|
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 be described
at each 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. Most are made
up of chips, transistors, a bus, etc. And, the physical laws
of electricity, optics and the like 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 consistent with
some well-specified semantics of the domain.
In
order to simplify the discussion, let use turn to the game of
Tic-Tac-Toe and try to use it to illustrate some of these distinctions.
An illustration of the idea that there are many ways to physically
realize something that is described computationally can be viewed
by clicking on Tic-Tac-Toe
Example. (We
have also included an article describing the construction of
a computer that plays Tic-Tac-Toe. What is interesting about this computer
is that it was constructed using Tinkertoys...a fact that is
only surprising if one one rejects the Levels Hypothesis. )
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;
- 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 to discover.
|
 |
|
Similarly,
at the level of the game, the set of legal move sequences includes
moves that we would view as quite "irrational". For
example, we find it strange if a player's next move could win
the game, but the player makes some other non-winning move. The
figure to the right provides an example of this "irrational"
case. The "semantics" of a game is to try to achieve
the goal of winning. Sequences of moves can violate this "semantics"
but still constitute a syntactically correct game. Thus, we have
the set of possible Tic-Tac-Toe games and the set of competitive
Tic-Tac-Toe games. And, this latter set is a subset of the former.
There
seems to be only a small set of devices which can also be viewed
at this semantic level where we consider not only what the device
can do but what it "ought" to do if it is considered
to be "rational." These remarks point to the potential
relevance of normative ideas and models to the study of reasoning
and intelligence. The levels hypothesis claims that the mind
can be viewed from these three related but distinct perspectives.
Hopefully, the Tic-Tac-Toe example will help you to remember
these differing perspectives.
|
 |
