Objective Concepts

Consider this post to be my reaction to the Concepts entry in the Stanford Encyclopedia of Philosophy:

Margolis, Eric and Stephen Laurence, "Concepts", The Stanford Encyclopedia of Philosophy (Fall 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/fall2023/entries/concepts/>.

Next, consider the title a bit provocative as I do not think that concepts stand for objects (or actions). I intentionally want to make this discussion emotional so that my readers remember my ideas and feel tempted to engage with criticism or support.

Concepts vs Objects

I will state my view on concepts first, and then will go through the entry to address the concerns of the authors.

We live in a real-time world of enormous variety and complexity. Our goal with respect to knowledge is to be able to recognize objects and to select actions that reliably get us closer to our everyday goals. Note that I am not talking about guaranteed results because in the presence of obstacles or competition those are only wishful thinking. Insufficient resources may also limit our ability to achieve goals. Therefore, we may only guarantee that our actions will move the needle but not that those efforts will suffice.

Concepts figure in both knowledge that and knowledge how. We only need to properly relate them to objects and actions. The key insight here is, "Objects have properties, actions change properties". Here I am talking about comparable properties. My claim is that concepts belong to the properties domain, and not to the domain of objects or actions.

The next key insight is, "Everything is recognized in comparison". Assume that we start with an empty concept toolbox. Everything around can be called an "object". Is it useful? No. Let's introduce a comparable property "tangibility". By using one simple criterion "is it tangible?" we can divide "objects" into "tangibles" and "intangibles". By using another criterion "is it animate?" based on another property, we divide "tangibles" into further subclasses. Note that this criterion does not automatically apply to the other class of "intangibles". The selection of the following criteria at each level depends on the previous path down the specialization tree. It is a semantic process.

Criteria should not be limited only to binary options. We may well use properties like "color" or "shape" that are far from binary. Possible options, binary or not, are necessarily ranges.

When we classify objects, we do not take into account all their properties. Take any of the known classes represented in natural languages with nouns and a respective object. The class is defined by the stack of all the criteria down the specialization tree to the level of that class. However, the real object classified in this way has many more properties. This is an important aspect of classification.

Take a class Chair. By considering the property "material", we may subdivide that class into Plastic Chairs and Wooden Chairs subclasses among many others. Note that the criterion for subdivision does not rely on the similarity of "many more properties" that all plastic chairs have - at this moment they are not even considered. The criterion relies on the differences between plastic chairs and non-plastic chairs. Classification is about differences from sibling subclasses and not about the similarities of intra-class instances.

Generalization, so intensively discussed recently, is about ignoring "differences from sibling subclasses". For example, ignoring differences in "material" we generalize plastic and wooden chairs to the parent class Chair. This adds another function to the specialization tree turning it into the specialization/generalization tree.

Note that any concept, which is just a range, is a multidimensional pocket/cube of the concept space. We cannot apply the term "complex concept" to Plastic Chair just because we do not have a single word for it. All concepts are complex, some of them are never considered, not to mention named. Naming is reserved only for frequently used, or crucial in other aspects, concepts.

How do we draw boundaries between ranges? They depend on actions and practical purposes. Each action takes input parameters and produces some output. Recall that actions change properties. Also, recall Einstein's definition of insanity - "doing the same thing over and over and expecting a different result." Based on our purposes, we decide what changes are "the same" and what are "different". But what does that tell us about the input parameters? And how does that use our specialization/generalization tree?

Exceptions or differences in results determine respective boundaries for inputs. Respective ranges on the tree may be connected with the "action tag".

Another important issue is vagueness. The SEP entry on Vagueness provides this advice on how the boundaries are determined, "Where there is no perceived need for a decision, criteria are left undeveloped." Consider the example of boundaries for a morning - 6 AM and 10 AM. Only philosophers a-la Gettier will correct a person who says "Good day!" at 9:59 AM or "Good Morning!" at 10:01 AM. Ordinary people are fault-tolerant when "there is no perceived need for a decision".

Another important issue about concepts is that they may be relative. Given two pencils, we may call one "short" and the other "long". Later looking at two trains, we may call one of them "short" even though it is way longer than the "long" pencil.

What does that suggest about our innate abilities to recognize concepts? I propose to consider a hypothesis that we have lots of "rulers" for different properties in our heads. Those rulers have "flexible" marks. When we classify objects in a given context we label those marks "up to this - short pencils" or "above this - long trains". But first, we use other rulers along the specialization/generalization tree to recognize pencils and trains.

