# Fittingness: Rational success in concept formation

## Epistemic status:

This post offers a philosophical argument for distinguishing truth and fittingness as parallel success concepts for two phases of rational inquiry. I have graduate degrees in philosophy, with relevant expertise in logic, type theory, epistemology, phenomenology, ontology, and philosophy of science. I am confident (0.9) about truth the central claims, and the fittingness of central concepts. At the end I include a brief and much more speculative section (0.5) on how these ideas might related to pattern recognition in the brain.

## Intro

The concept of truth is widely held to be a central concept of success for rational inquiry. It captures the notion of accuracy of beliefs in modeling reality. In this post, I suggest that truth needs a companion concept of fittingness. I will argue, that as truth is the essential success concept for rational belief, so fittingness is needed as a success concept for rational concept formation (equivalently: ontology building or type assignment). Both truth and fittingness capture an idea of accuracy in world modeling, but they operate at different type theoretic levels. Roughly, fittingness concerns the accuracy or appropriateness of how we divide reality by attaching concepts to it, by typing it, how we cut reality at the seams with language. Truth captures the accuracy of statements (propositions) within a given ontology. In order for questions about the truth of a proposition to be meaningful fruitful and salient, the concepts in which the proposition is expressed must be sufficiently fitting. [Slider’s comment below makes the point that truth conditions can be meaningful even when the concepts employed are not fitting. He gives the example of the concept grue from philosophy. This example also illustrates that even when a statement is truth evaluable it may not be fruitful or salient for the purpose of rational inquiry.]

## Fittingness in Inquiry

There are two phases of rational inquiry. These two phases do not occur in strict linear sequence, but rather as a cycle, frequently looping back and forth. In one phase I’m engaging with some domain (or a novel aspect of a domain) that is confusing, anomalous, or hard to make sense of. I don’t have good pre-existing concepts to describe or articulate what’s happening here. I’m not even sure what questions to ask, or how I should identify salient features of the domain.

Despite my ignorance, I can engage with this domain by looking at examples, by interacting and observing what happens. As I do this I may be struck by an association, metaphor, or a loose analogy with something I already understand (usually something in a seemingly unrelated domain). I notice this association and “try it on for size”. I attempt to map it to the current domain more closely to turn the intuitive association into something more rigorous. Sometimes, this mapping clicks into place. I keep observing my interactions with the domain, and the new analogy holds closely. Moreover, it might become a fruitful guide to my inquiry, suggesting new avenues of exploration, new questions to ask, etc. In time, if it proves to be particularly fruitful, coherent, and stable across the domain, it may solidify into a feature of the domain.

Once features (which might also be called properties, objects, relations, agents, or processes depending on context) start to form, we can move into the second phase of inquiry. We can formulate precise statements about these features and what might or might not hold between them. At this point, truth becomes relevant as the success concept for evaluating such statements. A question such as “Do objects characterized by property A enter into a process B?” has a truth value. It can be evaluated based on observation and argument. In contrast, the question of whether the domain is properly characterized by property A and process B, is not a question of truth, it is a question of fittingness.

Just as true has an opposite false, and it can (for some domains) admit of degrees called probability, we can similarly say that fitting has an opposite of distorting or ill-fitting, and there are degrees of fit.

## Spandrels: An Example of Fittingness in Biology

A scientific example to illustrate these phases. Stephen Jay Gould and Richard Lewontin introduced the term spandrel into evolutionary biology based on an analogy with an architectural feature of old churches.

Stephen Jay Gould; Richard Lewontin (1979), “The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme”, Proc. Roy. Soc. Lond. B, 205 (1161): 581–598.

Source

The spandrel was meant to capture the idea that a trait of organism could evolve as a structural byproduct or side effect of another trait that which evolved due to natural selection. Analogously, architectural spandrels arise from the necessary space left at the top of an archway. The analogy is fitting because with the spandrels due to arches, architects eventually made use of them for decorative flourishes, much as species with spandrel traits might eventually evolve uses for these traits that confer selective advantage. The conceptual mapping between architectural spandrels and biological spandrels is tight and multi-layered. It was not be obvious before it was suggested, but once one sees the connection it clicks into place.

