a kantian legacy in history and philosophy of science michael friedman oxford december 2, 2015

A Kantian Legacy in History and Philosophy of Science

Michael FriedmanOxford

December 2, 2015

1. Whatever agrees with the formal conditions of experience (in accor-dance with intuition and concepts) is possible.

2. That which is connected with the material conditions of experience (of sensation) is actual.

3. That whose connection with the actual is determined in accordance with general conditions of experience is (exists) necessarily.

(A218/B265-6)

The Postulates of Empirical Thought

Since the word nature already carries with it the concept of laws, and the latter carries with it the concept of the necessity of all determinations of a thing belonging to its existence, one easily sees why natural science must derive the legitimacy of this title only from its pure part—namely, that which contains the a priori principles of all other natural explanations—and why only in virtue of this pure part is natural science to be proper science. (Preface: 468-9)

Metaphysical Foundations of Natural Science

Since the word nature already carries with it the concept of laws, and the latter carries with it the concept of the necessity of all determinations of a thing belonging to its existence, one easily sees why natural science must derive the legitimacy of this title only from its pure part—namely, that which contains the a priori principles of all other natural explanations—and why only in virtue of this pure part is natural science to be proper science. (Preface: 468-9)

Metaphysical Foundations of Natural Science

[N]o law of either attractive or repulsive force may be risked on a priori conjectures. Rather, everything, even universal attraction as the cause of weight [Schwere], must be inferred, together with its laws, from data of experience. (Dynamics: 534)

1. In all alterations of corporeal nature the total quantity of matter remains the same, neither increased nor diminished. (4, 541)

2. All alterations of matter have an external cause. (Every body persists in its state of rest or motion, in the same direction and with the same speed, if it is not compelled by an external cause to leave this state.) (543) 3. In all communication of motion action and reaction are always equal to one another. (544)

The three Laws of Mechanics in the Metaphysical Foundations



The three Laws of Mechanics in the Metaphysical Foundations

LUGKEPLER

Kant and Newton(Dynamics)

Remark 2: [I]t is clear that the offense taken by his contemporaries, and perhaps even by Newton himself, at the concept of an original attraction set him at variance with himself: for he could absolutely not say that the attractive forces of two planets, e.g., of Jupiter and Saturn, manifested at equal distances of their satellites (whose mass is unknown), are proportional to the quantity of matter of these heavenly bodies, if he did not assume that they attracted other matter merely as matter, and thus according to a universal property of matter. (515)

Proposition 7: The attraction essential to all matter is an immediate action of it on others through empty space. (512)


A

B

aB

aB = kA/r2

r

“acceleration field” property


a1 = kS/r12

r1

r

a2 = kJ/r22

aJmJ = - aSmS

aJ/aS = kS/kJ = mS/mJ

a1

a2

r2

accelerations proportional to mass

immediacy&

universality

Proposition 7, Remark 2: [O]ne cannot adduce this great founder of the theory of attraction as one’s predecessor, if one takes the liberty of substituting an apparent attraction for the true attraction he did assert, and assumes the necessity of an impulsion through impact to explain the phenomenon of approach. He rightly abstracted from all hypotheses purporting to answer the question as to the cause of the universal attraction of matter, for this question is physical or metaphysical, but not mathematical. And, even though he says in the advertisement to the second edition of his Optics, “to show that I do not take gravity for an essential property of bodies, I have added one question concerning its cause,” it is clear that the offense taken by his contemporaries, and perhaps even by Newton himself, at the concept of an original attraction set him at variance with himself. (Dynamics: 515)

Kant and Newton(Principia, Book 1, Proposition 1)

Kant and Newton(Principia, Book 1, Proposition 1)

mathematical properties of forces can be derived from those of the corresponding motions

Kant and Newton(Principia, Book 3)

Proposition 3: The force by which the moon is maintained in its orbit is directed toward the earth and is inversely as the square of the distance of its places from the center of the earth. [T]he second part [is evident] from the very slow motion of the moon’s apogee. [calculation of how the exponent is just a little greater than 2] Now this motion of the apogee arises from the action of the sun (as will be pointed out below) and accordingly is to be ignored here.

Phenomenon 6: The moon, by a radius drawn to the center of the earth, describes areas proportional to the times. Actually, the motion of the moon is somewhat perturbed by the force of the sun, but in these phenomena I pay no attention to minute errors that are negligible.

I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses [hypotheses non fingo]. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this experimental philosophy, propositions are deduced from the phenomena and made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method. And it is enough that gravity should really exist, and act according to the laws that we have set forth and suffice for the explanation of all the motions of the heavenly bodies and of our sea.

Principia, General Scholium to Book 3

Pure rational cognition from mere concepts is called pure philosophy or metaphysics; by contrast, that which grounds its cognition only on the construction of concepts, by means of the presentation of the object in an a priori intuition, is called mathematics.

