1046 lines
75 KiB
HTML
1046 lines
75 KiB
HTML
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font color="#993366"><font face="Verdana, sans-serif"><b>S<img src="data:image/png;base64,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" name="OdkC31" align="right" width="62" height="34" border="0">econd
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law of thermodynamics.</b></font></font> The second law of
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thermo-dynamics may not seem like an issue in the nature of efficient
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causation. Its main philosophical implications are usually portrayed
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as the discovery of the inevitability of the so-called “heat death”
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of the universe. But since it is a global regularity about change, it
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does describe states of affairs that are temporally related, like
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efficient cause and effect, and having seen how it is related to the
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other global regularities, we can see that it involved in every
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connection between efficient causes and their effects. Dispositions,
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such as the shattering of a fragile object, which are the paradigm
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case of efficient causation, are irreversible structural global
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regularities, and structural causes doing work are the stuff of which
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reproductive cycles and their ontological effects are made. To start
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with the second law of thermodynamic is, therefore, to go the heart
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of the problem with apparently irreducible laws.</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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received explanation of thermo­dynamics, statistical mechanics,
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is often cited as a successful reduction of a theory to physics, but
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it is not completely successful in reducing these laws to the basic
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laws of physics. It is undoubtedly correct in taking heat energy to
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be the kinetic energy of the constituent molecules on the micro
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level, but statistical mechanics is not a reduction of the second law
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of thermo­dynamics to the basic laws of physics, because they do
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not entail that law. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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problem with the materialist reduction of the simplest case of
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entropy increase can be suggested by a very abstract puzzle about the
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direction of change in time. The second law of thermo­dynamics
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describes a regularity about change that is <i>a</i>symmetrical in
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time. But all the more basic laws of physics to which it would be
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reduced are temporally symmetrical. That is, the basic laws of
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physics can tell us, given the state of a system, how it will unfold
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over time. But those laws are just as valid for another system, just
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like the first, except that the objects (and photons) all have
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exactly opposite momentums. And they imply that the second system
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will unfold as if time were reversed in the first system. Thus, the
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basic laws of physics are symmetrical in time. But the second law of
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thermo­dynamics is not. It denies that time could be reversed.
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Entropy cannot decrease over time in an isolated system; it can only
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increase. The problem is how a time-<i>a</i>symmetrical law can be
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derived from time-symmetrical laws. This is sometimes called the
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puzzle about the “arrow of time.”<sup><a class="sdendnoteanc" name="sdendnote1anc" href="#sdendnote1sym"><sup>i</sup></a></sup>
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It is, as we shall see, the source of Loschmidt’s paradox.</font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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time-asymmetry of the tendency to randomness has an obvious
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explanation, according to spatio-materialism, because it is a regular
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change about the geometrical structures that holds of whole regions
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of dynamic processes over time. It is plausibly explained by space as
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an ontological cause, because both tendencies responsible for it are
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global change in the direction of a geometrical structure that
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resembles that of space itself. Potential energy becomes kinetic
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energy which becomes evenly distributed heat. It is the second
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tendency, the way in which kinetic energy is randomized, that is at
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issue in the reduction of the second law. What makes the tendency to
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randomness seem mysterious is overlooking the role of space itself. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Science
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does not recognize the existence of any substances not entailed by
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its efficient-cause explanations, and as we have seen, than means
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that space itself is not taken as a cause in explaining any
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phenomenon. Instead, physics gets by affirming only the truth of
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highly mathematical laws of nature and using them to predict
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quantitatively precise measurements. Though in this case, the
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mathematics is statistics, it still abstracts from the nature of
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space. Statistical mechanics is the attempt at a materialist
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reduction, rather than a spatiomaterialist reduction, and its
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inadequacy is shown by a paradox described by Loschmidt. The
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advantage of explaining the tendency to randomness to
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spatio-materialism can, therefore, be seen in how it removes that
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paradox. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
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was Boltzmann who first showed that random states of closed or
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isolated systems of material objects could be analyzed statistically.
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He defined randomness for a gas contained in a box as a <i>statistical
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equilibrium </i>about the positions and momentums of its constituent
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molecules. Although the microstate of a gas depends on the positions
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and momentums of all its molecules, many different microstates are
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indistinguishable from a macroscopic standpoint, and Boltzmann’s
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idea was to measure the probabilities of different kinds of
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macrostates by the number of different microstates that could realize
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them. This makes sense statistically, if the possible microstates of
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a gas are all equally probable. But that requires a way of measuring
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how many different kinds of microstates would realize each kind of
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macrostate, and so Boltzmann introduced the notion of a <i>six
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dimensional phase space </i>to represent the state of <i>each
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</i>molecule in the gas. Three dimensions of phase space were used to
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represent its spatial location, and another three dimensions were
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used to represent its momentum in each of the three spatial
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dimensions, giving each molecule of the gas a certain location in six
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dimensional phase space. Thus, if this phase space were divided up
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into very many, equally sized cells, each molecule would be located
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in one or another of the cells of phase space (the limits of phase
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space being determined by the total energy of the gas and the size of
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its container). But since exchanging any two molecules in different
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cells of phase space would leave the gas in the same kind of
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macrostate, Boltzmann argued that the most probable macrostate of the
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gas would be the one in which the number of ways that molecules could
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be exchanged (or permuted) among the cells is maximum, for it would
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correspond to the largest number of different possible microstates.
