How does the mathematician differ from the physicist?

How does the mathematician differ from the physicist?

Physical bodies contain surfaces and volumes, lines and points. These are the subject-matter of mathematics.

Is astronomy different from physics or a department of it?

It seems absurd that the physicist should be supposed to know the nature of sun or moon, but not to know any of their essential attributes.

The writers on physics discuss their shape, whether the earth and the world are spherical or not.

The mathematician also treats of these things. But he:

• does not treat of them as the limits of a physical body
• does not consider the attributes indicated as the attributes of such bodies.

That is why he separates them.

In thought, they are separable from motion, and it makes no difference. Nor does any falsity result if they are separated.

The holders of the theory of Forms do the same even if they are not aware of it. They separate the objects of physics, which are less separable than those of mathematics.

This becomes plain if one tries to state in each of the two cases the definitions of the things and of their attributes.

The following do not involve motion:

• ‘Odd’ and ‘even’
• ‘straight’ and ‘curved’
• ‘number’, ‘line’, and ‘shape'

But the following do:

• ‘flesh’ and ‘bone’
• ‘man’

These are defined like ‘snub nose’, not like ‘curved’.

Similar evidence is supplied by the more physical of the branches of mathematics, such as:

• optics
• harmonics
• astronomy.

These are in a way the converse of geometry.

Geometry investigates physical lines but not qua physical.

Optics investigates mathematical lines, but qua physical, not qua mathematical.

‘Nature’ has 2 senses:

1. The form
2. The matter

We must investigate its objects as we would the essence of snubness.

That is, such things are neither independent of matter nor can be defined in terms of matter only.

Here too one might raise a difficulty.

Since there are 2 natures, which one should the physicist be concerned with?

Should he investigate the combination of the two?

But if the combination of the two, then also each severally.

Does it belong then to the same or to different sciences to know each severally?

To the ancients, physics would be concerned with the matter.

• Empedocles and Democritus only very slightly touched on the forms and the essence.

But if on the other hand art imitates nature, and it is the part of the same discipline to know the form and the matter up to a point.

For example:

• the doctor has a knowledge of health and also of bile and phlegm. This makes him provide health
• the builder both of the form of the house and of the matter, namely that it is bricks and beams

If so, then it would be the part of physics also to know nature in both its senses.

Again, ‘that for the sake of which’, or the end, belongs to the same department of knowledge as the means. But the nature is the end or ‘that for the sake of which’.

For if a thing undergoes a continuous change and there is a stage which is last, this stage is the end or ‘that for the sake of which’.

That is why the poet was carried away into making an absurd statement when he said ‘he has the end for the sake of which he was born’.

For not every stage that is last claims to be an end, but only that which is best.) For the arts make their material (some simply ‘make’ it, others make it serviceable), and we use everything as if it was there for our sake. (We also are in a sense an end.

‘That for the sake of which’ has two senses: the distinction is made in our work On Philosophy.

Therefore, the arts which govern the matter and have knowledge are two:

1. The art which uses the product
2. The art which directs the production of it.

That is why the using art also is in a sense directive.

But it differs in that it knows the form, whereas the art which is directive as being concerned with production knows the matter.

The helmsman knows and prescribes what sort of form a helm should have, the other from what wood it should be made and by means of what operations.

In the products of art, however, we make the material with a view to the function, whereas in the products of nature the matter is there all along.

Matter is a relative term: to each form there corresponds a special matter.

How far then must the physicist know the form or essence? Up to a point, perhaps, as the doctor must know sinew or the smith bronze (i.e. until he understands the purpose of each): and the physicist is concerned only with things whose forms are separable indeed, but do not exist apart from matter.

Man is begotten by man and by the sun as well. The mode of existence and essence of the separable it is the business of the primary type of philosophy to define.