Preface to the Metaphysical Foundations

Pure rational cognition from mere concepts is called pure philosophy or metaphysics; by contrast, that which grounds its cognition only on the construction of concepts, by means of the presentation of the object in an a priori intuition, is called mathematics. Properly so-called natural science presupposes, in the first place, metaphysics of nature. For laws, that is, principles of the necessity of that which belongs to the existence of a thing, are concerned with a concept that cannot be constructed, since existence cannot be presented a priori in any intuition. (469)


Now to cognize something a priori means to cognize it from its mere possibility. But the possibility of determinate natural things cannot be cognized from their mere concepts; for from these the possibility of the thought (that it does not contradict itself) can certainly be cognized, but not the possibility of the object, as a natural thing that can be given outside the thought (as existing). Hence, in order to cognize the possibility of determinate natural things, and thus to cognize them a priori, it is still required that the intuition corresponding to the concept be given a priori, that is, that the concept be constructed. (470)


Pure rational cognition from mere concepts is called pure philosophy or metaphysics; by contrast, that which grounds its cognition only on the construction of concepts, by means of the presentation of the object in an a priori intuition, is called mathematics. Properly so-called natural science presupposes, in the first place, metaphysics of nature. For laws, that is, principles of the necessity of that which belongs to the existence of a thing, are concerned with a concept that cannot be constructed, since existence cannot be presented a priori in any intuition. (469)


These, then, are the three analogies of experience. They are nothing else but the principles for the determination of the existence of appearances in time with respect to all of its three modes, the relation to time itself as a magnitude (the magnitude of existence, i.e., duration), the relation in time as a series (successively), and finally [the relation] in time as a totality of all existence (simultaneously). This unity of time determination is thoroughly dynamical; that is, time is not viewed as that in which experience immediately determines the place of an existent, which is impossible, because absolute time is no object of perception by means of which appearances could be bound together; rather, the rule of the understanding, by means of which alone the existence of the appearances can acquire synthetic unity with respect to temporal relations, determines for each [appearance] its position in time, and thus [determines this] a priori and valid for each and every time. (A215/B262)



The Laws of Mechanics in the Metaphysical Foundations

Of these sciences [pure mathematics and pure natural science] one can appropriately ask: how are they possible; for that they must be possible is demonstrated by their actuality.*

*Some may still have doubts concerning the latter. But one need merely consider the various propositions that come forth at the outset of proper (empirical) physics, such as those of the permanence of the same quantity of matter, of inertia, of the equality of action and reaction, etc., and one will be quickly convinced that they constitute a physica pura (or rationalis), which well deserves to be separately established, as a science of its own, in its whole extent, whether narrow or wide. (B20-21/n)

Introduction to the Critique of Pure Reason (B)

Now how in general anything can be altered, how it is possible that upon a state at one point of time an opposite one could follow in the next—of these we have a priori not the least concept. For this acquaintance with actual forces is required, which can only be given empirically, e.g., the moving forces, or, what is the same, certain successive appearances (as motions), which indicate such forces.

Moving forces in the Second Analogy

Now how in general anything can be altered, how it is possible that upon a state at one point of time an opposite one could follow in the next—of these we have a priori not the least concept. For this acquaintance with actual forces is required, which can only be given empirically, e.g., the moving forces, or, what is the same, certain successive appearances (as motions), which indicate such forces.

One should well note that I do not speak of the alteration of certain relations in general, but rather of alteration of state. Therefore, if a body moves uniformly it does not alter its state (of motion) at all, but it certainly does if its motion increases or decreases. (A206-207/B252/n)

Moving forces in the Second Analogy

Kant and Newton(morals)

1. Kant accepts Newton’s abstract treatment of impressed force as a measurable mathematical magnitude, considered independently of any hypotheses concerning underlying mechanisms.


1. Kant accepts Newton’s abstract treatment of impressed force as a measurable mathematical magnitude, considered independently of any hypotheses concerning underlying mechanisms.2. But we must assume that gravitational force, in particular, has the mathematical properties required in order to facilitate theory-mediated measurements of both this force itself and other centrally important related quantities.

1. Kant accepts Newton’s abstract treatment of impressed force as a measurable mathematical magnitude, considered independently of any hypotheses concerning underlying mechanisms.2. But we must assume that gravitational force, in particular, has the mathematical properties required in order to facilitate theory-mediated measurements of both this force itself and other centrally important related quantities.3. Prominent among the latter is quantity of matter, the measure-ment of which, in the theory of universal gravitation, involves the direct application of action = reaction (conservation of momentum) between arbitrarily distant bodies.


4. This kind of abstract “structural” conception is not a version of contemporary “structural realism.” Rather, it concerns the methodological use of theory-mediated measurements in ongoing inferences that are more secure than either inductive (curve-fitting) or hypothetico-deductive arguments (George Smith).



5. The greater security of such inferences is a centrally important part of Kant’s anti-Humean conception of causal necessity.



6. These inferences are subject to later refinements along new and unanticipated dimensions that may become clear only post hoc.




6. These inferences are subject to later refinements along new and unanticipated dimensions that may become clear only post hoc.