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That state can be shown mathematically to be the one in which the
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molecules are most evenly distributed among the cells of six
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dimensional phase space. In that kind of macrostate, the molecules
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are said to be in statistical equilibrium. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Boltzmann’s
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definition clearly refers to the same kind of macrostate that was
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described in explaining the tendency to randomness, because an even
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distribution of molecules among the cells of his six dimensional
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phase space is equivalent to an even spatial distribution <i>in three
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dimensional space</i> of the three causally relevant factors: (1) the
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locations of molecules of each rest mass, (2) their kinetic energies,
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and (3) their directions of momentum. But these are basically
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different ways of defining randomness. Boltzmann’s definition is
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<i>statistical</i>, whereas the definition of randomness we have been
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using is <i>geometrical</i>. And whereas Boltzmann’s explanation is
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based on the assumption that all the possible microstates of a gas
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are equiprobable, no such assumption is needed to define randomness
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as evenness in the distribution of each of the causally relevant
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factors in real space. That is, instead of using a six dimensional
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phase space to <i>count </i>possible microstates of certain kinds, we
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||
used a geometrical fact about the distribution of causally relevant
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factors in uniform, three dimensional space not only to <i>define
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</i>non-randomness, but also to <i>explain </i>why such systems
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evolve in the direction of randomness over time. The unevenness in
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the spatial distribution of any of those factors is what causes it to
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be evened out, because any such unevenness entails that certain
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(symmetrically interacting) molecules will be in asymmetrical
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situations, and that will make them interact in ways that tend to
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equalize their distribution in space. That tendency will continue
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until there is no longer any unevenness to drive it. It is a change
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in the geometrical structure of the whole region.</font></font></font></p>
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||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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authority of mathematics may lead some contemporary naturalists to
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argue that Boltzmann’s statistical definition of randomness is just
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a mathematically more rigorous way of stating the geometrical
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definition. But it is not, for his six dimensional phase space is a
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mathematical abstraction that precludes explaining the tendency to
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randomness geometrically. To be sure, Boltzmann’s definition of
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randomness as a statistical equilibrium implies that it is
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overwhelmingly probable that any system we happen to examine will be
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random. But that does not explain why the system has a tendency to
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become more random over time. Indeed, his statistical explanation
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denies that there is any real tendency toward randomness, if that
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means that change really has a direction in time, for it holds <i>only
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</i>that we will almost always find them in random states, if one
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samples many such systems at many different times. But that does not
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explain the tendency to randomness by showing that change really has
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that direction over time. </font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">On
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the contrary, Boltzmann’s definition of randomness gives rise to
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Loschmidt’s reversibility paradox. The basic laws of physics are
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time-symmetrical, which means that, if the molecules all have the
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same locations, but exactly opposite momentums, change will take
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place as if time were reversed. That means, as Loschmidt pointed out,
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that for every non-random microstate that evolves toward randomness,
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there must be another microstate that evolves toward non-randomness.
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Indeed, since the statistics by which Boltzmann defines randomness
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assume that every possible microstate is equally probable, his
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definition <i>implies </i>that for every non-random microstate that
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evolves toward randomness, there must be another microstate—the one
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in which the momentums of all the molecules are exactly reversed—that
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proceeds towards the non-random state. Changes in either direction
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should occur equally often. But in fact, we never observe closed
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systems becoming non-random spontaneously.<sup><a class="sdendnoteanc" name="sdendnote2anc" href="#sdendnote2sym"><sup>ii</sup></a></sup>
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</font></font></font>
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</p>
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<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
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basic source of Loschmidt’s reversibility paradox is overlooking
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space as an ontological cause. It was Boltzmann who first overlooked
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space when he argued that randomness is a “statistical equilibrium”
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about the molecules in the gas. And the reason our ontological
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explanation does not generate Loschmidt’s reversibility paradox is
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that it does not have to assume that all possible microstates of the
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system are equally probable. This is not to deny that, among the
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abstractly possible microstates that would appear to be random from
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the macroscopic standpoint, there are some that would evolve into
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non-random macrostates, if they occurred. That possibility is a
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consequence of the time symmetry of the basic laws of physics, which
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we accept as part of the essential nature of matter. But the
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geometrical explanation need not admit that such microstates <i>ever
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actually occur </i>as the result of the motion and interaction of
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molecules that are already random. Nor is that problematic, since no
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one has ever given a good reason to believe that all mathematically
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possible microstates are equally probable.<sup><a class="sdendnoteanc" name="sdendnote3anc" href="#sdendnote3sym"><sup>iii</sup></a></sup></font></font></font></p>
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<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Loschmidt’s
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||
paradox is a rigorous way of showing that the statistical definition
|
||
of randomness does not explain the time-asymmetry of this most basic
|
||
instance of the second law of thermo­dynamics. We can now see
|
||
that his reversibility paradox comes from using a statistical
