Sunday, February 1, 2009

Leibniz



In The World As Will And Representation, Arthur Schopenhauer says Immanuel Kant's idea that space is not a material object can first be found in Pierre Maupertuis.

In Volume II, Chapter IV, Schopenhauer writes:

But what are we to say when we find Kant's most important and brilliant doctrine, that of the ideality of space and of the merely phenomenal existence of the corporeal world, expressed already thirty years previously by Maupertuis? ... Maupertuis expresses this paradoxical doctrine so decidedly, and yet without the addition of proof, that it must be supposed that he also obtained it from somewhere else. It is very desirable that the matter should be further investigated, and as this would demand tiresome and extensive researches, some German Academy might very well make the question the subject of a prize essay.
Well it turns out Schopenhauer was right. It wasn't Kant or Maupertuis's original idea. It was Leibniz's and he may have gotten it from Descartes and Aristotle.

"Space without matter is something imaginary." -- Gottfried W. Leibniz, polymath, 1689

"There is no vacuum." -- Gottfried W. Leibniz, polymath, 1689

Leibniz has always been the antidote to Newton as Leibniz thought Newton's gravity hypothesis was utterly absurd (probably because it is).

"Like Huygens, Leibniz never accepted Newtonian gravitation." -- Ezio Vailati, philosopher, 1997

And Leibniz stated General Relativity in 1689 with no need for gravity:

"Since we have already proved through geometrical considerations the equivalence of all hypotheses with respect to the motions of any bodies whatsoever, however numerous, moved only by the collision with other bodies, it follows that not even an angel could determine with mathematical rigor which of the many bodies of that sort is at rest, and which is the center of motion for the others." -- Gottfried W. Leibniz, polymath, 1689

"To summarize my point, since space without matter is something imaginary, motion, in all mathematical rigor, is nothing but a change in the position [situs] of bodies with respect to one another, and so, motion is not something absolute, but consists in relation. This already follows from the Aristotelian definition of place, for motion is the change of place, and place is the surface of the surrounding body, so when this changes, motion occurs, and either the surrounding body or the thing in the place can be assumed to have moved away, leaving the other at rest." -- Gottfried W. Leibniz, polymath, 1689

"When formerly I regarded space as an immovable real place, possessing extension alone, I had been able to define absolute motion as change of this real space. But gradually I began to doubt whether there is in nature such an entity as is called space; whence it followed that a doubt might arise about absolute motion." -- Gottfried W. Leibniz, polymath, 1695 (quoted by Russell 1900)

"...to establish it [gravity] as original or primitive in certain parts of matter is to resort either to miracle or an imaginary occult quality." -- Gottfreid W. Leibniz, polymath, July 1710

Leibniz, G.W., On Copernicanism and the Relativity of Motion, 1689

Leibniz, G.W., First Letter To Hartsoeker, 1710

Schopenhauer, A., The World as Will and Idea, Volume II, 1819

Russell, B., A Critical Exposition of the Philosophy of Leibniz, 1900

Jolley, N., The Cambridge Companion to Leibniz, 1995

Vailati, E., Leibniz & Clarke: A Study of Their Correspondence, 1997

Schönfeld, M., The Philosophy of the Young Kant, 2000

8 comments:

Quantum_Flux said...

Yeah, well, it was Newton's Theory of Gravitation that allowed NASA to put a man on the moon.

Where does that leave Leibniz except for in the same boat as the dogmatic Pope who also didn't believe in Newtonian Gravitation? I think it was Leibniz who was incorrect and that it was Newton who was correct in that one.

Seth said...

The Naval Academy still teaches Ptolemaic astronomy for celestial navigation purposes, because it is extremely precise and easy to calculate. It is not, however, an accurate picture of reality, just mathematically precise. The same is true for Gravity and the Theories of Relativity. They work, but are not true.

OilIsMastery said...

QF, how did Newton's hypothesis of gravitation allow NASA to put a man on the moon?

Leibniz invented the differential calculus that allowed NASA to put a man on the moon. No gravity required.

Seth,

For the most part I agree although I couldn't tell you in what sense epicycles and Dark Matter are extremely precise and accurate.

Quantum_Flux said...

The calculus that is required for landing humans on the moon requirs the computation of the amount of fuel necessary to navigate from gravitational orbit around the Earth to the gravitational orbit around the Moon.

By the way, Leibniz never developed the vector calculus necessary to perform such a trip, Newton did.

OilIsMastery said...

Newton's gravitational hypothesis never predicted how much fuel it would require to land on the moon. According to Newton's gravitational hypothesis it requires zero fuel since, according to Newton, without divine intervention the moon should fall to the Earth at 9.8 meters/second squared.

Quantum_Flux said...

No, but you can't deny that the gravitational formulas:

F = G*M1*Mo/(ro1)^2 = Mo*(V)^2/(ro1)

U = G*M1*Mo/(ro1) = (1/2)*Mo*V^2

Were used.

Quantum_Flux said...

Newton's predictions do not say the moon has a gravitational acceleration toward the Earth of 9.81 m/s^2 at all, but it did show that an approximation for the gravitational rate of acceleration toward the Earth at Sea Level has that value.

Seth said...

OilIsMastery, The theory of epicycles is precise in the sense that using it, you can predict with precision where a planet will be in the night sky many years into the future. The theory of gravity under the general theory of relativity lets us predict with certain verifiable precision, say, to what degree light will be bent when passing around a star. Dark matter does not allow precise predictions at all.