Recognition is fast because it uses only the defining features of concepts. Consider the game 20 Questions - in up to 20 simple comparisons one may figure out one of a million concepts. Remarkable performance! The game deserved the attention of Charles Sanders Peirce for a reason.

Natural languages use words to refer to ranges. One word may refer to several ranges (of different properties) making it a polysemous word. Several words may refer to the same range of the same property making them synonyms.

References filter relevant objects from the current context by picking the properties of those objects that differentiate them. If one word is not enough we stack filters.

Concepts from the SEP Entry

Regarding "the ontological status of a concept. The three main options are to identify concepts with mental representations, with abilities, and with abstract objects such as Fregean senses."

Probably my approach is closer to the last option. The only difference is that I rely on the stack of ranges of different properties. This stack is abstract so that many objects will fit its combined filter.

"The classic contemporary treatment maintains, instead, that the internal system of representation has a language-like syntax and a compositional semantics. According to this view, much of thought is grounded in word-like mental representations. This view is often referred to as the language of thought hypothesis (Fodor 1975)."

I have a different view on language. It has very limited capabilities. A word referring to a concept only encodes the "defining features" ignoring "much more properties". Those properties are registered by perception and stored in memory. When we think we juggle all the available properties of those objects and not their limited representations.

Language simplifies our thoughts leaving us only their "defining features". Thoughts are richer. It is not that thoughts function like language. It is that language tries to mimic our thoughts.

"One of the most influential arguments along these lines claims that mental representations are explanatorily idle because they reintroduce the very sorts of problems they are supposed to explain."

My approach introduces the specialization/generalization tree. At each level, we may introduce rules. For example, "all birds fly". At the level below, we may introduce exceptions/subrules, "chickens, penguins, and ostriches don't". It makes knowledge compact.

"For proponents of this view, concepts, as meanings, mediate between thought and language, on the one hand, and referents, on the other. An expression without a referent (“Pegasus”) needn’t lack a meaning, since it still has a sense. Similarly, the same referent can be associated with different expressions (e.g., “Eric Blair” and “George Orwell”) because they convey different senses. Senses are more discriminating than referents. Each sense has a unique perspective on its referent—a mode of presentation which represents the referent in a particular way. Differences in cognitive content trace back to differences in modes of presentation."

I respect human imagination and its inhabitants like Pegasus. Whatever we can talk about, even if it's an imaginary object, deserves its share of our cognitive resources. Otherwise, we would not be able to generate hypotheses which are crucial in expanding our knowledge.

I agree with the "unique perspective on its referent" but again it is most often used to differentiate the referent from context.

"Critics of the sense-based view have questioned the utility of appealing to such abstract objects (Quine 1960). One difficulty stems from the fact that senses, as abstract entities, stand outside of the causal realm. The question then is how we can access these objects."

We do not access abstract "objects". Those are filters for fitting real (Pegasus included) objects. Fitting objects pass through respective ranges of those multiple rulers in our heads.

"According to the classical theory, a lexical concept C has definitional structure in that it is composed of simpler concepts that express necessary and sufficient conditions for falling under C."

This is a clear misunderstanding of how definitions work. Class C is all the instances of its ancestor class A that are different from other instances of A by that their property P falls into the range R. In other words, we define a class through the reference to its parent class and the identification of an additional property that serves as a differentiating criterion for the sibling subclasses of the parent class. We never introduce one class. At the very least, we introduce a class and a non-class. If we ignore the defining property at this level we should generalize to the parent class. Hence, we should consider all the ranges of the defining property.

"Categorization can be understood as a psychological process in which a complex concept is matched to a target item by checking to see if each and every one of its definitional constituents applies to the target. And reference determination, we’ve already seen, is a matter of whether the definitional constituents do apply to the target."

It's a filtering process based on the comparison of ranges.

"the classical theory receives further motivation through its connection with a philosophical method that goes back to antiquity and that continues to exert its influence over contemporary thought. This is the method of conceptual analysis. Paradigmatic conceptual analyses offer definitions of concepts that are to be tested against potential counterexamples that are identified via thought experiments. Conceptual analysis is supposed to be a distinctively a priori activity that many take to be the essence of philosophy."

"if the definitions aren’t there to be discovered, this would seem to put in jeopardy a venerable view of what philosophy is and how philosophical investigations ought to proceed"

According to Heraclitus, "No man ever steps in the same river twice. For it's not the same river and he's not the same man." Everything is unique, even the same object is different at different points in time. But from the practical perspective, for some purposes, some objects are interchangeable.

