Geometric Method

BL’s book contains the best explanation of BS’s Geometric Method

So let’s outline what I am trying to do in this website. I am not attempting a philosophical or “academic” analysis, but a “pedagogical extrapolation” of what a Spinozist theory of teaching and learning might look like. There are quite a few academic articles which explore the pedagogy of Spinoza, but they are aimed at an academic audience cognizant of the full range of scholarship about Spinoza, and, excellent as they are, not readily accessible to your average teacher.

I wanted to use Spinoza’s ideas as a springboard for my own reflections upon my life as a learner and an educator in schools for over a quarter of a century. In this sense, the project is “auto-ethnographic” in that I am using Spinoza’s idea to trigger a reflective commentary upon my own experiences as a teacher and learner. At certain apposite moments, I have illustrated how many of Spinoza’s precepts are now endorsed and further explored by other philosophers, psychologists, educational research and learning theories.

Spinoza wrote famously in what is termed the “Geometric Method”, using Euclid’s Geometry as a guideline for how to write Ethics. This involved Spinoza setting out his treatise with clear “Axioms” (self-evident truths) and “Definitions” at the beginning of each section, then proceeding forward with a series of “Propositions” which build upon one another in a “reasoned” way. Each Proposition could contain all or some of the following in order to justify it fully: a Demonstration (D: a demonstration of the proposition in action); Corollary (C: a proposition that follows from one already proved); Scholium (S: supposedly marginal notes which are much more than that in Ethics); a lemma (L: a subsidiary or intermediate theorem in an argument or proof); a postulate (Post: a thing suggested or assumed as true as the basis for reasoning, discussion, or belief).

There are many excellent books on Spinoza’s Geometric Method, and I have in no way explored the issue in this blog, but I have made a “gesture” towards the Geometric Method here in that every section contains a memorable phrase which I believe encapsulates the essence of Spinoza’s thought. I have then followed this phrase with the Spinozist equivalent of a Scholium: a marginal note. Sometimes, I have offered Axioms and Definitions where I have felt that they might be helpful. My website does not pretend to be “geometric” in any fashion. It aims for readability though, and its argument should have some kind of internal logic, based on Spinoza’s thinking. The structure of Spinoza’s Ethics has assisted with the structure of my blog: I have loosely followed the five different sections of Ethics in the trajectory of my blog.

Spinoza’s Chapter The Joy of Teaching
I.  Of God Chapter 1: God’s Learning
II. Of the Nature and Origin of the Mind Chapter 2: The Mind’s Learning
III. Of the Origin and Nature of the Affects Chapter 3: Affective Learning
IV. Of Human Bondage, Or The Powers of the Affects Chapter 4: Power and Learning
V. Of the Power of the Intellect, or on Human Freedom Chapter 5: Learning to be Free

This blog is a process of learning about Spinoza and about learning, it does not pretend to be authoritative, it is an exploration; the act of writing has been a profound learning experience for me; writing this has been a chance for me to learn more about Spinoza.

I’m aiming this blog not only at teachers of all subjects but also any interested person. I believe that science teachers may well be just as interested in his philosophy as an English teacher like me because his philosophy is truly “holistic”: it can readily embrace the lessons of science today, as much as having relevance to the teaching of literature. It has an openness and range which is unusual.

I try at all times to write in a clear style which an “intelligent” teenager could understand.

I have punctuated the text with “Journey into Joys” which are questions, exercises, thought experiments, creative visualisations for readers to pursue if they want to; they are there to help the reader understand my conceptions of Spinoza and learning in an active fashion.



Strength of Character

Spinoza does something of vital importance in the last three sections of Ethics. As I’ve indicated, he shows how adequate thinking creates joy which necessarily leads to people living ethical lives.

Ethical living is a necessary consequence of adequate thinking. Joy is the vital link here: when you think adequately about something you will feel joy which will necessarily make you realise certain vital truths, the most important of which is that love is always the best rational response to hatred. Chapter 3 of this website, Affective Learning, goes into more depth on this, but I would like to outline some concepts here which I believe are hugely useful for teachers.

A vital affect which Spinoza believes is a central component of a free thinking individual is “self-esteem”, which Spinoza defines as “joy accompanied by the idea of an internal cause” (Spinoza, 1994a, p. 86) or “a joy born of the fact that a man considers himself and power of acting”. Most teachers know that children with low self-esteem are difficult to teach because they feel like they are worthless and therefore there is nothing worth learning. They have lost their “powers of acting”. I like this diagram which illustrates some of the issues involved:


Figure 1 Self-esteem chart

For Spinoza, as for many psychologists today, self-esteem is about the internal dialogue that we have with ourselves: if we tell ourselves that we are capable of generating our own joy, if we believe there is something “within” us which is intrinsically joyful then we will acquire a degree of self-esteem. This, for Spinoza, is a “necessary truth” because we are all part of what he calls “God or Nature” (more on this later) and God/Nature is intrinsically joyful.

