Concepts and Models

[Brief summary of this post]

In The process of mind I discussed the reasoning process as
the second phase of the RRR loop (recollection, reasoning, and reaction). That discussion addressed procedural elements of reasoning, while this discussion will address the nature of the informational content. Information undergoes a critical shift in order to be used by the reasoning process, a shift from an informal set of associations to explicit relationships in formal systems, in which thoughts are slotted into buckets which can be processed logically into outcomes which are certain instead of just likely. Certainty is dramatically more powerful than guesswork. The buckets are propositions about concepts and the formal systems are an aspect of mental models (which I will hereafter call models).

I have previously described this formal cataloging as a cartoon, which you can review here. So is that it then, consciousness is a cartoon and life is a joke? No, the logic of reasoning is a cartoon but the concepts and models that comprise them bridge the gap — they have an informal side that carries the real meaning and a formal side that is abstracted away from the underlying meaning. So there is consequently a great schism in the mind between the formal or rational side and the informal or subrational side. Both participate in conscious awareness, but the reason for consciousness is to support the rational side. Reasoning requires that the world be broken down, as it were, into black and white choices, but to be relevant and helpful it needs to remain tightly integrated to both external and internal worlds, so the connections between the cartoon world and the real world must be as strong as possible.

So let’s define some terms in a bit more detail and then work out the implications. I call anything that floats through our conscious mind a thought. That includes anything from a sensory perception to a memory to a feeling to a concept. A concept is a thought about something, i.e. an indirect reference to it, and this indirect reference is the formal aspect that supports reasoning, a thought process that uses concepts to form propositions to do logical analysis. (A concept may also be about nothing; see below.) What concepts refer to doesn’t actually matter to logical analysis; logic is indifferent to content. Of course, content ultimately matters to the value of an analysis, so reasoning goes beyond logic to incorporate meaning, context, and relevance. So I distinguish reasoning from rational thought in that it leverages both rational and subrational thinking. And concepts as well leverage both: though they may be developed or enhanced by rational thinking, they are first and foremost subrational. They are a way of grouping thoughts, e.g. sensory impressions or thoughts about other thoughts, into categories for easy reference.

We pragmatically subdivide our whole world into concepts. The divisions are arbitrary in the sense that the physical world has no such lines — it is just a collection of waves and/or particles in ten or so dimensions. But it is not arbitrary in the sense that patterns emerge that carry practical implications: wavelets clump into subatomic particles, which clump into atoms, which clump into molecules, which clump into earth, water, and air or self-organize into living things. These larger clumps behave as if causes produce effects at a given macro level, which can explain how lakes collect water or squirrels collect nuts. The power that organizes things into concepts is generalization, which starts from recognizing commonalities between two or more experiences. Fixed reactions to sensory information, e.g. to keep eating while hungry, are not a sufficiently nuanced response to ensure survival. No one reaction to any sight, sound or smell is helpful in all cases, and in any case, one never sees exactly the same thing twice. Generalization is the differentiator that provides the raw materials that go into creating concepts. Our visual system contains custom algorithms to differentiate objects based on hardwired expectations about the kinds of boundaries between objects that we encountered in our ancestral environment that we benefited most from being able to discriminate. Humans are adapted to specialize in binocular, high-resolution, 3-D color vision of slowly moving objects under good lighting, even to the point of being particularly good at recognizing specific threats, like snakes1. Most other animals do better than us with fast objects, poor lighting, and peripheral vision. My point here is just that there are many options for collecting visual information and for generalizing from it, and we are designed to do much of that automatically. But being able to recognize a range of objects doesn’t tell us how best to interact with them. Animals also need concepts about those objects that relate their value to make useful decisions.

Internally, a concept has two parts, its datum and a reference to the datum, which we can call a handle after the computer science term for an abstract, relocatable way of referring to a data item. A handle does two things for us. First, it says I am here, I am a concept, you can move me about as a unit. Second, it points to its datum, which is a single piece of information insofar as it has one handle, but connecting to much more information, the generalizations, which together comprises the meaning of the concept. A datum uniquely collects the meaning of a given concept at a given time in a given mind, but other thoughts or concepts may also use that connected information for other purposes. This highly generalized representation is very flexible because a concept can hold any idea — a sensation, a word, a sentence, a book, a library — without restricting alternative formulations of similar concepts. And a handle with no datum at all is still useful in a discussion about generic concepts, such as the unspecified concept in this clause, which doesn’t point to anything!

To decompose concepts we need to consider what form the datum takes. This is where things start to get interesting, and is also the point where conventional theories of concepts start to run off the rails. We have to remember that concepts are fundamentally subrational. This means that any attempt to decompose them into logical pieces will fail, or at best produce a rationalization2, which is an after-the-fact reverse-engineered explanation that may contain some elements of the truth but is likely to oversimplify something not easily reducible to logic. For a rational explanation of subrational processes, we should instead think about the value of information more abstractly, e.g. statistically. The datum for the concept APPLE (discussions of concepts typically capitalize examples) might reasonably include a detailed memory of every apple we have ever encountered or thought about. If we were to analyze all that data we might find that most of the apples were red, but some were yellow or green or a mixture. Many of our encounters will have been with products made from apples, so we have a catalog of flavors as well. We also have concepts for prototypical apples for different circumstances, and we are aware of prototypical apples used by the media, as well as many representations of apples or idiomatic usages. All of this information and more, ultimately linking through to everything we know, is embedded in our concept for APPLE. And, of course, everyone has their own distinct APPLE concept.

