Abduction is hypothetic and diagnostic reasoning. It is backward reasoning, that goes from an observed fact, considered to be a sign, to the most plausible explanation. It is a First, in the Peircean sense of the word.
Deduction is rule-based prognostic reasoning. It is foreward reasoning, that goes from an observed fact and the appropriate rule, to a conclusion. It is a Second.
A car driver looking at his dashboard may see certain indicator tell him that he will soon be out of petrol and that his car will refuse to carry him further on. This is deduction.
It happens that a car stops without giving any announcing sign. Poor driver. He has to do some backward reasoning, to make an effort to understand what causes his disconfort. He will try to find a good explanation enabling him to act adequately in order to solve his problem. This is abduction.
Let us admit that the most plausible explanations for the stopping of the car are:
* it is out of petrol.
* the battery is dead.
The driver looks at his dashboard. The indicator tells him that a lack of petrol is not the problem. He then switches to another abductive reasoning:
* The car stops.
* When the battery is dead, a car stops.
* The battery may be dead.
The important element in this mode of inference is the existing knowledge of a general rule. That the driver is able to mobilize such a rule makes us conclude that the driver has at his disposition an expert system concerning the functioning of his car. He may rely on this expert system when he starts his inferential mecanism to operate. The presence of the general rule ‘when a battery is dead, a car stops’ brings a deductive element in the driver’s abduction. This is why this type of abduction may be called deductive abduction. It is essential that the driver is aware of the existence of the rule, or, if not, that it can be easily made explicit.
The format of deductive abduction is:
* If p, than q
Things are different when one is confronted with an illimited profusion of possible explanations.
There is the exemple of the joke about the man seeing another man walking every day in his street with a carrot in each ear. This makes the first man very curious. But he does not dare to ask the man why he does so. One day he sees the man, now carrying a ballpoint in each ear. The observer is so overwhelmed by his curiosity that he runs out of his house into the street and asks the man for an explanation. That explanation is simple. The carrots were sold out this morning, says the other.
This was an explanation the curious man has certainly not thought of. In his guessing at the riddle, in his abductive reasoning, he may have thought of all kinds of existing or imaginable rules that may lead to some explanation, but in this particular case he had to create a rule that was really beyond any logic, any reasonable imagination.
We can imagine a man who would have thought of an enormous number of explanations for the fact that the other man was carrying ballpoints in his ears:
* It gives the man an unusual erotic pleasure.
* He tries out new ways of carrying small objects.
* He considers it to be esthetic.
* He wants to be an original.
* He makes some kind of sales promotion.
And so on.
For all these inferences basic general rules are not available. The interpreting person has, in this case, to create his own basic rules. This is why we may speak of creative abduction.
The format of creative abduction is:
* If p, then q
I think we may consider creative abduction as the most basic way of inferring. The most wide-spread may-be. Descartes supposed that common sense is the most well spread quality among mankind. An amendment to this dictum could be: creative abduction, which is the basis of common sense, is the best spread quality among mankind. Any human being has the gift for creating general rules that can function in new situations. Any human being is able of creative abduction.
Chess cannot be played without knowledge of basic rules. It is basic that you know what a chessboard is and how to place it between the players, white square on the right side. If your intended opponent takes a damboard or if he places the chessboard the wrong way (black square right), you may conclude: this man is not a chessplayer.
There is an enormous number of rules for the course of the pieces. Beginning chessplayers have sometimes to be instructed, even during the game, about the conditions of castelling, about taking a piece ‘en passant’ and so on.
We may postulate the beginning chessplayers spend most of their energy on the integration, in their minds, of the elementary rules of the game – and we may characterize their way of playing as predominantly deductive. Beginning chess–players are like people starting to learn a foreign language; they are in their drill-phase, they apply recently learned grammar rules to simple exercices, in order to internalize these rules. Habit taking is the goal in this learning phase, just as it will be during a whole lifetime.
The first chess computer operating in the Netherlands brought on its first move the white king’s knight from its beginning position (g1) to f3. This is an acceptable move. It is effective in this sense that it brings the knight to development; from its new position it has a threatening power over two fields in the centre (d4 and e5). After the opponent’s reply, black’s first move, the second move of the computer was amazing: the machine brought back the knight to its starting position.
Why is that move so amazing? It is correct. It is a correct application of some of the basic rules of the game. The chess player is entitled to play the same piece in consecutive moves. A knight may go forwards and backwards. The computer could eventually have continued to repeat the knight’s manoeuvre as long as his opponent would have given him opportunity to doing so. But the computer’s second move is amazing because it is such a stupid move. It is absolutely ineffective. It gives away all the benefit of the first move.
The move breaks with a basic rule of chessplayer’s experience that prescribes good positioning of pieces in the opening phase of the game – you must ‘develop’ your pieces, occupy important squares, make your general position strong.