So, while the diagram above has some elements in common with Spinoza, it is not entirely Spinozist. It’s worth explaining this because it might help me show you why I feel Spinoza’s philosophy is more helpful than many more modern psychological theories. The diagram above is a simplified version of what is known as Cognitive Behavioural Therapy (CBT) which aims to re-orient a depressed person’s thinking about themselves by changing the things we say to ourselves in our heads. So I think it is perfectly true that many reluctant learners in school frequently say to themselves (and other people): “I won’t do it”; “I can’t do it” etc. However, what tends to happen in schools and, in therapy, is that an instrumental view of the depression is taken. So the teacher might cajole a student into saying “I want to do it” by giving them either a bribe or a threat: you’ll get a good mark if you have a go, or a detention if you don’t do it. The therapist might not be so brutal, but will nevertheless say something like if you tell yourself you want to do it, you’ll stop feeling so depressed. The reward here is a better mood. Developing Spinozist self-esteem wouldn’t, I believe, involve quite this approach; it would encompass the reluctant learner/depressed person developing an understanding of who they are, which would necessarily increase their powers of action. So the Spinozist pedagogue would help the reluctant learner reframe the interior dialogue in this way, with the first comments at the bottom of the pyramid being the ones the teacher/therapist would nurture first:

Figure 2 Develop Spinozist self-esteem

The diagram illustrate how putting understanding at the heart of developing self-esteem is absolutely central to Spinozist pedagogy. Understanding always and necessarily increases one’s powers of action. There are no rewards and punishments in a Spinozist pedagogy, understanding is the reward and it is through understanding that the learner finds his/her self-esteem. This understanding is developing through “reason”: Spinoza’s definition of reason is quite different from definitions we have of it today. Spinoza was not a “logician” or “rationalist” in the way we frequently define these terms today. Beth Lord writes: “While Spinoza believes that the truth is known through reason, he also believes that rational knowledge could not be attained without experience and experiments” (Lord, 2010, p. 4).

In order to develop this self-esteem, it is necessary to acquire “strength of character”, which consists of two elements: “tenacity” and “nobility”. Tenacity is “the desire by which each one strives, solely from the dictate of reason, to preserve his being”. For Spinoza this means being tenacious in the pursuit of adequate ideas because to preserve one’s being fully one must be joyful. Spinoza’s conception of tenacity is similar to modern ideas of “resilience” or “grit” (Perkins-Gough, 2013) in that it suggests that adequate thinking involves overcoming set-backs, problem-solving, sticking to the task at hand, even if this is difficult. However, Spinoza’s concept of tenacity is not as instrumental as modern pedagogies of “resilience” which tend to focus upon “grit” as a way to get great exam results, a place at a top university and then a well-paid job. This way of thinking about resilience views it as a “means to an end” and, as a result, the idea has an instrumental quality to it; it is a “tool” for learning. Spinoza would reject such conceptions and would argue that being tenacious is worthwhile in itself because the moment you are tenacious, you increase your powers of action and therefore your joy. The process is the point, not the end product. As we will see again and again, living in the “here and now” is absolutely central to Spinoza; he is a philosopher of “immanence”. There no real “end points” in Spinoza, only processes or passages from one state to another.

The other component to strength of character is “nobility”. This is a wonderful appropriation of a word which has connotations of being upper-class, aristocratic and courageous in the English language. Nobility for Spinoza is: “the desire by which each one strives, solely from the dictate of reason, to aid other men and join them to him in friendship” (Spinoza, 1994a, p. 103). In other words, when we think adequately about things, we will see that we want to help other people. This is important for teachers because it means that nurturing collaboration and friendship is more than a useful tool for nurturing learning, but is actually a necessary prerequisite for an ethical life. Urging your students to be “noble” in a Spinozist sense is not only important but absolutely necessary. For me, this means that collaborative learning is an absolute given in any Spinozist pedagogy; it is the noble virtue to be cultivated continuously. In order to do this though, in a world which riven with conflicts and competition, a teacher needs to be “tenacious”: thus we can see that tenacity and nobility are inextricably bound together.

The teacher needs to be tenacious in his pursuit of nobility and noble in his pursuit of tenacity because preserving your being (tenacity) necessarily involves helping others (nobility) and helping others necessarily means you preserve yourself.

The upshot of developing self-esteem, tenacity and nobility in oneself will be cheerfulness. This is the one affect that you can never have too much of in Spinoza’s view. He argues that you can have an excess of joy (and sadness), but cheerfulness is a unique affect because it always maintains an equilibrium.

Figure 3 Understanding and the Joyful Affects

The linking between all these affects is particularly important for a teacher to understand. They all have a reciprocal relationship with one another: a person guided by Spinozist reasoning will necessarily be tenacious but won’t solely pursue their self-interest but will be noble in their helping of others as well. Understanding this makes you have true strength of character. You need to help yourself and other people: indeed, through the dictats of reason, we must understand that the one cannot exist without the other. Similarly, self-esteem is only acquired through an understanding that there is something inherently lovable about you – your very nature – and that necessarily means you know that helping other people builds your self-esteem because you are aiding the very thing that you love within yourself because we are all part of one thing: God/Nature.

For me, Spinoza squares the circle of bondage and freedom, selfishness and altruism, competition and collaboration etc., which is a problem many teachers confront on a very “nitty-gritty” level every day. Most teachers understand that when students collaborate with each other they learn more (Education Endowment Foundation, 2016) but they often have a real job of work trying to sell the idea to their students, particularly the “more able” ones who feel that they are being held back if they help people “less able”. Spinoza gives the teacher a language to frame why students should collaborate: it is “noble” to collaborate and it necessarily builds your “self-esteem” if you do it properly, making you cheerful in the process. It has both cognitive and emotional benefits.