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What Even Is Philosophy?

Philosophy comes from the Greek word philo (love of) and sophos (wisdom) and so means 'love of wisdom'. Every person and every culture has some form of 'wisdom', guides to live by, ways of thinking.

Some Branches Of Philosophy

Epistemology: truth and knowledge - What is true and how do we know?

Metaphysics: 'first philosophy', dealing with the most abstract and general considerations. What is being? What is a substance and a quality? How can one and many exist? Is mind immaterial? etc.

Ontology: being and reality - What is there?

Ethics: relations among people, especially morals ('should' in contrast to 'is'). How should we act?

Logic: the rules for valid reasoning. What is a valid argument? How do we draw conclusions from one thing to another?

Rhetoric: the art of making a convincing argument.

Natural Philosophy/Physics: what we now call science and engineering.

Some schools or categories of Philosophy

These summaries are gross generalisations and within each group there may be many sub groups sometimes in strong opposition to each other, and every thinker has their own arguments to offer. This is intended as a rough guide to familiarise, not an authoritative list.


Medieval and Renaissance

Modern Philosophy



Philosophers On Philosophy

What is philosophy? Ask philosophers and see what they say they are doing when they do philosophy.

This chapter is an effort to build an ironic political myth faithful to feminism, socialism, and materialism. Perhaps more faithful as blasphemy is faithful, than as reverent worship and identification. Blasphemy has always seemed to require taking things very seriously... Irony is about contradictions that do no resolve into larger wholes, even dialectically, about the tension of holding incompatible things together because both or all are necessary and true. Irony is about humour and serious play. It is also a rhetorical strategy and a political method, one I would like to see more honoured within socialist-feminism. At the centre of my ironic faith, my blasphemy, is the image of the cyborg.

Haraway, A Cyborg Manifesto, 1985

In late 20th century philosophy there was a turn away from a search for certain and/or universal truths towards rhetoric, politics, power and construction of identity. Rhetoric in particular is very much a branch of philosophy from antiquity - the art of making a convincing argument. This is part of a view that 'knowledge' and 'truth' are constructed. For Haraway here, 'irony', 'play' and 'blasphemy' are a way to resist. This attitude harks back to Socrates, perhaps the most important figure in all Western philosophy, who called himself a 'gadfly' because he annoyed the Athenian state and people by reminding them of uncomfortable truths, pointing out hypocrisy, and so on. For Haraway and Socrates philosophy is a means of resisting what powers tell us to accept by questioning and critiquing. Though while Haraway does this for resistance and self determination, Socrates says it is for society, to save it from itself.

The history of (the only) metaphysics, which has, in spite of all differences, not only from Plato to Hegel (even including Leibniz) but also, beyond these apparent limits, from the pre-Socratics to Heidegger, always assigned the origin of truth in general to the logos: the history of truth, of the truth of truth, has always been-except for a metaphysical diversion that we shall have to explain-the debasement of writing, and its repression outside the 'full' speech.

Derrida, Of Grammatology, p3, 1967

Derrida makes critiques the whole history of Western philosophy, exposing assumptions and agendas many of which emerged at the beginning and persisted throughout. For Derrida Western philosophy has always been biased to 'logos'. In ancient rhetoric, a good argument would be comprised of ethos (the reputation and reliability of the speaker), pathos (an appeal to emotion) and logos (the reasonable or logical argument, also the Greek word for 'word'). Derrida isn't suggesting we look instead to ethos and pathos, but critiques or 'deconstructs' 'logos'. Derrida can be difficult to follow, which is part of the point, but he argues that Western Philosophy is dominated by the misconception that reason may make 'truth' and other things, 'present'. Philosophy is reasoning aimed at obtaining truth - but for Derrida this is a misconception.

Whoever plans an 'Introduction to Philosophy' presupposes that those who are to be introduced to philosophy stand initially outside of it. Philosophy itself thus counts as an area somewhere that consists of knowledge and principles, which many people might bypass throughout their lives and from which they might thus remain closed off. Although this notion of philosophy is widespread, it misses the essence of philosophy insofar as there is no such outside - separated from the human essence - that could constitute the abode of philosophy where humans would first need to proceed in order to be in philosophy.