|
||
approach that abstracts from the geometrical structure of space. Our
|
||
ontological reduction of the tendency to randomness avoids
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||
Loschmidt’s paradox and explains why the change has a direction in
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||
time, because instead of relying on mathematical abstractions, it
|
||
takes the wholeness of space into account as an ontological cause.
|
||
The material objects (with their kinetic energies and directions of
|
||
motion) have certain locations in the whole region, and that gives
|
||
the region the geometrical structure as a whole which is, as we have
|
||
seen, the cause of the tendency to randomness. Our ontological causes
|
||
enable us to <i>see</i> intuitively why non-random states tend to
|
||
become random over time. In the uniform geometrical structure of
|
||
space, any unevenness in the distribution of causally relevant
|
||
factors is a <i>geometrical structure </i>about the whole region of
|
||
molecules that causes them to be evened out. It puts molecules in
|
||
local situations where their motion and symmetrical, elastic
|
||
interactions will add up over time in the structure of space to
|
||
randomness, that is, toward their being evenly distributed on the
|
||
micro level. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">This
|
||
is not to deny that Boltzmann’s statistical definition may provide
|
||
thermo­dynamics with a useful way of measuring randomness (and
|
||
lack of randomness) or representing them mathematically. Indeed, the
|
||
confirmation of quantitative predictions of statistical mechanics
|
||
suggests that it is. But a measure of randomness is not the same as
|
||
an explanation of why systems tend to become random over time. For
|
||
that, we must reduce the mathematical representations to
|
||
spatio-materialist ontology. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">This
|
||
is to resolve one of the anomalies that arises in the program of
|
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reductionistic materialism, where it is assumed that regularities are
|
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explained by deducing them from the basic laws of physics, initial
|
||
and boundary conditions, and relevant mathematical theorems. Bus as
|
||
we can now see, the attempt to give an efficient-cause explanations
|
||
of the second law of thermodynamics is the mistake. It requires an
|
||
ontological explanation, that is, an explanation of the same kind
|
||
that explains why the basic laws of physics are true. Those
|
||
time-symmetrical laws physical laws are relevant in explaining this
|
||
time-asymmetrical regularity, but only because they characterize the
|
||
essential nature of the matter contained in the region of space. It
|
||
is the how such bits of matter work together with the wholeness of
|
||
space that explains the tendency to randomness, for as we have seen,
|
||
it is the geometrical structure about the distribution of any of the
|
||
three causally relevant factors that puts material objects in
|
||
situations where their behavior in accordance with physical laws will
|
||
tend to even out their distribution, resulting in evenly distributed
|
||
heat. Indeed, geometrical structures about the locations, motions and
|
||
interactions of the material objects in which entropy can increase
|
||
are what geometrical structures of material objects must coincide
|
||
with in order for them to use the free energy to do work.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
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||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
explanation of the second law of thermodynamics requires thinking
|
||
outside the box. In this case, the box is the assumption that to
|
||
explain is to give an efficient-cause explanations. What does not
|
||
come under discussion in disputes about the status of the law of
|
||
entropy increase is the assumption that any adequate explanation must
|
||
fit the deductive-nomological model. It must be shown to follow from
|
||
the laws of physics together with relevant initial and boundary
|
||
conditions. And since there is nothing temporally asymmetrical about
|
||
those laws (or the initial and boundary conditions), the second law
|
||
of thermo­dynamics seems to be irreducible. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
time-asymmetry can be explained ontologically, because it replaces
|
||
the laws of physics with matter of the appropriate kind and
|
||
recognizes that they coincide with a substance with an opposite kind
|
||
of essential nature. Though the regularities in the motion and
|
||
interaction of such matter in space can be described by laws of
|
||
physics using the language of mathematics, that is to abstract the
|
||
local regularities about what happens in a spatiomaterial world like
|
||
ours and to leave the global regularities behind. By bringing the
|
||
ontological causes of the laws of physics to the surface, we
|
||
recognize that they depend as much on the structure of space as they
|
||
do on the nature of matter. But the structure of space entails its
|
||
wholeness. All possible spatial relations among bits of matter fit
|
||
together as part of the geometrical structure of space, and by seeing
|
||
the distribution of the causally relevant factors (their locations,
|
||
kinetic energies and directions of motion) against the background of
|
||
the wholeness of space, we see it as a geometrical structure in the
|
||
region as a whole. That is to recognize the efficient cause that
|
||
produces the greater randomness, for it is that geometrical structure
|
||
that puts material objects in situations where they tend to wipe out
|
||
the geometrical structure. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">To
|
||
be sure, this efficient cause is what is measured by the statistical
|
||
improbability developed by Boltzmann. But by abstracting geometrical
|
||
structure as an arithmetic measure of randomness, Boltzmann hides the
|
||
connection between this efficient cause and its effect. We can <i>see</i>
|
||
how the geometrical distribution of causally relevant factors in the
|
||
region tends to wipe itself out, because we have a factual of
|
||
rational imagination, which includes spatio-temporal and
|
||
structuro-temporal imagination, and we understand how the motion and
|
||
interactions of the material objects tends to change their spatial
|
||
relations, kinetic energies and directions of motion. As time passes,
|
||
it adds up in the region to randomness. The connection between the
|
||
efficient cause and its effect is necessary, because it is caused
|
||
ontologically by the endurance of these substances through time. But
|
||
this causal connection cannot be represented in a
|
||
deductive-nomological explanation, because the only way it can be
|
||
represented by a mathematical formula, like a law of nature, it as a
|
||
basic law, like the second law of thermodynamics, which is
|
||
irreducible to the other basic laws of physics. Hence, there is no
|
||
solution as long as the only kind of explanation that is recognized
|
||
to be legitimate are efficient-cause explanations. That is to be
|
||
locked in the box of the deductive-nomological model of explanation. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><font color="#993366"><font face="Verdana, sans-serif"><b>M<img src="data:image/png;base64,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" name="OdkC32" align="right" width="64" height="34" border="0">echanical
|
||
principles.</b></font></font><font color="#993366"> </font>A less
|
||
obvious doubt about the reducibility of the causal connections in
|
||
scientific explanation to the basic laws of physics has to do with
|
||
the principles of mechanics. The irreducibility of the structural
|
||
aspects of mechanical principles has been used by Hilary Putnam and
|
||
others to cast doubt on using physics as the foundation for a
|
||
complete explanation of the world. Their arguments have contributed
|
||
to general consensus about rejecting all forms of reductionism. But
|
||
the problems to which they are pointing are solved by
|
||
spatiomaterialism. Just as Loschmidt’s’ reversibility paradox
|
||
arises from failing to recognize how material global regularities can
|
||
be explained ontologically, these critic are pointing to three
|
||
problems that arise from failing to recognize how structural global
|
||
regularities can be explained ontologically. The significance of
|
||
ontological philosophy is, in part, therefore, the restoration of the
|
||
good name reductionism. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><b>Putnam’s
|
||
Board-and-Peg Argument.</b> Many years ago, Hilary Putnam (1975,
|
||
296-7) cited a simple regularity that he argued was not reducible to
|
||
the basic laws of physics as required by the materialists’
|
||
reductionistic program. It can, however, be reduced to
|
||
spatiomaterialism by way of the ontological explanation of structural
|
||
global regularities. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Putnam
|
||
illustrated a basic problem about reductive explanations with a
|
||
simple physical system – “a board with two holes, a circle one
|
||
inch in diameter and a square one inch high, and a cubical peg
|
||
one-sixteenth of an inch less than one inch high.” The peg passes
|
||
through the square hole, but not the round hole. This regularity
|
||
would not be explained, Putnam holds, even if it could be deduced
|
||
from the laws of physics governing the behavior of matter in this
|
||
system.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000">“<font face="Times New Roman, serif"><span lang="en-US">One
|
||
might say that the peg is, after all, a cloud or, better, a rigid
|
||
lattice of atoms. One might even attempt to give a description of
|
||
that lattice, compute its electrical potential, worry about why it
|
||
does not collapse, produce some quantum mechanics to explain why it
|
||
is stable, etc. The board is also a lattice of atoms, I will call the
|
||
peg ‘system A’, and the holes ‘region 1’ and ‘region 2’.