When an analogical mapping is fitting, when the fit is tight and consistent, and when it illuminates the structure of a domain it quickly morphs into a literal feature. Within a few years of Gould and Lewontin’s original paper, the term spandrel was replaced by the more biological sounding term “exaptation”. This became a new standard concept in the conceptual repertoire of evolutionary biology. It is no longer a mere analogy, but a literal feature. Biologists can use this new concept to ask precise scientific questions such as “Did bilateral symmetry arise in animals as an exaptation or an adaptation?” Such questions can be evaluated in terms of truth or falsity. Insofar as such statements are taken seriously in actual scientific research, They presuppose conceptual fluency with the relevant concepts they presuppose the fittingness of the concepts used in their formulation [updated based on Slider’s comment]. We cannot fruitfully engage with truth evaluation until we’ve already embraced the fittingness of the concepts used to pose the question.

## Can fittingness be reduced to truth?

To anticipate a potential object to the true-fitting distinction. I acknowledge that questions of conceptual fit can be turned into questions of truth by asking whether the statement, “X is fitting for domain D” is true. However, this is a meta-statement about the relation of our concepts to the domain, it is not a truth-evaluable statement within our target domain. So the cost of converting fittingness questions to truth questions is to shift the relevant domain of inquiry into a meta-domain. Ascending to such a meta-domain does not help us evaluate fit. We must still rely our ground-level judgements of fit as we engage/​interact with the domain while trying on different concepts for size.

## Why is this Distinction Important?

### Intractable Disagreement

I think that often when disagreements persist between well meaning intelligent people, it is because of a mismatch in the taken-for-granted concepts and word meanings we use to try to discuss the issues at hand. We can try to resolve such mismatches by offering explicit definitions and disambiguation of terms, but these measures do not adequately address the questions of whether a given term, definition, or concept is relevant, useful, natural, illuminating, etc.

When disagreements resist straightforward approaches based on evidence and argument, when they seem to turn on different views of what is salient to talk about, this is a good clue that we need to shift from a truth-focused inquiry to a fittingness-focused inquiry.

### Sub-Optimal Concepts

The culture of rationalism (and science generally) may have an unacknowledged bias towards truth-focused inquiry over fittingness-focused inquiry. Inquiring into fittingness can feel messy, childish, too subjective, certainly not what a respectable researcher should be focused on. Rationalists like clean lines and sharp distinctions, not loose analogies, metaphors, and associations. However, this means we might end up rushing the first phase of inquiry, leaving us stuck with ill-fitting concepts. When we try to formulate truth claims in terms of these ill-fitting concepts, we may give the illusion of clarity and precision, while actually obfuscating the domain we wish to understand.

The concept of fittingness can help us avoid this tendency by allowing us to explicitly signal when we need to shift modes between the two phases of inquiry. Rather that this seeming like some illegitimate move in the discussion, it can become a well accepted and non-mysterious oscillation between two well-defined phases of inquiry. In short, I am arguing the the concept of fittingness is fitting for the domain of rational inquiry.

## Conclusion

In general, questions of fittingness concern the correct formation of the concepts, ontologies, or types (in a type theoretic sense) that we use to structure our statements about a domain. In contrast, questions of truth concern the evaluation of statements made within an already formed scheme/​ontology/​typing of the domain.

What does fittingness-focused inquiry look like? It is about orienting to a domain, examining examples, connecting the dots, drawing analogies, telling stories. We get our hands dirty with the domain while looking for conceptual connections. This can lead us to an experience a spontaneous shift in our perception of how the domain is organized as it is interpreted through a new conceptual lens. Not just any shift will do; for it to be fitting, the shift must be one that transitions our experience of the domain to become more intelligible or rationally structured. The domain becomes less confusing, more navigable, more naturally divisible, and more compositional.

