History teaches us 1: Democritus, Plato, Galileo, Newton, Locke, Descartes, Hume                                                    2, 3, 4



I wish to demonstrate in a little more detail the very strange state of affairs already noticed in a famous fragment of Democritus of Abdera the strange fact that on the one hand all our knowledge of the world around us, both that gained in everyday life and that revealed by the most painstaking laboratory experiments, rests entirely on immediate sense perception, while on the other hand this knowledge fails to reveal the relations of the sense perceptions to the outside world, so that in the picture or model that we form of the outside world, guided by our scientific discoveries, all sensual qualities are absent.

If you ask a physicist what is his idea of yellow light, he will tell you that it is transversal electromagnetic waves of wavelength in the neighborhood of 590 millimicrons. If you ask him: But where does yellow come in? he will say: In my picture not at all, but these kinds of vibrations, when they hit the retina of a healthy eye, give the person whose eye it is the sensation of yellow.


Plato, in an ideal world

Socrates: So they are, my boy, quite without culture. But others are more clever, whose secret doctrines I am going to disclose to you. For them the beginning, upon which all the things we were just now speaking of depend, is the assumption that everything is real motion and that there is nothing besides this, but that there are two kinds of motion, each infinite in the number of its manifestations, and of these kinds one has an active, the other a passive force.

From the union and friction of these two are born offspring, infinite in number, but always twins, the object of sense and the sense which is always born and brought forth together with the object of sense. Now we give the senses names like these: sight and hearing and smell, and the sense of cold and of heat, and pleasures and pains and desires and fears and so forth. Those that have names are very numerous, and those that are unnamed are innumerable. Now the class of objects of sense is akin to each of these; all sorts of colors are akin to all sorts of acts of vision, and in the same way sounds to acts of hearing, and the other objects of sense spring forth akin to the other senses. What does this tale mean for us, Theaetetus, with reference to what was said before? Do you see?


The pendulum oscillates.

Swept on by the inherent necessities of this mathematical metaphysic, Galileo, like Kepler, was inevitably led to the doctrine of primary and secondary qualities, only with the Italian genius the doctrine appears in a much more pronounced and developed form. Galileo makes the clear distinction between that in the world which is absolute, objective, immutable, and mathematical; and that which is relative, subjective, fluctuating, and sensible. [...] The Copernican astronomy and the achievements of the two new sciences must break us of the natural assumption that sensed objects are the real or mathematical objects. They betray certain qualities, which, handled by mathematical rules, lead us to a knowledge of the true object, and these are the real or primary qualities, such as number, figure, magnitude, position and motion [...] qualities which also can be wholly expressed mathematically. The reality of the universe is geometrical; the only ultimate characteristics of nature are those in terms of which certain mathematical knowledge becomes possible. All other qualities, and these are often far more prominent to the senses, are secondary, subordinate effects of the primary.

Of the utmost moment was Galileo's further assertion that these secondary qualities are subjective. In Kepler there had been no clear statement of this position; apparently for him the secondary qualities were out there in the astronomical world, like the primary, only they were not so real or fundamental.



Then, as regards body in particular, we have only the notion of extension, which entails the notions of shape and motion; and as regards the soul on its own, we have only the notion of thought, which includes the perceptions of the intellect and the inclinations of the will...

digital brain

These long chains of perfectly simple and easy reasoning by means of which geometers are accustomed to carry out their most difficult demonstrations had led me to fancy that everything that can fall under human knowledge forms a similar sequence; and that so long as we avoid accepting as true what is not so, and always preserve the right order of deduction of one thing from another, there can be nothing too remote to be reached in the end, or too well hidden to be discovered.


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I would rather discover a single causal
connection than win the throne of Persia.

The Intellect:

By convention there is color,

By convention sweetness,
By convention bitterness,
But in reality there are
atoms and space

The Senses:

Poor intellect, do you hope to defeat us
while from us you borrow your evidence?
Your victory is your defeat.


Where does the yellow come in?
Where does the yellow come in?

Science is nothing but perception.