Given this very broad and even all-encompassing subrational structure for APPLE, it is not hard to see why theories of concepts that seek to provide a logical structure for concepts might go awry. The classical theory of concepts3, widely held until the 1970’s, holds that necessary and sufficient conditions defining the concept exist. It further says that concepts are either primitive or complex. A primitive concept, like a sensation, cannot be decomposed into other concepts. A complex concept either contains (is superordinate to) constituent concepts or implies (is subordinate to) less specific concepts, as red implies color. But actually, concepts are not comprised of other concepts at all. Their handles are all unique, but their data is all shared. Concepts are not primitive or complex; they are handles plus data. Concepts don’t have discrete definitions; their datum comprises a large amount of direct experience which then links ultimately to everything else we know. Rationalizations of this complex reality may have some illustrative value but won’t help explain concepts.

The early refinements to the classical theory, through about the year 2000, fell into two camps, revamp or rejection. Revamps included the prototype, neoclassical and theory-theory, and rejection included the atomistic theory. I’m not going to review these theories in detail here; I am just going to point out that their approach limited their potential. Attempts to revamp still held out hope that some form of definitive logical rules ultimately supported concepts, while atomism covered the alternative by declaring that all concepts are indivisible and consequently innate. But we don’t have to do down either of those routes; we just have to recognize that there are two, or at least two, great strategies for information management: mental association and logic. Rationality and reasoning depend on logic, but there are an unlimited number of potentially powerful algorithmic approaches for applying mental associations. For example, our minds subconsciously apply such algorithms for memory (storage, recall and recognition), sensory processing (especially visual processing in humans), language processing, and theory of mind (ToM, the ability to attribute mental states — beliefs, intents, desires, pretending, knowledge, etc. — to oneself and others). Logic itself critically depends on the power of association to create concepts and so is at least partially subordinate to it. So an explanation of reasoning doesn’t result in turtles (logic) all the way down. One comes first to logic, which can be completely abstracted from mental associations. One then gets to concepts, which may be formed purely by association but usually includes parts (that are necessarily embedded in concepts) built using logic as well. And finally one reaches associations, which are completely untouchable by direct logical analysis and can only be rationally explained indirectly via concepts, which in turn simplify and rationalize them, consequently limiting their explanatory scope to specific circumstances or contexts.

I have established that concepts leverage both informal information (via mental association) and formal information (via logic), but I have not said yet what it means to formalize information. To formalize means to dissociate form from function. Informal information is thoroughly linked or correlated to the physical world. While no knowledge can be literally “direct” since direct implies physical and knowledge is mental (i.e. relational, being about something else), our sensory perceptions are the most direct knowledge we have. And our informal ability to recognize objects, say an APPLE, is also superficially pretty direct — we have clear memories of apples. Formalization means to select properties from our experiences of APPLES that idealize in a simple and generalized way how they interact with other formalized concepts. On the one hand, this sounds like throwing the baby out with the bathwater, as it means ignoring the bulk of our apple-related experiences. But on the other hand, it represents a powerful way to learn from those experiences as it gives us a way to gather usable information about them into one place. I call that place a model; it goes beyond a single generalization to create a simplified or idealized world in our imagination that follows its own brand of logic. A model must be internally consistent but does not necessarily correspond to reality. It is, of course, usually our goal to align our models to reality, but we cognitively distinguish models from reality. We recognize, intuitively if not consciously, that we need to give our models some “breathing room” to follow the rules we set for them rather than any “actual” rules of nature because we don’t have access to the actual rules. We only have our models (including models we learn from others), along with our associative knowledge (because we don’t throw our associative knowledge out with the bathwater; it is the backbone beneath our models). Formally, models are called formal systems, or, in the context of human minds, mental models. Formal systems are dissociated from their content; they are just rules about symbols. But their fixed rules make them highly predictable, which can be very helpful if those predictions could be applied back to the real world. The good news is that many steps can be taken to ensure that they do correlate well with reality, converting their form back into function.

