Newton’s Influence on Kant:
Forces in the
Metaphysical Foundations of
Dynamics
Jonathan Everett
Department of Science and Technology Studies
UCL
Jonathan.everett.09@ucl.ac.uk
1
Introduction
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
• Aims:
1. Examine Kant’s concept of force in the
Dynamics.
2. Assess Friedman’s reading of
Metaphysical Foundations (MFNS) in
light of this.
A suggested
reading of MFNS
2
Jonathan Everett – UCL – Dept. Science and Technology Studies
MFNS as a Critical Project
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
• Friedman: MFNS should be understood as attempt to ground
Newtonian mechanics within Critical project.
• Evidence:
1. Concerned with Newton:
• Many mentions of Newton throughout, broadly
concerned with same are of science.
2. Critical project:
• Expresses need for critical analysis of mathematical
sciences.
• Carries matter through all 4 functions of judgement.
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Jonathan Everett – UCL – Dept. Science and Technology Studies
Some supporting quotes
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
• “Thus these mathematical physicists could certainly not avoid
metaphysical principles, and among those certainly not such as make the
concept of their proper object, namely matter, a priori suitable for
application to outer experience: as the concepts of motion, the filling of
space, inertia etc. However they rightly held that to let merely empirical
principles govern these concepts would be absolutely inappropriate to the
apodictic certainty they wished their laws of nature to possess; they
therefore preferred to postulate such principles, without investigating them
in accordance with their a priori source.”(4:472)
•“The concept of matter had therefore to be carried through all four of the
indicated functions of the concepts of the understanding (in four chapters),
where in each a new determination of this concept was added.” (4:476)
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Jonathan Everett – UCL – Dept. Science and Technology Studies
An alternative reading
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
• In pre-critical work Kant undertook to
reconcile aspects of Leibniz’s philosophy
with Newton’s natural science.
• MFNS also serves to bring aspects of preCritical work in to line with Critical turn.
A suggested
reading of MFNS
5
Jonathan Everett – UCL – Dept. Science and Technology Studies
Part 1
“Matter fills a space…through a
particular moving force”
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Jonathan Everett – UCL – Dept. Science and Technology Studies
Matter in the Dynamics
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
• Matter fills a space, not through its mere
existence, but through a particular moving
force. (4:496)
• Mechanical: matter fills space through its
solidity, it is incompressible
• Dynamical: matter fills space through
repulsive force, it is compressible
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Jonathan Everett – UCL – Dept. Science and Technology Studies
Kant’s Proof
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
“Penetration into a space (in the initial moment this is called a
striving to penetrate) is a motion. Resistance to motion is the cause
of its diminution, or even the change of this motion into rest. Now
nothing can be combined with a motion, which diminishes it or
destroys it, except another motion of precisely the same moveable in
the opposite direction (Phoron. Prop.). Therefore, the resistance that
a matter offers in the space that it fills to every penetration by other
matters is a cause of the motion of the latter in the opposite direction.
But the cause of motion is called a moving force. Thus matter fills its
space through a moving force, and not through its mere existence.”
(4:497)
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Jonathan Everett – UCL – Dept. Science and Technology Studies
Kant’s question
MFNS: A Critical
Project?
But:
A particular
moving force…
The Balancing
Argument
What are the consequences of matter filling space
through a repulsive force?
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
9
Jonathan Everett – UCL – Dept. Science and Technology Studies
Part 2
The balancing argument
Jonathan Everett – UCL – Dept. Science and Technology Studies
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Repulsion-entails-Attraction
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
•
•
Matter has this tendency to expand, and,
There is no limit to the extension of this repulsive force “because
smaller degrees are possible to infinity for any moving force”.
Therefore:
• “matter, by its repulsive force…would, alone and if no other
moving force counteracted it, be confined within no limit of
extension; that is it would disperse itself to infinity, and no
specified quantity of matter would be found in any specified
space. Therefore, with merely repulsive forces all spaces would
be empty, and thus, properly speaking, no matter would exist at
all.” (4:508)
Jonathan Everett – UCL – Dept. Science and Technology Studies
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The Modus Tollens Formulation
MFNS: A Critical
Project?
(i)
A particular
moving force…
The Balancing
Argument
(ii)
Are Kant’s forces
Newtonian?
(iii)
If P then Q: if matter fills space only through
repulsive force then “no specified quantity of
matter would be found in any specified space”.
¬Q: but specified quantities of matter are
found.
Therefore ¬P: therefore matter cannot
fill space through repulsive force alone.
A suggested
reading of MFNS
Jonathan Everett – UCL – Dept. Science and Technology Studies
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An interpretive problem
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
So, in setting the argument out in modus tollens form,
it is clear that it is not very good.