## Speculation: Fittingness and Pattern Recognition in the Brain

It seems likely that on a neurological level, inquiry that leads to fitting concepts is grounded in the brain’s basic pattern recognition abilities. This is an automatic process that learns patterns in experience without pre-existing abstract concepts. While the brain can learn innumerable patterns, our pallet of linguistically articulable concepts is much more limited. Since we can’t name every micro-pattern we are able to learn, we must find an economical way to express the most important patterns, ideally by re-purposing and extended existing concepts through analogy. A judgement of fittingness is the perception of a higher-order structural match between the pattern of a concept and the pattern we’ve learned to recognize non-linguistically in the domain.

Note: this previous paragraph is a just a hypothesis of how fittingness may relate to the brain. The main philosophical arguments of this post do not depend on the correctness or even plausibility of this hypothesis.

• I agree, but to me this idea is already captured by the concept we variously call telos, purpose, care, or concern. That is, fitness as you described it seems to be a natural consequence of truth necessarily being in the service of some concern, this making truth ready at hand. In this way fitness is something like the extent to which a category serves the purpose its discerner intended.

• Fittingness is not the same as telos/​purpose/​concern. It is a success concept for a specific telos/​purpose/​concern, namely that belonging to rational inquiry. In other words, it indicates that one has formed a concept or ontology which is successful for the purpose of rational inquiry. Of course, there might be other purposes governing concept formation which would have their own success concepts. For example, if one’s purpose is to craft deceptive propaganda then the relevant success concept might be slipperyness or something.

• Oh, but then why have a special word for success to the purpose of rational inquiry? To my ear “fitness” seems like something general we could say about anything, as in it’s “fitness for X”, like “fitness for rational inquiry” or “fitness for convincing others”.

• The term I introduced is “fittingness” not fitness. Fittingness is meant to evoke both fit, as in whether a pair of shoes fit my feet, and also fitting, as in “that is a fitting word choice for this sentence”. It is possible that there is another term which would be a better label for the underlying concept. If you have suggestions for alternatives I would love to hear them.

I think it’s important that the word is specific, not general. As you point out, we could use a general term qualified with a lengthy phrase like: “success with respect to concept formation in the context of rational inquiry,” but that clunker is difficult to sprinkle throughout an argument. The advantage of a single term to encapsulate an important idea should be obvious. Nobody suggests we should replace the term truth with the phrase, “success with respect to belief in the context of rational inquiry.” Moreover, the metaphorical associations of fit and fitting give a clue about what this kind of success actually involves. It involves concepts fitting the structures found in reality, without implying the unsustainable idea that we can know what the natural structures are in advance of inquiry. We can size a shoe without knowing our foot size in advance, just by trying on lots of different shoes until one fits.

I admit that the concept I call fittingness is not often used at present. Indeed I believe in present discourse fittingness is often muddled either with truth or instrumental usefulness. This precise muddle leads to difficulties in understanding how Kuhnian paradigm shifts (or pre-paradigmatic science) can be understood as legitimate expressions of rational inquiry. I didn’t do more than hint at such problems in the post, maybe I’ll write another post about this.

The point of my post is to diffuse these muddles and make it easier to appeal to fittingness on the regular. I want it to be a part of our ready-to-hand conceptual repertoire as rationalists, in the same way that we have easy access to terms like truth, probability, evidence, etc. I make a case for why this would be of benefit in the section titled, “Why is this Distinction Important?” If you don’t find that section convincing please let me know what you see as the specific shortcomings and I will try to address them.

• I think I can simultaneusly say that “grue” is not a fitting color word but still be able to determine truth values involving the concept.

You need to be able to be understand the claims to evaluate truth but fluency is a different thing than fittingness.

• Thanks, you are correct. I have updated the post to reflect this.

• That is a weird way you think it reflects on the content. I think I can fruitfully engage in truth evaluation of grue things wihtout agreeing or supposing that grue is fitting.

