# Concept

This article by Dan Polansky is about the concept of concept. It gives a first idea, raises some questions, and collects interesting further reading publicly available online. (The article may later be moved to "One man's look at concept" since it occupies the Concept head that others could also want to use.)

## Introduction

A concept is to be distinguished from a word or phrase. As a first approximation, a concept is a word meaning. Thus, a single word covers multiple concepts, and a single concept is named by multiple words. By means of example, the concept of cat-domestical-animal is named by word "cat" but also by word "grimalkin". And the other way around, the word "cat" covers the concept of cat-domestic-animal but also cat-felid-feline. We use the hyphenated names to unambiguously identify the concepts, hoping that listing a set of synonyms will serve to disambigute. Thus, each WordNet's synset is intended to match a single concept.
However, there are multiple reasons to think a concept does not have to be a word meaning. One reason is that at least some concepts seem to exist without words. Thus, pre-linguistic humans were probably able to rank observed individuals, e.g. individual trees, under a single mental category. The same is probably true of other primates. Such a sophisticated animal as a chimpanzee cannot operate in their environment without this kind of conceptual ability, the ability to rank individual observed objects into classes, and to interconnect classes by meaningful relationships. Thus, concepts would be some kind of mental objects different from word meaning. It would still be true that words point to concepts, but not each concept would need to be a word meaning.
Sum of parts concepts are also concepts. Thus, white-cat is also a concept, even if it is just cat that is white. Thus, it would seem any noun phrase ambiguously identifies a concept. Indeed, noun-phrase-that-ambiguously-identified-a-concept is also a concept.
As was pointed above, there is no unique way to name concepts. Thus, we can say cat-domestical-animal or cat-animal-in-the-narrow-sense. The former seems much better.

## Concepts for individual entities

Concepts may also correspond to individual instances, at least to abstract instances. Since, "blueness" is a name of concept, a quality, and that is an individual instance.
One may be less ready to consider concepts for concrete individual entities, including individual people or trees. It is unclear what qualities a concept for, say, Albert Einstein contains: it rather seems that the Kripkean view is of import, that "Albert Einstein" is a rigid designator rather than a package of properties to select by. If one accepts the Russelian theory of names as descriptions, there are also concepts for individual instances, having a certain selection of properties as uniquely identifying these instances. One may object that these concepts are not really belonging to the individuals since they would not belong to them across possible worlds. This needs clarification and discussion.
The idea of concepts corresponding to concrete individual entities via descriptions suggests that different descriptions uniquely identifying an individual entity in this world could correspond to difference concepts, Fregean senses. Thus, Hesperus would pick the individual entity via a different concept than Phosphorus: one has the appearance in the morning sky as part of the concept whereas the other one in the evening sky.
We may wonder whether the idea of Kripkean rigid designation can inspire us to construct a concept that applies across possible worlds without the selecting description so applying:
* The person, in this world or a possible world, who is in this world named Albert Einstein and who in this world has discovered special theory of relativity, regardless whether he did so in the particular world under consideration.
Here, the description would be used to pick the individual entity in this world, and the connection to possible worlds would be via the idea of trans-world numerical identity that disregards which parts of the selecting description are necessary and which merely contingent.

## Disjunctive concepts

Literature also talks about concepts that are disjunctive, using OR to connect criteria. This raises questions about whether any OR combination is a concept, including the following:
* Multi-genus: A star or a house.
* Multi-genus: A star or a house or a mineral or an inflected form or a computable function.
* A person who is tall or is Albert Einstein or has ever been to Canada.

## Complexity of concepts

Possible complexity of concepts points to one set of questions that are to be answered. For a start, does each of the following descriptions correspond to a concept?
* A cat that is white, weighs at least 10 kg and has not broken a vase.
* The concept of metric space in mathematics, that is, a structure that meets all of certain axioms.
Is there any limit to a complexity of description or a specification of a concept? To put it in technical terms, given a particular language of first order logic, does any formula with one free variable correspond to a concept? If it does, it seems impossible for each concept to fit into human consciousness.