Armchair thought experiments are fine as long as they specify the difference between "the same" and "different" for the considered task. Claiming that "Good morning!" is unacceptable at 10:01 AM would be unacceptable in the Middle Ages. Who cared?

"For psychologists, the main problem has been that the classical theory has difficulty explaining a robust set of empirical findings. At the center of this work is the discovery that certain categories are taken to be more representative or typical and that typicality scores correlate with a wide variety of psychological data (for reviews, see Smith & Medin 1981, Murphy 2002). For instance, apples are judged to be more typical than plums with respect to the category of fruit, and correspondingly apples are judged to have more features in common with fruit."

"more typical items are categorized more efficiently."

I do not agree with "apples are judged to have more features in common with fruit". According to my theory, all fruits, whether apples or plums, have the same number of properties in common with Fruit. The problem may be with the classification of apples and plums, more specifically, whether they are sibling subclasses or maybe apples are aunts of plums, if not grand aunts. In the latter case, it just takes more generalization steps to reach from plums to Fruit than from apples. Also, it may be possible that some boundaries are more clearly cut leading to faster processing.

"Since Edmund Gettier (1963) first challenged the traditional definition of KNOWLEDGE (as JUSTIFIED TRUE BELIEF), there has been widespread agreement among philosophers that the traditional definition is incorrect or at least incomplete (see the entry the analysis of knowledge)). But no one can seem to agree on what the correct definition is. Despite the enormous amount of effort that has gone into the matter, and the dozens of papers written on the issue, we are still lacking a satisfactory and complete definition. It could be that the problem is that definitions are hard to come by. But another possibility—one that many philosophers are now taking seriously—is that our concepts lack definitional structure."

I propose several questions to guide the process. Where is the parent concept? It is Belief. What is the criterion for differentiation of sibling subclasses? I propose to drop “true” and go with “justified”. Then we may consider the property “source” and its ranges “reliable” and “unreliable”. If we believe that a clock is working and accurate (when it is not) based on information from a reliable source then we have to respect the data from the clock as reliable. We will hold erroneous knowledge without knowing it. When another reliable source provides us with conflicting information we will reconcile those two blocks of information and go with the more reliable one. But if we knew from the start that the clock was broken then its data is of no relevance to us. Note the difference in our attitude. This difference is due to the check of one property. Concepts in the first place are recognized in comparison.

"A non-classical alternative that emerged in the second half of the twentieth century is the prototype theory (e.g., Hampton 2006). According to this theory, a lexical concept C doesn’t have definitional structure but has probabilistic structure in that something falls under C just in case it satisfies a sufficient number of properties encoded by C’s constituents. The prototype theory has its philosophical roots in Wittgenstein’s (1953/1958) famous remark that the things covered by a term often share a family resemblance, and it has its psychological roots in Eleanor Rosch’s groundbreaking experimental treatment of much the same idea (Rosch & Mervis 1975, Rosch 1978). The prototype theory is especially at home in dealing with the typicality effects that were left unexplained by the classical theory. One standard strategy is to maintain that, on the prototype theory, categorization is to be understood as a similarity comparison process, where similarity is computed as a function of the number of constituents that two concepts hold in common."

The prototype theory shares a fatal flaw with the exemplar theory. To understand this flaw and why it is critical, ask yourself a few questions. How many concepts do we know? Does the theory explain why we should not compare a given object to the prototypes of each concept out there? Are all the properties equally important for comparison with the prototype?

"the prototype theory has its own problems and limitations. One is that its treatment of categorization works best for quick and unreflective judgments. Yet when it comes to more reflective judgments, people go beyond the outcome of a similarity comparison."

Object classification as explained above should not rely on "similarity comparison". Prototypes and exemplars rely on intra-class comparisons of unspecified properties. This is doomed to show poor performance.

"Another criticism that has been raised against taking concepts to have prototype structure concerns compositionality. When a patently complex concept has a prototype structure, it often has emergent properties, ones that don’t derive from the prototypes of its constituents (e.g., PET FISH encodes properties such as brightly colored, which have no basis in the prototype structure for either PET or FISH). Further, many patently complex concepts don’t even have a prototype structure (e.g., CHAIRS THAT WERE PURCHASED ON A WEDNESDAY)"

"a patently complex concept" as explained above is different from primitive concepts in only one aspect - no one cares about the former to give it a one-word name. Regarding "bright colors", I do not agree that they are the "defining features" of PET FISH.

"concepts have conceptual cores, which specify the information relevant to more considered judgments and which underwrite compositional processes. Of course, this just raises the question of what sort of structure conceptual cores have."

