Mathematics

Mathematics is the part of natural philosophy which is commonly made a principal part.

• It has the same rank as special physics and metaphysics

But I think it should be a branch of metaphysics.

This is because it:

• is based on relative quantities

• belongs to philosophia prima

Quantity, determined or proportionable, is one of the essential forms of things. In Nature, it causes a number of effects.

• Democritus ascribed shapes to the first seeds of things
• Pythagoras supposed numbers to be the principles and originals of things.

Of all other forms, quantity is the most abstracted and separable from matter.

Quantity is therefore most proper to metaphysics which has likewise been the cause why it hath been better laboured and inquired than any of the other forms, which are more immersed in matter.

The human mind:

• delights in the spacious liberty of generalities, as in a champagne region.
• delights not in the enclosures of particularity
  • Mathematics is the goodliest field to satisfy that appetite.

Mathematics as a science is not much material.

• It has our partitions that we use to observe a kind of perspective so that one part may cast light on another.

Mathematics is either:

• pure or
• mixed.

Pure mathematics are those sciences belonging which handle quantity determinate, merely severed from any axioms of natural philosophy. These are 2:

1. Geometry

This handles quantity continued.

2. Arithmetic

This handles quantity dissevered.

Mixed hath for subject some axioms or parts of natural philosophy, and considereth quantity determined, as it is auxiliary and incident unto them.

Mathematics and its perspectives in music, astronomy, cosmography, architecture, engineery, etc. is necessary to:

• invent many parts of Nature through sufficient subtlety
• demonstrate many parts of Nature with sufficient perspicuity
• use many parts of Nature with sufficient dexterity

The only deficiency in mathematics is that men do not sufficiently understand this excellent use of pure mathematics.

They remedy and cure many defects in the wit and intellectual faculties.

• If the wit be too dull, pure mathematics sharpens it.
• If too wandering, pure mathematics fixes it.
• If too inherent in the sense, pure mathematics abstracts it.

Tennis itself is useless game.

• But it is useful in making the eye quick and body ready to put itself into all postures.

Likewise, mathematics is used to improve the intellect as mentioned above.

I predict that mixed mathematics will develop into more kinds as Nature grows further disclosed. Thus much of natural science, or the part of Nature speculative.

For natural prudence is the operative part of natural philosophy.

I divide it into 3 parts:

1. Experimental
2. Philosophical
3. Magical

When active, these 3 parts correspond with the 3 speculative parts:

1. Natural history
2. Physic
3. Metaphysic

Many operations have been invented:

• sometimes by a casual incidence and occurrence
• sometimes by a purposed experiment.

Those operations which have been found by an intentional experiment:

• some have been discovered by varying or extending the same experiment.
• some have been discovered by transferring and compounding diverse experiments the one into the other
  • This kind of invention an empiric may manage.

The knowledge of physical causes leads to many indications and designations of new particulars.

But these are but coastings along the shore, premendo littus iniquum.

There can hardly be discovered any radical or fundamental alterations and innovations in Nature, either by:

• the fortune and essays of experiments, or
• the light and direction of physical causes.

Since metaphysic is deficient, then natural magic, which is related to it, is also deficient.

The natural magic now is mentioned in books containing:

• credulous and superstitious conceits
• observations of sympathies and antipathies and hidden proprieties
• some frivolous experiments, strange by concealement

These are more different in truth of Nature than the story of King Arthur is different from Cæsar’s Commentaries

Cæsar did greater things de vero than those imaginary heroes did.

• But he did them not in that fabulous manner.

Of this kind of magical learning is the fable of Ixion.

• He wanted to enjoy Juno, the goddess of power.
• He had sex with a cloud instead of her, which became pregnant with centaurs and chimeras.

In this way, whoever entertains vaporous imaginations begets hopes and beliefs of strange and impossible shapes.

The degenerate sciences of natural magic are alchemy, astrology, and the like.

These sciences hold so much of imagination and belief.

In their propositions, the description of the means is even more monstrous than the pretence or end.

For it is a thing more probable that he that

A person might know the a metal’s nature in terms of:

• weight, colour
• pliant and fragile in respect of the hammer
• volatile and fixed in respect of the fire, etc.

He can use this knowledge to superinduce on some metal the nature and form of gold.

• He can make this better than using some grains of medicine that would turn into gold.

Likewise, a person might know the body’s nature in terms of:

• arefaction
• assimilation of nourishment to the thing nourished
• how it increases and clears of spirits
• how the spirits cause depredations on the humours and solid parts

He can use this knowledge to create diets, bathings, anointings, medicines, motions, and the like to:

• prolong life, or
• restore some degree of youth or vivacity

He can do this better than using a few drops or scruples of a liquor or receipt.

True natural magic gets its great liberty and latitude of operation from the knowledge of forms. This is deficient.

Its operations are derived and deduced from metaphysic.

This can be improved through:

1. Preparation

We could create a calendar that resembles an inventory of a man’s estate. It contains all the existing inventions (being the works or fruits of Nature or art).

