This is a fragment of my notes on Percian semiotics (so it's not particularly readable). Why semiotics? Meaning-making, or how we come to make sense of the world around us is an integral part of inquiry into the mind. While exceptionally fragmented, Peirce's introduction to semiotics is focused on finding from first-principles what the most basic components which make up thought and meaning are.

While a number of terms are over-loaded in cultural every-day usage, it's important to point out that terms like concept--the components of thoughts--do have a particular meaning.

From Perice's perspective, a concept or a sign is made of three indecomposable elements which Peirce calls firstness, secondness, and thirdness. These three components are the building blocks upon which everything we can think about are built. In short, firstness is feeling, secondness is resistance, and thirdness is experience.

I relate these in less anachronistic terms to:

1. Sensation prior to awareness
2. Relations and Properties
3. Experiences and Generalities

It's not exactly intuitive, and my notes rely heavily on extended quotations to explain the concepts.

Firstness: Sensation Prior to Awareness

Before we have an abstraction which helps us understand the environment, there must be---absent of any categorization, modelling, or understanding---the information or sensation which is used to construct the abstraction. Firstness is "feeling, as distinct from objective perception, will, and thought" (CP 1.302)[1]. It is prior to perception and thought.

A pure nature, or quality, in itself wihtout parts or features, and without embodiment. (CP 1.303)

When you hear firstness, think the raw observations. The fundamental building block for everything that can be present to the mind is what is immediately sensed in a primary sense: the raw stream of information which we use to form perceptions of the environment. Not the sense of experiencing the feelings, but sensorimotor sensation prior to judgements such as feelings and awareness.

That is a phaneron [present to the mind] peculiar to metaphysical thought, not involved in the sensation itself, and therefor not in the quality of feeling, which is entirely contained or superseded , in the actual sensation. The Germans usually call these qualities feelings, feelings of pleasure or pain. To me this seems to be mere repetition of a tradition, never subjected to the test of observation. I can imagine a consciousness whose whole life, alike when wide awake and when drowsy or dreaming, should consist in nothing at all but a violet colour or a stink of rotten cabbage. it is purely a question of what I can imagine and not of what psychological laws permit. The fact that I can imagine this, shows that such a feeling is not in general, in the same sense in which the law of gravitation is general. For nobody can imagine that law to have any being of any kind if it were impossible that there should exist any two masses of matter, or if there were no such things as motion. A true general cannot have any being unless there is to be some prospect of its sometime having occasion to be embodied in a fact, which is itself not a law or anything like a law. A quality of feeling can be imagined without any occurrence, as it seems to me. Its mere may-being gets along with any realisation at all. (CP 1.304)

When Peirce says phaneron, he means what is present to the mind with no claims as to whether or not it is present in reality; he has drawn comparisons to what he means when he says phaneron and what some mean when they say idea (CP 1.284). He is saying that there's no reason there couldn't be primary elements of our conceptualisation of the world which exist independent of any other---pieces which could be composed to make all of our conceptualisation.

Peirce invites us to consider what we think the building blocks of concepts, or thought, might be if we begin with this firstness of sensation as the first piece:

Suppose I begin by inquiring of you, Reader, in what particulars a feeling of redness or of purple without beginning, end, or change...that should constitute the entire universe, would differ from a substance? I suppose you will tell me that no such thing could be alone in the universe because, firstly, it would require a mind to feel it, which would probably not be the feeling itself; secondly the colour...would consist of vibrations; thirdly, none of them could last forever without a flow of time; fourthly, each would have a quality, which would be a determination in several respects, the colour in hue, luminosity, chroma, and vividness...and fifthly, each would require a physical substratum altogether disparate to the feeling itself. (CP 1.305)

And he supposes we propose five pieces starting with Firstness as sensation:

1. A mind which experiences the sensation
2. The vibrations of the colour
3. Time for the vibrations to vary over
4. The qualities the colour could be measured over
5. The physical realm which this all happens in

But I point out to you that these things are only known to us by extraneous experience; none of them are [seen in the colour]... Consequently, there can be no logical difficulty in supposing them to be absent, and for my part, I encounter not the slightest psychological difficulty in doing so. To suppose, for example, that there is a flow of time, or any degree of vividness, be it high or low, seems to me quite as uncalled for as to suppose that there is freedom of the press or a magnetic field. (CP 1.305)

Peirce then outlines how all of these additions are reducible. The flow of time and minds as perceivers of the sensation of red are all constraints which we put in place given additional understanding. On a personal level, none of them are required to experience sensations such as redness, or whistling.

It is clear that although these notions aren't necessary for the sensation which peirce treats as primary, we do use notions of time and understanding of the properties of things we sense to conceptualise and reason about the world.

Peirce acknowledges this, pointing out that while it's conceivable to just experience the world on a moment-to-moment sensory basis, that such an agent or system would be cognitively limited.

