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Idealization is necessary in the face of complexity
(whether consequence of non-discreteness, or on top of discreteness)
for pragmatic reasons, to effectively make statements about reality.
«The world of physics is extremely complicated, and scientific
reseach succeeded only at the price of abstraction and schematisation,
to isolate from this world groups of phenomena
und unify them in a comprehensive theory»
[Broglie 267 >, my translation]
Without idealization,
«Consider, for example, what would be required to calculate ... what we normally conceive of as
the graviational attraction between two bodies. In such a scenario there
would be no "bodies," strictly speaking; instead, there would only be an
infinitely extensive real-valued density function defined over all of space
... [And if we clarify] that we are interested in the gravitational force
excerted on a finite region, then one can imagine that the answer should
itself be a manifold, defined over the region, whose value at each point
is the net gravitional force impinging on the
point» [OOO 178 <>].
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Idealized Model of Reality
But if we "collapse the mass-density fields into point masses,"
then this is nothing ontic -- not a claim that the masses are actually point-wise
(nor an actual collapse in the real world),
but something epistemic -- we have 'created' an idealization of reality,
an idealized view of reality: a model.
«[The successes of theoretical physics] proved
that numerous categories of phenomena can be accomodated in a logical schema,
in a frame therefore which is constructed purely rationally.
...
[But:] Are static ideas, which have clear and sharp outlines,
really applicable to a moving reality of infinite complexity?»
[Broglie 267 <, my translation]
«The very term "idealization" ... is an
admission that things are not this way, which in turn betrays the fact that
the idealized circumstances -- alledged point masses, for example -- are
features of the epistemic situation, not of the ontological one. ...
[T]hese idealizations part company not only with the way the world is in
some potentially ineffable sense, but with the way that physical theory
itself registers the world as being. It is a recognition of
a theory-internal gap or split, not a recognition or partiality or
approximateness of the theory itself. Moreover, to repeat the central
point, it is a coherently structured gap, between how the theory takes the
world as being, and how the theorist must register the world, in order to
do any predictive or calculative or other kind of useful work»
[OOO 179f <>, my underlining].
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E.g. Particle and Wave - Two Competing Idealizations
«[T]he and of de Broglie's discovery does not have the direct meaning
that both waves and corpuscles exist at the same time, but has the indirect
meaning that the same physical reality admits of two possible interpretations,
... [T]he and ... does not refer to physical objects,
but to possible descriptions of physical object ... [Reichenbach 1951].»
[Compl 5].
«The corpuscle [or particle] located at a point of space
and the completely determined dynamic state represented by a strictly monchromatic wave
are ...
abstractions, which can in certain cases correspond with quite large precision
to the details of observed facts,
but which are never a precise, literal translation of the facts.»
[Broglie 270, my translation and underlining]
«In the macroscopic experiment, that is when looking at things in the large,
an unsharply defined corspuscle concept is entirely usable and adequate
for the interpretation of the facts.
But if one turns with refined methods towards the phenomena of the microscopic and atomic scale,
and if one simultaneously wants to define the image of a point-shaped corpuscle
with completely precision, then one realizes that this image is, although not wrong,
not perfectly conforming to the minute description of the observed phenomena»
[Broglie 268f]
«A physical unit [eg. electron] loses, when bound in a system,
to a large degree its individuality ...
This becomes especially clear in the case of particles of the
same nature, and from it completely unexpected consequences result,
to which the classical notions never could have lead,
but which conform with a large number of experimental facts
(new statistics, exclusion principle, etc.)»
[Broglie 271, my underlining]
Even in situations where the wave view applies,
the wave is not an ideal wave:
«[T]he wave connected with a material unit [eg. electron]
is never strictly monochromatic, it is always constituted by the overlaying
of monochromatic waves, which occupy a finite spectral interval.
The concept of dynamic state, which satisfies in macroscopic physics,
proves to be, investigated more closely, an idealization as well,
which is never strictly applicable to reality»
[Broglie 269f]
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The Individual Object Abstraction
«[I]ndividuality is not made out of purely physical stuff; it will
have to be assembled out of some kind of more expensive ingredient»
[OOO 183 <].
«[O]ne of the things that individuals have, that physical phenomena
lack, is concreteness's opposite: abstraction»
[OOO >183?]:
«In order to be distinguished from a background, a given (individual) object
must be viewed as different from that background:
... difference in the sense of being differentiable.
In order to be distinguished from other objects of the same type,
an individual must similarly be viewed as different from them:
... difference in the sense of being distinct. ...
[I]n order for an individual to be taken as a unity, any internal variation
in behavior or constitution must be ignored, or at least contained, so that
the whole can be treated as one thing - and in that sense the same.
The internal difference that is caused by my thumb's striking the space bar
does not violate the keyboard's logical integrity, its integrity as a
spatio-temporally enduring individual.
This sameness across difference ... shows that abstraction is
intrinsically implicated in the notion of an individual. It will also be
required in order to support a notion of reidentifying the same object,
at a different place or time.» [OOO 121f, my underlining]
In this picture,
«all "objects"---hammers ... trees ...---qua registered objects,
involve a degree of abstraction» [OOO 141].
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Breakdown of the Abstraction
Take the "Perseus's ship" example [Parts]:
During the voyage through the Mediterranean Sea,
one piece after the other of Perseus's ship is replaced in different ports.
In the end, none of the original parts is left.
- Is this ship the same individual, the same object
with which Perseus started his voyage?
- Or, if we collect all the replaced parts from the ports
and assemble them to a ship -
could that be the ship with which Perseus started his voyage?
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