Reduction and Elimination in Philosophy and the Sciences

Of course we don’t have scale models in the brain.
But this does not mean that an analog account of the brain
is impossible as there is a more abstract ‘second-order’
form of resemblance (Shepard and Chipman 1970). First
order resemblance occurs when two things share one or
more physical properties. For example the paint cards you
get at the hardware store represent the colour of the paint
by replicating the colour of the paint. It is implausible that
the ground of mental content is first-order resemblance
because we are capable of representing many things with
which the brain shares no physical properties. But there is
a more abstract ‘second-order’ notion of resemblance. 'In
second-order resemblance, the requirement that
representing vehicles share physical properties with their
represented objects can be relaxed in favour of one in
which the relations among a system of representing
vehicles mirror the relations among their objects' (O'Brien
and Opie 2004, p.10). Consider for example a mercury
thermometer. It represents temperature because the
relation between variations in the volume of the mercury
resembles the relations between variations in the
temperature of the substance that the thermometer is in
contact with. For example, if volume x is greater than
volume y then the temperature which corresponds to x is
hotter than the temperature that corresponds to y.
Because of this relational similarity between the volume of
the mercury and the temperature of the substance it is in
contact with, it is possible to use variations in the volume
of mercury to represent variations in temperature.
Importantly, the structure and nature of the
constituents of the representing vehicles determines their
content for second-order resemblance. As with the scale
model, the meaning of a mercury thermometer depends on
the structure of the parts. If you change the structure by
stomping on it, you would change the meaning. Also like
the scale model, the nature of the constituents determines
the meaning in the thermometer. It is because mercury is a
substance that expands when heated that it can be used
to represent temperature; you cannot make a thermometer
out of wood or custard. So meaning in a mercury
thermometer is at a mereologically higher-level to its
constituents.
Connectionism provides a model of how to
implement analog computation in the brain. We can see
second-order resemblance in the activation space of many
artificial neural networks. Activation space is a multidimensional
space that enables us to represent the
relations between patterns of activation across the units of
a layer of an artificial neural network. Each dimension of
activation space corresponds to the possible levels of
activation of one of the units. Each point in activation
space represents one pattern of activation across a layer.
Patterns of activation that are near each other in activation
space will be similar in that they consist of similar patterns
of activity across the units whereas dissimilar patterns of
activation across the units will be further apart in activation
space. The similarity relations between the patterns of
activation can be represented in activation space via the
distance between the points.
Importantly it has been shown that the activation
space of many artificial neural networks resembles aspects
of the task domain. Consider for example Cotrell’s face
recognition network, which is able to recognize familiar
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Making the Mind Higher-Level — Elizabeth Schier
faces, distinguish between faces and non-faces, and
determine the gender of unfamiliar faces (Churchland
1995). When the patterns of activation across the hidden
units were mapped in activation space it was discovered
that all the patterns of activation that represent images of a
particular individual are clustered closely together in
activation space. What this means is that they are
represented with patterns of activation that are quite
similar. The patterns of activation that represent images of
faces of the same gender are clustered together in a larger
region of activation space. Finally all of the patterns of
activation that represent faces are located in a large region
of activation space that is separate from the patterns of
activation that represent non-face images. In general,
similar faces are represented with similar patterns of
activation and dissimilar faces are represented with
dissimilar patterns of activation. The relations between
patterns of activation resemble the relations between
faces.
So we can see second-order, relational similarity at
work in artificial neural networks. Importantly the structure
and nature of the constituents of the representing vehicles
determines their content in such networks. We can see this
by realising that the similarity relations between patterns of
activation that are mapped in activation space are based in
the intrinsic structure of the patterns of activation. Although
individual patterns of activation are represented in
activation space by points, the basis of their location in
activation space, and the basis of their similarity relations,
is their internal structure. Two patterns of activation will be
located near each other in activation space because they
consist of similar levels of activity across the units.
Conversely, if two patterns consist of different levels of
activity of the various units then they will be located in
different regions of activation space. If you change the
nature of a pattern of activation you will move it within
activation space and therefore change what it resembles
and means. And patterns of activation have the structure
that they do because of the electrical nature of the
units/neurons that constitute them; you cannot build a
network out of beer cans or bricks. For the connectionist,
meaning does depend on the structure and nature of the
parts, so meaning is mereologically higher-level to the
parts. It is only when you organise neurons into the right
firing patterns that you have representing vehicles with
meaning. Meaning is neurons arranged in a particular way
in the same way that water is H20 arranged in a particular
way. So the meaning of a pattern of activation across
neurons is at a higher mereological level to the neurons
that constitute it. This means that the meaning of
connectionist representing vehicles is not in competition for
causally efficacy with their neural constituents.
We can see that on an analog connectionist account
of the mind the meaning of a representing vehicle is at a
mereolgocially higher-level to its constituents. So meaning
can play a causal role over and above that played by its
neural constituents. Yet, because the causal powers of the
representing vehicles are determined by the nature of their
constituents, meaning is a physical property. So, like
water, meaning is higher-level, real, physical and causally
efficacious. Connectionism makes the mind higher-level
and therefore, by everyone’s standards, real, causally
efficacious and physical.