How should we interpret it?
• Friedman: treats argument as a transcendental one.
• Warren: perhaps there is a hidden assumption…
A suggested
reading of MFNS
Jonathan Everett – UCL – Dept. Science and Technology Studies
13
Friedman’s defence of the argument
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
“In the simplest case of hydrostatic equilibrium, for example,
atmospheric air is maintained in an equilibrium state by a balancing of
its internal expansive pressure by the gravitational attraction of the
earth—the “weight” of the air towards the (center of) the earth—where
this weight or compressive pressure depends on the height above the
earth’s surface: the higher the region of the atmosphere under
consideration, the smaller is the weight of the air. It is necessary for a
state of equilibrium, then, that the air form concentric layers above the
earth’s surface where, at equal distances from the surface, all points of a
given layer have the same pressure and density, such that, as the
distance increases, the pressure and density decrease accordingly.”
(2010, p.609)
Jonathan Everett – UCL – Dept. Science and Technology Studies
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Part 3
Are Kant’s forces Newtonian?
Jonathan Everett – UCL – Dept. Science and Technology Studies
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A clue…
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
“Rather it would be far more appropriate to call dead forces
those, such as the original moving forces of dynamics, whereby
matter acts on another, even when we abstract completely from
its own inherent motion, and also even from its striving to move;
by contrast one could call living forces all mechanical moving
forces, that is, those moving by inherent motion without
attending to the differences of speed, whose degree may be
infinitely small—if in fact these terms for dead and living forces
still deserve to be retained.” (4:539)
A suggested
reading of MFNS
Jonathan Everett – UCL – Dept. Science and Technology Studies
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Translation problems
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
“The merely dynamical concept [of matter] could consider
matter also as at rest; for the moving force there dealt with
had merely to do with the filling of a certain space,
ohne daßone’s
die Materie,
die ihn erfüllte,
selbst the
als bewegt
without
being permitted
to regard
matter
angesehen
werden
durfte.
that filled the
space
as being itself moved.
without the matter filling it needing to be seen as itself moved.
Repulsion was therefore an originally moving force for
imparting motion. In mechanics by contrast, the force of
matter set in motion is considered as communicating this
motion to another.” (4:536, my underlining)
Jonathan Everett – UCL – Dept. Science and Technology Studies
17
How does Kant treat force in the Dynamics?
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
“Attractive force is that moving force whereby a matter can be
the cause of the approach of matter to itself (or, equivalently,
whereby it resists the withdrawal of other matter from itself).
Repulsive force is that whereby a matter can be the cause of
making other matters withdraw from itself (or equivalently
whereby it resists the approach of other matter to itself).” (4:498)
“There can be found beyond every extensive force a greater
moving force which can work against the former and would thus
diminish the space that the extensive force is striving to expand.”
(4:500)
Jonathan Everett – UCL – Dept. Science and Technology Studies
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A possible solution
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
The Dynamics deals with situations with zero “quantity
of motion”, i.e. no inertial properties/ no “quantity of
matter”.
If force understood as affecting motion alone, rather
than “quantity of motion”, the first premises in the
balancing argument can be defended.
A suggested
reading of MFNS
Jonathan Everett – UCL – Dept. Science and Technology Studies
19
Concluding Remarks
A suggestion for reading the
Metaphysical Foundations
Jonathan Everett – UCL – Dept. Science and Technology Studies
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A suggestion for reading MFNS
MFNS: A Critical
Project?
A particular
moving force…
The Balancing
Argument
Are Kant’s forces
Newtonian?
A suggested
reading of MFNS
• Is this not, in fact, even less charitable to Kant to
say that he's mistaken about force than allowing the
balancing argument just to be bad?
• Kant's forces are more Newtonian in the Mechanics:
point is that they are not yet Newtonian in the
Dynamics.
• MFNS should be read "cumulatively"
• Such a reading assigns Kant's pre-Critical work a
crucial role to play in overall argument of MFNS.
Jonathan Everett – UCL – Dept. Science and Technology Studies
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Bibliography
• Friedman, M. (2010): ‘Synthetic History Reconsidered’,
in Domski & Dickson (eds.) Discourse on a New Method.
• Kant, I. (1786): Metaphysical Foundations of Natural
Science, trans. M. Friedman (CUP, 2004)
• Warren, D. (2010): ‘Kant on attractive and repulsive
force: the balancing argument’, in Domski & Dickson
(eds.) Discourse on a New Method.
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Newton’s Influence on Kant:
Forces in the
Metaphysical Foundations of
Dynamics
Jonathan Everett
Department of Science and Technology Studies
UCL
Jonathan.everett.09@ucl.ac.uk
23