There are multiple alternative theories of concepts. I want to list them, compare them, consider how an integral model can combine and replicate all their features, and explore how a dimensional model can completely describe anything we might call a concept. ** The classical theory of concepts is one of the five primary theories of concepts, the other four being prototype or exemplar theories, atomistic theories, theory-theories, and neoclassical theories. The classical theory implies that every complex concept has a classical analysis, where a classical analysis of a concept is a proposition giving metaphysically necessary and jointly sufficient conditions for being in the extension across possible worlds for that concept. https://iep.utm.edu/conc-cl/ What is a concept? Disputes about concepts Reconciling models of concepts Classical theory of concepts Prototype theory of concepts Fuzzy theory of concepts Synthetic dimensional model of concepts

What is a concept? Sketch | Back What is a concept? Some scholars have defined a concept as "a building block of thought". What is the structure of that building block? What is is "made out of"? How can we represent that structure in abstract symbolic terms -- such as words and letters and symbols? In this Closed Loop project, we are exploring ways that concepts can be constructed from "synthetic dimensions". We propose to "build concepts" by defining them as algebraic structures constructed from synthetic dimensions. Are we saying that people have a library of algebraic dimensions in their brains, by which they define all concepts? The answer to that question is -- let's talk about it. Maybe yes, maybe no, maybe it varies from person to person. A synthetic dimension is a recursively defined dimension, such that its values -- its "units" -- can be composite and "multi-dimensional " objects, such as "apple" or "beautiful", rather than simple linear units, such as "1 inch". The term "property" can be understood as a synonym for "synthetic dimension". This is also true for other related terms, such as "characteristic" or "attribute" or "quality". We are proposing to build concepts out of synthetic dimensions, by defining a concept as an intersect of dimensions. This is workable because the values of a synthetic dimension are complex constructed objects rather than simple linear values. In this way, we could use synthetic dimensions to construct the abstract conceptual object "beautiful 10 inch apple pie". That dimensional intersect would be our "concept." What is a pie? What is an apple? What is beautiful? Each of those questions can be answered by values in dimensions. Employing dimensional descriptions, all objects that are "pies" can be distinguished from all objects that are "not pies", such as horses or cakes. how can concepts be defined as constructed from dimensions? What does it mean to speak of the "digital integration of conceptual form"? We are proposing to model actual human behavior in digital terms We are creating a definition of "concept" that we believe is consistent with cognitive psychology and philosophy We are not saying that people think in terms of "digital structures" Sat, May 8, 2021 Reference Without concepts, mental life would be chaotic. If we perceived each entity as unique, we would be overwhelmed by the sheer diversity of what we experience and unable to remember more than a minute fraction of what we encounter. And if each individual entity needed a distinct name, our language would be staggeringly complex and communication virtually impossible. Fortunately, though, we do not perceive, remember, and talk about each object and event as unique, but rather as an instance of a class or concept that we already know something about. When entering a new room, we experience one particular object as a member of the class of chairs, another as an instance of desks, and so on. Concepts thus give our world stability. They capture the notion that many objects or events are alike in some important respects, and hence can be thought about and responded to in ways we have already mastered. Concepts also allow us to go beyond the information given; for once we have assigned an entity to a class on the basis of its perceptible attributes, we can then infer some of its nonperceptible attributes. Having used perceptible properties like color and shape to decide an object is an apple, we can infer the object has a core that is currently invisible but that will make its presence known as soon as we bite into it. In short, concepts are critical for perceiving, remembering, talking and thinking about objects and events in the world. http://originresearch.com/docs/SmithAndMedin.docx URL http://originresearch.com/docs/SmithAndMedin.docx

Disputes about concepts Placeholder | Back Stanford Plato says there are five issues surrounding the study of concepts The five issues are: (1) the ontology of concepts, (2) the structure of concepts, (3) empiricism and nativism about concepts, (4) concepts and natural language, and (5) concepts and conceptual analysis. https://plato.stanford.edu/entries/concepts/ Thu, Apr 29, 2021

Reconciling models of concepts Placeholder | Back The synthetic dimensionality model of concepts is supposedly capable of reconciling and combinging all the various alternatives theories that are listed in mainline academic literature. By gahering up a complete list of concept theories and defining their particulars and what particular problem they solve, we'll explore whether combing all these aspects together into one model is really possible The power of synthetic dimensionality suppoedly residess in its flexibility and adaptability -- one language and contrustive method capable of building all these basic logical/semantic/mathematical objects Thu, Apr 29, 2021

Classical theory of concepts Placeholder | Back Table of contents from https://iep.utm.edu/conc-cl/ Historical Background and Advantages of the Classical View Concepts in General Concepts as Semantic Values Concepts as Universals Concepts as Mind-Dependent or Mind-Independent Concepts as the Targets of Analysis The Classical View and Concepts in General Classical Analyses Necessary and Sufficient Conditions Logical Constitution Other Conditions on Classical Analyses Testing Candidate Analyses Apriority and Analyticity with respect to Classical Analyses Objections to the Classical View Plato’s Problem The Argument from Categorization Arguments from Vagueness Quine’s Criticisms Scientific Essentialist Criticisms References and Further Reading Thu, Apr 29, 2021