Heidegger, Introduction To Philosophy - Thinking and Poetizing, p1944

For Heidegger we are already doing philosophy, simply because we are human and that's what humans do. For Heidegger though Philosophy isn't simply cold reason. For Heidegger we are doing philosophy when we pause and reflect on the sense we have of things, and beyond this, on being itself. One example he gives is when our tools break and instead of concentrating on our task we pay attention to that tool, as tool. We don't notice the floor until it falls from under us. Philosophy is the moment we notice the floor. It's difficult to explain, but I would paraphrase his conclusion to 'What is philosophy', as 'Philosophy is digging the music of Being.'

We remain unknown to ourselves, we seekers after knowledge, even to ourselves - so how should we one day find ourselves?... Imagine someone who, when woken suddenly from divine distraction and self-absorption by the twelve loud strokes of the noon bell, asks himself: 'What time is it?' In much the same way, we rub our ears after the fact and ask in complete surprise and embarassment: 'What was that we just experienced?, or even 'Who are we really?' Then we count back over in retrospect, as I said, every one of the twelve trembling strokes of our experience, our life, our being - and alas! lose our count in the process... And so we necessarily remain a mystery ourselves, we fail to understand ourselves, we are bound to mistake ourselves. Our eternal sentence reads: 'Everyone is furthest from himself' - of ourselves, we have no knowledge..."

Nietzsche, On The Genealogy Of Morals, p3. 1887


'Know thyself' is a well known inscription at the cave of the oracle of Delphi.

Nietzsche was an inflammatory philosopher, who didn't suffer fools lightly. He was a Romantic, writing after the Enlightenment and so moved away from abstract searches for universal truths, writing polemics and aphorisms. He was none the less deeply concerned with what it means to be human and how to go about living, particularly with will and power. Here Nietzsche mocks those naive enough to think we might possible 'know' ourselves and, in this book, On The Genealogy Of Morals, proceeds with a 'geneaology' of how and why we have the morals that we do. He shows that they are not 'necessary' or 'true' but have developed due to historical circumstances. In this sense we might say Nietzsche sees philosophy as a means of understanding and criticising, and as giving insights into how to live, rather than a way of 'knowing'. He was very influential on later philosophers.

It is plainly not the effect of the levity, but of the matured judgement* of the age, which refuses to be any longer entertained with illusory knowledge, It is, in fact, a call to reason, again to undertake the most laborious of all tasks—that of self-examination, and to establish a tribunal, which may secure it in its well-grounded claims, while it pronounces against all baseless assumptions and pretensions, not in an arbitrary manner, but according to its own eternal and unchangeable laws. This tribunal is nothing less than the critical investigation of pure reason.

[*Footnote: We very often hear complaints of the shallowness of the present age, and of the decay of profound science. But I do not think that those which rest upon a secure foundation, such as mathematics, physical science, etc., in the least deserve this reproach, but that they rather maintain their ancient fame, and in the latter case, indeed, far surpass it. The same would be the case with the other kinds of cognition, if their principles were but firmly established. In the absence of this security, indifference, doubt, and finally, severe criticism are rather signs of a profound habit of thought. Our age is the age of criticism, to which everything must be subjected. The sacredness of religion, and the authority of legislation, are by many regarded as grounds of exemption from the examination of this tribunal. But, if they are exempted, they become the subjects of just suspicion, and cannot lay claim to sincere respect, which reason accords only to that which has stood the test of a free and public examination.]

I do not mean by this a criticism of books and systems, but a critical inquiry into the faculty of reason, with reference to the cognitions to which it strives to attain without the aid of experience; in other words, the solution of the question regarding the possibility or impossibility of metaphysics, and the determination of the origin, as well as of the extent and limits of this science. All this must be done on the basis of principles.

