2. Philosophy - Stefano Franchi

F ORM AND CONTENT
completely different interpretations or, even more interestingly, that two different formal
systems can be attached to the same content through different interpretations. Chess, for ex-
ample, can be formally analyzed as composed by a square, 8x8 chessboard and 2 sets of 16
pieces belonging to 6 different kinds (King, Queen, Bishop, Knight, Rock and Pawn) plus
a few rules for movement, check and capture. But an indefinite number of alternative rep-
resentations is possible. We can define chess played on sticks, spheres and cubes, with
wooden chessman, iron chessman and so on and so forth. Here, for example, is one (not so
original) variation: “monodimensional” chess, a game obtained by replacing the square
board by a long stick divided in 64 units, conveniently numbered from 0 to 63. Pieces are
as usual but movement rules become very complicated. 14
Although it is doubtful that anyone would find much fun in playing monodimensional
chess, from the standpoint of Artificial Intelligence the two games are the same: two iso-
morphic realizations of a same structure. (The fact that people, in fact, do have fun, when
playing the game of chess, whereas monodimensional chess, while being “equivalent” to
it, is hardly playable by humans should alert us to the existence of a possible problem.) The
important thing here is that AI’s definition of formality is such that the hypothetical content
assigned to a position in the ideal structure is exactly maintained if the rules have been care-
fully defined.
In other words, the attribution of meaning to symbols occurring within the structure
can always be performed at the last minute because the (syntactic) rule governing the
movements of the pieces do not touch it at all. According to the formalist, symbols have
14. Consider pawns, the simplest piece, and let us limit to White's pieces: at the beginning they occupy
cases 8-15 and the possible moves for each of them can be found by adding 8 (or 16, for their first
move) to the original position. The rule for capture is a bit more complex: a pawn can capture a piece
which is 7 or 9 units far from him. Rules for all the other pieces can be given -- although the exercise
starts to be boring very quickly -- so that an exact 1-to-1 translation from one representation to other
can be given which respects all the relations among the pieces. For example, if we number the cases
from 0 to 63, the first two moves of the Sicilian opening (1. e2-e4 e7-e5 2. Kg8-f6 Kb8-c6) become:
1. 12-28 52-36 2. K6-21 K57-42). The example is in fact quite simple, since it preserves the distinction
between a fixed chessboard and pieces moving on them. But the relationship could be reversed: we
might imagine a game chess played on a moving (and topologically quite interesting) chessboard with
fixed pieces. John Haugeland exploits a trick of this kind in his example of a different version of solitaire
given in Artificial Intelligence…, 60 ff.
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