7. Kant is less explicit about—and in the end less open to—such refinements than is Newton (but see A662-3/B690-1)



Kant and Newton(gravitational perturbations)

[W]e arrive at unity of the genera of these paths according to their form [at circular, elliptic, parabolic, and eventually hyperbolic orbits]; and we thereby further arrive, however, at unity of the cause of all the laws of their motion (i.e., gravitation). From there we afterwards extend our conquests further, seeking also to explain all variations and apparent deviations from these rules from the same principle. (A663/B691)

Kant and Newton(gravitational perturbations)

[W]e arrive at unity of the genera of these paths according to their form [at circular, elliptic, parabolic, and eventually hyperbolic orbits]; and we thereby further arrive, however, at unity of the cause of all the laws of their motion (i.e., gravitation). From there we afterwards extend our conquests further, seeking also to explain all variations and apparent deviations from these rules from the same principle. (A663/B691)

The Newtonian explanation breaks down, however, in the case of the perihelion of Mercury; it is then replaced by the Einsteinian explanation, which essentially involves a non-Euclidean spatial geometry.

Kant and Einstein

Kant and Einstein(the electro-magnetic field)

The Maxwell field is an abstract measurable magnitude, like Newtonian gravitational force. Unlike the latter, however, this field of force is dynamical—and, in particular, it is propagated through space with a definite finite velocity c. It is thus an “actor” in the physical world along with the matter upon which it acts (Howard Stein).


Hertz’s experiments with radio waves securely established the “structural” properties of the electro-magnetic field via theory-mediated measurements, just as the corresponding properties of gravitational force were similarly established by Newton’s “deductions from the phenomena.” Hertz thereby experimentally realized, in particular, the Maxwellian displacement current (Stein).


1857-1894

Kant and Einstein(Maxwell vs. Newton)

The light-cone is not Galilean invariant. The “structural” properties of Maxwellian (finitely propagated) causality are in fundamental ten-sion with those of Newtonian (instantaneously propagated) causality.

Space-time itself is Lorentz invariant. The “structural” properties of Maxwellian (finitely propagated) causality are also those of the new spatio-temporal background structure (Minkowski space-time).

Kant and Einstein

Interferometer experiments of Michelson, Morley, et. al. securely established these “structural” properties of the spatio-temporal background structure in the same sense that the corresponding properties of the Maxwell field were established by Hertz.

Kant and Einstein

Kant and Einstein(general relativistic space-time)

Kant and Einstein(general relativistic space-time)

The variable light-cone structure determines the two species of four-dimensional geodesics representing motions in a

gravitational field: time-like and light-like.

Kant and Einstein(bending of light in a gravitational field)

three-dimensional spatial geometry of variable negative curvature

Kant and Einstein

Observations and photographic measurements established these “structural” relations between Einsteinian and Newtonian gravity in the same sense as in the previous experiments.

Hertz’s experiments with radio waves securely established the “structural” properties of the electro-magnetic field via theory-mediated measurements, just as the corresponding properties of gravitational force were similarly established by Newton’s “deductions from the phenomena.” Hertz thereby experimentally realized, in particular, the Maxwellian displacement current (Stein).


Kant and Einstein

Interferometer experiments of Michelson, Morley, et. al. securely established the “structural” properties of the spatio-temporal background structure in the same sense that the corresponding properties of the Maxwell field were established by Hertz.

Kant and Einstein

Observations and photographic measurements established the “structural” relations between Einsteinian and Newtonian gravity in the same sense as in the previous experiments.

Kant’s Metaphysics of Experience

Hence all natural philosophers who have wished to proceed mathematically in their occupation have always, and must have always, made use of metaphysical principles (albeit unconsciously), even if they themselves solemnly guarded against all claims of metaphysics upon their science. Undoubtedly they have understood by the latter the folly of contriving possibilities at will and playing with concepts, which can perhaps not be presented in intuition at all, and have no other certification of their objective reality than that they merely do not contradict themselves. (472)

The Preface to the Metaphysical Foundations

All true metaphysics is drawn from the essence of the faculty of thinking itself, and it is in no way fabricated [erdichtet] on account of not being borrowed from experience. Rather, it contains the pure actions of thought, and thus a priori concepts and principles, which first bring the manifold of empirical representations into the law-governed connection through which it can become empirical cognition, that is, experience. (472)


Thus these mathematical physicists could in no way avoid metaphysical principles, and, among them, also not those that make the concept of their proper object, namely, matter, a priori suitable for application to outer experience, such as the concept of motion, the filling of space, inertia, and so on. But they rightly held that to let merely empirical principles govern these concepts would in no way be appropriate to the apodictic certainty they wished their laws of nature to possess, so they preferred to postulate such [principles], without investigating them with regard to their a priori sources. (472)


Newton’s Axioms or Laws of Motion


1643-1727 1724-1804 1646-1716

The Relativized (but still Constitutive) A Priori

1851-1953

MF on Scientific Revolutions

The “a priori sources” of Constitutive PrinciplesSuch principles are a (synthetic) priori in the relativized sense as enabling conditions for a procedure of theory-mediated measure-ment capable of bestowing a more than inductive and more than hypothetical epistemic status on properly empirical laws.

a kantian legacy in history and philosophy of science michael friedman oxford december 2, 2015

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