The "Symbol Grounding Problem" was formulated by Harnad (1990). He pointed out that the symbols in an information processor can only be internally described by using an address to obtain other symbols which can only be described by looking up yet further symbols and so on. There is nothing within an information processor that gives its internal symbols any meaning.
The Symbol Grounding Problem can be seen as another way of stating Aristotle's regress. In Aristotle's regress it is argued that perception is problematic because the image on the eye must be seen by an inner eye that in turn must be seen by another inner eye whilst in a computer the contents of a data store are categorised by being related to data in another data store but unfortunately the content of this data store is just another set of symbols that can only be categorised by relating them to another data store and so on.
The symbol grounding problem is a scientific way of describing Searle's Chinese Room Argument (Searle 1980) in which a person translates English into Chinese by following a set of instructions (ie: by manually implementing a computer program) and might appear to know Chinese without actually knowing Chinese at all.
Both the symbol grounding and Chinese room problems had already been explored by Aristotle when he pointed out that perception would create an infinite regress or require a sense that is self aware. In the symbol grounding problem an infinite regress would occur in a processor if it sought for any internal meaning for its symbols and in the Chinese room the symbols only acquire meaning when they are passed outside the processor to a recipient that is self aware.
Leibniz knew about the problem of mechanical systems being no more than parts that act upon each other three hundred years ago:
"One is obliged to admit that perception and what depends upon it is inexplicable on mechanical principles, that is, by figures and motions. In imagining that there is a machine whose construction would enable it to think, to sense, and to have perception, one could conceive it enlarged while retaining the same proportions, so that one could enter into it, just like into a windmill. Supposing this, one should, when visiting within it, find only parts pushing one another, and never anything by which to explain a perception. Thus it is in the simple substance, and not in the composite or in the machine, that one must look for perception." Leibniz. Monadology, 17.
The Symbol Grounding Problem is directly related to Leibniz's windmill, computers being machines in which electrons are just "parts pushing one another". Even if a computer were attached to a robotic arm and recorded its own actions all it would have internally would be a set of symbols.
All that has changed in the past three hundred years is that modern people really love their machines. The idea that our own creations might be conscious is not new, for instance the ancient Greeks loved their ceramics like we love computers and believed that Man himself was made by the gods breathing on a clay man.
The symbol grounding problem does not seem to apply to us. Unlike a digital computer, we know what we are doing, for instance if I fill a hole by digging soil with a spade my mind contains the directedness of the loaded spade towards the hole as a real extension in time (see Time and conscious experience). It is this extension in time that allows me to know my own symbols.
Harnad (1990) shows that symbols can be grounded by association with real objects in the world but this demonstration only means that we can construct machines that work, not that the machines have any internal conscious experience.
Harnad, S. (1990) The Symbol Grounding Problem. Physica D 42: 335-346.
Searle, J.R. 1980. Minds Brains and Programs. The Behavioral and Brain Sciences, vol. 3. Copyright 1980 Cambridge University Press. http://members.aol.com/NeoNoetics/MindsBrainsPrograms.html
It is curious that the symbol grounding problem is really a restatement of Heisenberg's Uncertainty Principle: we cannot simultaneously observe the position and momentum (elapsed time) of an event. Information is always physically instantiated so uncertainty applies as much because two sets of information must be generated to represent both position and momentum as because, in Heisenberg's original example, a measuring photon will perturb the electron that it strikes to make a measurement. (See Entropic uncertainty principle