## Phenomenal concepts

A concept can probably be expressed in terms of the manner in which it is observed without knowledge of or differentiation of the underlying kind of entity. Thus, we would have the concept of a star as that which reveals itself as bright dot in the sky, without knowing whether the entity causing the dot is a ball of matter or a hole through which something shines or whether we are talking about a single kind of underlying entity rather than a single produced kind of observation. We can classify such stars into fixed stars, slowly moving stars and falling stars. Without deeper knowledge, we could think that some bright dots in the sky are a result of shining balls of matter whereas other bright dots are a results of fires shining through holes.
An example of a concept perhaps less phenomenal but still rather phenomenal is zebra, which can informally defined as striped horse-like animal. There are multiple species of zebra. What makes it phenomenal is that the selection of animals into the concept in part does not depend on underlying genetic affinities only but rather on external appearance. The underlying genetic affinities can be thought of as hidden essences, as if truer or deeper natural joints into which the natural world is cut, sliced or articulated.

## Name-based concepts

A concept can be probably constructed based on words referring to things only. Thus, the following would be concepts:
* Any person named Peter.
* Any entity called cat in whatever sense of the word. (Generally multiple disparate genera.)
* Any entity called by the German word "Katze" in any sense of the word. (Allows embedding of foreign language.)
* Any entity described by the German phrase "schwarze Katze" in any senses of the component words. (Embedding of whole phrases.)
The above may seems strange, but it is often that which is cognitively given in a situation. Thus, if one hears unknown people talk in another room without seeing them, and if one hears "Peter, come here please", a valid even if uncertain inference is that there is someone named Peter, which is not a proper noun manner of reference but rather a common noun manner and thus much more of a candidate to be or correspond to a concept. And "someone named Peter" is as much as one can validly think about that individual entity represented in some way in the mind, together with the inferred "human" and "male". Peter has not spoken so there is not even a way to associate particular voice with that entity.

## Very specific concepts

The possibility of great specificity of concepts needs to be analyzed. Thus, it is to be clarified whether the following are concepts:
* A person shown on the photograph so and so.
* A person with fingerprint so and so.
This question, combined with the one about complexity, leads to the question whether the following defines a concept:
* A person that corresponds to the knowledge that person X (who has seen a photograph) has about Albert Einstein.
The above would imply the existence of many detailed very specific concepts corresponding to individual entities, where different people would have a different concept about the individual entity based on what they know, and the concept would keep on being enlarged with more knowledge gained. There is something implausible about this idea. If one further combines the idea with the idea of arbitrarily combining concepts via OR, we could construct a concept corresponding to knowledge of, say, 50 individual people a certain person has. This construction seems to be at odds with the reason why the concept of concept was introduced in the first place, to correspond to something like relatively general categories under which observed things and other things fall, where "relatively general" is left unspecified.

## Equivalent definitions of the same class

For individual entities, we have seen that Hesperus and Phosphorus could correspond to different concepts even if the same individual entity. There could be a similar situation with classes, for instance of ellipse. An ellipse can be defined as a set of points with a particular constant sum of distances from the focal points or as a set of points generated by applying sine and cosine function to a parameter. These two equivalent definitions identify the same class, but in a different manner, and if two different ways of accessing Hesperus correspond to different concepts, so could the two different ways of accessing the class of ellipses.

## Nativism of concepts

One can ask whether some or all concepts are innate or rather learned. It seems implausible that complex concepts are innate. At the same time, it seems hard to believe that no concept at all is innate.
If we take natural kinds such as biological species or minerals as corresponding to concepts, it seems hard to believe they would be innate. There is not enough environmental information and adaptive survival/reproduction advantage for an organism to have them all innate. For instance, assuming that humans evolved in Africa, it is unclear how the evolutionary analogue of learning consisting in generic and phenotypic variation and elimination would learn about Americas-only species. Similar puzzle applies to learning about species living only deep in the ocean or the concept of bacteria.
By contrast, it is superficially plausible to think that e.g. the concepts of animal (excluding humans), tree and river could be innate, driven by applications relating to survival and reproduction, or more accurately genetic fitness, and based on environmental information readily available to humans no less than chimpanzees.
The subject is covered in Stanford Encyclopedia of Philosophy.