|
||
One could compute all possible trajectories of system A (there are,
|
||
by the way very serious questions about these computations, their
|
||
effectiveness, feasibility, and so on, but let us assume this), and
|
||
perhaps one could deduce from just the laws of particle mechanics or
|
||
quantum electrodynamics that system A never passes through region 1,
|
||
but that there is at least one trajectory which enables it to pass
|
||
through region 2.”</span></font><sup><font face="Times New Roman, serif"><span lang="en-US"><a class="sdendnoteanc" name="sdendnote4anc" href="#sdendnote4sym"><sup>iv</sup></a></span></font></sup></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Putnam
|
||
argued that a deduction of this regularity from physics, if it is
|
||
possible at all, is not really an explanation. What explains why the
|
||
square peg fits in the square hole, but not in the round hole, is not
|
||
the basic laws of physics governing the ultimate constituents. It is
|
||
the higher level structure. All that matters is that “the board is
|
||
rigid, the peg is rigid, and as a matter of geometrical fact, the
|
||
round hole is smaller than the peg, the square hole is bigger than
|
||
the cross-section of the peg.” This explanation would hold
|
||
regardless of what the peg and board are made of, as long as they are
|
||
rigid, and so Putnam argues that such higher-level structural
|
||
explanations are “autonomous” and not reducible to physics. It is
|
||
our interests, Putnam claims, that make it look as if irreducible
|
||
higher-order structures like these are causally relevant. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">What
|
||
Putnam is getting at in his example is obviously, however, structural
|
||
ontological causation. It is just an instance of a reversible
|
||
structural global regularity, like our example of the box of gas.
|
||
What is regular in this case is that certain material objects moving
|
||
and interacting in the region always have unchanging geometrical
|
||
structures. That is a global regularity, even though all of the
|
||
global changes are reversible, for it means that the region itself
|
||
has a kind of geometrical structure that does not change over time.
|
||
The bare existence of those material structures moving around
|
||
randomly in the region includes the fact that the peg is sometimes in
|
||
one hole, but not the other. By denying that the structure of this
|
||
dynamic process can be deduced from the laws of physics, Putnam is,
|
||
in effect, making the case for recognizing material structures and
|
||
the global aspect of space (that is, its wholeness) as ontological
|
||
causes. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Putnam
|
||
is not, however, arguing for spatio-materialism. He accepts the
|
||
materialist ontology, and he argues that these explanations refer to
|
||
geometrical structures only because “we are much more interested in
|
||
generalizing to other structures which are rigid and have various
|
||
geometrical relations, than we are in generalizing to the next peg
|
||
that has exactly this molecular structure.”<sup><a class="sdendnoteanc" name="sdendnote5anc" href="#sdendnote5sym"><sup>v</sup></a></sup>
|
||
That role of special interests is what leads him to argue that
|
||
“structural features” are a “higher level” that is
|
||
“autonomous” from physics.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Let
|
||
me emphasize, however, that space is an ontological cause of this
|
||
simple global regularity in two ways. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">First, the
|
||
global aspect of space, which is entailed by its structure, is an
|
||
ontological cause, along with these derivative ontological causes, of
|
||
the simple global regularity being explained. It connects the
|
||
geometrical structures of different material objects as parts of the
|
||
same world and enables them to interact as geometrical structures. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Second, the
|
||
global aspect of space is an essential ontological cause of the
|
||
formation of the unchanging geometrical structures of these material
|
||
objects, since material structures are derivative ontological causes.
|
||
They are by-products of the tendency of potential energy to become
|
||
kinetic. And since the spatial relations of the parts of the material
|
||
object are constituted by the space that contains them, the
|
||
geometrical structures of the board and peg are not universals, but
|
||
no less <i>concrete </i>than the material objects that embody them.
|
||
What enables the board and peg to move across space without changing
|
||
their geometrical structures is that every region of space contains
|
||
every possible geometrical structure. It is hard to avoid the
|
||
conclusion that the anomaly in this case comes from materialists
|
||
overlooking that space is a substance, because to account for this
|
||
simple global regularity, all we need is to recognize that space has
|
||
the same ontological status as matter.</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><b>The
|
||
Supervenience of Dispositional Properties. </b>Other philosophers
|
||
trying to carry out the materialist reductionistic program have
|
||
noticed certain anomalies that arise in the reduction of
|
||
dispositional properties. For example, Bigelow and Pargetter (1987,
|
||
p. 190) call fragility a “supervenient” property, because it
|
||
cannot be reduced to the laws of physics. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Properties
|
||
are said to be “supervenient” when they cannot be reduced to
|
||
physical properties in the sense of being defined in terms of them. A
|
||
definition would pick out exactly the same objects by identifying in
|
||
terms of physical properties what is meant by the supervenient
|
||
property, which would be another way identifying the same property.
|
||
But such definitions cannot be given in some cases. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">The most
|
||
obvious are functional properties, such as “being a clock,” which
|
||
may be realized by objects whose physical structures range from
|
||
machines worn on the wrist to tree rings, sun dials, and the amount
|
||
of radioactive decay. There is no way to pick out all clocks by their
|
||
physical properties, because when one looks for physical properties,
|
||
one is force to start listing all the different kinds of physical
|
||
objects that could serve as clocks. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
|
||
particular causes, supervenient properties are thought to be
|
||
identical to the physical properties of the object having the
|
||
supervenient property. Thus, they hold that any object that is
|
||
physically similar to one that has a supervenient property must also
|
||
have the supervenient property. But supervenient properties are not
|
||
reducible, because it is not possible to describe the physical
|
||
properties that are both necessary and sufficient for supervenient
|
||
properties. There are just too many different kinds of cases and no
|
||
principle by which a list of them can be completed. The reduction
|
||
involves, at most, therefore, only an identity between the tokens on
|
||
the two levels, not an identity between types. That is what it means
|
||
to say that the properties <i>supervene </i>on physical traits.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">Reduction
|
||
would require an identity between the functional and the physical
|
||
types, or what is called “type-identity.” But since functional
|
||
properties are supervenient, all the holds is that the functional
|
||
property <i>in this case </i>is nothing but the physical properties.
