The so-called Levels Hypothesis claims
that some devices can be described at a variety of levels...it
will suffice to distinguish three such levels. They are:
- the Physical Level;
- the Symbolic or Computational Level; and
- the Semantic or Knowledge Level.
Computers and humans are, according to this
hypothesis, both devices which can appropriately described at
each of these levels. (A lump of coal, a red apple, etc. are
examples of things that aren't appropriately described at these
various levels...only rather special things can be described
at all of these levels.)
What is a level? Intuitively, it is a way
of describing things. When we speak of our brain, its neurons,
their organization, and the like we are describing things at
the Physical Level. In addition to the way we carve
up and name the "stuff" at this level, there are also
laws, in this case physical laws, that describe the way in which
the "stuff" behaves. Computers can be described at
the hardware level, chips, transistors, bus, etc. And, the physical
laws of electricity hold in describing this level. Thus, a level
represents a kind of commitment to the existence and lawful behavior
of certain kinds of entities.
The Symbolic or Computational Level
is a level at which we describe symbols, expressions composed
from symbols, processes that map from expressions to expressions,
and the like. The Turing Machine was, of course, a description
at this level. Now, the idea is that there are usually many ways
to physically realize or instantiate a computational
device. Nonetheless, the computational description and laws describe
the device quite independently of its physical instantiation.
The Semantic or Knowledge Level
is the level at which we describe the notion of a rational agent.
One sense of this is that a device is rational to the extent
that it uses its knowledge to attempt to satisfy its goals. Another,
broader and more technical sense, is that a computational device
realizes some semantics if and only if it generates outputs that
are derivable from some well-specified semantics of the domain.
The three different physical settings within
which Tic Tac Toe could be played are clearly quite different.
However, all that matters about the physical setting is that
it provide a way in which to represent the computational ideas
of a move; of the entities controlled by each player at each
point in the game; and finally, a relation that holds over 8
subsets of size 3 of the entities. Viewing the animation of a
game in these three settings illustrates that the physical similarity
between the traces of a game can be fairly substantial to non-existent.
Now, reflect for a moment on the various possible
sequences of events that are possible at each level. At the physical
level, any physically realizable sequence of moves is possible.
For example, as depicted in the figure to the right, 3 X
moves could immediately be made across the top row. This sequence
violates the rules of Tic Tac Toe, but certainly no physical
law prevents it. Thus, if we find that only "legal"
Tic Tac Toe sequences are observed, then either we must assume
that these regularities arise from some other level or there
is some Physical "Tic Tac Toe" Law that we have yet