When I read how our first dutch computer had played in its first game, I have thougt of the experience of a researcher about the behaviour of schizophrenic patients. He had played chess with a schizophrenic patient and noticed that this patient had a tendency never to make moves that would bring pieces too close to the position of the opponent. The researcher compared this tendency to stay on his own territory on the chess board to the tendency of schizophrenic patients to create in their rooms a kind of marked off territory where they could feel themselves on private ground, in safety. And so I thought of this beginning chess computer as showing at least one symptom of schizophrenia.
My amazement made me aware of the fact that even the most stupid beginner has to do with two different kinds of general rules: the rules of the game and the rules of experience. Experience should have learned the computer that he should have chosen a better second move. Any experienced chess player seeing the computer make that bad second move would have known that white is going to loose. Any experienced chessplayer disposes in his mind of rules of experience that give him an indication about what to do and what not to do in the opening phase of the game and in certain situations. There are such rules already for the very first move: it would be stupid to move forward pawns on the extreme sides of the field (a2 or h2) or to bring the knights to these sides (Ka3 or Kh3). So, the beginning chess player is not only bound to know the rules of the game. He has to do immediately with rules of experience. His interpretation of the situation on the board and his inferential behaviour during the play are based on a very complex set of rules.
3. The role of the rules
Knowledge of the rules of the game is a necessary condition for playing chess. Knowledge of the rules of experience is a necessary condition for being a reasonable strong player. Knowledge of the rules of experience are obtained by personal experience and by learning from other players’ experience in studying their games. Human as wel as mechanical players can do that. And they do.
Chess is a thinking game. The thinking in chess can be accounted of in logical formats of the if–then type.
* If the situation is thus, then the best move is ... (major premise)
* The situation is thus. (case – minor premise)
* The best move is ... (conclusion)
The pleasure of chess is dependant of the fact that general rules as quoted are not available for alle the many situations that are possible. There are situations in which it is absolutely impossible to say what is the very best move. In these cases a lot of moves can be excluded as being bad, but there stays a certain number of moves that are equally good. The best example of such a position with equal chances for different moves is the starting position of every game. Several first moves can be considered to be equally good. The day a best first move will be found and, accordingly, an algorithm that makes White always winner, chess will be dead. God forbid. It would be as if some athlete would have brought back the world record on the hundred meters to zero seconds.
As long as the best first move has not been found, even excellent players will have to play with general rules in uncertainty. If they do so, we may say that their inferring is deductive abductive.
4. Deductive abduction
Chessgame after move 25
Botvinnik Capablanca After 25. Re1:
We speak of deductive abduction, when the interpretation of a situation is made on the basis of a rule that is not given but that is self invented (created). When a chess player makes his decision about the best move to play in a given situation, we say that he makes his decision on the basis of intuition.
A good exemple of (deductive) abduction in chess we find in Hans Müler’s excellent book Botwinnik lehrt Schach, 1949 (I read it in dutch translation, Zó speelt Botwinnik, Van Goor, 1950), when Müller analyses Botvinnik’s brilliant game against Capablanca in 1938 during the AVRO-tournament. In this game Capablanca (Black) develops an attack ont the queen’s side, while Botvinnik (White) aims for an attack ont the king’s wing. Müller notes, with Botvinnik’s 16th move (Ra1-e1) Guided by his very refined positional insight, Botvinnik sacrifies his pawn (on a4). He foresees that the loss of material is sufficiently compensated by the better possibilities of his pieces on the e- and f-lines that, later, will be opened.
At first sight, Müller’s remark may suggest that Botvinnik’s superiority, under these circumstances, lies in his better prognostics. He foresees better than his opponent. But one may also say it this way: Botvinnik’s strategic, or creative, insight is better. His hypothesis, his assessment of the situation, is the better one. This hypothesis is established on the basis of inductive abduction, that is the creation of general rules acquired in previous ecperiences. Our conclusion may be: there are elements of induction, deduction as well as abduction in Botvinnik’s superior inferential capabilities.
I make a little digression here. The question if indeed Botvinnik’s hypothesis is indeed superior to Capablanca’s is not solved until the 30d move, when Botvinnik sacrifies a bishop (on a3). This sacrifice, Hans Müller says, is ‘the beginning of a brilliant combination’. And so it is. The sacrifice has to be accepted. If not, Black looses the game immediately. The game thus comes into a phase of fatality. Capablanca, after this move, does not make a single mistake. We see that things cannot go otherwise than the way they go. That gives us a feeling of the cruelty of fate, the feeling that is so so essential in tragedies. In tragedies heroes fight a hopeless fight against the will of gods. The cruelty of fate gives the game its extreme beauty. What makes the game thrilling is that after the first sacrifice comes a second one on the next move (the 31st one), when Botvinnik gives away a knight on the other end of the chessboard, and that black still fights back, trying to obtain eternal chess during thirteen thrilling moves, until he surrenders (at the 41st move) seeing that mate is inevitable. This long agony makes Capablanca human, Botvinnik an almighty god – and the game a thrilling tragedy.)
