In this article I try to summarize the main idea’s in Piaget’s 1968 series of lectures about his Genetic epistemology.
Piaget’s approach claims that knowledge is so far a process which is constantly changing and has no linear direction.
Understanding the nature of scientific knowledge has to do with our ability to conceptualize, for example :
- Fundamental operations : one-to-one correspondence
- The notion of simultaneity as seen in Einsteins general theory of relativity, is seen an example of a notion which is not a primitive notion – (otherwise Einstein’s theory would be a very drastic crisis in sciences). Human beings do not perceive simultaneity with any precision. Piaget claims that the basic notion of humans is one of speed not of time, time in an intellectual construct.
The ability of perception and of conceptualization as part of human biology can be studied through observing child development. How do we go from a state of less sufficient knowledge to a state of higher knowledge ? How do we abstract and conceptualize ?
The psychological foundations of a notion, which are seen in our early development, has implications for the later epistemological understanding of this notion. Psychological factors are usually not taken into consideration by scientists operating in the context of scientific knowledge but is seen as transparent (having no effect that is).
The logical positivists, not taking psychology into account of their epistemology, affirm that logical being and mathematical being are nothing but linguistic structures – using general syntax, general semantics or general pragmatics. Logic and mathematics are nothing but specialized linguistic structures.
Piaget asks – is there any logical behavior in children before language develops ?
Chomsky asserts, not that logic is based on and derived for language, but, on the contrary, that language is based on logic. So a human is born this capability, and contrary to the logical positivists it is not just a linguistic convention.
There is an importance of formalization in epistemology, but, it cannot be sufficient by itself, for these reasons :
- There are many types of logics and not only a single one. No single logic is sufficient for the total construction of human knowledge and all different logics are not sufficiently coherent with each other to serve as a foundation for human knowledge. This is why formalization alone cannot reflect all human knowledge.
- Gödel’s theorem – There are limits to formalization. Any consistent system sufficiently rich to contain elementary arithmetic cannot prove its own consistency. So what does knowledge formalize ? What lies underneath the indemonstrable axioms and the undefinable notion ?
- Knowledge is not purely formal. There are other aspects to it. (suggested : behavior in animals in general ? The process of verification of behavior and thought can be based on biological and social parameters – normative aspects).
In a child’s development Piaget defines two complementary aspects :
- Figurative : Imitation of states, momentary and static.
- Operative : Transformations of one to another. These include The intellectual operations which are essentially systems of transformations.
The figurative as aspects are always subordinated to the operative aspects.
For Piaget, to know is to transform reality into systems of transformations, to know is to understand how a certain state is brought about. Piaget breaks off from the ‘knowledge as a (static) copy of reality’ model (knowledge as an image in the shape of reality, mimesis). He claims we can create isomorphic models of interaction with reality. Knowledge then, is a system of transformation that become progressively adequate.
Logical and mathematical structures are abstract whereas physical knowledge (the one based on experience) is concrete. Why is logical and mathematical abstract ? There are two possibilities :
- Empirical : Our knowledge is derived from the object itself. Experimentation.
- Operational : When we are acting upon an object we have to take into account the action or operation itself, since the transformation can be carried out mentally. This means the abstraction is drawn from the action itself. Piaget thinks this is the basis of logical and mathematical abstraction.
As an example Piaget shows that by counting objects we don’t relate to the order of the objects themselves, but we relate to the action of counting. The rule of logic we find is the commutativity rule is in mathematics : the sum is independent of the order. This is an example of abstract knowledge based upon action.
Piaget characterizes an operation / action by these fundamental characteristics :
- Operation is an action that can be internalized, carried out in though as well as materially.
- A reversible action:
a. reversibility by inversion or negation +1 -1 = 0
b. reversibility by reciprocity (exchange) A=B and reversal of order B=A
c. supposition of conservation (transformation). 5+1 / 4+2 / 3+3
d. no operation exists alone. Operation relates to a system of operation, structure.
Piaget then mentions Bourbaki’s (1939, French group) three mother structures: algebraic, topological, and order, these isomorphic structures were achieved by regressive analysis (‘archityping’). Piaget asks : are those corresponding to anything natural / psychological or axionomatical / mathematical ?
The way of analysis was reaching the elementary form by a non a-priori analysis, an inductive search. Piaget goes deeper into explaining the mother structures, shortly :
Algebraic : classes and numbers.
Order structure : relationships
Topological : notions such as neighborhood, border and approaching limit.
These notions or abstractions, as abilities, can be found in children as young as 6 or 7 years old in approximation. The example that Piaget brings is the one, in which a child can tell the relation between birds (relationships, Order structures), ducks (items, Algebraic) and the fact of having to count them to tell their estimated ratio of all other birds in the woods (approaching limit / Topological), therefore roughly exercising control over three mother structure.
The three types of mother structures are also present in geometry (and math) : the Greek Euclidean as algebraic, projected geometry (suggested by Greeks, and 17th century) as ordered structure, and finally modern topological geometry. Piaget claims that, concerning child development, it’s actually the topological intuition that develops first. The first operation of dividing space and ordering in space are more similar to the topological operations that the Euclidean, algebraic ones. Children at early age would draw copies of squares and triangles as circles. Geometry is an intellectual structure that is develops later and is also used to conceptualize time. The ability to conceptualize time develops from a notion of duration in early development.
Piaget shows that one mother structure alone is not adequate, a number, for example, is a synthesis of class inclusion and relationships of order and even more complicated relations between the mother structures.
What Piaget is actually suggests here is that we have a natural / biological / evolutionary tendency towards certain typologies, meaning we come to the world with certain sets of default preferences.