|
||
Since only the token of the functional property is identical to the
|
||
token of the physical property, or what is called “token-identity.”</font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
|
||
the case of the disposition, fragility, what Bigelow and Pargetter
|
||
(1987, p. 190) apparently mean by “supervenience” is that fragile
|
||
objects of the same and different kinds can break up or shatter in
|
||
different ways in different situations. Different physical properties
|
||
are responsible for what happens in different cases, and there is no
|
||
physical property that they all have in common by which all the kinds
|
||
of cases can all be included. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Supervenience
|
||
theorists are eager to reassure us, however, that they are not saying
|
||
that non-physical causes are responsible for the exhibition of such
|
||
supervenient properties. In each particular case, it is possible, in
|
||
principle, to explain physically what happened, and any case that is
|
||
physically like it in all relevant respects will also break up in the
|
||
same way (or not break up at all). But the disposition is not
|
||
reducible to those physical properties (and their effects according
|
||
to basic laws of physics), because there is no natural physical kind
|
||
or type that is identical to this <i>type </i>of disposition, that
|
||
is, which includes all and only fragile objects, making fragility a
|
||
supervenient property. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Physical
|
||
dispositions can be explained, as we have seen, by spatiomaterialism
|
||
as forms of structural global regularities. In addition to the
|
||
wholeness of space, the structural ontological causes of the global
|
||
regularities are the geometrical structures of the material objects
|
||
involved and free energy that is supplied somehow by the conditions
|
||
under which the disposition is exhibited. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">What
|
||
makes fragility irreducible to the laws of physics is the difficulty
|
||
in identifying the structural cause of the irreversible change in the
|
||
object before it occurs. A fragile object will break up in different
|
||
ways, depending on the precise way free energy is supplied under the
|
||
test conditions. That is because different structural causes are
|
||
embedded in the same material object. The structural cause in each
|
||
case is all the parts of the composite object that do not come apart
|
||
(though breaking up may involve a series of such structural causes),
|
||
for they are the unchanging structures that determine how objects
|
||
break up. That is, fragile objects are just machines that use the
|
||
free energy provided by the conditions of its expression to do the
|
||
mechanical work of separating chucks of itself from one another. But
|
||
they are complex machines that do it different ways in different
|
||
cases, depending on how free energy is supplied. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Does
|
||
the existence in the material object of many different structural
|
||
causes generating many different global regularities mean that
|
||
fragility is a supervenient property? That can’t be correct, for if
|
||
it were, we wouldn’t be able to <i>see </i>how all the global
|
||
regularities are alike. And we can. Given that the bonds among the
|
||
parts of the object are inelastic and cannot absorb much of the free
|
||
energy supplied by the impact, we can see how the forces are
|
||
communicated by their bonds and spread out geometrically so that
|
||
whole groups of bonds break together or not at all. For example, we
|
||
can see why a wine glass dropped on concrete will shatter, but when
|
||
dropped on a rug which absorbs some of the initial shock, it is more
|
||
likely to break at the stem. What happens is just a result of how the
|
||
motion and interaction of bits of matter add up in space over time,
|
||
including how forces are communicated among the parts of the fragile
|
||
object, and with our capacity for spatio-temporal imagination, we can
|
||
“see” the similarity about what happens in each case. The
|
||
similarities among cases of objects breaking up under impact
|
||
(including different kinds of fragile objects) are basically
|
||
geometrical, but nonetheless real. Thus, there is a type-type
|
||
identity between the ontological causes and the disposition (or
|
||
global regularity) they determine. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Supervenience
|
||
is just an appearance that a spatiomaterialist world has because
|
||
science seeks only efficient-cause explanations. What makes fragility
|
||
seem to be irreducible is the assumption that the reductive
|
||
explanation must be formulated as a deductive argument from laws of
|
||
physics together with initial conditions and mathematics theorems. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
basic laws of physics are local regularities about change that are
|
||
constituted jointly by space and matter. They depend on the structure
|
||
of space as much as the essential natures of the forms of matter
|
||
contained by space. Thus, when the laws of physics are taken as basic
|
||
in an efficient-cause explanation, only some of the relevant aspects
|
||
of the ontological causes are represented. The structure is space is
|
||
included only insofar as it helps constitute the local regularities
|
||
described by the laws, but that is to abstract from the wholeness
|
||
that is also entailed by the geometrical structure of space. The
|
||
wholeness of space is just as relevant to how change unfolds over
|
||
time as the aspects of space that are represented by the laws of
|
||
physics. It includes all the geometrical aspects of the motions and
|
||
interactions of the bits of matter that add up over time to a certain
|
||
structural effect. But the wholeness of space is excluded, according
|
||
to the deductive-nomological model, from efficient-cause
|
||
explanations. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
is not easy to translate the geometrical factors that are relevant
|
||
such an ontological reduction of dispositions into mathematical
|
||
formulas that can be used in conjunction with the laws of physics to
|
||
derive a description of the breaking up or shattering. The motion and
|
||
interaction of material structures do not add up to simple
|
||
quantities, like those involved in the conservation of momentum and
|
||
energy. They add up to geometrical structures. But limitations in the
|
||
capacity of mathematical formulas to represent geometrical structures
|
||
should not be taken as grounds for denying their role or the role of
|
||
the geometrical structure of space itself in the ontological
|
||
reduction of dispositions. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
is not necessary to construct deductions using mathematical formulas,
|
||
because the cause that explains the <i>kind </i>of structural global
|
||
regularity is a material structure and how its motion and interaction
|
||
add up in the wholeness of space, and that can be understood by using
|
||
spatio-temporal imagination. It is a matter of seeing how the forces
|
||
imposed by the impact are communicated to other parts and how they
|
||
build up in certain locations. Insofar as the structural effects
|
||
depend on quantitative aspects, such as the strength of the forces
|
||
and the distances over which they are exerted, they can be
|
||
approximated by computer models that take into account both the
|
||
forces and the geometrical structures of each molecule or atom and
|
||
their spatial relations to one another in the composite whole. This
|
||
is, of course, how materials science has been explaining the
|
||
properties of bulk matter ever since computers became widely
|
||
available. The capacity of computer simulations to do what formal
|
||
mathematical deductions cannot do is evidence of the relevance of the
|
||
geometrical structures of the material objects and the geometrical
|
||
structure of space itself as ontological causes of these global
|
||
regularities.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Fragility
|
||
and other such dispositions are, therefore, supervenient properties
|
||
only in the sense that they cannot be deduced mathematically from the
|
||
basic laws of physics together with appropriate initial and boundary
|
||
conditions. But they are not supervenient relative to our ontology,
|
||
because when we recognize that the dispositions are constituted by
|
||
bits of matter that coincide with space as a substance, we can see
|
||
how the wholeness of space so constrains the motion and interaction
|
||
of the material structures that they add up over time to global
|
||
regularities of certain kinds.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
example of fragility is complicated by the fact that one of its
|
||
ontological causes is derivative. Material structures are not basic
|
||
ontological causes, but depend on the tendency of potential energy to
|
||
become kinetic, and fragility is a disposition in which the very
|
||
existence of the ontological cause is at stake. It involves, in other
|
||
words, the <i>generation </i>and <i>corruption </i>of (derivative)
|
||
substances in our ontology, and thus, is special in way that
|
||
parallels the generation and corruption of primary substances in
|
||
Aristotle’s ontology.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
complication about generation and corruption encountered in the case
|
||
of fragility is, however, general, for it holds of chemical
|
||
interactions generally. They are unlike the interactions in which
|
||
molecules serve as catalysts (or enzymes), for in those cases, the
|
||
molecules have geometrical structures that persist through the
|
||
change, making them ontological causes. But in chemical interactions,
|
||
molecules have geometrical structures that contain many different
|
||
structural ontological causes, like fragile objects, because their
|
||
global regularities also depend on how the free energy that drives
|
||
the irreversible processes is supplied. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 3.81cm; margin-right: 2.03cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif">A typical
|
||
chemical interaction involves an exchange of clusters of atoms
|
||
between two original molecules that result in two new molecules.