But why do we formalize knowledge into models? Might not the highly detailed, associative knowledge remembered from countless experiences be better? No, we instead simplify reality down to bare-bones cartoon descriptions in models to create useful information. The detailed view misses the forest for the trees. Generalization eliminates irrelevant detail to identify commonality. The mind isolates repetitive patterns over space and time, which inherently simplifies and streamlines. This initially creates a capacity for identification, but the real goal is a capacity for application. Not just news, but news you can use. So from patterns of behavior, the mind starts to generalize rules. It turns out that the laws of nature, whatever they may ultimately be, have enough regularity that patterns pop up everywhere. We start to find predictable consequences from actions at any scale. We call these cause and effect if the effect follows only if the cause precedes, presumably due to some underlying laws of nature. It doesn’t matter if the underlying laws of nature are ever fully understood, or even if they are known at all, which is good because we have no way of learning what the real laws of nature are. All that matters is the predictability of the outcome. And predictability does approach certainty for many things, which is when we nominate the hypothesized cause as a law. But we need to remember that what we are really doing is describing the rules of a model, and both the underlying concepts in the model and their rules can never perfectly correspond to the physical world, even though they appear to do so for all practical purposes. Where there is one model, there can always be another with slightly different rules and concepts that explains all the same phenomena. Both models are effectively correct until a test can be found to challenge them. This is how science vets hypotheses and the paradigms (larger scale models) that hold them.

Having established that we have models and why, we can move on to how. As I noted above, while logic can be abstracted from mental associations, it is not turtles (i.e. logical) all the way down. Models are a variety of concept, and concepts are mostly subrational, the informal products of association: we divine rules and concepts about the world using pattern recognition without formal reasoning. We can and often do greatly enrich models (and all concepts) via reasoning, which ultimately makes it difficult to impossible to say where subrational leaves off and rational begins.4 As noted above, we can’t use reason to separate subrational from rational, because that is rationalizing, whose output is rational. Rational output has plenty of uses, but can’t help but stomp on subrational distinctions. But although we can’t identify where the subrational parts of the model end and the rational parts begin, it does happen, which means we can talk about an informal model that consists of both subrational and rational parts, and a formal model consisting of only rational parts. When we reason, we are using only formal models which implicitly derive their meaning from the informal model that contains them. This is a requirement of formal systems: the rules of logic operate on propositions, which are statements that are true or false affirmations or predicates about a subject, which itself must be a concept. So “apples are edible” and “I am hungry” are propositions about the concepts APPLE, EDIBLE, and HUNGRY (at least). Our informal model in this scenario consists of the aspects of the data (plural of datum) of these concepts and all related interactions we recall or have generalized about in the past. To create a formal model with which we can reason we add propositions such as: “hunger can be cured by eating” and “one must only eat edible items”. From here, logical consequences (entailments) follow. So with this model, I can conclude as a matter of logical necessity that eating an apple could cure my hunger. So while our experience may remind us (by association) of many occasions on which apples cured hunger, reasoning provides a causal connection. Furthermore, anyone would reach that conclusion with that model even though the data behind their concepts varies substantially. The conclusion holds even if we have never eaten an apple and even if we don’t know what an apple is. So chains of reasoning can provide answers where we lack first-hand experience.

So we form idealized worlds in our heads called models so we can reason and manage our actions better. But how much better, exactly, can we manage them than with mental association alone? At the core of formal systems lies logic, which is what makes it possible for everything that is true in the system to be necessarily true, which in principle can confer the power of total certainty. Of course, reasoning is not completely certain, as it involves more than just logic. As Douglas Hofstadter put it, “Logic is done inside a system while reason is done outside the system by such methods as skipping steps, working backward, drawing diagrams, looking at examples, or seeing what happens if you change the rules of the system.”5 I would go a step beyond that. Hofstadter’s methods “outside the system” are themselves inside systems of rules of thumb or common sense we develop that are themselves highly rational. We might not have formally written down when it is a good idea to skip steps or draw diagrams, but we could, so these are still what I call formal models. But that still only scratches the surface of the domain of reason. Reasoning more significantly includes accessing conscious capacities for subrational thought across informal models, and so is a vastly larger playing field than rational thought within formal models. In fact it must be played in this larger arena because logic alone is is an ivory tower — it must be contextualized and correlated to the physical world to be useful. Put simply, we constantly rebalance our formal models using data and skills (e.g. memory, senses, language, theory of mind (ToM), emotion) from informal models, which is where all the meaning behind the models lies. I do still maintain that consciousness overall exists as a consequence of the simplified, logical view of rationality, but our experience of it also includes many subjective (i.e. irrational) elements that, not incidentally, also provide us with the will to live and thrive.

  1. We May Have Snakes To Thank For Our Acute Vision, Barbara J. King, NPR, Mar 19, 2015
  2. Webster: ”rationalize: to bring into accord with reason or cause something to seem reasonable”, Your Dictionary: “rationalize: to make rational; make conform to reason”, Collin’s: “rationalize: to justify (one’s actions, esp discreditable actions, or beliefs) with plausible reasons, esp after the event”
  3. The Classical Theory of Concepts, Internet Encyclopedia of Philosophy
  4. The German philosopher Martin Heidegger explored the junction between the subrational and the rational. His idea of disclosure supposes that the meaning of a word or thing depends upon the context in which we encounter it. His “first order disclosure” is akin to a model in which no rational enrichment has taken place, and his “second order disclosure” is akin to a model enriched by rational reflection.
  5. Gödel,Escher, Bach, 1979, Douglas Hofstadter

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