). Experiments can demonstrate the laws by taking measurements (facts) and using thinking, all maner of application of useful laws of thought to ultimately say whether the facts or consistent or not with the models (law) they construct.
Let's examine a quality, green, or in pure firstness, having a color, possibly green. In many fields that have developed a lot since Pierce wrote, we can produce different cognitive descriptions and the phenomenogy they produce. Color perception is a process essential to the autopoiesis of a great many species. Speculatively, our close relatives have similar or related color awareness as adapted by use in hunting, gathering and pro-creating (process networks). The point here is that there is a deep thirdness embedded in the very question of color perception and by implication color experience (green as firstness). The green in secondness of chlorophil and the history of interactions in the environment as conditioned by a history interacting living processes in both plants and animals.
And red, plants signal their ripeness in their red color, and other colors. Primates are adapted by histories of eating ripe fruit that contrasts with the green vegitation. The point of all of this is that our experiential environment, the phenomenology of human beings as firstness, already has encoded in it quite a great deal of thirdness.
In secondness, the facts of color are the energy spectrum of photons and the response curves of the rods and cones in human eyes. Then there is the whole visual processing system that will even try to tell your awareness that an object is green even when the reflected light is not green at all. It compensates at a level below awareness for ambient light. So that something that is green in mid-day sun is also green at dusk or grey skys, phenominalogically, that is. This compensation is a fact observable in relation to different ways to define greeness in fact and experience.