|
||
Their shapes determine how the original molecules fit together and,
|
||
so, which parts of each molecule interact with which parts of the
|
||
other, and the total force exerted at such moments determines whether
|
||
or not the molecules will interact chemically and exchange subgroups
|
||
of atoms, forming new kinds of molecules. The free energy comes from
|
||
the potential energy of the forces that parts of molecules exert on
|
||
one another, but it is structured by spatial relations among parts
|
||
that are not changed.<sup><a class="sdendnoteanc" name="sdendnote6anc" href="#sdendnote6sym"><sup>vi</sup></a></sup>
|
||
The structural causes in these cases are the clusters of atoms (or
|
||
smaller molecules) that do not change their geometrical structures
|
||
during the interaction, since only <i>unchanging </i>geometrical
|
||
structures of matter are ontological causes. Thus, molecules will
|
||
contain different structural causes depending on which other kinds of
|
||
molecules are combined with them. But that does not mean that
|
||
chemical interactions are supervenient properties or otherwise
|
||
ontologically irreducible, at least, not when we recognize that
|
||
substantival space is an ontological cause. </font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><b>Putnam’s
|
||
Argument from Countervailing Conditions.</b> Although Putnam does not
|
||
say that they are supervenient, he also argues that dispositions are
|
||
often irreducible. His reason is that they are tendencies that hold
|
||
only “other things being equal.” Putnam (1987) illustrates the
|
||
irreducibility of disposition by considering the solubility of a
|
||
sugar cube in water.<sup><a class="sdendnoteanc" name="sdendnote7anc" href="#sdendnote7sym"><sup>vii</sup></a></sup>
|
||
</font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
might not dissolve when placed in water, he argues, because the water
|
||
might already be saturated with sugar. Or because the water might
|
||
freeze before the cube can dissolve. Finally, he appeals to
|
||
Loschmidt’s reversibility paradox as a countervailing condition.
|
||
The water might happen to be in a state that is the exact
|
||
time-reversal of a state that occurs when a larger cube was
|
||
dissolving, so that the motions and interactions in this special case
|
||
make the cube un-dissolve out of the water and form a crystal. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">It
|
||
is materialist reduction that Putnam is talking about, for the
|
||
irreducibility of these disposition comes from trying to deduce them
|
||
from premises that are “formulas in the language of fundamental
|
||
physics”<sup><a class="sdendnoteanc" name="sdendnote8anc" href="#sdendnote8sym"><sup>viii</sup></a></sup>
|
||
which cannot take into account of all the various exceptional
|
||
conditions that might prevent the expression of the disposition. On
|
||
the deductive-nomological model of explanation, the only way to
|
||
predict what will happen is to trace precisely the motion and
|
||
interaction of all the objects in the region over a region of time
|
||
and see where it leads, and Putnam denies that all the conditions
|
||
that might be relevant to the exhibition of the disposition can be
|
||
included in such a deductive argument. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
dissolving of the sugar cube in water is, according to the
|
||
spatiomaterialist reduction, just a structured thermo­dynamic
|
||
process. The free energy is the potential energy that comes from the
|
||
forces that would form weak hydrogen bonds between the sugar and
|
||
water molecules. The structural causes are the shapes of the water
|
||
molecules, the shapes of the sugar molecules, and the material
|
||
structure that results from packing sugar molecules together in the
|
||
crystal. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">In
|
||
dissolving, weak bonds holding sugar molecules together in the
|
||
crystal are replaced by weak bonds with water molecules as a result
|
||
of their random motion and interaction with one another in the
|
||
region. Opposite electric charges on opposite sides of the water
|
||
molecules fit with similar charges on sugar molecules in such a way
|
||
that the sugar molecules exchange their bonds with one another for
|
||
stronger, less energy-rich bonds with water molecules, freeing
|
||
kinetic energy in the process. Thus, when their random motion and
|
||
interaction brings these molecules together, sugar molecules are
|
||
released from their bonds in the crystal to form bonds with water,
|
||
and a new kind of static order comes to exist. That is how matter, as
|
||
energy, flows through geometrical structures from potential energy to
|
||
evenly distributed heat in this case. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Putnam’s
|
||
doubts about reducibility come from the impossibility of including
|
||
countervailing conditions in the deduction. But if the disposition is
|
||
recognized to be a <i>global </i>regularity, there can be no
|
||
countervailing conditions that are not taken into account, because
|
||
all the bits of matter in the region are involved in how their motion
|
||
and interaction add up over time. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">If
|
||
what prevents the sugar cube from dissolving is that the water is
|
||
already saturated with sugar molecules, it is simply the absence of
|
||
the free energy in the region that the material structures use to do
|
||
the work of freeing them from the crystal. The potential energy
|
||
depends on certain spatial relations between the molecules exerting
|
||
the forces, and since all the water molecules in the region are
|
||
already bound to sugar molecules, the relevant spatial relations do
|
||
not exist, and so there is no thermo­dynamic flow of matter from
|
||
potential energy to evenly distributed heat to be structured. That
|
||
condition is already taken into consideration, if it is explained
|
||
ontologically as a global regularity by structural causes and the
|
||
global aspect of space.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">On
|
||
the other hand, if what keeps the sugar cube from dissolving is a
|
||
sudden freezing of the water, that is also something that is already
|
||
taken into account by treating it as a global regularity. Global
|
||
regularities are regularities about whole regions of space, and that
|
||
means they must either be closed or else one must keep track of what
|
||
is flowing in and what is flowing out of the region. Although a
|
||
sudden freeze would certainly stop the irreversible special theory of
|
||
relativity, there is no way it could happen unnoticed. Heat is a form
|
||
of matter (that is, kinetic energy is explained ontologically as
|
||
kinetic matter), and as a kind of substance, it cannot simply go out
|
||
of existence. The tendency to randomness spreads heat throughout the
|
||
region, and it can be removed from the region only if there is
|
||
