Leibniz Rationalism vs. Newton Empricism. Newtons space Three dimensional Infinite (in all...

Leibniz Rationalism vs. Newton Empricism

Newton’s space

Three dimensional

Infinite (in all directions)

Homogeneous (isotropic)

Newton’s time

t

Newton’s absolute space

A “stage” where all physical phenomena take place:3-d, infinite, homogeneous;Not affected by the phenomena;“Rest” means “absolute rest”.

t

Newton’s absolute space

t

Absolute space, in its own nature, without relation to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is commonly taken for immovable space; … Absolute and relative space are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the earth remains always the same, will at one time be one part of the absolute space into which the air passes …

Newton’s absolute time

t

Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Absolute simultaneity is possible!

The fixed stars:

t

But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes, and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions, whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.

Gottfried Wilhelm Leibniz (1646-1716)


Time consists only in the successive Order of Things

Space consists only in the Order of coexisting Things

Relative Space and Time


Time consist only in the successive Order of Things … I hold space to be an Order of Coexistences, as Time is an Order of Successions. For Space denotes, in Terms of Possibility, an Order of Things which exist at the same time, considered as existing together; without enquiring into their Manner of Existing.


An extreme rationalist

Metaphysics is prior to physics

His philosophical ideal: to understand the world (including God) via the ratio

Leading Principle: the pre-established harmony between nature and human understanding

A committed empiricist

Relative time and space



Physics is prior to metaphysics

Absolute time and space

The Newton-Leibniz Controversy

A Clash of Titans

Caroline, Marquees of

Brandenburg-Ansbach

(1683-1737)

Princess of Wales – 1714

Queen of England – 1727 (George II)

Caroline, Marquees of

Brandenburg-Ansbach

(1683-1737)

Leibniz became her preceptor at Hannover – 1704

Corresponded until Leibniz’s death - 1717

The Newton-Leibniz ControversyA clash of Titans

Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Newton’s Theory threatens the status of religious belief in England!!”

Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Natural Religion it self, seems to decay [in England] very much. Many will have Human Souls to be material: Others make God himself a corporeal Being.”

Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Sir Isaac Newton says, that Space is an Organ, which God makes use of to perceive Things by. But if God stands in need of any Organ to perceive Things by, it will follow, that they do not depend altogether upon him, nor were produced by him.”

Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Sir Isaac Newton, and his Followers, have also a very odd Opinion concerning the Work of God. According to their Doctrine, God Almighty wants to wind up his Watch from Time to Time: Otherwise it would cease to move. He had not, it seems, sufficient Foresight to make it a perpetual Motion. Nay, the Machine of God's making, is so imperfect, according to these Gentlemen; that he is obliged to clean it now and then by an extraordinary Concourse, and even to mend it, as a Clockmaker mends his Work; ”

Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Who must consequently be so much the more unskilful a Workman, as he is oftner obliged to mend his Work and to set it Right. According to My Opinion, the same Force and Vigour remains always in the World, and only passes from one part of Matter to another, agreeably to the Laws of Nature, and the beautiful pre-established Order. And I hold, that when God works Miracles, he does not do it in order to supply the Wants of Nature, but those of Grace. Whoever thinks otherwise, must needs have a very mean Notion of the Wisdom and Power of God.”

God must necessarily intervene occasionally to tune up the solar system and restore order

Is the universe stable?



Nov. 1715: Leibniz to Caroline of Ansbach, Princess of Wales“Newton’s Theory threatens the status of religious belief in England!!”

The Princess to Samuel Clarke: “What?”

Samuel Clarke (1645-1729): Anglican priest, close to Newton

Leibniz-Clark Correspondence

10 Letters1715-1716


• Space and Time: absolute or relative

• Space as the “Sensorium Dei”

• Existence or inexistence of the void

• The need for God’s continual intervention in the functioning of the universe

• The mysterious nature of gravitation

• The principle of sufficient reason

• The principle of the identity of indiscernibles


10 Letters1715-1716


1709-1716: priority controversy on the calculus

1713: the Royal Society establishes a committee to discuss it

The decision: Newton invented – Leibniz copied


10 Letters1715-1716


May 10, 1715 (Leibniz to Caroline): A French journalist has suggested that the dispute is between Germany and England rather than simply between Leibniz and Newton. Consequently, king Georg I should appoint him historiographer of England to demonstrate that Leibniz was esteemed as much as Newton, who was then Minister of the Mint, and thus to restore the honor of Hanover and Germany.

