Transcript Slides - Faculty of Philosophy

A Kantian Legacy in History and Philosophy of
Science
Michael Friedman
Oxford
December 2, 2015
The Postulates of Empirical Thought
1. Whatever agrees with the formal conditions of experience (in accordance 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)
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
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)
[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)
The three Laws of Mechanics in the Metaphysical Foundations
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
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)
KEPLER
LUG
Kant and Newton
(Dynamics)
Proposition 7: The attraction essential to all matter is an
immediate action of it on others through empty space. (512)
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)
Kant and Newton
(Dynamics)
Proposition 7: The attraction essential to all matter is an
immediate action of it on others through empty space. (512)
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)
Kant and Newton
(Dynamics)
B
r
aB
aB = kA/r2
A
“acceleration field” property
Kant and Newton
(Dynamics)
a1 = kS/r12
r1
a1
a2 = kJ/r22
r
a2
immediacy
&
universality
r2
aJmJ = - aSmS
aJ/aS = kS/kJ = mS/mJ
accelerations proportional to mass
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)
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.
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.
Principia, General Scholium to Book 3
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.
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.
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)
Preface to the Metaphysical Foundations
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)
Preface to the Metaphysical Foundations
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)
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)
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
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)
Introduction to the Critique of Pure Reason (B)
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)
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.
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)
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.
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.
2. But we must assume that gravitational force, in particular, has
the mathematical properties required in order to facilitate theorymediated measurements of both this force itself and other centrally
important related quantities.
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.
2. But we must assume that gravitational force, in particular, has
the mathematical properties required in order to facilitate theorymediated measurements of both this force itself and other centrally
important related quantities.
3. Prominent among the latter is quantity of matter, the measurement of which, in the theory of universal gravitation, involves the
direct application of action = reaction (conservation of momentum)
between arbitrarily distant bodies.
Kant and Newton
(morals)
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).
Kant and Newton
(morals)
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.
Kant and Newton
(morals)
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.
Kant and Newton
(morals)
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.
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)
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).
Kant and Einstein
(the electro-magnetic field)
Kant and Einstein
(the electro-magnetic field)
1857-1894
Hertz’s experiments with radio waves securely established the
“structural” properties of the electro-magnetic field via theorymediated 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
(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.
Kant and Einstein
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
(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.
Kant and Einstein
(the electro-magnetic field)
Hertz’s experiments with radio waves securely established the
“structural” properties of the electro-magnetic field via theorymediated 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
The Preface to the Metaphysical Foundations
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
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)
The Preface to the Metaphysical Foundations
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)
The Preface to the Metaphysical Foundations
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
Kant’s Metaphysics of Experience
Kant’s Metaphysics of Experience
Kant’s Metaphysics of Experience
1643-1727
1724-1804
1646-1716
The Relativized (but still Constitutive) A Priori
1851-1953
MF on Scientific Revolutions
MF on Scientific Revolutions
MF on Scientific Revolutions
The “a priori sources” of Constitutive Principles
Such principles are a (synthetic) priori in the relativized sense as
enabling conditions for a procedure of theory-mediated measurement capable of bestowing a more than inductive and more than
hypothetical epistemic status on properly empirical laws.
The “a priori sources” of Constitutive Principles
Such principles are a (synthetic) priori in the relativized sense as
enabling conditions for a procedure of theory-mediated measurement capable of bestowing a more than inductive and more than
hypothetical epistemic status on properly empirical laws.
The “a priori sources” of Constitutive Principles
Such principles are a (synthetic) priori in the relativized sense as
enabling conditions for a procedure of theory-mediated measurement capable of bestowing a more than inductive and more than
hypothetical epistemic status on properly empirical laws.
The “a priori sources” of Constitutive Principles
Such principles are a (synthetic) priori in the relativized sense as
enabling conditions for a procedure of theory-mediated measurement capable of bestowing a more than inductive and more than
hypothetical epistemic status on properly empirical laws.
The “a priori sources” of Constitutive Principles
Such principles are a (synthetic) priori in the relativized sense as
enabling conditions for a procedure of theory-mediated measurement capable of bestowing a more than inductive and more than
hypothetical epistemic status on properly empirical laws.