something colder in the region to which it can flow. That would be a
|
||
thermo­dynamic flow of matter toward evenly distributed heat in
|
||
the region that is clearly relevant in explaining the dissolving as a
|
||
global regularity. Finally, nothing outside the region could make it
|
||
freeze without violating the principle of local action. Thus, a
|
||
sudden freezing is not an exception to an explanation of dissolving
|
||
as a structural global regularity. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">The
|
||
final countervailing condition Putnam mentions is not explained by
|
||
this reduction to spatiomaterialism, for it is just an illusion that
|
||
comes from the attempt to carry out a materialist reduction of the
|
||
tendency to randomness. Putnam is using Loschmidt’s paradox as a
|
||
countervailing condition. But as we saw in the last chapter, when the
|
||
tendency to randomness is explained geometrically, rather than
|
||
mathematically, by statistics, there is no reason to believe the
|
||
water and sugar molecules would ever be in a microstate that
|
||
corresponds to one in which the sugar cube is dissolving except for
|
||
all the molecules having exactly opposite momentums. Only the
|
||
statistical definition of randomness requires us to believe that all
|
||
possible microstates are equally probable.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">None
|
||
of the countervailing conditions to exhibiting solubility that Putnam
|
||
mentions would be overlooked, therefore, by an explanation of this
|
||
disposition as a global regularity, because when the global aspect of
|
||
space is recognized as an ontological cause, the whole region where
|
||
it occurs is causally relevant. Dispositions are not properties
|
||
inherent in the nature of matter, but rather kinds of structural
|
||
global regularities, which depend on structural causes, free energy
|
||
supplied by a thermo­dynamic flow of matter toward evenly
|
||
distributed heat, and a region of space where their geometrical
|
||
structures coincide. What makes it seem that exceptional conditions
|
||
preclude the ontological reduction of dispositions is the assumption
|
||
that a reductive explanation must deduce a description of the
|
||
regularity from “formulas in the language of fundamental physics,”
|
||
as if the disposition had to follow from the basic laws of physics
|
||
without taking account of how structural causes can channel the
|
||
thermo­dynamic flow of forms of matter toward evenly distributed
|
||
heat in the region. The role of space in imposing those regularities
|
||
may make it hard to formulate these ontological explanations as
|
||
deductions, but the reduction to the ontology of spatio-materialism
|
||
leaves no room for surprises.</font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 1.27cm; margin-right: 2.54cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Finally,
|
||
other apparently irreducible phenomena can be explained in similar
|
||
ways. </font></font></font>
|
||
</p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000"><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt">Prigogine
|
||
(1980), for example, points to the phenomenon of self-forming objects
|
||
as irreducible.<sup><a class="sdendnoteanc" name="sdendnote9anc" href="#sdendnote9sym"><sup>ix</sup></a></sup>
|
||
He recognizes that it does not occur when entropy is maximum, but
|
||
depends on open systems, in which there is a flow of mass and energy
|
||
(so-called “dissipative systems”). But far from being an anomaly,
|
||
this kind of phenomenon is entailed in a spatiomaterial world like
|
||
ours, because self-forming objects are just instances of the tendency
|
||
of potential energy to become kinetic.<sup><a class="sdendnoteanc" name="sdendnote10anc" href="#sdendnote10sym"><sup>x</sup></a></sup>
|
||
See the discussion of crystal formation and the conformation of
|
||
protein molecules in <font face="Verdana, sans-serif">Structural
|
||
global regularities.</font></font></font></font></p>
|
||
<p lang="en-US" class="western" align="left" style="margin-left: 2.54cm; margin-right: 1.27cm; margin-top: 0.49cm; margin-bottom: 0.49cm; line-height: 100%; widows: 0; orphans: 0">
|
||
<font color="#000000">“<font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">Chaos”
|
||
is likewise cited as evidence of emergent phenomena. These are
|
||
situations in which structural global regularities suddenly appear
|
||
from apparently chaotic, or random, dynamic processes, such as a
|
||
turbulent flow suddenly becoming highly structured. What makes them
|
||
seem inexplicable, however, is failing to take space into account in
|
||
one way or another, either by not recognizing the structural causes
|
||
at work in the region, by not taking the geometrical structure of the
|
||
boundary conditions of the system into account, or by ignoring the
|
||
structure of the space within those boundaries. When they are taken
|
||
into account, it is not surprising that the quantitative aspects of
|
||
the motion and interaction of bits of matter in the region would fit
|
||
together geometrically with those spatial structures so that their
|
||
motion and interaction add up over time to certain regular, repeated
|
||
patterns.</span></font></font><sup><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US"><a class="sdendnoteanc" name="sdendnote11anc" href="#sdendnote11sym"><sup>xi</sup></a></span></font></font></sup><font face="Times New Roman, serif"><font size="3" style="font-size: 12pt"><span lang="en-US">
|
||
They are just structural global regularities. The anomalies all come
|
||
from overlooking structural ontological causes and how they work
|
||
together with the global aspect of space. </span></font></font></font>
|
||
</p>
|
||
<div id="sdendnote1">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote1sym" href="#sdendnote1anc">i</a>
|
||
L. Sklar (1992) reviews these issues and gives references to the
|
||
literature in Chapter 3, “The Introduction of Probability into
|
||
Physics”. He puts the problem of reducing them to the basic laws
|
||
of physics as being unable to show that the probabilistic
|
||
assumptions of statistical mechanics are “nonautonomous” (p.
|
||
121). See also Sklar (1993)).
|
||
</p>
|
||
</div>
|
||
<div id="sdendnote2">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote2sym" href="#sdendnote2anc">ii</a>
|
||
Loschmidt’s paradox does not mean that Boltzmann’s statistical
|
||
explanation of this tendency is falsified by observation, for it can
|
||
be held that the reason we never observe random systems
|
||
spontaneously becoming nonrandom is that the random microstates that
|
||
lead to nonrandom states are statistically so overwhelmingly
|
||
improbable that they virtually never occur in nature. And the reason
|
||
why we <i>do </i>observe many cases of nonrandom states becoming
|
||
random can be explained by the existence of other kinds of processes
|
||
in nature that impose nonrandom initial states on closed systems.