A committed empiricist

Relative time and space



Physics is prior to metaphysics

Absolute time and space

Physics vs. Metaphysics

Leibniz’s rationalist theology

God's Perfection requires, that all his Actions should be agreeable to his Wisdom; and that it may not be said of him, that he has acted without Reason; or even that he has prefer'd a weaker Reason before a stronger.

Principle of the Want of a Sufficient Reason



There are not in Nature two real, absolute Beings, indiscernible from each other; because if there were, God and Nature would act without Reason, in ordering the one otherwise than the other; therefore God does not produce Two Pieces of Matter perfectly equal and alike.

Principle of the Identity of Indiscernibles



This Supposition of two Indiscernables, such as two Pieces of Matter perfectly alike, seems indeed to be possible in abstract Terms; but it is not consistent with the Divine Wisdom, by which nothing is admitted without Reason. The Vulgar fancy such Things, because they content themselves with incomplete Notions. And this is one of the Faults of the Atomists.

Principle of the Identity of Indiscernibles



The great Foundation of Mathematicks, is the principle of Contradiction, or Identity, that is, that a Proposition cannot be true and false at the same time; and that therefore A is A, and cannot be not A. This single Principle is sufficient to demonstrate every part of Arithmetick and Geometry, that is, all Mathematical Principles.

Principle of Contradiction;



But in order to proceed from Mathematicks to Natural Philosophy, another Principle is requisite: … I mean, the Principle of a sufficient Reason, viz. that nothing happens without a Reason why it should be so, rather than otherwise.

Principle of Contradiction;



I do not say, the Material World is a Machine, or Watch, that goes without God's Interposition; and I have sufficiently insisted, that the Creation wants to be continually influenc'd by its Creator. But I maintain it to be a Watch, that goes without wanting to be Mended by him: Otherwise we must say, that God bethinks himself again. No; God has foreseen every thing; He has provided a Remedy for every thing before-hand; There is in his Works a Harmony, a Beauty, already pre-established.

God’s role in the Universe



If God is oblig'd to mend the Course of Nature from time to time, it must be done either supernaturally or naturally. If it be done supernaturally, we must have recourse to Miracles, in order to explain Natural Things: Which is reducing an Hypothesis ad absurdum: For, every thing may easily be accounted for by Miracles. But if it be done naturally, then God will not be Intelligentia Supramundana: He will be comprehended under the Nature of Things; that is, He will be the Soul of the World.

God’s role in the Universe



To say that God can cause the whole Universe to move forward in a Right Line, or in any other Line, without making otherwise any Alteration in it; is another Chimerical Supposition. For, two States indiscernible from each other, are the same State; and consequently, 'tis a change without any change. Besides, there is neither Rhime nor Reason in it. But God does nothing without Reason;

On absolute space and time



It is a like fiction, (that is) an impossible one, to suppose that God might have created the World some Millions of Years sooner. They who run into such kind of Fictions, can give no answer to one that should argue for the Eternity of the World. For since God does nothing without Reason, and no Reason can be given why he did not create the World sooner; it will follow, either that he has created nothing at all, or that he created the World before any assignable time, that is, that the World is Eternal.




The Author contends, that Space does not depend upon the Situation of Bodies. I answer: 'Tis true, it does not depend upon such or such a situation of Bodies; but it is That Order, which renders Bodies capable of being situated, and by which they have a Situation among themselves when they exist together; as Time isThat Order, with respect to their Successive position. But if there were no Creatures, Space and Time would be only in the Ideas of God.




In like manner, to admit a Vacuum in Nature, is ascribing to God a very imperfect Work: 'Tis violating the grand Principle of the necessity of a sufficient Reason;

On vacuum



'Tis impossible there should be any Principle to determine What Proportion of Matter there ought to be, out of all the possible degrees from a Plenum to a Vacuum, or from a Vacuum to a Plenum. Perhaps it will be said, that the one should be equal to the other: But, because Matter is more perfect than a Vacuum, Reason requires that a Geometrical Proportion should be observed, and that there should be as much more Matter than Vacuum, as the former deserves to have the preference before the latter. But then there must be No Vacuum at all; for the Perfection of Matter is to that of a Vacuum, as Something to Nothing.

On vacuum



I say then, that if Space was an absolute Being, there would Something happen, for which it would be impossible there should be a sufficient Reason. Which is against my Axiom. And I prove it thus. Space is Something absolutely Uniform; and, without the Things placed in it, One Point of Space does not absolutely differ in any respect whatsoever from Another Point of Space. Now from hence it follows, (supposing Space to be Something in it self, besides the Order of Bodies among themselves,) that 'tis impossible there should be a Reason, why God, preserving the same Situations of Bodies among themselves, should have placed them in Space after one certain particular manner, and not otherwise; why every thing was not placed the quite contrary way, for instance, by changing East into West.