This path—the only one now remaining—has been entered upon by me; and I flatter myself that I have, in this way, discovered the cause of—and consequently the mode of removing—all the errors which have hitherto set reason at variance with itself, in the sphere of non-empirical thought. I have not returned an evasive answer to the questions of reason, by alleging the inability and limitation of the faculties of the mind; I have, on the contrary, examined them completely in the light of principles, and, after having discovered the cause of the doubts and contradictions into which reason fell, have solved them to its perfect satisfaction. It is true, these questions have not been solved as dogmatism, in its vain fancies and desires, had expected; for it can only be satisfied by the exercise of magical arts, and of these I have no knowledge. But neither do these come within the compass of our mental powers; and it was the duty of philosophy to destroy the illusions which had their origin in misconceptions, whatever darling hopes and valued expectations may be ruined by its explanations. Kant, Critique Of Pure Reason, 1781

For Kant, as with other Enlightenment philosophers the purpose of philosophy was to find the most fundamental and basic knowledge in the most general and universally applicable sense. These would ground further conclusions in various fields. For Kant the word 'critique' meant examining the conditions of possibility for something. For Kant, before we can even consider what is true or false, what exists or not, we must first consider what we are capable of thinking. This determines what knowledge, if any, we could possibly have. For example, Kant's view was that we think spatially and temporally so we cannot conceive of anything that isn't in space and time. Also that although things might have a reality beyond ourselves the only way we can experience them is through our senses - so although we may reason about those experiences, things are unknowable in themselves. Kant thought he had finally figured it all out once and for all. For Kant, Philosophy is a way of establishing the conditions of possibility for reason itself.

I will, nevertheless, make an effort, and try anew the same path on which I had entered yesterday, that is, proceed by casting aside all that admits of the slightest doubt, not less than if I had discovered it to be absolutely false; and I will continue always in this track until I shall find something that is certain, or at least, if I can do nothing more, until I shall know with certainty that there is nothing certain. Archimedes, that he might transport the entire globe from the place it occupied to another, demanded only a point that was firm and immovable; so, also, I shall be entitled to entertain the highest expectations, if I am fortunate enough to discover only one thing that is certain and indubitable.

2. I suppose, accordingly, that all the things which I see are false (fictitious); I believe that none of those objects which my fallacious memory represents ever existed; I suppose that I possess no senses; I believe that body, figure, extension, motion, and place are merely fictions of my mind. What is there, then, that can be esteemed true ? Perhaps this only, that there is absolutely nothing certain.

3. But how do I know that there is not something different altogether from the objects I have now enumerated, of which it is impossible to entertain the slightest doubt? Is there not a God, or some being, by whatever name I may designate him, who causes these thoughts to arise in my mind ? But why suppose such a being, for it may be I myself am capable of producing them? Am I, then, at least not something? But I before denied that I possessed senses or a body; I hesitate, however, for what follows from that? Am I so dependent on the body and the senses that without these I cannot exist? But I had the persuasion that there was absolutely nothing in the world, that there was no sky and no earth, neither minds nor bodies; was I not, therefore, at the same time, persuaded that I did not exist? Far from it; I assuredly existed, since I was persuaded. But there is I know not what being, who is possessed at once of the highest power and the deepest cunning, who is constantly employing all his ingenuity in deceiving me. Doubtless, then, I exist, since I am deceived; and, let him deceive me as he may, he can never bring it about that I am nothing, so long as I shall be conscious that I am something. So that it must, in fine, be maintained, all things being maturely and carefully considered, that this proposition (pronunciatum ) I am, I exist, is necessarily true each time it is expressed by me, or conceived in my mind.

Descartes, Meditations, 1641

Descartes is probably the best known modern philosopher and is often credited with starting modern philosophy with his statement, "Cogito ergo sum." or "I think therefore I am". Probably the most famous phrase in all philosophy. As stated in his method, for Descartes, Philosophy is a way of arriving at the most fundamental, certain truths (in his case by doubting), from which to then draw conclusions.

If one clings to what others have said and tries to understand Zen by explanation, he is like a dunce who thinks he can beat the moon with a pole or scratch an itching foot from the outside of a shoe.

Mumon Wumen Huikai, The Gateless Gate, c.1200

If you have to ask...

1. The beginning of first philosophy

First Chapter: the number of philosophical sciences For each science there is a subject matter the condition of which is investigated by that science. Subject matter is of two kinds: the one which depends for its being on our action, and the other which does not depend for its being on our action... The one which informs us of the condition of our action is named practical science... The other informs us about the nature of the being of objects... This science is named speculative science.

