Preface
Vygotsky (in his previously unpublished notes) acknowledges the remnants of Cartesian dualism in his work, including an overemphasis of the intellectual over affect and the practical ...
To overcome these remants in his own work, Vygotsky turned to the philosopher Baruch Spinoza, who had postulated that there was on one substance that has body (Extension) and Thought as attributes. Accordingly, there are not two substances, body and thought (mind), biology and culture, or nature and nurture, but only one substance that manifests itself in different, mutually exclusive ways. This one substance is the thinking body, however, it is not the material human body: 'Thought can ... only be understood through investigation of its mode of action in the system thinking body - nature as a whole' ...
The most fundamental idea in The German Ideology is the primacy of social relations to anything that distinguishes humans from other species. Consciousness, the ideal, and the general all are societal in nature - not just as per their origin but also in their very existence. The ideal, such as a mathematical 'abstraction' or a mathematical 'idea', exists in the form of human relations. This insight led me to the title of this book, The Mathematics of Mathematics. That is, mathematics is not 'socially constructed' because humans have produced with others (ie. 'socially') and 'negotiated' some idea. In this way of approaching mathematics, 'the social' is incidental. In any event, any mathematical discovery is ascribed to individuals and, thus, is understood not socially: something like Fermat's Last Theorem is considered to have been an individual construction before it became social. This, however, is not consistent with how Marx or the late Vygotsky thought, where any higher psychological function was a relation with another person. Therefore, what is mathematical in mathematics is not merely (contingently) social but exists in the form of (universal) societal relations. Children learn mathematics and mathematical forms because they exist in public, that is, because these exist as relations in which the children are an integral part. Because, according to the Ideology, consciousness is conscious being, mathematics becomes individual when the child becomes conscious of the relation with others where the mathematical form exists as joint praxis....
these ideas are challenged by this book (existing awareness --> new awareness):
a) mediational nature of the sign (language) --> semiotic (sense-giving) speech field
b) meaning --> sense
c) the zone of proximal development --> the primacy of the social
d) thought --> unity / identity of intellect, affect and praxis
e) thinking --> thinking and speaking as two lines of development in communication
f) the distinction between intra and intersubjectivity (inside-outside) --> intra-inter subjectivity...
Episodes mostly from elementary school mathematics classrooms but some also involving scientists are used for developing and exemplifying the theory and method ...
Comment (BK): One challenge is how should we conceive / think about the individual, eg. Fermat, Marx, Spinoza etc. Didn't they have superior insights into society than other individuals? Shouldn't that aspect of their individuality be acknowledged? Their insights derived from the social but they were better at articulating what was happening than others. In this view of history individuals are important because individuals make breakthroughs and then those breakthroughs can be spread through painstaking education to the masses or society as a whole. We honour those individuals because we recognise their exceptional talents.
Reference to Preface:
Maxine Sheets-Johnstone, The Corporeal Turn: An Interdisciplinary Reader
Evald V Ilenkov, Dialectical Logic: Essays on it History and Theory
Marx & Engels, The German Ideology
Benedict de Spinoza, The Ethics