We can, it is true, see what a feeling in general is like; that, for example, this or that red is a feeling; and it is perfectly conceivable that a being should have that color for its entire consciousness, throughout a lapse of time, and therefore at every instant of time. But such a being could never know anything about its own consciousness. It I could not think anything that is expressible as a proposition. It could never know anything about its own consciousness. it could have no idea of such a thing. It would be confined to feeling that colour. (CP 1.310)

The point being made that which is first can only be an exact reproduction of itself. Simply having the same sensation, or subset of sensations, in the same mind at a different time is something different from the firstness itself. Or, if in a different mind, the identity would depend on the mind, violating the reproduction.

A collection of other snippets which are explanatory:

"a pure nature, or quality, in itself without parts, or features, or embodiment" (CP 1.303).

that which "involves no analysis, comparison, or any process whatsoever, nor consists in whole or in part of any act..." (CP 1.306)

"A state, which is in its entirety in every moment of time as long as it endures"

Secondness: Relations and Properties

While sensation is integral to how we conceive of our world, it's also clear that we do not understand our world using the raw, unprocessed sensation from the environment alone. We can see the influence things beyond sesnation in how we perceive our environment: there are blind spots in our vision which we do not perceive. Optical illusions can convince us perceptually that things are not as they truly are. There is some processing which enables us to understand our environment in terms of an abstraction.

Contemplate anything by itself---anything whatever that can be so contemplated. Attend to the whole and drop the parts out of attention altogether. On can approximate nearly enough to the accomplishment of that to see that the result of its perfect accomplishment would be that on quality of feeling. This quality of feeling would in itself, as so contemplated, have no parts. It would be unlike any other such quality of feeling. In itself, it would not even resemble any other; for resemblance has its being only in comparison. contemplate, however complex may be the object, it follows that there is nothing else in immediate consciousness. To be conscious is nothing else than to feel. (CP 1.317)

Pierce then makes the observation "what room, then, is there for secundans and tertians?" Why is there anything else other than instantaneous feeling as an irreducible building block of building symbols?

Understanding of the environment is not just based on the perceptions of the environment, but also the relationship between things. Redness has a character or has properties to it which we can understand in terms of relations between different moments or different independent sensations.

To explain this, we turn to actions and their consequences. Pierce explores this by discussing an agent's effort and the consequences of it.

An effort is not a feeling, nor anything priman or protoidal. There are feelings connected with it: they are the sum of consciousness during the effort. By it is conceivable that a man should have it in his power directly to summon up all those feelings, or any feelings. He could not, in any world, be endowed with the power of summoning up an effort to which there did not happen to be a resistance all ready to exist. (CP 1.321)

Here, I choose to read effort as action, or more generally as behaviour. The point he makes here is that the actions an agent takes in its environment are fundamentally separate from the raw feelings of the agent. They may influence the feelings which are felt during the instants during which the behaviour is being executed, but they are not the same as the behaviours being executed.

By struggle, I must explain that I mean mutual action between two things regardless of any sort of third or medium and in particular regardless of any law of action. (CP 1.325)

For example, an agent in its environment may bump into a wall. There is a relationship between the wall and the agent. The agent took an action, leading it to bump into the wall. Resistance in the environment caused a sensation of force against the agent's bump sensor.

The effort and resistance---the action and the sensation---are secondness. Using this example, we can describe a sense of 'other-ness'.

Secondness isn't limited to 'otherness'. Things which we wish to express about the world which are relations between two different moments are secondness. Peirce draws connections to causation and statistics as examples which related to seconds by drawing relations between two senses.

The idea of second is predominant in the ideas of causation and statical force. For cause and effect are two; and statical forces always occur between pairs. Constraint is a secondness. In the flow of time in the mind, the past appears to act directly upon the future, its effect being called memory, while the future only acts upon the past through the medium of thirds. Phenomena of this sort in the outward world shall be considered below. I sense and will , there are reactions of Secondness between the ego and the non-ego. (which non-ego may be an object of direct consciousness). In will, the events leading up to the act are internal, and we say that we are agents more than patients. In sense, the antecedent events are not within us; and besides, the object of which we form a perception (though not that which immediately acts upon the nerves) remains unaffected. Consequently, we say that we are dominant; for the real is that which insists upon forcing its way to recognition as something other than the mind's creation. (CP 1.325)

Relating these notions back to machine intelligence: methods which perform classification or regression are secondness. Focusing specifically on Reinforcement Learning methods, we could consider a policy evaluation method---a method which estimates either the value or some accumulation of sensation for a given state---to be a second. There is a relation drawn between an action and a response.

As an aside, Pierce makes an interesting observation: before English adopted the word two, we simply used other.

Thirdness: Experiences and Generalities

Finally, there must be something which connects the relation to the instances which are a party to it: the seconds to the firsts. This is what Peirce considers that which connects is the third.