|
||
This bias in our sample of systems makes what is just an atemporal
|
||
statistical fact about such systems appear to be a tendency to
|
||
become more random over time.</p>
|
||
<p lang="en-US" class="sdendnote-western">This may save the
|
||
appearances, but it does not salvage Boltzmann’s definition of
|
||
randomness as an explanation of the <i>tendency </i>to randomness.
|
||
To be sure, there are sources of usable, or “free”, energy in
|
||
nature that can impose nonrandom initial states on closed systems,
|
||
and a more general version of the second law of thermo­dynamics
|
||
would have to cover the systems of which they are parts. These
|
||
sources of free energy include not only other systems with nonrandom
|
||
distributions of elasticly interacting objects, but also systems in
|
||
which the objects have potential energy because of forces they exert
|
||
on one another. But their existence does not explain the tendency to
|
||
randomness as a change with a direction in time. It only explains
|
||
why there are so many examples of that tendency in our surroundings.
|
||
There is still no reason to believe that systems that start off in a
|
||
nonrandom state will become random, except that most such systems
|
||
examined must be in a random state, if all possible microstates are
|
||
equally probable. At best, the existence of natural processes that
|
||
impose nonrandom initial states on closed systems will so bias our
|
||
sample that it will <i>appear </i>that change has a direction in
|
||
time. But that is no part of the statistical explanation of the
|
||
tendency to randomness, for if its statistics did take into account
|
||
the existence of such natural processes, it could not assume that
|
||
all possible microstates are equally probable.
|
||
</p>
|
||
</div>
|
||
<div id="sdendnote3">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote3sym" href="#sdendnote3anc">iii</a>
|
||
Attempts to show the equiprobability of all possible microstates
|
||
introduce another kind of phase space to represent the microstates
|
||
of the gas. The position and momentum of each molecule in a box can
|
||
be represented by six numbers, three each for its position and
|
||
momentum, and since the state of the whole box can be represented by
|
||
six numbers for each molecule, it is possible to think of the
|
||
microstate of the box as the location of a single point in a “space”
|
||
whose number of dimensions is six times the number of molecules.
|
||
This is misleadingly similar to the real, three dimensional space
|
||
from which it abstracts, for changes in the state of the box, which
|
||
actually depend on the molecules all moving and interacting in real
|
||
space according to the laws of physics, are represented as the
|
||
“motion” of this “phase point” in a “phase space” with
|
||
an enormous number of dimensions (the limits of the phase space
|
||
being determined by the total energy of the gas and the size of its
|
||
container). Although it can be shown that the phase point will <i>not
|
||
</i>move around to every point, it can be shown that it will
|
||
eventually spend the same amount of time in every small region of
|
||
this phase space. This theorem (the ergodic theorem) is used to
|
||
justify the assumption that all the points in phase space are
|
||
equally probable. But as long as it shows only that the phase point
|
||
will visit every <i>region </i>of phase space equally often, and not
|
||
every <i>point</i>, there is no good reason to believe that the
|
||
kinds of random microstates that would lead to non-random states
|
||
will ever occur, because there is no reason to believe that minor
|
||
differences in micro states will not add up to big differences, such
|
||
as not being non-random on the macro level. The importance of such
|
||
small differences is an example of the “butterfly effect” to
|
||
which chaos theorists have recently been drawing attention. See J.
|
||
Gleick, <i>Chaos: The Making of a New Science</i> (New York: Penguin
|
||
Books, 1987).</p>
|
||
</div>
|
||
<div id="sdendnote4">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote4sym" href="#sdendnote4anc">iv</a>
|
||
“Philosophy and Our Mental Life”, Putnam (1975, pp. 295-6).
|
||
Putnam (1978, pp. 42-3) calls it the “Laplacean super-mind’s
|
||
deduction”.</p>
|
||
</div>
|
||
<div id="sdendnote5">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote5sym" href="#sdendnote5anc">v</a>
|
||
For Putnam (1975, pp. 296-7), structural features are singled out
|
||
because of our interests, because of what is salient from our
|
||
special point of view, or because of the “pur­poses for which
|
||
we use the notion of explanation”, rather than because of the role
|
||
of material structures in constituting global regularities about
|
||
change over time.</p>
|
||
</div>
|
||
<div id="sdendnote6">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote6sym" href="#sdendnote6anc">vi</a>
|
||
For many chemical interactions, the molecules must collide with
|
||
enough energy to distort one another’s geometrical structures so
|
||
that their parts are in a position to exert the forces that result
|
||
in exchanging parts of themselves with one another, and thus, the
|
||
likelihood of such reac­tions depends on the mean kinetic energy
|
||
of their random motion and interaction, or tempera­ture.
|
||
Although combustion does not start spontaneously, once it does
|
||
start, it can be self-sustaining. Once some molecules interact
|
||
energeti­cally enough to form the stronger, lower-energy bonds,
|
||
they release enough energy to put other molecules in a position to
|
||
do the same.</p>
|
||
</div>
|
||
<div id="sdendnote7">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote7sym" href="#sdendnote7anc">vii</a>
|
||
Putnam also uses this argument elsewhere, for example, in Putnam
|
||
(1992, p. 62).</p>
|
||
</div>
|
||
<div id="sdendnote8">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote8sym" href="#sdendnote8anc">viii</a>
|
||
Putnam, 1987, p. 11.</p>
|
||
</div>
|
||
<div id="sdendnote9">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote9sym" href="#sdendnote9anc">ix</a>
|
||
See also Kauffman (1993, 1995).</p>
|
||
</div>
|
||
<div id="sdendnote10">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote10sym" href="#sdendnote10anc">x</a>
|
||
The more elaborate examples in which one kind of chemical reaction
|
||
is followed by another in cycles can also be explained as global
|
||
regularities, for they are simply cases in which the free energy of
|
||
the thermo<font color="#000000">­dynamic processes </font>to be
|
||
structured is supplied by the forces exerted by the molecules in the
|
||
region on one another and the chemical interactions are changing the
|
||
kinds of molecules that are present in the region.</p>
|
||
</div>
|
||
<div id="sdendnote11">
|
||
<p lang="en-US" class="sdendnote-western" style="margin-top: 0cm; margin-bottom: 0.25cm">
|
||
<a class="sdendnotesym" name="sdendnote11sym" href="#sdendnote11anc">xi</a>
|
||
See Gleick (1987).</p>
|
||
</div>
|
||
</body>
|
||
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