From each of these two sciences we derive three sciences. There are three practical sciences. The first is the science of public management which assures us about associations for which tehre is a need to be orderly. And this is of two kinds. The first concerns the nature of religious laws, and the second concerns the nature of the science of politics... Another is the science of household management which is meant to regulate the associations taking place in a house between husband and wife, father and child, and master and slave. The third is the science of the self, specifying how man should be with his own self. Somce it is man's condition to be alone or to be in association with others, and since associations are either with members of a household or with fellow citizens, there are three kinds of practical sciences governing these associations: that of civic management, that of household management, and finally that of management of the self.

The speculative science is of three kinds: one is named first philosophy, the science of primordials of that which is beyond nature; another is an intermediate science which is called the science of syntax and mathematics; the other is called a natural science or inferior science to the fact that things are classified only into three kinds. Either their being (ie: that the subject matter of these sciences) is in no way connected to sensible matter, mixture and motion... Or (2) there are other kinds of subjects whose beings are not separated from sensible matter and things in motion... Or (3) other kinds fo subjects that are such that their being is in materials, and defining and imagining them are related to matter and to the nature of motion, as was clarified by means of our previous example.

- Avicenna, Metaphysica, pp11-12

For surely to be wise is the most desirable thing in all the world. It is quite impossible to imagine anything better, or more becoming for a human being, or more appropriate to his essential nature. That is why the people who try to reach this goal are called philosophers, because that is precisely what philosophy means, the love of wisdom. And wisdom, according to the definition offered by early philosophers, signifies the knowledge of all things, divine and human, and of the causes which like behind them.

Cicero, On Duties II

We have said in the Ethics what the difference is between art and science and the other kindred faculties; but the point of our present discussion is this, that all men suppose what is called Wisdom to deal with the first causes and the principles of things; so that, as has been said before, the man of experience is thought to be wiser than the possessors of any sense-perception whatever, the artist wiser than the men of experience, the masterworker than the mechanic, and the theoretical kinds of knowledge to be more of the nature of Wisdom than the productive. Clearly then Wisdom is knowledge about certain principles and causes.

Since we are seeking this knowledge, we must inquire of what kind are the causes and the principles, the knowledge of which is Wisdom. If one were to take the notions we have about the wise man, this might perhaps make the answer more evident. We suppose first, then, that the wise man knows all things, as far as possible, although he has not knowledge of each of them in detail; secondly, that he who can learn things that are difficult, and not easy for man to know, is wise (sense-perception is common to all, and therefore easy and no mark of Wisdom); again, that he who is more exact and more capable of teaching the causes is wiser, in every branch of knowledge; and that of the sciences, also, that which is desirable on its own account and for the sake of knowing it is more of the nature of Wisdom than that which is desirable on account of its results, and the superior science is more of the nature of Wisdom than the ancillary; for the wise man must not be ordered but must order, and he must not obey another, but the less wise must obey him.

Such and so many are the notions, then, which we have about Wisdom and the wise. Now of these characteristics that of knowing all things must belong to him who has in the highest degree universal knowledge; for he knows in a sense all the instances that fall under the universal. And these things, the most universal, are on the whole the hardest for men to know; for they are farthest from the senses. And the most exact of the sciences are those which deal most with first principles; for those which involve fewer principles are more exact than those which involve additional principles, e.g. arithmetic than geometry. But the science which investigates causes is also instructive, in a higher degree, for the people who instruct us are those who tell the causes of each thing. And understanding and knowledge pursued for their own sake are found most in the knowledge of that which is most knowable (for he who chooses to know for the sake of knowing will choose most readily that which is most truly knowledge, and such is the knowledge of that which is most knowable); and the first principles and the causes are most knowable; for by reason of these, and from these, all other things come to be known, and not these by means of the things subordinate to them. And the science which knows to what end each thing must be done is the most authoritative of the sciences, and more authoritative than any ancillary science; and this end is the good of that thing, and in general the supreme good in the whole of nature. Judged by all the tests we have mentioned, then, the name in question falls to the same science; this must be a science that investigates the first principles and causes; for the good, i.e. the end, is one of the causes.