An Example: Ambulance Sirens

It may seem unclear why we should need a third. We have moments which we sense, and we have the perception which relations between moments give rise to. What else could there be?

Typically, we categorize the pipeline as having two parts: 1) immediate sensation and 2) perception. Peirce breaks what we would usually consider perception into a third category: experience (CP 1.335). The reasoning behind this is that perception of events is not cognition of change.

If an ambulance is racing towards you and suddenly passes, due to the doppler effect the sound of the siren will lower as it passes you. You have a sensation of the whistle, which gives rise to the perception of the whistle, but the cognition and understanding of the change in tone---awareness of the changes and contrasts of awareness---is experience.

Thirdness as Generalities

By the third, I mean the medium or connecting bond between the absolute first and last. The beginning is first, the end second, the middle third. The end is second, the means third. The thread of life is a third; the fate that snips it, its second. A fork in the road is a third, it supposes three ways; a straight road, considered merely as a connection between two places is second, but so far as it implies passing through intermediate places it is third. Position is first, velocity or the relation of two successive positions second, acceleration or the relation of three successive positions third. But velocity in so far as it is continuous also involves a third. Continuity represents Thirdness almost to perfection. Every process comes under that head. Moderation is a kind of Thirdness. The positive degree of an adjective is first, the superlative second, the contemplative third. All exaggerated language, "supreme," "utter," "matchless," "root and branch," is the furniture of minds which think of seconds and forget thirds. Action is second, but conduct is third. Law as an active force is second, but order and legislation are third. Sympathy, flesh and blood, that by which I feel my neighbour's feelings, is third. (CP 1.337)

This description is a touch melodramatic. Extending on the metaphor of a road: a place is a first because it is simply a location in relation to nothing else. When we make a road connecting two places---two firsts---we create a second by drawing a relation between the two firsts.

If we reflect back on the previous robot example, an analogy can be made between the the immediate sensation and the value estimate. It has some estimation which predicts that it will bump into the wall. The estimate for that state is a second, the estimator for all given states is third.

It is impossible to resolve everything in our thoughts into those two elements. We may say that the bulk of what is actually done consists of Secondness--or better, Secondness is the predominant character of what has been done. The immediate present, could we seize it , would have no character but its Firstness. Not that I mean to say immediate consciousness...would would be Firstness, but the quality of what we are immediately conscious of... is Firstness. (CP 1.343)

When we categorize what we think about, it's clear that a lot of what our thoughts consist of can fit into firstness and secondness. Moments are clearly influencing our thoughts on a moment to moment basis (Firstness). These sensations give rise to perception and an understanding of relations between the moments, including how our behaviour influences sensation on a moment-to-moment basis (Secondness).

In general, we may say that meanings are inexhaustible. We are too apt to think that what one means to do and the meaning of a word are quite unrelated meanings of the word 'meaning', or that they are only connected by both referencing some operation of the mind... (CP 1.343)

This is kind of a classic pragmatic point to make: that the meaning of some word is not unrelated to behaviour. The use of a concept and the consequences of a behaviour are directly responsible for constructing meaning.

In tuth the only difference is that when a person means to do anything he is in some state in consequence of which the brute reactions between things will be moulded into conformity to form to which the man's mind itself moulded, while the meaning of a word really lies in the way in which it might, in a proper position in a proposition believed, tend to mould the conduct of a person into conformity to that to which it is itself moulded. (CP 1.343)

This is drawing a comparison demonstrating how meaning in a linguistic sense is related to meaning in an active behavioural sense: we judge meaning in both cases based on their consequences.

Not only will meaning always, more or less, in the long run, mould reactions itself, but it is only in doing so that its own being consists. For this reason, I call this element of the phenomenon or object of thought the element of Thirdness. It is that which is what it is by imparting a quality to the reactions in the future. (CP 1.343)

Primacy of Firstness, Secondness, and Thirdness

it is a priori impossible that there should be an indecomposable element which is what it is relatively to a second, a third and a fourth, The obvious reason is that which combines two will by repetition combine any number. Nothing could be simpler; nothing in philosophy is more important. We find then a apriori that there are three categories of undecomposable elements to be expected in the phaneron: those which are simply positive totals, those which involve dependence but not combination, those which involve combination. Now let us turn to the phaneron and see what we find in fact. (CP 1.298-299)

Thinking it Through: Examples Of Firsts, Seconds, and Thirds

• Position: First
• Velocity: Second
• Acceleration: Third
• Observations from the environment: First
• A General Value Function predicting an observation for some behaviour policy over some time-scale: Second
• A model: Third
• A Sensor reading: First
• An exponential moving average of sensor readings: Second
• A model of the process which the sensor records: Third

[1] I use Percian citations which are standard for citing Peirce's works. Here CP m.n stands for Collected Papers volume m paragraph n.

Thanks to Oliver Oxton for the helpful chats.