5. Examples: Kasparov, Alekhine
In 1981 eighteen year old Garry Kasparov played in the USSR championship with White an Anti Meran opening against Timoshchenko. He was confronted with Black’s plan that, as Kasparov notes in his book Fighting Chess, 1995, was deeply worked out by Botvinnik. The game followed the Botvinnik-variation of the Anti Meran opening as applied in a previous game, Anikayev–Sveshnikov, up to the 22d move. In this position Anikayev had made a bad move and had loosed. Kasparov writes: But even such a failure did not dissuade ‘seekers of secrets’.
His opponent in the Championship game, Timoshchenko, was such a seeker of secrets. He came up with a move that he had played earlier, that had proven to be bad. Of course Kasparov was surprised to Timoshchenko play that variation again. Both players, Kasparov and Timoshchenko had been playing rapidly the well known first moves. They had done their home work. When, in the beginning of a game, players make their moves quickly, they are in their deductive phase. They have their rules for the actual situations at their immediate disposal. It is not before they fall in deep thought that they enter the abductive phase of the game. Then they are confronted with novelties. The power of such novelties lies in the difficulty for the opponent to leave the prepared analysis and to turn to independent analysis at the board, as Kasparov calls it. At the board it costed him 53 minutes to find an answer to Timoshchenko’s novelty. A good answer it was (until the contrary has been proven!), because Kasparov succeeded to win.
The next day, in the same tournament, Dorfman played against Kasparov the same variation of the Anti Meraner. He followed the Kasparov-Timeshchenko game until the 30d move. The Dorfman came up with a novelty. And was crashed by a surprising Kasparov response. Since that day the variation was not played some time. It stayed, as I would like to say, in a deduction box.
In the summer of 1983 Kasparov played for Azerbaidzhan the Spartiakad. In this tournament, he met as an opponent Mikhail Tal, the Latvian exworld champion. Tal played the Botvinnikvariation of the Anti Meran opening. Kasparov thought; Tal is playing down the main line. Where does the surprise await me? in other words: we are in our deductive phase. When will we turn to abduction? When will I have to be creative? Tal followed the Black moves played in the games Kasparov–Timoshchenko and Kasparov–Dorfman. Kasparov mentions in his book that he spent 20 minutes to fix in his mind the course of events in these previous games.
It was a special but not unusual situation chess-masters can be in. They start playing along deductive lines, waiting for the moment the moment forces them to switch to abduction.
Chessgame after move 22
Kasparov Tal After 22. ... Ke5!
With his 21st move, Tal places a knight on the middle of the board (e5) in stead of giving it a more defensive position (a5) as Timoshchenko and Dorfman did. In his book, Kasparov writes that he realized: Here is Tal’s novelty.; Kasparov then considers several possibilities. They seem too risky to him. Therefore I set off along the beaten track (as in the other games) although I felt dangers radiating from the knight at e5. It did not mean that he played in a defensive way. To play in a defensive way is not Kasparov’s style. He just sticks to moves that have proven to be effective in the games with Timoshchenko and with Dorfman. Even in changed circumstances he sticks to deductive procedures, we may say. He just changes the order of the moves. He takes with his bishop a pawn (on a7) on the 27th move in stead of on the 30th in the other games. Thus he forces his opponent, Tal, to assume the responsibility of finding a new move. He passes on the burden of abduction.
Abduction is not a heavy burden to Tal. He is known for for his gift of finding unexpected moves. The game develops in a very interesting way. There were threats on both sides, created by White as well as by Black. They did not lead to a decisive attack – the game ended in a draw.
During the game Kasparov had rejected a possible 23d move. Why? By intuition, as he wrote. Afterwards he checked, in his analysis of the game, if his intuition had not betrayed him. In a Postscript to the Tal game he exposes and considers an impressive amount of beautiful variations that at first sight show that Kasparov’s fear of the consequences of the rejected moves had been unjustified. It looked as if he could have won brilliantly. He writes:
It’s easy to imagine my disillusionment on finding these variations. I was left regretting missed opportunities and wondering which future opponent would set off along these paths.
These lines show us Kasparov as a ‘seeker of secrets’. The use of the word path, in his text, reminds me of another seeker of secrets, namely Augustin Meaulnes, the hero of Alain-Fournier’s novel Le Grand Meaulnes. Mealnes, in this book, is characterized as un chercheur de pistes. He is indeed ‘a seekker of new ways’. Kasparov has in common with Meaulnes that he is a ‘chercheur de pistes’. The difference between both men, the real chess master and the fictive school boy, is that their goals are different. Kasparov seeks ‘new ways’ in order to surprise his opponent, and in order to avoid a surprise that his opponent can confront him with. Meaulnes is after new adventures, has no opponent. But the chess–master playing fighting chess is certainly also seeking ‘new adventures’, just as Alain–Fournier’s marvellous hero.