Piaget mentions the fact that, in studying children, we see that the logical mathematical structures exist, before the appearance of language. While language appear more or less in the middle of the second year, sensory motor intelligence appears on the around the end of the first year.
Piaget calls a schema : whatever that is repeatable and generalizable in an action. There is a logic of schemes, while a given schema by itself does not have a logical component. Schemes can be coordinated with one another.
Piaget through a series of examples shows, that actions through early childhood, build logic by the relation of the individual, its actions and the inner relation between objects taking part, in other words : logic is order between means and a goal, through actions. What is new about the concept in the context of the 20th century is that knowledge in the context of math and logic, and as a structure, is being seen as a process developed so far as in early age in the context of behavior, in terms of actions, and their conceptualizations.
Basic sensory-motor operation develop at the age of one year to more developed operations that can track successive change of position, a conceptualization of a permanence of an object and later notions of conservation at the operational level.
In the age of 1½ and the age of 7 or 8 years the operations are going through a process of being internalized, of taking shape in thought at the level of representation rather than the actual carrying of actions.
Instead of being represented by language, actions can also be represented by a sign or a symbols (Head: the symbolic function vs the semiotic function). In deaf individuals they can be gestures as an example.
Piaget talks about a number of experiments in which he tried to investigate how children conceptualize, in terms of function relationships and identities, such as the case of the phenomenon of apparent motion (stroboscopic motion). Conceptualization of identity and movement is done, like in a 24 frame per second film, with disregard of gaps or non-linearity. Motion and identity is only apparent, to say only made possible only through the disregard of other elements or variable. Enduring things, equal things, things, substances, bodies… all are constructions of the mind.
In one experiment children are shown a growing plant, and being asked to draw the plant in various growth stages, then being asked if that’s being the same plant ? Often that answer is no. The children are asked to draw themselves in different growth phases in their past life, acknowledging they were always themselves. After the experiment, some children were able to relate the plant to themselves and were able to conceptualize that the plant maintains the same identity through its growing phases.
As we grow older the notion of identity changes. Often the philosophical question is being asked, under which condition things stay the same. Piaget mentions the fact, that through a persons life and even through western literature, there is never one equilibrate state of physical or psychological identity. Existence is a process of change.
The notions of identity and motion are made possible through the dismissal of other irrelevant factors. How do we know which factors are irrelevant ? Depends on what we focus our attention on, depends on the criteria of action we are conceptualizing at the time.
This makes me think about the notion we have about science in the context of Empiricism : If we conceptualize the orbit of the planets in the solar system, we have to disregard a huge amount of variables, arguably (and surprisingly) most of them can be said to be rooted in behavior, action, human interaction. Why should Occam’s razor, be the superior scientific criteria ? It functions in this sense, by making sure we can communicate one to the other efficiently, efficient being matching our actions to the desired outcome. Truth becomes not the nature of the world, not a copy or a representation (= image) of the world, but something pragmatic, in the sense of efficiency in terms of matching our actions towards desired results. This is a possible explanation why different groups have a different definition of a truth.
If we reached the moon, it’s not because ‘we managed to describe the things as they really are’ – that is an ideal taken from the enlightenment period. According to the pragmatic explanation, we managed to get to the moon because it was our aim or desired result in the context of society and culture.
How is that made possible ? A group of people managed to agree on a method of conceptualization of space and time, managed to agree about a desired outcome, coordinated their actions and found the power and control that this sort of successful process brings useful. According to this model truth is not a metaphysical ‘essence of things’, but verification of actions against desired results.
Piaget discusses the topic of speed and time. He acknowledges the referential circularity of (western, scientific) language in which :
- speed is defined by change in location in space in time
- time can only be measured in the context of constant speed
Piaget sees movement as a more primitive, complex and less differentiated notion. In conceptualizing space we are ignoring speed while in conceptualizing of time we are not in terms of coordinating movements.
We cannot actualize time like we do with space. Meaning we are not able to project its linearity. The moments of time are lost and irreversible, we cannot find them back, we can’t act them in reverse.
Piaget gives two examples of experiments in which children recognized one object being faster than the other, that happened only if it was visible to them that an overtaking was taking place. This means that the property of speed is conceptualized at an early age by an action and not by advanced abstraction of space (length) – that might be something like Euclidean geometry.
Again, Piaget, through a series of experimentation with children supported the idea that absolute time is an intellectual construction. Children experience duration as their main notion of time, and so time is relative to their actions, or to the surrounding actions. It is only adults (and sometimes of certain cultures) that construct an idea of absolute linear time, the time of watches, that might relate to universal patterns such as the orbit of the planets, earth rotation or electromagnetic radiation in atomic clocks.
When talking about subjective or psychological time, the subjective time depends on our actions and those around us. Time seems shorter when we are doing something that seems to interest us, and slows down while we go to the dentist or while we wait for something. Interest reinforces or accelerates the speed with which work is done.
While intelligible thinking build reversible structures, time is only reversible in our thoughts.
Conclusion : Piaget asks how do we keep on making new relevant knowledge ? Knowledge is a process, not a static state or a goal. The empiricist approach, calls it a ‘discovery’ like there is no construction of new realities, and knowledge is always accessible through our interface with the world. The approach of apriorists is that knowledge is always predetermined inside the subject.
Genetic Epistemology sees knowledge as a process of continues construction. A move from one step to the other is done by formulating steps that did not exist before, either in the external world or in the subject’s mind. The main catalyst is change. The main challenge of this approach is the discovery of the mechanism of this construction, reflexive abstraction and self-regulation.