Concepts are ordered stacks of defining features. That stack is the core. All other properties of the fitting objects are irrelevant for classification purposes.

"Another and currently more popular suggestion is that cores are best understood in terms of the theory theory of concepts. This is the view that concepts stand in relation to one another in the same way as the terms of a scientific theory and that categorization is a process that strongly resembles scientific theorizing"

It is not just that "concepts stand in relation to one another". Plastic Chair and Wooden Chair are related to one another differently than Plastic Chair to Democracy.

Another comment I find important to add is that we should respect scientific experiments more than theories when it comes to concepts. The core principle of scientific experiments is to change one property keeping all the others the same. This is not sufficient for figuring out complicated interdependencies between properties but it is definitely a good start for discovering basic dependencies.

"A radical alternative to all of the theories we’ve mentioned so far is conceptual atomism, the view that lexical concepts have no semantic structure (Fodor 1998, Millikan 2000). According to conceptual atomism, the content of a concept isn’t determined by its relation to other concepts but by its relation to the world."

I only hope that you will compare this "radical alternative" to the above and decide for yourself on the merits of each approach.

"One way of responding to the plurality of conceptual structures is to suppose that concepts have multiple types of structure. This is the central idea behind conceptual pluralism. According to one version of conceptual pluralism, suggested by Laurence & Margolis (1999), a given concept will have a variety of different types of structure associated with it as components of the concept in question. For example, concepts may have atomic cores that are linked to prototypes, internalized theories, and so on. On this approach, the different types of structure that are components of a given concept play different explanatory roles. Reference determination and compositionality have more to do with the atomic cores themselves and how they are causally related to things outside of the mind, while rapid categorization and certain inferences depend on prototype structure, and more considered inferences and reasoning depend upon theory structure."

Approaches like "conceptual pluralism" are proposed in the absence of a clear picture. I wonder if there are precise guidelines with respect to when to prefer “atomic cores” over “prototypes”.

"One of the oldest questions about concepts concerns whether there are any innate concepts and, if so, how much of the conceptual system is innate. Empiricists maintain that there are few if any innate concepts and that most cognitive capacities are acquired on the basis of a few relatively simple general-purpose cognitive mechanisms. Nativists, on the other hand, maintain that there may be many innate concepts and that the mind has a great deal of innate differentiation into complex domain-specific subsystems."

Rulers are innate, marks on them are learned.

"Perhaps the most influential discussion of concepts in relation to the nativism/empiricism debate is Jerry Fodor’s (1975, 1981) argument for the claim that virtually all lexical concepts are innate. Fodor (1975) argued that there are theoretical problems with all models of concept learning in that all such models treat concept learning as hypothesis testing. The problem is that the correct hypothesis invariably employs the very concept to be learned and hence the concept has to be available to a learner prior to the learning taking place. In his (1981), Fodor developed this argument by allowing that complex concepts (and only complex concepts) can be learned in that they can be assembled from their constituents during the learning process. He went on to argue that lexical concepts lack semantic structure and consequently that virtually all lexical concepts must be innate—a position known as radical concept nativism."

"Fodor has convinced many that primitive concepts are in principle unlearnable (see, e.g., Pinker 2007)."

I wonder at what age children differentiate short and long pencils and trains. To learn concepts is to learn how to demarcate the rulers in one's head. The boundaries are flexible at first and later get more stable. It is not that we may randomly guess the "correct hypothesis", it is that we can confirm it with testing.

"Even if it’s agreed that it is possible to have concepts in the absence of language, there is a dispute about how the two are related. Some maintain that concepts are prior to and independent of natural language, and that natural language is just a means for conveying thought (Fodor 1975, Pinker 1994). Others maintain that at least some types of thinking (and hence some concepts) occur in the internal system of representation constituting our natural language competence (Carruthers 1996, 2002, Spelke 2003) or that natural language augments our concepts in significant ways (Lupyan 2012)."

I clearly go with the former view.

"For many, philosophy is essentially the a priori analysis of concepts, which can and should be done without leaving the proverbial armchair."

I developed my theory predominantly in that proverbial armchair (figuratively speaking). I performed only thought experiments and consumed the required knowledge through textual sources.

I am interested in intelligence and natural languages. It is easy to run thought experiments in those domains from the proverbial armchair. But let's ignore the differences between domains to generalize. It is hard to produce valuable concepts about football or swimming from the proverbial armchair. Hence, in general, I propose when in Rome to do as Romans do. Concepts are about relevant differences. If one cannot experience them in the proverbial armchair then one is better to go out in the search for the source of information.