Wonder [said Socrates] is very much the affection of a philosopher; for there is no other beginning of philosophy than this.

Better a little which is well done, than a great deal imperfectly.

Wise people talk because they have something to say; fools, because they have to say something.

And what, Socrates, is the food of the soul? Surely, I said, knowledge is the food of the soul.

Beauty of style and harmony and grace and good rhythm depend on simplicity.

Knowledge is true opinion.

The punishment which the wise suffer, who refuse to take part in government, is to live under the government of worse men.

It is a common saying, and in everybody's mouth, that life is but a sojourn. The learning and knowledge that we have, is, at the most, but little compared with that of which we are ignorant.

Knowledge which is acquired under compulsion has no hold on the mind. Therefore do not use compulsion, but let early education be rather a sort of amusement; this will better enable you to find out the natural bent of the child.

There are three classes of men; lovers of wisdom, lovers of honor, and lovers of gain.

The spiritual eyesight improves as the physical eyesight declines.



Plato  Home vision

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But it does move.

Hence I think that these tastes, odors, colors, etc., on the side of the object in which they seem to exist, are nothing else than mere names, but hold their residence solely in the sensitive body [...]

In questions of science the authority of a thousand
is not worth the humble reasoning of a single individual.

But where the senses fail us, reason must step in.

All truths are easy to understand once they are discovered; the point is to discover them.

Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

My dear Kepler, what would you say of the learned here, who, replete with the pertinacity of the asp, have steadfastly refused to cast a glance through the telescope? What shall we make of this? Shall we laugh, or shall we cry?

I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use.


The reading of all good books is like a conversation with
the finest minds of past centuries.

With me everything turns into mathematics.

In order to improve the mind, we ought less to learn, than to contemplate.

When writing about transcendental issues, be transcendentally clear

Thus what I thought I had seen with my eyes, I actually grasped solely with the faculty of judgment, which is in my mind.


Descartes Home


Sir Isaac Newton

Truth is ever to be found in the simplicity, and not 
in the multiplicity and confusion of things.

 [The] science of colors becomes a speculation as truly mathematical as any other part of physics.

No great discovery was ever made without a bold guess.

I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smooth pebble, or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.

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For the Rays (of light) to speak properly are not colored. In them there is nothing else than a certain Power and Disposition to stir up a Sensation of this or that Color. [...] in the Rays they are nothing but their Dispositions to propagate this or that Motion into the Sensorium, and in the Sensorium they are Sensations of those Motions under the form of Colors.


spectral theory

It became Him who created it to set it in order; and if he did so, it is unphilosophical to seek for any other origin of the world, or to pretend that it might arise out of a chaos by the mere laws of Nature.

What I have done is due to patient thought.

Zeal without knowledge is like expedition to a man in the dark.

It is the glory of geometry that from so few principles, fetched from without, it is able to accomplish so much.





These I call original or primary qualities of the body, which I think we may observe to produce simple ideas in us, viz., solidity, extension, figure, motion or rest, and number.

Secondly, such qualities which in truth are nothing in the objects themselves, but powers to produce various sensations in us by their primary qualities, i.e. by the bulk, figure, texture, and motion of their insensible parts, as colour, sounds, tastes, etc., these I call secondary qualities.

The ideas [perceptions] of primary qualities of bodies are resemblances of them, [i.e., of qualities of matter] and their patters do really exist in the bodies themselves; but the ideas produced in us by these secondary qualities have no resemblance of them at all. [...] What is sweet, blue or warm in idea, is but bulk, figure, and motion of the insensible parts in the bodies themselves, which we call so ... A piece of manna of a sensible bulk, is able to produce in us the idea of a round or square figure; and by being removed from one place to another, the idea of motion.

This idea of motion represents it, as it really is in the manna moving; a circle or square are the same, whether in idea or existence; in the mind or in the manna.

