I recommend reading the first footnote before starting
It started with Plato, but it didn't end there1. This fact isn't often discussed.
Plato lived in Athens in Ancient Greece about 2400 years ago. He himself studied informally under Socrates, and Plato in turn had his own students and disciples at a school (of sorts) called The Academy2. The very first person to succeed as head of The Academy was one of Plato's nephews, Speusippus, who led the Platonic school from Plato's death (348/7 BCE) for eight years until he himself died in 339/8 BCE. After Seusippus' death the Academy was headed by Xenocrates. The Academy continued to exist until 83 BCE.
It is no surprise that Speusippus' metaphysics were a derivation and development of Plato, who was his teacher for many years3. What may however come to a surprise to many people, especially those who depend on Plato's own writings as indicators of his thought, is that Plato's late philosophy took a strong turn in a Pythagorean direction. Plato still maintained his ideas about Forms, but he also postulated The One and the Indefinite Dyad as key concepts. Speusippus' ideas should be considered as a response to these aspects of Platonic thought.
The architecture of Speusippus' metaphysics is quite unwieldy, so it is worth outlining it before discussing what it sought to achieve and how it grew out of Plato's own ideas.
Like Plato, Speusippus begins with two primary principles: the One and Multiplicity (plethos in Greek, and which corresponds to Plato’s Indefinite Dyad). Whereas the One is the epitome of unity (and is by nature indivisible), Multiplicity is the epitome of a continuum, that is, that which is continually divisible. To Speussipus’ mind, the entire universe can be seen as a product of these two basic aspects. One and Multiplicity combine to form the principle of Number. Through Number, the One is able to form the first of the number series, namely the number one. From the number one the rest of the numbers are derived, including the numbers 1,2,3,4 which made up the Tetractys which was important to Speusippus for mystical reasons, as together they add to make the number ten. So One and Number make the numbers, and on the other side Multiplicity and Number make Figure (as in the essence of geometry). Figure and One together manifest the point (i.e. the single point) from which are derived all other geometrical shapes. The geometrical entities can interact with Multiplicity to form Soul, which is defined as the form of dimensionality, the very essence of existing in space. From the Soul come the forms of the souls and bodies that form our world.
Certainly not the most intuitive set-up. This metaphysical architectonic is summarized below:
||The One and Multiplicity combine to form Number
||Number and The One form Numbers, and Number and Multiplicity form Figures
||The One and Numbers forms one, and The One and Figure forms point
||Point makes geometrical shapes
||Geometrical shapes and Multiplicity make Soul
||Soul makes all the bodies and souls of the world
As indicated above, Speuspippus' principles were seen to fit into tiers. The first three tiers out of five have been described. It is not clear but it seems likely that tiers IV and V were populated respectively with inanimate and animate things.
Speusippus did not develop any complicated ethical theory akin to his metaphysical one, and in fact, seems to have been only a single principle. This principle is that the best life is that which sees "freedom from disturbance" which is understood as being a state intermediate to pain and (as we normally use the word) pleasure.
Both Plato and Aristotle took Speusippus to task for this philosophy, accusing him of not explaining how pleasure could be bad. And while this is true, he did seem to hold that pain and (naive) pleasure were both bad extremes, his problem was a problem of nomenclature. Speusippus lacked the technical terminology of the later Stoics, whose philosophy he would have admired. To a certain extent, Stoic philosophy can be seen as a sophisticated elaboration of Speusippus' ethics, although it is not clear to what extent he actually influenced or informed them.
From what I can tell, Speusippis didn't have any coherent unified system of epistemology. Nonetheless I will list a few of his ideas in this general area.
- Sense perception mixes with rationality to produce our perceptions. I interpret this, not so much as a meta-epistemological doctrine, but rather as a theory of perception. I expect that Speusippus is trying to explain what the relationship is between pure sense perception (e.g. sounds) and evaluated sense perceptions (e.g. melody).
- We don't fully know something unless we can explain how it differs from everything else in its class. This is one of those ideas that really bothered Aristotle, and it's easy to imagine why. A sympathetic interpretation is that Speusippus is talking primarily about his first principles and their offspring, in particular geometrical entities and the number series (see the section on metaphysics above). In these cases it seems reasonable that one could in theory explain how one number (e.g. the number seven) differs from all other numbers in the series. A corollary of this is that for Speusippus knowledge of earthly objects cannot approach the certainty of principle objects (e.g. numbers and figures).
It's not clear whether there are any lessons that can be taken from Speusippus. His metaphysical schema is laborious. His ethics appears to be no more than a precursor to Stoicism. And his epistemology feels like an afterthought. Nonetheless there are two ideas in Speusippus' philosophy that I'd like to dwell on here and which I believe can be taken as valuable lessons. The first is his method for deriving the world out of first principles, and the second is his use of the word pleasure.