## Coupling to language

The opening paragraphs started with the first approximation that concepts are word meanings. This raises the questions:
* Are there any concepts without words?
* Does language enhance one's work with concepts?
* Does it cognitively matter whether a concept is bound to a word, even if a compound word, or rather a phrase?
We have answered the first question in the affirmative. The answer to the second question seems true as well. Thus, for a mathematical example, the concept of metric space is easier to work with and arrive at if the concept has a name ("metric space") and if it is linked to other concept's names via axioms. Moreover, the use of new words and phrases forces one to create a classification or conceptual scheme that ranks individual objects under the word or phrase, forcing concept formation.
An interesting window on the concept-language coupling is offered by German (and similar languages), a language with a tendency to form long compounds. Does the existence of ready-made long German compounds enhance one's capacity to think and work with concepts?
The subject is covered in Stanford Encyclopedia of Philosophy.
Further reading:
* 4. Concepts and natural language in Concepts, Stanford Encyclopedia of Philosophy

## Definitions of concepts

In so far as concepts are or correspond to word and phrase senses, they can be defined. One can define a concept using words, but that is ambiguous. One can less ambiguously define concepts using concepts, provided one finds a way to unambiguously identify concepts using words or their groups. Thus, one can define cat-domestic-animal as domestic-animal that meows. Here we use a hyphen convention reminiscent of the programming language LISP to identify concepts less ambiguously than single words can.

## Adjectival and verbal concepts

Further to be clarified is whether there are adjectival concepts and verbal concepts; there are such word senses. Since, instead of saying X is blue, we may say X has the quality or state of blueness, and thus we do not need any concept for adjective "blue". Similarly, instead of saying that X operates, we may say that X is in the process of operation. If concepts are by definition nominal (corresponding to nouns and noun phrases), here would be another difference between concept and word sense.

## Applications

The concept of concept can be used to study human and animal behavior. The term "concept" is used in standards for thesauri for information retrieval and in a related interchange data format.

## Concept vs. notion

It seems that some literature has some uses of the word notion that are synonymous with concept. Uses of the form "the notion of X" where X is a noun or a noun phrase are suggestive of this kind of use. Narrower uses suggestive of synonymy are "define the notion of X". An example of this apparent use is the publication What is a Word? About the Notion of Word from GRIN Verlag, apparently written by German native speaker or speakers.
One way to shed some light on this question is to use a German-English dictionary to translate the German word Begriff. If we use Cambridge dictionary, we get two different translations as different senses, one notion and one concept.. Langenscheidt features both notion and concept as possible translations. Collins mentions concept but not notion.
A similar way is to start with Czech pojem. Lingea gives both concept and notion as possible translations, as different senses.
The above exercise could be expanded with coverage of other languages. Starting with the two languages picked and the results, it would seem possible that native English speakers do not usually use the word notion as a synonym of concept whereas non-native speakers could do so under influence of translation dictionaries, by picking the wrong translation for the sought sense. But this is just a guess.
Notion being a synonym of concept is suggested by the definition of concept in Meriam-Webster 1913: "An abstract general conception; a notion; a universal."
One possible terminological deliberation and choice could be this. Even if notion is sometimes used synonymously with concept, it is concept that is the headword of Britannica 1911 article, modern Britannica online and Stanford Encyclopedia of Philosophy; and thus, concept would be the preferred name and notion the dispreferred name (that's an if).
To support the above terminological choice, we can consider the rates in Google Ngram Viewer (GNV) of narrower concept vs. narrower notion and broader concept vs. broader notion. In both comparisons, the variant with concept comfortably wins but the variant with notion sees significant use.
Let us look at the NGV rates of undefined concepts and undefined notions.. The picture is remarkable: in 19th century, undefined concepts sees almost no use, unlike undefined notions; in 20th century, undefined concepts takes a lead while undefined notions still sees wide use. But it is above all terms that are undefined.
Further reading:
* notion, merriam-webster.com

## Names in other languages

Let us have a look at the names of the concept of concept in other languages. These can be meaningfully groupped by language family.
* English concept, Italian concetto, French concept
* German Begriff but also Konzept, Danish begreb
* Czech pojem, Russian понятие, Polish pojęcie

## Frege's Begriffsschrift

Frege's Begriffsschrift can be translated as concept/conceptual script (collection of letters). From what I understand, in the formalism developed in Begriffsschrift, there is a one-to-one correspondence between concept letters and concepts; there remains no ambiguity.
Further reading:
* Begriffsschrift, wikipedia.org