Aristotle, Metaphysics 3rd century BC

For Aristotle, philosophy meant establishing rules and criteria for valid reasoning and applying this to all subjects of enquiry.

'Is not what we call death a freeing and separation of the soul from the body?'

'Certainly,' he said.

'And the desire to free the soul is found chiefly, or rather only, in the true philosopher; in fact the philosopher's occupation consists precisely in the freeing and separation of soul from body. Isn't that so?'


'Well then, as I said at the beginning, if a man has trained himself throughout his life to live in a state as close as possible to death, would it not be ridiculous for him to be distressed when death comes to him?'

'It would, of course.'

'Then it is a fact, Simmias, that true philosophers make dying their profession, and that to them of all men death is least alarming.'

Plato, Phaedo, [Penguin, 1993] c.400BC

It's impossible to consider Plato and Socrates without each other, since Plato was reporting on what Socrates said. Whether ideas are Plato's or Socrates' is not always clear. In this quote we see the well known 'Socratic method' which consists of asking questions rather than making assertions, so that the student arrives at the truth, knowledge or learning on their own. Clearly many of the questions are leading questions, though. Here we see the common tendency in philosophy to view detachment of the mind or soul from the body as an ideal. This detachment gives an ability to reason clearly resulting in an ability to cope with situations peacefully that others find distressing. Note that Socrates refers more to philosophy as the identity of someone. Philosophy is what philosophers do. For Socrates philosophy is something lived, not merely a method of enquiry, reasoning or ethics, but applying those uncompromisingly to ones life.

The way that can be spoken of

Is not the constant way;

The name that can be named

Is not the constant name.

The nameless was the beginning of heaven and earth;

The named was the mother of the myriad creatures.

Hence always rid yourself of desires in order to observe its secrets;

But always allow yourself to have desires to in order to observe its manifestations.

These two are the same

But diverge in name as they issue forth.

Being the same they are called mysteries,

Mystery upon mystery -

The gateway of the manifold secrets.

Lao Tzu, Tao Te Ching, 1, 6th-century BC

One of these lines is often translated differently, which have an opposite meaning. eg:

But if desire always within us be,

Its outer fringe is all that we shall see. http://www.sacred-texts.com/tao/taote.htm or

Caught in desire, you see only the manifestations. http://thetaoteching.com/taoteching1.html

Note several other translations: https://www.yellowbridge.com/onlinelit/daodejing01.php

Bear in mind that much of what we understand of a philosopher may be determined by choices made by the translator. This is a particularly interesting case because the dualities that are always reiterated in Taoism suggest that both these meanings are intended, particularly given the following line - 'These two are the same.' Ie: that when desiring we are mislead or blinded by illusion, but we also need to allow ourselves to have and carry out these desires in a detached observational way, in order to understand them and the way the world works, as implied by the preceding line. Taoism, here then does not simply recommend not having desire - with Taoism there tends always to be a duality, not an absolute or a victory of one thing over another - on the contrary if we are to avoid succumbing to the manifestations and illusions of desire, we must have desire, to have desire assumes we are aware of it as something that is resistable. This strategy of thought is echoed in the critical method, 'Deconstruction' of Poststructuralism.

If a person can so control his senses, in him is wisdom established. If a man things about sensual objects, this gives birth to attachment about those. From attachment is created desire and desire gives birth to anger. Anger gives birth to delusion and delusion leads to confusion of memory. From confusion of memory comes loss of intellect and loss of intellect results in destruction. But he who has controlled his mind is freed from attachment and hatred. Having used himself to control his senses, he uses these to enjoy objects and satisfy himself. When there is such serenity, in him is eliminated all unhappiness. Because in the mind of someone at peace, wisdom is quickly established.... Therefore, he whose senses have been withdrawn from objects in every way, in him has wisdom been steadily established.

