1. First-Order Concepts

First-order concepts refer to percepts that refer to objects; from this reference they derive their semantic value.

There are two types of sentences: sentences about the world and sentences about language. Unfortunately, these types of sentence are sometimes confused with one another.[99]

To understand the need for two types of sentences, let us examine when concepts can and cannot be defined in terms of other concepts. Suppose you pick up a dictionary in order to find the definition of a certain word. It is certainly possible that the definition of the word itself contains a word that you do not know. If you are insufficiently learned (or quite unlucky), you might encounter this problem repeatedly, spending hours trying to find the definition of a single word. If you did not know the definition of any words to begin with, the circularity would be complete; you necessarily cannot learn the meaning of any word.

To illustrate the way this vicious cycle is broken, imagine trying to define an “apple” to a child:

Us: “An apple is a fruit.

Child: “What is a fruit?

Us: “A fruit is a sweet red thing.

Child: “What is a red thing?

Us: [Hmm...] “A red thing is a...” [what is a red thing, anyway?] “A red thing is a thing that is not blue, green, or yellow.

Child: “What is not blue, green, or yellow?

Us: [pointing] “ That thing is an apple. Look. Here.

If we cannot convey the information necessary to define a word using other words, we must point to an actual red thing. In other words, if we are unable to describe a concept with concepts that the child already comprehends, we encourage the child to create a concept based directly on percepts. We could say “Look, that is a red thing” , pointing to a red shirt, “that is a red thing” , pointing to a stop sign: in this way, the child learns what a red thing is. The child forms a set of experiences in which two things repeatedly co-occur: the percept of a red thing, and someone saying “red thing” .

To learn what “apple” is, as a first-order concept, we must have direct experience of an apple and some motivation to learn. If this happens a number of times, we generalize from the set of experiences in which the apple appears. If we enjoy the experience of eating an apple, we might learn that “apple” is a good thing: the concept “apple” comes to be associated with the pleasant eating experience. Perhaps we will learn to speak the word “apple” , particularly if that behavior is rewarded: in order to do so, it is not necessary to equate the word with the object.

At some point, however, the word “apple” may become more than just a behavior that is performed in order to get apples. This first-order concept may be named: the utterance “apple” may become a symbol , which is capable of evoking the concept of an apple (instead of eliciting a subsequent behavior). This process of using percepts to represent concepts gives rise to a new possibility: language, the calculus of symbols. By performing basic manipulations on concepts using their symbolic representations, we enable the expression of novel concepts (as well as facilitating their formation). These concepts may in turn be given new names, recursively.

To illustrate how sentences are of exclusively two kinds, those that define words and those about events, here are several examples of sentences about events:

1. The apples fell to the ground.

2. Leibniz tossed an apple in the direction of Sir Isaac.

3. You should eat an apple a day.

The first two sentences clearly correspond to events in the world. The correspondence of the third sentence to an event in the world is less obvious. However, given that possibility is a dimension of linguistic reality (at the very least), we may interpret this sentence as a recommendation of a particular five-dimensional event (which may be construed as a six-dimensional event, where the additional dimension indicates some valuation or goodness).

Some types of sentences, such as questions, are difficult to categorize as either events or definitions. On one hand, a question may be viewed as the definition of a word which is intended to be supplied by the answerer. On the other, questions may be understood as sentences about high-dimensional events which vary along a modal dimension that spans all possibilities (for more information, see the section called “Constructing Dimensions”). In either case, questions have a part of their specification missing (that part is supplied by the answer to the question). This missing part of speech is indicated with a placeholder such as “what” or “where” . The interrogative nature of questions requires the answer to specify a position on that undetermined dimension. For example, “Is it going to rain tomorrow” requires selecting either the true or false coordinate on the dimension of possibility.[100]

To summarize, first-order concepts are categories of percepts. For example, “water” is a concept that we may have learned through the perception (or sensation) of water. While we may later learn the definition of water in terms of other concepts, it is also possible to learn this concept directly (i.e. based on percepts).

[99] A sentence may be about objects, percepts or concepts. However, although sentences can be about perception, this seems to be relatively infrequent: if someone tells you about what they are seeing, they are most often making statements about objects themselves (i.e. in the world). Even percepts such as anger are most often directed toward external objects as opposed to indicating our internal states. In this section, sentences about percepts are treated as a special case of sentences about the world, as opposed to sentences about language.

[100] Many questions make use of linguistic variables, which may be understood as references which have not been dereferenced yet: that final dereference is achieved by the answer to the question. So, in the question “who was that in the coffee shop” , we may treat “who” as a reference for which a dereference (i.e. a more exact reference, such as a proper name) is sought.