[Retros] Conventions in Retroanalysis

Peter Fayers fayers at freeuk.com
Sun Aug 3 11:15:18 EDT 2003

Here is the full text of the review (by Cedric Lytton, FIDE judge for retros) in this month's Problemist.
As well as buying direct from Alexander, people in Europe can order it via the British Chess Problem Society - please send a 5-Euro note (at your own risk) to me at
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Text follows:

Conventions in Retroanalysis, by Alexander George. (An updated version of the same author's article: diagrammes July-Sept. 1994, pp.25-34.)

Available from the author at Department of Philosophy, Amherst College, Amherst, MA 01002 price $5.00, or from Peter Fayers price £3.00. Both prices include postage. Shipment will be from the USA, so please allow 28 days for delivery.

Reviewed by Cedric Lytton.

This is a well-documented text with most or all of the major relevant references cited. It concentrates on direct-mates in which retro-analysis (RA) permits the deduction of various mutually-exclusive combinations of en-passant and of White and Black castling, and the text divides into two parts.

In the first part, the author shows that the "common convention for castling" (CCC), which simply declares a particular castling legal unless it can be proved otherwise, leads to various contradictions if applied with strict logic to some well-known problems. Now, in most of these problems the composer's reasoning is obvious and the solver intuitively modifies the CCC to avoid these contradictions, in the direction either of Partial Retrograde Analysis (PRA), aka Retro-Variants (RV), or of A Posteriori Proof (APP), once known as the Adamson type; but the perfect logician avoids intuition and seeks an exact reformulation of the CCC to cover all cases. Certainly attempts to reconcile the dichotomy of PRA and APP have taxed the logical powers of many great experts, and Colin Vaughan wrote in The Problemist, some time in the early 1970s: "We cannot see that either side has a monopoly of that favoured commodity, logic." However, it is one thing to assert dissatisfaction and quite another actually to provide such a reformulation.

In the second part the author does attempt a stricter formulation, "Complete Retroanalysis by Cases" (CRAC) and applies this to further classic direct-mates, ending with the great five-part #3 by Jim Mauldon, BCM June 1666 (version, 1667) which this reviewer admits was new to him. Even now, the author is not happy. For one thing, he proves within the axioms of CRAC that any problem involving White castling as a keymove is necessarily unsound - a result guaranteed to upset all classical-RA lovers of this great corpus. For another, he maintains (and in a carefully-written Appendix we discover why) that in strict conjunctivistic logic, inter alia one cannot assert that a proposition X is either true or false (axiomatic to a classical logician). The reviewer thinks this is probably a consequence of Bertrand Russell's work on classes of classes, within which there are statements that are neither true nor false (for example, "The barber shaves every man who doesn't shave himself"). But this means that. eg. the author cannot assert the disjunctive statement "White can capture ep. or Black cannot castle" where the solution requires it, again denying himself the pleasure that classical RA-lovers get from this body of problems, including Mauldon's #3 cited above. On the other hand, in Gerd Rinder's Die Schwalbe 35 (1975), 2b5/1pPp1p1p/3p1P1k/3PpKpP/4P1P1/4P3/5p2/8, draw (APP), the author would presumably be very happy with the solution: neither ep. capture is legal because neither can be proved possible for all proof games; white is stalemate! Maybe the author would be equally happy with AP(osteriori)P helpmates or retractor helpmates (not discussed here) in which both sides cooperate logically as well as over the board.

This little book, then, can be viewed as an anthology of nice RA direct-mates, several of which will be new to most readers, all of which can simply be enjoyed for their own sake while keeping in mind and respecting the author's strictly logical standpoint. This reviewer is glad to have his copy.

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