Krishna to Arjuna in Mahabharata, 8th and 9th centuries BCE

Indian philosophy is exceptionally old. As such it has developed countless branches and infinite nuances. It is impossible even to scratch the surface of this vast depth of philosophy in an introduction. (My own knowledge is limited to cursory overviews and a closer study of the Mahabharata - the greatest epic in the history of the world.) None the less, debate over whether, or to what extent we should resist desire and avoid attachment to worldly things is a recurring theme throughout Indian philosophy. While Western philosophy is taken to have begun with the Pre-socratics, the first of these actually lived in Asia, in the town of Miletus on the coast of modern Turkey. The Persian empire stretching from Greece to the Indus valley was established soon after that time. Prior to this there were other connected civilisations between Greece and India. Miletus was a major trading town. It seems disingenuous to suggest there was not at least some transmission of ideas from India to Ancient Greece.

There is some similarity of Krishna's words to Socrates's words in Plato's Phaedo. This doesn't demonstrate a connection with India though, since it's a common enough belief among humans that detachment from bodily concerns is virtuous. Anyone, anywhere might have enough wisdom to not satisfy their desires immediately in anticipation of greater rewards later.

Philosophy is a way of life, reason, criteria for valid reasoning, the conditions of possibility for reasoning, a critical attitude, a guide to good living, a means to knowing ourselves, a contemplation of 'being', a way to resist power, means of finding truth, a way to be free. Many of these answers to the question, 'What is philosophy?' would be familiar to us in the way we use the word philosophy usually. Rather than trying to pin the meaning of the word down to one thing only it is worth understanding the sources of these different meanings of 'philosophy'. That helps us understand at least why we think what we think and what assumptions we have, and the actions we take that are based on those assumptions. Only then can we question what we think and what actions we take and decide whether and how they are wrong or should be changed. Philosophy is also a means to be free.


Another way to answer the question is to look at when philosophy first emerged, to identify what distinguishing characteristics it has that separate it out from other things. Those qualities that make it distinct tell us what it is and how we identify it. Western philosophy begins with the Pre-socratics.

Pre-Socratic philosophers lived in Greece and Greek colonies in the Mediterranean Sea, including the coast of modern day Turkey, the south of Italy and in Sicily. Most of what is known about the Pre-Socratic philosophers is available only through short and fragmentary references in later texts writing about them. Given the Persian Empire extended from Greece to the Indus valley in modern day Pakistan, and began soon after the earliest Greek philosopher, and trade was already extensive, and philosophers sought learning from Babylonia and Egypt, and given their similarity many concepts must have been derivative of, or mingled with concepts from much earlier Indian philosophy.

Many of the arguments made by Pre-Socratics sound silly to us today. For example, that one said everything comes from water, another argued that it comes from air and another from fire and another says they are all mixed together and always in flux, and then one says there is only one unchanging whole and movement is an illusion, while another says there are only numbers, and yet another that there are countless many tiny little indivisible material things called 'atoms' - it seems as if they are simply taking in turns in contradicting each other. But these claims are often supported by well reasoned arguments and mark a distinct change how people thought. Some of the main characteristics of philosophy, and many of it's ongoing debates emerge in this time:

It's remarkable how persistent the concepts developed in this time can be. As an example we find in Sartre's tome Being and Time a brilliant discussion freedom and free will. He makes the point that having freedom depends on non-being. We are in a situation where things are as they are, or 'being', so for us to be able to change them, we must be able to imagine things being not as they are, 'non-being'. Sometimes philosophy points out what was so obvious we didn't notice it, but this simple point forms the basis of a demonstration that our freedom can never be taken away from us (Sartre had been a prisoner of war), and that we always remain responsible for our own actions (this is significant in the context of the aftermath WWII and the 'Nuremburg defence' where soldiers claimed they were 'only following orders') and that we are always in a process of inventing ourselves, among other things. Sartre had read Heidegger while a prisoner of war. Heidegger (who incidentally pointed out that we don't notice the obvious until it breaks) had a great interest in the Pre-Socratics.

Now, the Pre-Socratic philosopher Parmenides had argued that it is impossible for us to imagine any particular thing not-being. If we imagine it, we imagine it existing, and it at least exists in our imagination. Also, we cannot imagine any such thing as non-being generally since we would imagine it 'being' which is self contradictory. Therefore there is only being. Now consider change. If we were to imagine something to change from one state to another, it would necessarily have changed from what it was to what it wasn't, which requires that there be some 'non-being' that it wasn't. Since we already showed there can't be non-being, change is impossible. So there is only one unchanging unchanging. We can pick holes in this but is a very abstract and sophisticated argument, counter-intuitive to our basic beliefs - things which have become characteristic of Philosophy. The atomists, later argued that there is such thing as non-being, in the physical sense, as empty space allowing atoms to move about, thus allowing for the principle of change that we see in the world around us.