When, later, Kasparov carefully reconsidered the possible variations after the rejected move, he discovers new ones. They show him that Black could have had the possibility of inflicting a terrible reckoning, setting White with difficult if not insuperable problems. And he concludes that meeting with such a surprise during a game would be most unpleasant. This is to say that Kasparov, although confident in the abductive power of his thinking, realizes that creative reasoning is good but that well prepared deduction is better. This is the justification of the many hours grandmasters spend in finding prepared variations. These prepared variations are no other than the results, frozen deductions, of what originally was intuition, the living source of abduction. In Peirce’s terms: the prepared variations are Thirds that were Seconds and that started as Firsts.
Alekhine, who was a chess genius, has in an intuitive way implicitely expressed, but very differently from Kasparov, the essential difference between the role of deduction and abduction in chess. He said: Nichts ist schädlicher als Schablone. Nothing is more unprofitable than walking the beaten tracks. I think these words must be interpreted as follows: victory, in chess, comes from abduction, and it is very dangerous to have too much confidence in the apparent safety of deduction. Alekhine expressed the same idea in an indirect way, when he said Das Geheimnis meines Erfolges? Ganz einfach: ich zwinge meine Gegner mit jedem Zug Selbständig zu denken! (The secret of my success? I force my opponents with every move to think by his own.) There is of course an implicit contempt in Alekhine’s words. What he says is finally this: when it comes to independent thinking, I, Alekhine, am the stronger one, compared to my opponents. When we admit that independent thinking is abductive thinking, we may conclude that Alekhine means that the abductive thinker is the better chessplayer.
I think he is right.
© Aart van Zoest, February 2001
Botwinnik Capablanca Kasparov Tal
AVRO tournooi 1938 Spartakiad
1. d4 Knf6 1. d4 Knf6
2. c4 e6 2. c4 e6
3. Knc3 Bb4 3. Knf4 d5
4. e3 ... 4. Knc3 c6
Image 1 5. Bg5 c3:
4. ... d5 6. e4 b5
5. a3! Bc3:+ 7. e5 h6
6. c3: c5 8. Bh4 g5
7. d5: d5: 9. Kng5: g5:
8. Bd3 0-0 10. Bg5: Knbd7
9. Kne2 b6 11. f6: Bb7
10. 0-0 Ba6! 12. g3 c5
11. Ba6: Knxa6 13. d5 Qb6
12. Bb2 Qd7 14. Bg2 000
13. a4 Rfe8? 15. 00 b4
14. Qd3 c4 16. Kna4 Qb5
15. Qc2 Knb8 17. a3 Knb8
16. Rae1 Knc6 18. b4: b4:
17. Kng3 Kna5 19. Be3 Bd5:
18. f3 Knb3 20. Bd5: Rd5:
19. e4 Qa4 21. Qe2 Knc6
20. e5 Knd7 22. Rfc1 Kne5!
21. Qf2 g6 Image 3
22. f4 f5 23. b3 c3
23. f6: Knf6: 24. Knc3: c3:
24. f5! Re1: 25. Rc3:+ Kb8
25. Rf1: ... 26. Qc2 Bd6
Image 2 27. Ba7:+ Kb7
25. ... Re8 28. b4! Knc6
26. Re6! Re6: 29. Be3 Be5
27. e6: Kg7 30. Rc6: Ba1:
28. Qf4! Qe8 31. Rc7+ Kb8
29. Qe5! Qe7 32. Ba7+ Ka8
30. Ba3! Qa3: 33. Be3 Kb8
31. Knh5+ h5: 34. Ba7+ Ka8
32. Qg5+ Kf8 35. Bc5 Kb8
33. Qf6:+ Kg8 36. Rf7: Be5!
34. e7 Da3+ Image 4
35. Kf2 Dc2+ 37. Ba7+ Ka8
36. Kg3 Dd3+ 38. Be3 Rd7!
37. Kh4 De4+ 39. Qa2+ Kb8
38. Kh5: De2+ 40. Ba7+ Kc8
39. Kh4 De4+ 41. Qe6: Qd5
40. g4 De1+ 42. Qa6+ Qb7
41. Kh5 ... 43. Qc4+ Qc7
1 0 1/2 1/2
Chessgame after move 25
Image1 Botvinnik Capablanca After 25. Re1:
Chessgame after move 25
Image2 Botvinnik Capablanca After 25. Re1:
Chessgame after move 22
Image3 Kasparov Tal After 22. ... Ke5!
Chessgame after move 22
Image4 Kasparov Tal After 22. ... Ke5!