Speusippus and first principles
There were various problems with Plato's own metaphysical doctrines which Speusippus' theories seem to address. One problem is that the identity of Forms seems somewhat haphazard (which Speusippus overcomes by focusing on more basic principles, like geometry and number series). Another problem is for Plato to explain how two intrinsically homogeneous principles - The One and the Indefinite Dyad - can combine to form more than one thing.
As described above, Speusippus doesn't face this second problem because his hierarchy of principles acts incestuously - in other words, any given principle (e.g. Number) can go off an mate with its parent principle (e.g. Number interacts with Multiplicity) to produce its own novel offspring. This is significant.
The details and nomenclature of Speusippus' metaphysics are far from being intuitive. It is useful to take a step back and consider just the format that's being used in itself, which resembles what we would need if we wanted to provide a complete theory of everything: We would need logical principles which we could use to derive the mathematical principles which we could then presume in order to characterize our world's geometry, the behavior of which are determined by the same logical principles with which we started. Of course our attitude to this is empirical, and so would presume to start from the facts of the world and build upwards into increasingly abstract theorems. Nonetheless we could imagine the possibility of knowing the first principles that predict the world, at which point we would then have to ask: "Is the world a tautology?"
Speusippus and pleasure qua evil
Speusippus' ethics lacked the technical terminology of later thinkers. For example the Stoics developed an idea of equanimity which they termed apatheia, while the Epicureans developed an idea of ataraxia involving tranquility. The significant point in both these cases is that the Stoics and Epicureans were able to clearly differentiate pleasure depending on whether it was desirable or not.
Although it seems like Speusippus' ethics is fated to be interpreted as a primitive Stoicism, its limitation offers an unusual advantage. It's worth restating Speusippus' position, which is based on three possible states. One state is pain, which is bad and which people know to avoid. Another state is called pleasure, and is also bad even though it is thought by many to be good. The third state sits in between these two extremes and is called "freedom from disturbance" (henceforth simply "Freedom"). For Speusippus pleasure is bad. This is not because his is an ascetic. Rather it seems likely that Speusippus is concerned with the problem that many pleasures are dependent on relief of pain: for instance interest contrasts boredom, satiety contrasts hunger, and so forth. Any state which is enjoyed but which is also dependent on a prior pain is bad. A truly good activity is one that is both satisfied and sustainable.
This becomes interesting but also problematic. Are all activities that are either pain or pleasure (and so are not Freedom) bad? Whilst tranquilly studying can I not enjoy the pleasure of the sun on my back? And is it bad to jog if it causes discomfort? Perhaps Speusippus would have allowed that one may suffer pain or enjoy pleasure if it does not detract (or if it in fact adds) to one's sense of Freedom: the perfect state of life is to achieve a state of freedom from all disturbance; this requires one avoid base pain or pleasure except where they serve this first goal.
1 Because Speusippus is generally passed over as a minor figure in philosophy I have chosen not to expand on other topics which could nonetheless shed light on his character and ideas. For example I do not expound Plato's theory of Forms. I would recommend some familiarity with Plato's philosophy as a primer to what I've written here. Similarly I do not discuss some of the other pre-Socratic philosophers and Sophists who would certainly have influenced Speusippus. These and more are interesting topics worth following up on. Also "how the hell do you pronounce this guys name?" I've seen a few different pronunciations online, and have chose this one:spu-sip-us.
Postscript: thanks to DonJaime, Speusippus is spelled Σπεύσιππος, which is pronounced spε-OO- sip-pos.
2 There is a lot that could be said of Plato's Academy. This is not the place. Suffice it to say at this point that it seems to have been an informal institution, and one which did not demand adherence to any particular set of dogmas. The role of the dialogues which Plato wrote, and which are all that remain of his teachings first hand remains arguable, and it seems likely that one of the main purposes of The Academy was to provide a forum for philosophical debates.
3 Caveat: My main reference has been a book by Dillon which is an extremely sympathetic interpretation of Speusippus. Many of the primary texts it depends on are either fragments, not obviously about Speusippus, or else have been interpreted beyond what they literally say.
References: The most significant reference was the book "The Heirs of Plato: A Study of the Old Academy (347-274 BC)" by John Dillon. It is an excellent book, full of pithy observations and with a strong awareness of other opinions. The rest is general knowledge based on readings of Plato, and some facts (especially dates) were checked against that paragon of knowledge: Wikipedia. The guide to pronouncing Speusippus' name is from a book (via Google Books) with the gargantuan full title of A pronouncing and explanatory dictionary of the English language: founded on a correct developement of the nature, the number, and the various properties of all its simple and compound sounds, as combined into syllables and words; to which is added a vocabulary of Greek, Latin and Scripture proper names with their correct pronunciations by James Knowles (1835)! Thanks for reading.