And this, both motion and figure are really in the manna, whether we take notice of them or not. This everybody agrees to. Besides, manna by the bulk, figure, texture and motion of its parts has a power to produce the sensation of sickness, or sometimes of acute pains or gripings in us. That these ideas of sickness and pain are not in the manna, but effects of its operations on us, and are nowhere when we feel them not: this also everyone readily agrees to. And yet men are hardly to be brought to think, that sweetness and whiteness are not really in manna ...


artificial retina

[All] chemical binding is electromagnetic in origin, and so are all phenomena of nerve impulses.

[...] the whole spatial world becomes a vast machine, including even the movements of animal bodies and those processes in human physiology which are independent of conscious attention. This world has no dependence on thought whatever, its whole machinery would continue to exist and operate if there were no human beings in existence at all. On the other hand, there is the inner realm whose essence is thinking, whose modes are such subsidiary processes as perception, willing, feeling, imagining, etc.,

In which realm, then, shall we place the secondary qualities? The answer given is inevitable. We can conceive the primary qualities to exist in bodies as they really are; not so the secondary.

"In truth they can be representative of nothing that exists out of the mind." They are, to be sure, caused by the various effects on our organs of the motions of the small insensible parts of the bodies.


David Hume



A wise man proportions his belief to the evidence. 

Be a philosopher; but amidst all your philosophy, be still a man.

Among well-bred people a mutual deference is affected, contempt of others is disguised; authority concealed; attention given to each in his turn; and an easy stream of conversation maintained without vehemence, without interruption, without eagerness for victory, and without any airs of superiority.

Curiosity, or the love of knowledge, has a very limited influence, and requires youth, leisure education, genius and example to make it govern any person.

Liberty of thinking, and of expressing our thoughts, is always fatal to priestly power, and to those pious frauds on which it is commonly founded.

The sweetest and most inoffensive path of life leads through the avenues of science and learning; and whoever can either remove any obstruction in this way, or open up any new prospect, ought, so far, to be esteemed a benefactor to mankind.

What a peculiar privilege has this little agitation of the brain which we call 'thought'.

"The sublime," says Longinus, "is often nothing but the echo or image of magnanimity"; and where this quality appears in any one, even though a syllable be not uttered, it excites our applause and admiration.



If we imagine a machine so constructed as to produce thought, sensation, perception, we may conceive it magnified to such an extent that one might enter it like a mill. This being supposed, we should find in it on inspection only pieces which impel each other, but nothing which can explain a perception. It is in the simple substance, therefore, not in the compound, or in the machinery, that we must look for that phenomenon [...] 


Although the whole of this life were said to be nothing but a dream and the physical world nothing but a phantasm, I should call this dream or phantasm real enough, if, using reason well, we were never deceived by it.


Since this is the best (or worst) of all possible worlds, the laws of physics can best be described by variational principles.




John Locke

Education begins the gentleman, but reading, good
and reflection must finish him.

No man's knowledge here can go beyond his experience.

Logic is the anatomy of thought.

The great art to learn much is to undertake a little at a time.

The power of perception is that which we call the understanding.

Whatsoever the mind perceives of itself, or is the immediate object of perception, thought, or understanding, that I call an idea.

We are taught to clothe our minds, as we do our bodies, after the fashion in vogue; and it is accounted fantastical or something worse, not to do so.

All men are liable to error; and most men are, in many points, by passion or interest, under temptation to it.

Experience: in that all our knowledge is founded; and from that it ultimately derives itself. Our observation employed either about external or sensible objects or about the internal operations of our minds, perceived and reflected on by ourselves, is that which supplies our understandings with all the materials of thinking.

Firmness or stiffness of the mind is not from adherence to truth, but submission to prejudice.

General observations drawn from particulars are the jewels of knowledge, comprehending great store in a little room.

Habits wear more constantly and with greatest force than reason, which, when we have most need of it, is seldom fairly consulted, and more rarely obeyed.

Reading furnishes the mind only with materials of knowledge; it is thinking that makes what we read ours.



The world as described by natural science has no obvious place for colors, tastes, or smells. Problems with sensory qualities have been philosophically and scientifically troublesome since ancient times, and in modern form at least since Galileo in 1623 identified some sensory qualities as characterizing nothing real in the objects themselves [...]