But if Space is nothing else, but That Order or Relation; and is nothing at all without Bodies, but the Possibility of placing them; then those two States, the one such as it now is, the other supposed to be the quite contrary way, would not at all differ from one another. Their Difference therefore is only to be found in our Chimerical Supposition of the Reality of Space in it self. But in truth the one would exactly be the same thing as the other, they being absolutely indiscernible; and consequently there is no room to enquire after a Reason of the Preference of the one to the other.



Newton’s replies (via Clarke)

The Uniformity of all the parts of Space, is no Argument against God's acting in Any part, after what manner he pleases. God may have good reasons to create finite Beings, and Finite Beings can be but in particular Places. And, all places being originally alike, (even though Place were nothing else but the Situation of Bodies;) God's placing one cube of matter behind another equal cube of matter, rather than the other behind That; is a choice no way unworthy of the Perfections of God, though Both these Situations be perfectly equal: Because there may be very good reasons why Both the Cubes should exist, and they cannot exist but in one or other of equally reasonable Situations.




If Space was nothing but the Order of Things coexisting; it would follow, that if God should remove in a streight Line the whole Material World Entire, with any swiftness whatsoever; yet it would still always continue in the same Place: And that nothing would receive any Shock upon the most sudden stopping of that Motion. And if Time was nothing but the Order of Succession of created Things; it would follow, that if God had created the World Millions of Ages sooner than he did, yet it would not have been created at all the sooner. Further: Space and Time are Quantities; which Situation and Order are not.




It was no impossibility for God to make the World sooner or later than he did: Nor is it at all impossible for him to destroy it sooner or later than it shall actually be destroyed. As to the Notion of the World's Eternity; They who suppose Matter and Space to be the same, must indeed suppose the World to be not only Infinite and Eternal, but necessarily so; even as necessarily as Space and Duration, which depend not on the Will, but on the Existence of God. But they who believe that God created Matter in what Quantity, and at what particular Time, and in what particular Spaces he pleased, are here under no difficulty. For the Wisdom of God may have very good reasons for creating This World, at That particular Time he did.



Newton’s replies

The Rotating Bucket Experiment

The shape of the surface of water is not determined by the motion of water relative to the bucket.


Principia, Book 1: Scholium

Water moves with respect to absolute space. The motion of water is absolute motion.

If a vessel, hung by a long cord, is so often turned about that the cord is strongly twisted, then filled with water, and held at rest together with the water; after, by the sudden action of another force, it is whirled about in the contrary way, and while the cord is untwisting itself, the vessel continues for some time this motion; the surface of the water will at first be plain, as before the vessel began to move; but the vessel by gradually communicating its motion to the water, will make it begin sensibly to revolve, and recede by little and little, and ascend to the sides of the vessel, forming itself into a concave figure...



This ascent of the water shows its endeavour to recede from the axis of its motion; and the true and absolute circular motion of the water, which is here directly contrary to the relative, discovers itself, and may be measured by this endeavour. ... And therefore, this endeavour does not depend upon any translation of the water in respect to ambient bodies, nor can true circular motion be defined by such translation. ...; but relative motions...are altogether destitute of any real effect. ...It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motions of particular bodies from the apparent; because the parts of that immovable space in which these motions are performed, do by no means come under the observations of our senses.



Ernst Mach (1836-1916)

Newton’s experiment with the rotating vessel of water simply informs us, that the relative rotation of the water with respect to the sides of the vessel produces no noticeable centrifugal forces, but that such forces are produced by its relative rotation with respect to the mass of the earth and the other celestial bodies. No one is competent to say how the experiment would turn out if the sides of the vessel increased in thickness and mass till they were ultimately several leagues think. The one experiment only lies before us, and our business is, to bring it into accord with other facts known to us, and not with the arbitrary fictions of our imagination.

Science on Mechanics (1883)

Shape of Water Surface

Rel. motion of B & W

Newton: Abs. Motion of W

Mach: Rel. Motion of W & S

Initial state of rest flat none none none

B begins rotating flat yes none none

B continues rotating curved none yes yes

B suddenly stopped curved yes yes yes

Final state of rest flat none none none

Leibniz Rationalism vs. Newton Empricism

Leibniz Rationalism vs. Newton Empricism. Newtons space Three dimensional Infinite (in all...

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