We can see a relationship between this Pre-socratic debate around being and nothingness, and how change depends on nothingness, and Sartre's argument about being, nothingness and free will. Philosophy is a long debate over thousands of years over fundamental questions.

There isn't time to look at them all in detail, so here is a quick overview before looking in more detail at the Anaximander fragment.

In answer to a question on Pythagoras during the chat that I didn't answer fully:

Is this true, everything is made of numbers?

For Pythagoreans, in a way yes: Numbers are more real than things in the world. Things in the world come in to being, have imperfect shapes and pass away. The truths of mathematics are perfect, eternally and indubitably true. 2 + 2 = 4 is always true regardless of whether you are adding apples or oranges, but apples and oranges are never perfect apples and oranges and they decay. In this sense numbers and geometry are more 'real' than material things. Can we even imagine a possible universe in which it is not true? Everything in the Pythagorean Universe is built up, imperfectly, from basic mathematical forms such as circles, triangles, squares, and so on and the way they interact depends on the properties of these shapes. Considering a primary concern for Pre-Socratics was the nature of the Universe, what is is made from and how things come to be and Pythagoreanism was quite esoteric, we might say they thought the universe was made of numbers or of geometry.

The Anaximander Fragment


τῶν δὲ ἓν καὶ κινούμενον καὶ ἀπειρον λεγόντων Ἀ. μἐν Πραξιάδου Μιλήσιος Θαλοῦ γενόμενος διάδοχος καὶ μαθητὴς ἀρχήν τι καὶ στοιχεῖον εἴρηκε τῶν ὄντων τὸ ἄπειρον, πρῶτος τοῦτο τοὔνομα κομίσας τῆς ἀρχῆς. λέγει δ' αὐτὴν μήτε ὕδωρ μήτε ἄλλο τι τῶν καλουμένων εἶναι στοιχείων, ἀλλ' ἑτέραν τινὰ φύσιν ἄπειρον, ἐξ ἧς ἅπαντας γίνεσθαι τοὺς οὐρανοὺς καὶ τοὺς ἐν αὐτοῖς κόσμους· ἐξ ὧν δὲ ... τάξιν [Β 1], ποιητικωτέροις οὕτως ὀνόμασιν αὐτὰ λέγων.

Anaximander of Miletos, son of Praxiades, a fellow-citizen and associate of Thales, said that the material cause and first element of things was the Infinite, he being the first to introduce this name for the material cause. He says it is neither water nor any other of the so-called elements, but a substance different from them, which is infinite, from which arise all the heavens and the worlds within them. And into that from which things take their rise they pass away once more, "as is ordained; for they make reparation and satisfaction to one another for their injustice according to the appointed time," as he says in these somewhat poetical terms. —Phys. Op. fr. 2 (R. P. 16).

Translated by Nietzsche (and then into English):

Whence things have their origin, there they must also pass away according to necessity; for they must pay penalty and be judged for their injustice, according to the ordinance of time.

But where things have their origin, there too their passing away occurs according to necessity; for they pay recompense and penalty to one another for their recklessness, according to firmly established time.

Translated by Heidegger:

Whence emergence is for what respectively presences also an eluding into this (as into the Same), emerges accordingly the compelling need; there is namely what presences itself (from itself), the fit, and each is respected (acknowledged) by the other, (all of this) from overcoming the unfit according to the allotment of temporalizing time. https://www.beyng.com/grk/anax1.html

Google translate:

of the two, and of the moving and endless, with Praxiadou Milesios Thalos, a successor and student, first and foremost, of those who were born in the first place before the name of the queen of the Anarchy. neither do they say, nor do they say anything that is called, but they are of another nature, that when they come to be the blame, and to them in these worlds; for they are more innocent than they say

More quotes from Anaximander: https://history.hanover.edu/texts/presoc/anaximan.html