Out of this is a list of what other inventions are possible.

For any impossible invention, add the currently-invented thing which approaches closest to it.

These optatives and potentials will make man’s inquiry more awake in deducing direction of works from the speculation of causes.

2. Caution

These experiments which have an immediate and present use should not be the only ones esteemed.

More importance should be given to those which:

• are of most universal consequence for invention of other experiments
• give most light to the invention of causes should be given

The invention of the compass gives the direction. It is just as beneficial for navigation than the invention of the sails which give the motion.

5. There remains a division of natural philosophy that does not concern the matter or subject.

It is positive and considerative. It reports either an assertion or a doubt.

These doubts are of 2 sorts:

1. Particular

2. Total

The Calendar of Doubts

An example is in Aristotle’s Problems. This should be continued.

The registering of doubts has 2 excellent uses:

1. It saves philosophy from errors and falsehoods

This happens when that which is not fully appearing is not collected into assertion, whereby error might draw error, but reserved in doubt.

2. The entry of doubts are as so many suckers or sponges to draw use of knowledge

Insomuch as that which if doubts had not preceded, a man should never have advised, but passed it over without note, by the suggestion and solicitation of doubts is made to be attended and applied.

But both these commodities do scarcely countervail and inconvenience, which will intrude itself if it be not debarred; which is, that when a doubt is once received, men labour rather how to keep it a doubt still, than how to solve it, and accordingly bend their wits.

Of this we see the familiar example in lawyers and scholars, both which, if they have once admitted a doubt, it goeth ever after authorised for a doubt.

But that use of wit and knowledge is to be allowed, which laboureth to make doubtful things certain, and not those which labour to make certain things doubtful.

Therefore, these calendars of doubts I commend as excellent things.

So that there he this caution used, that when they be thoroughly sifted and brought to resolution, they be from thenceforth omitted, discarded, and not continued to cherish and encourage men in doubting.

To which calendar of doubts or problems I advise be annexed another calendar, as much or more material which is a calendar of popular errors: I mean chiefly in natural history, such as pass in speech and conceit, and are nevertheless apparently detected and convicted of untruth, that man’s knowledge be not weakened nor embased by such dross and vanity.

As for the doubts or non liquets general or in total, I understand those differences of opinions touching the principles of nature, and the fundamental points of the same, which have caused the diversity of sects, schools, and philosophies, as that of Empedocles, Pythagoras, Democritus, Parmenides, and the rest.

For although Aristotle, as though he had been of the race of the Ottomans, thought he could not reign except the first thing he did he killed all his brethren; yet to those that seek truth and not magistrality, it cannot but seem a matter of great profit, to see before them the several opinions touching the foundations of nature.

We cannot expect any truth in those theories.

The same phenomena in astronomy are satisfied by this received astronomy of the diurnal motion.

The proper motions of the planets, with their eccentrics and epicycles, and likewise by the theory of Copernicus, who supposed the earth to move, and the calculations are indifferently agreeable to both, so the ordinary face and view of experience is many times satisfied by several theories and philosophies;

Whereas to find the real truth requireth another manner of severity and attention.

For as Aristotle saith, that children at the first will call every woman mother, but afterward they come to distinguish according to truth, so experience, if it be in childhood, will call every philosophy mother, but when it cometh to ripeness it will discern the true mother.

So as in the meantime it is good to see the several glosses and opinions upon Nature, whereof it may be everyone in some one point hath seen clearer than his fellows, therefore I wish some collection to be made painfully and understandingly de antiquis philosophiis, out of all the possible light which remaineth to us of them: which kind of work I find deficient.

But here I must give warning, that it be done distinctly and severedly; the philosophies of everyone throughout by themselves, and not by titles packed and faggoted up together, as hath been done by Plutarch.

For it is the harmony of a philosophy in itself, which giveth it light and credence; whereas if it be singled and broken, it will seem more foreign and dissonant.

For as when I read in Tacitus the actions of Nero or Claudius, with circumstances of times, inducements, and occasions, I find them not so strange; but when I read them in Suetonius Tranquillus, gathered into titles and bundles and not in order of time, they seem more monstrous and incredible: so is it of any philosophy reported entire, and dismembered by articles.

Neither do I exclude opinions of latter times to be likewise represented in this calendar of sects of philosophy, as that of Theophrastus Paracelsus, eloquently reduced into an harmony by the pen of Severinus the Dane; and that of Tilesius, and his scholar Donius, being as a pastoral philosophy, full of sense, but of no great depth; and that of Fracastorius, who, though he pretended not to make any new philosophy, yet did use the absoluteness of his own sense upon the old; and that of Gilbertus our countryman, who revived, with some alterations and demonstrations, the opinions of Xenophanes; and any other worthy to be admitted.

(6) Thus have we now dealt with two of the three beams of man’s knowledge; that is radius directus, which is referred to nature, radius refractus, which is referred to God, and cannot report truly because of the inequality of the medium.

There resteth radius reflexus, whereby man beholdeth and contemplateth himself.