The qualities of size, figure (or shape), number, and motion are for Galileo the only real properties of objects. All other qualities revealed in sense perceptioncolors, tastes, odors, sounds, and so onexist only in the sensitive body, and do not qualify anything in the objects themselves. They are the effects of the primary qualities of things on the senses. Without the living animal sensing such things, these 'secondary' qualities (to use the term introduced by Locke) would not exist.

Much of modern philosophy has devolved from this fateful distinction. While it was undoubtedly helpful to the physical sciences to make the mind into a sort of dustbin into which one could sweep the troublesome sensory qualities, this stratagem created difficulties for later attempt to arrive at some scientific understanding of the mind. In particular, the strategy cannot be reapplied when one goes on to explain sensation and perception. If physics cannot explain secondary qualities, then it seems that any science that can explain secondary qualities must appeal to explanatory principles distinct from those of physics. Thus are born various dualisms.


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The fundamental principle of that philosophy is the opinion concerning colors, sounds, tastes, smells, heat and cold; which it asserts to be nothing but impressions in the mind, deriv'd from the operation of external objects, and without any resemblance to the qualities of the objects.


This principle being once admitted, all other doctrines of that philosophy seem to follow by an easy consequence. For upon the removal of sounds, colors, heat, cold, and other sensible qualities, from the rank of continu'd independent existences, we are reduced merely to what are called primary qualities,as the only real ones, of which we have any adequate notion. These primary qualities are extension and solidity, with their different mixtures and modifications; figure, motion, gravity and cohesion. The generation, encrease, decay and corruption of animals and vegetables, are nothing but changes of figure and motion; as also the operations of all bodies on each other; of fire, of light, water, air, earth, and of all the elements and powers of nature [...]

Thus there is a direct and total opposition betwixt our reason and senses [...] When we reason from cause and effect, we conclude, that neither color, sound, taste, nor smell have a continued and independent existence. When we exclude these sensible qualities there remains nothing in the universe, which has such an existence.



There is nothing besides perceptions and their changes to be found in the simple substance.

There are two kinds of truths: those of reasoning and those of facts. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible.

Even in the games of children there are things to interest the greatest mathematician.

I have said more than once, that I hold space to be something purely relative, as time; an order of coexistences, as time is an order of successions.

We must, in addition to purely mathematical principles, recognize metaphysical ones [in physics].

Music is a hidden metaphysical exercise of the soul, which does not know that it is philosophizing.


Leibniz   monads
Berkeley Berkeley


All the choir of heaven and furniture of earth in a word, all those bodies which compose the frame of the world have not any subsistence without a mind.

The eye by long use comes to see even in the darkest cavern: and there is no subject so obscure but we may discern some glimpse of truth by long poring on it.

Truth is the cry of all, but the game of few.

Others indeed may talk, and write, and fight about liberty, and make an outward pretence to it; but the free-thinker alone is truly free.


The trivial proposition which I propose to dispute is this: esse is percipi. This is a very ambiguous proposition, but, in some sense or other, it has been very widely held. That it is, in some sense, essential to Idealism, I must for the present merely assume. What I propose to show is that, in all the senses ever given to it, it is false.

What I dislike in this kind of argumentation is the basic positivistic attitude, which from my view is untenable, and which seems to me to come to the same thing as Berkeley's principle, esse est percipi.


The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature.


The real color of a thing is that one color-sensation which it gives us when most favorably lighted for vision. Soon its real size, its real shape, etc. these are but optical sensations selected out of thousands of others, because they have aesthetic characteristics which appeal to our convenience or delight. But I will not repeat what I have already written about this matter, but pass on to our treatment of tactile and muscular sensations, as 'primary qualities,' more real than those 'secondary' qualities which eye and ear and nose reveal. Why do we thus so markedly select the tangible to be the real? Our motives are not far to seek. The tangible qualities are the least fluctuating. When we get them at all we get them the same. The other qualities fluctuate enormously as our relative position to the object changes.

Wm James

History 2Young, Helmholtz, Mach, Riemann, Maxwell, Weyl, Schrödinger, Heisenberg, Dirac, Einstein


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