Prototype theory of concepts Placeholder | Back Family resemblance in terms Sat, May 8, 2021 Reference Prototype theory came out of problems with the classical view of conceptual structure. Prototype theory says that concepts specify properties that members of a class tend to possess, rather than must possess. Wittgenstein, Rosch, Mervis, Berlin, Anglin, and Posner are a few of the key proponents and creators of this theory. Wittgenstein describes the relationship between members of a class as family resemblances. There are not necessarily any necessary conditions for membership; a dog can still be a dog with only three legs. This view is particularly supported by psychological experimental evidence for prototypicality effects. Participants willingly and consistently rate objects in categories like 'vegetable' or 'furniture' as more or less typical of that class. It seems that our categories are fuzzy psychologically, and so this structure has explanatory power. We can judge an item's membership of the referent class of a concept by comparing it to the typical member—the most central member of the concept. If it is similar enough in the relevant ways, it will be cognitively admitted as a member of the relevant class of entities. Rosch suggests that every category is represented by a central exemplar which embodies all or the maximum possible number of features of a given category. Lech, Gunturkun, and Suchan explain that categorization involves many areas of the brain. Some of these are: visual association areas, prefrontal cortex, basal ganglia, and temporal lobe. The Prototype perspective is proposed as an alternative view to the Classical approach. While the Classical theory requires an all-or-nothing membership in a group, prototypes allow for more fuzzy boundaries and are characterized by attributes. Lakoff stresses that experience and cognition are critical to the function of language, and Labov's experiment found that the function that an artifact contributed to what people categorized it as. For example, a container holding mashed potatoes versus tea swayed people toward classifying them as a bowl and a cup, respectively. This experiment also illuminated the optimal dimensions of what the prototype for "cup" is. Prototypes also deal with the essence of things and to what extent they belong to a category. There have been a number of experiments dealing with questionnaires asking participants to rate something according to the extent to which it belongs to a category. This question is contradictory to the Classical Theory because something is either a member of a category or is not. This type of problem is paralleled in other areas of linguistics such as phonology, with an illogical question such as "is /i/ or /o/ a better vowel?" The Classical approach and Aristotelian categories may be a better descriptor in some cases. URL https://en.wikipedia.org/wiki/Concept

Fuzzy theory of concepts Placeholder | Back Membership in the category is fuzzy or ambiguous Sun, May 9, 2021 Reference A fuzzy concept is a concept of which the boundaries of application can vary considerably according to context or conditions, instead of being fixed once and for all. This means the concept is vague in some way, lacking a fixed, precise meaning, without however being unclear or meaningless altogether. It has a definite meaning, which can be made more precise only through further elaboration and specification - including a closer definition of the context in which the concept is used. The study of the characteristics of fuzzy concepts and fuzzy language is called fuzzy semantics. The inverse of a "fuzzy concept" is a "crisp concept" (i.e. a precise concept). A fuzzy concept is understood by scientists as a concept which is "to an extent applicable" in a situation. That means the concept has gradations of significance or unsharp (variable) boundaries of application. A fuzzy statement is a statement which is true "to some extent", and that extent can often be represented by a scaled value. The best known example of a fuzzy concept around the world is an amber traffic light, and indeed fuzzy concepts are widely used in traffic control systems.[4] The term is also used these days in a more general, popular sense - in contrast to its technical meaning - to refer to a concept which is "rather vague" for any kind of reason. In the past, the very idea of reasoning with fuzzy concepts faced considerable resistance from academic elites. They did not want to endorse the use of imprecise concepts in research or argumentation. Yet although people might not be aware of it, the use of fuzzy concepts has risen gigantically in all walks of life from the 1970s onward. That is mainly due to advances in electronic engineering, fuzzy mathematics and digital computer programming. The new technology allows very complex inferences about "variations on a theme" to be anticipated and fixed in a program. New neuro-fuzzy computational methods make it possible to identify, measure and respond to fine gradations of significance with great precision.[6] It means that practically useful concepts can be coded and applied to all kinds of tasks, even if ordinarily these concepts are never precisely defined. Nowadays engineers, statisticians and programmers often represent fuzzy concepts mathematically, using fuzzy logic, fuzzy values, fuzzy variables and fuzzy sets.[7] URL https://en.wikipedia.org/wiki/Fuzzy_concept

Synthetic dimensional model of concepts Placeholder | Back We want to define a general/universal theory of conceptual form that combines all these definitional properties of the concepts we have listed We think this approach is more powerful, more generally useful, and part of a broader and stronger way to represent conceptual, logical and mathematical form Thu, Apr 29, 2021