A theory of learning concepts
After listening to a talk by Aaron Sloman, I endeavoured to clarify my thinking with respect to variation theory and formulating concepts. Aaron seems to contend that things like mathematical concepts can not be formed from the recognition of differences or variations. In some respects, this applies to any abstract concept.
As I look around me, I visually recognise colour, distance, movement, shade, etc. I also hear sounds and feel objects. The human body has a wide range of sensory input that we recognised as different signals and yet possibly related to the same object or phenomenon.
An individual eye recognises colour and shade. The combination of two eyes gives us depth and to some extent direction (direction is probably recognisable with a single eye but two adds the depth to the perception of direction). An ear allows us to recognise variation in sound. A constant sound may be ignored unless we give it focal attention. Two ears helps us determine direction of the sound. Our nose allows us to detect the direction of the smell. Each of these is a dimension of variation detected by the body's sensors.
The brain doesn't scramble or confuse the different sensors. It recognises the different sensors origins and recognises when the sensors are providing information about the same object.
The question is how does the brain learn that a particular combination of noise, visual queues, or smell relate to the same object. Sometimes, we have to explore or experiment to confirm our suspicions. Once we have made the connection, the recognition is reasonably automatic although from time to time we recognise that we have made a mistaken identification. The most frequently happens with sound or smell clues but visual clues are also at times confused especially when the vision lacks clear focus.
I am going to argue that at times, we recognise that we have perceived a difference but we lack the conceptual framework to clearly identify what that difference means. I am thinking here in terms of visible objects but this may also apply to more abstract concepts such as mathematical concepts or virtual objects. Through language acquisition, we link agreed names (sound forms or visual word forms) to our observations. At some point in this process, we also accept names for the sensor groups (i.e. visual, smell, touch). These are abstract concepts that relate to more concrete signals that we receive. As I write this, I am conscious that how language relates to concepts is another abstraction that at this point, I have little theoretical knowledge of. I am writing this in English and as far as I am aware my thought processes are in English. Others for who English is not their primary language may claim to be thinking in another language. However, we all see and recognise the same phenomena. It is simply that in arriving at a naming convention, we have used different sound or symbol forms. I can only speculate whether the human brain uses some more abstract form for thought processes. However; I recognise that not all my thought processes are linguistic (language based) in nature. I may also conceive ideas in visual or sound form. I am thinking of art or models or music. At different times, our brain seems to reflect our thoughts using the different forms of sensory channels of our bodies. Our thoughts and sensory ability seem to have some linkage.
When we experience a new dimension of variation, we seek to apply some mechanism of identification. This leads to the formation of a new concept since the dimension of variation doesn't fit any existing concepts. I want to argue that our ability to reason also throws up new dimensions of variation or the recognition of new areas of similarity. The result is some times a struggle to name the concept but overall higher level concepts come from recognising similarities and differences in lower level concepts (vision draws together colour, contrast, depth, ...) and endeavouring to assign names.
Is reasoning simply becoming aware of new similarities or differences? I struggle to clearly express my current thoughts in part because I am on the edge of a domain that I have not previously given much attention. I recognise connections that I am making and to some extent my lack of language to express them.
Aaron is particularly interested in mathematical concepts but I wonder whether this may simply be utilising a different language for expressing our thoughts and reasoning. I see mathematical notation and recognise its origin but having not worked consistently with the notation, I struggle with its meaning but does this mean that I can not apply the reasoning that might be expressed in that mathematical notation. There seems to be a similar issue with language acquisition or expression of ideas. Two people reasoning in different languages or notations may apply the same process or come to the same conclusion by different processes but does that mean one or the other lacks the ability to reason about the phenomenon being studied. Surely the issue is one of acquiring the notation that is common to both.
It is clear that being able to communicate with a specific notation can aid in communicating to others in a particular field and to show that you are able to reason in that field. However, the lack of knowledge of a notation doesn't mean an inability to reason in that field or to recognise concepts in that field.
Ultimately, we assess a person's ability to reason and understand a field of study by their ability to communicate their reasoning and understanding. So maybe what we are really talking about is the ability to acquire particular notational skills.
So in teaching, I endeavour to draw existing knowledge, concepts, and terminology to foster understanding of what we argue is new knowledge, concepts and terminology. We attempt to make visible similarities and differences so that the learner becomes aware of new possibilities. At this point I will argue that abstractions come from seeing the similarities or commonalities while recognising the differences. The abstraction is developed simply to enable a reduction in the notational baggage when talking about phenomena that possess those commonalities. The learner may need help to see these commonalities and therefore the possible abstractions.
Here I really lack current knowledge of robotic techniques. However, a robot has an innate ability to retrieve data (bit streams) and to identify those bit streams based on their sensor source. Remove the knowledge of the sensor source and the bit stream is a meaningless set of signals. We can say the robot has vision or hearing based on its ability to process particular data streams.
The next step is to be able to associate the different signals so that it can combine sight, sound, location, smell, ... Through this process, it begins to develop a more complete picture of a phenomenon. As it continues this process of combining and separating, it could develop a conceptual framework possibly including the recognition of notations.
Giving it the ability to explore relationships and connections between signals may see it develop human like abilities to reason.
Humans may give focal attention to particular sensory inputs but I would contend that we don't discard signals simply because it doesn't seem to fit a particular strand of reasoning. Maybe the difficulty with robotic research is that the focus is narrowed too much so that certain signals necessary to develop some concepts are missed from the equation.