The Works of George Berkeley Part 7

We have learn'd from Mr. Locke that there may be, and that there are, several glib, coherent, methodical discourses, which nevertheless amount to just nothing. This by him intended with relation to the Scholemen. We may apply it to the Mathematicians.

Qu. How can all words be said to stand for ideas? The word blue stands for a colour without any extension, or abstract from extension. But we have not an idea of colour without extension. We cannot imagine colour without extension.

Locke seems wrongly to a.s.sign a double use of words: one for communicating & the other for recording our thoughts. 'Tis absurd to use words for recording our thoughts to ourselves, or in our private meditations(75).

No one abstract simple idea like another. Two simple ideas may be connected with one & the same 3d simple idea, or be intromitted by one & the same sense. But consider'd in themselves they can have nothing common, and consequently no likeness.

Qu. How can there be any abstract ideas of colours? It seems not so easily as of tastes or sounds. But then all ideas whatsoever are particular. I can by no means conceive an abstract general idea. 'Tis one thing to abstract one concrete idea from another of a different kind, & another thing to abstract an idea from all particulars of the same kind(76).

(M39) Mem. Much to recommend and approve of experimental philosophy.

(M40) What means Cause as distinguish'd from Occasion? Nothing but a being wch wills, when the effect follows the volition. Those things that happen from without we are not the cause of. Therefore there is some other Cause of them, i.e. there is a Being that wills these perceptions in us(77).

(M41) [(78)It should be said, nothing but a Will-a Being which wills being unintelligible.]

One square cannot be double of another. Hence the Pythagoric theorem is false.

Some writers of catoptrics absurd enough to place the apparent place of the object in the Barrovian case behind the eye.

Blew and yellow chequers still diminishing terminate in green. This may help to prove the composition of green.

There is in green 2 foundations of 2 relations of likeness to blew & yellow. Therefore green is compounded.

A mixt cause will produce a mixt effect. Therefore colours are all compounded that we see.

Mem. To consider Newton's two sorts of green.

N. B. My abstract & general doctrines ought not to be condemn'd by the Royall Society. 'Tis wt their meeting did ultimately intend. V. Sprat's History S. R.(79)

Mem. To premise a definition of idea(80).

(M42) The 2 great principles of Morality-the being of a G.o.d & the freedom of man. Those to be handled in the beginning of the Second Book(81).

Subvert.i.tur geometria ut non practica sed speculativa.

Archimedes's proposition about squaring the circle has nothing to do with circ.u.mferences containing less than 96 points; & if the circ.u.mference contain 96 points it may be apply'd, but nothing will follow against indivisibles. V. Barrow.

Those curve lines that you can rectify geometrically. Compare them with their equal right lines & by a microscope you shall discover an inequality. Hence my squaring of the circle as good and exact as the best.

(M43) Qu. whether the substance of body or anything else be any more than the collection of concrete ideas included in that thing? Thus the substance of any particular body is extension, solidity, figure(82). Of general abstract body we can have no idea.

(M44) Mem. Most carefully to inculcate and set forth that the endeavouring to express abstract philosophic thoughts by words unavoidably runs a man into difficulties. This to be done in the Introduction(83).

Mem. To endeavour most accurately to understand what is meant by this axiom: Quae sibi mutuo congruunt aequalia sunt.

Qu. what the geometers mean by equality of lines, & whether, according to their definition of equality, a curve line can possibly be equal to a right line?

If wth me you call those lines equal wch contain an equal number of points, then there will be no difficulty. That curve is equal to a right line wch contains the same points as the right one doth.

(M45) I take not away substances. I ought not to be accused of discarding substance out of the reasonable world(84). I onely reject the philosophic sense (wch in effect is no sense) of the word substance. Ask a man not tainted with their jargon wt he means by corporeal substance, or the substance of body. He shall answer, bulk, solidity, and such like sensible qualitys. These I retain. The philosophic nec quid, nec quantum, nec quale, whereof I have no idea, I discard; if a man may be said to discard that which never had any being, was never so much as imagin'd or conceiv'd.

(M46) In short, be not angry. You lose nothing, whether real or chimerical. Wtever you can in any wise conceive or imagine, be it never so wild, so extravagant, & absurd, much good may it do you. You may enjoy it for me. I'll never deprive you of it.

N. B. I am more for reality than any other philosophers(85). They make a thousand doubts, & know not certainly but we may be deceiv'd. I a.s.sert the direct contrary.

A line in the sense of mathematicians is not meer distance. This evident in that there are curve lines.

Curves perfectly incomprehensible, inexplicable, absurd, except we allow points.

(M47) If men look for a thing where it's not to be found, be they never so sagacious, it is lost labour. If a simple clumsy man knows where the game lies, he though a fool shall catch it sooner than the most fleet & dexterous that seek it elsewhere. Men choose to hunt for truth and knowledge anywhere rather than in their own understanding, where 'tis to be found.

(M48) All knowledge onely about ideas. Locke, B. 4. c. 1.

(M49) It seems improper, & liable to difficulties, to make the word person stand for an idea, or to make ourselves ideas, or thinking things ideas.

(M50) Abstract ideas cause of much trifling and mistake.

Mathematicians seem not to speak clearly and coherently of equality. They nowhere define wt they mean by that word when apply'd to lines.

Locke says the modes of simple ideas, besides extension and number, are counted by degrees. I deny there are any modes or degrees of simple ideas.

What he terms such are complex ideas, as I have proved.

Wt do the mathematicians mean by considering curves as polygons? Either they are polygons or they are not. If they are, why do they give them the name of curves? Why do not they constantly call them polygons, & treat them as such? If they are not polygons, I think it absurd to use polygons in their stead. Wt is this but to pervert language? to adapt an idea to a name that belongs not to it but to a different idea?

The mathematicians should look to their axiom, Quae congruunt sunt aequalia.

I know not what they mean by bidding me put one triangle on another. The under triangle is no triangle-nothing at all, it not being perceiv'd. I ask, must sight be judge of this congruentia or not? If it must, then all lines seen under the same angle are equal, wch they will not acknowledge.

Must the touch be judge? But we cannot touch or feel lines and surfaces, such as triangles, &c., according to the mathematicians themselves. Much less can we touch a line or triangle that's cover'd by another line or triangle.

Do you mean by saying one triangle is equall to another, that they both take up equal s.p.a.ces? But then the question recurs, what mean you by equal s.p.a.ces? If you mean _spatia congruentia_, answer the above difficulty truly.

I can mean (for my part) nothing else by equal triangles than triangles containing equal numbers of points.