Maybe a bigger example would be that we can do quantum mechanics without really understanding the mathematics. The field of interpretations of quantum mechanics is underdeveloped. Understanding there is not a prerequisite to build tech on it or to verify the outcomes of experiments. I think there was a deveoplement stage where we knew there were statistical regularities and the fittingness of the field went forward when the concept of “entanglement” was used to get a handle on it. Understanding helps in being and getting correct and it is the primary path and approach of some but it is not a rerequisite in that its neglect would lead to failure.

• I think I can fruitfully engage in truth evaluation of grue things wihtout agreeing or supposing that grue is fitting.

As indicated in the post, fittingness is dependent on the domain D under study. If we take grue to be a term in the study of colour, it is profoundly ill-fitting. I think it is a fair assessment that no researcher who studies colour would find it fruitful or salient to evaluate the truth of propositions involving grue. The picture changes however if we let D be philosophy of science. In that case, grue is fitting, precisely because it illuminates an important paradox in our theories of induction. Here the truth evaluation of statements formulated using grue is fruitful, but that’s not a problem because grue is fitting.

A true counter example to my claim would require that a concept C is ill-fitting for a given domain D and yet it is fruitful (for the purpose of rational inquiry into D) to evaluate the truth of statements which are formulated with C.

Regarding the quantum mechanics example, I would need more details to fully understand your claim. My hunch is that the mathematical concepts used to formulate QM could be fitting for the domain of physics even if we don’t have a good meta-interpretation of them. If you think this isn’t the case, please elaborate on why not.

• In my head it is fuzzy whether fittigness is supposed to be the same or different as some concepts being in fashion.

I think it is possible to dedtermine the truth of statements which use grue as a concept to deal with color. “Grue is a shade of red” is a statement in the domain of color and it can be determined to be false. That grue isn’t very fitting for color is connected to phenomena like statements like “Is grue a shade of green?” which is not effectively or truthfully answered with a plain yes or no answer. But I think this has a correct answer and the truth can be evaluated. Grue can feel discontinous if explained in terms of green and blue, but a representation of green can be given in the grue-style color understanding which would make green the “ill-fitting one” for that concept group.

I feel like “fruitful” in this context has multiple possible meaning that might be relevant. One of them is “bears fruit” ie you can make something happen with it, it produces theorems, or other result-type objects. Another would be fruitful in the sense of inciting excitement in the field forward or getting the acceptance of the group. In this sense heliocentrism would be unfruitful in a world of strong catholic geocentrism. In contrast epicycles would be a symptom of fudging, making an ill-fitting theory make correct predictions.

The whole motto of “shut up and calculate” seems to suggest a direction where constructing narratives is seen as anti-progress or just leading people astray. One could think that biology could suffer in a same kind of thing where if people antropomorphise and attribute human like wants and needs to evolutionary pressures then incorrect results could be doled out. But it seems the concepts surrounding biology are able to push forward without undue drag from other concepts. However difference between “inclusive genetic fitness” and “every animal just tries really hard to survive and some succeed” seems like it needs to be done again and again in popularizations. But like grue statements can be examined, examining a really biology ill-fitting overtly-machivellian view of evolution can be done. Then things like “every animal tries to survive” turns into a falsehood through not all animals representing to themselfs their survival making them impossible to want to survive.

Under certain conceptions of fruitfullness it would seem that if somebody achieved an interesting or important result via some method even if the method was obscure before then by the fact of the importance of the discovery the method would become fitting. This would seem like it is so resistant to counter-examples that the concept becomes empty by proving too much.

Suppose that somebody asks “Did the witch board the train?” and I believe that “witch” refers to Rebecca and I infact in my believe Rebecca did step into the train. If I say “yes” to the question do I implicitly think that referring to rebecca as “the witch” is a good idea? A more socially smart answer would probably be that “Rebecca is not a witch, she did board the train”. But even if I do so I have answered the question that I think is ill-fittingly asked. But one doesn’t need to share or agree to the conception to be interoperable or able to cooperate. Refusing or not being able to make the connection is epistemologically suboptimal.