In the same way, a thought about what is achievable in a given chess position refers to the abstract model that reflects what is in common to all equivalent chess positions. It is also important to note that the abstract structure focused upon in a chess game is conceived in entirely relational terms.
What is represented is a spatial arrangement, with pieces whose nature is exhausted by formally specified relational possibilities. The moral here is that when we conceive of a chess piece as such, the intrinsic character is not relevant. A chess piece can be made of wood, plastic, metal or old bits of kneaded dough. Its shape can vary, likewise. An imaginative grasp of the future possibilities open to a piece is essential to our recognition of a piece for what it is.
But the possibilities that in this way determine the nature of a piece are purely spatial. Only the potential relations of the piece to other squares and other pieces on 10 See, for example, the classic work by Binet More recent studies confirm the finding that blindfold players imagine the chess pieces in terms of the "lines of force" they exert: see Chabris and Hearst This idea, that the relational role or function of a piece is what is essential to our understanding of its nature, is one important feature that throws light upon the nature of our perception of everyday objects.
Despite their abstract nature, from a phenomenological point of view, chess positions take on a vivid reality. From the good player's perspective, the pieces on the board come alive in a game. They are not treated merely as representations in some abstract formal system.
Positions and pieces on the board can take on a meaningful presence, and have a strong emotional resonance. In part, the fact that positions take on significance has to do with practical goals, when a player strives to win the game. But in addition, the combinations that arise in practical play - and also in composed studies - can be assessed disinterestedly, in aesthetic terms, for beauty, elegance, wit and other related higher-level properties.
In his famous book, The Luzhin Defence - arguably the greatest novel about the game - Vladimir Nabokov captures some of these aspects of chess through his portrayal of the central figure of Luzhin, the doomed chess master whose thought processes, when playing blindfold chess, are described as follows: [Luzhin] saw then neither the knight's carved mane nor the glossy heads of the pawns - but he felt quite clearly that this or that imaginary square was occupied by a definite concentrated force, so he envisioned the movement of a piece as a discharge, a shock, a stroke of lightning - and the whole chess field quivered with tension In commenting on the final game of his return match with Euwe, Alekhine wrote of the capture of his opponent's piece as 'removing the most hated knight of the match', and such a comment is typical of the passionate way that players engage with the game.
The chess style of Petrosian was characterised by the way that he would exert a "python-like" grip on his opponent, depriving him of all counterplay. Nimzovitsch spoke of a passed pawn as 'a criminal, who should be kept under lock and key'; the passed pawn has a 'lust to expand'.
In these, and in multiple other ways, the manner in which chess players talk about the game reflects the fact that chess positions are full of meaning for them, figurative meaning that goes far beyond a grasp of formal structure.
This feature of the way that we see chess positions has implications for theories about perception and the nature of physical world.
In order to do this, they have to bracket off groupings of pieces on the board that are less central to their main focus. The player needs to treat some groupings of pieces on the board as semi-permanent units, like complex objects, which have no direct bearing on the task in hand.
If the immediate task is, for example, to find a direct sacrifice to expose the opponent's king to a possible mate, then the player may ignore pieces on the other side of the board, at least in a temporary way, while exploring the initial sacrificial possibilities. An example here will illustrate what I mean, and clearly shows the difference between the way computers "think" or compute in chess, and the way that humans explore the tactical possibilities in positions.
This is from a very interesting endgame study by Mihai Neghina, first posted on the internet in The position was initially published without a solution, accompanied by the claim that computers were unable to evaluate the position correctly. D 12 Neghina Endgame Study position version. White to play and win. This position is a forced win for White. However, even after some introductory moves, the computer wrongly calculates that Black has a winning advantage: 1 Nd4 Qg7ch 2 Kh3 Qxh6 3 Nf4 Kc8 Because of the threat of a knight fork on e6, if the knight on f4 is captured 4 Nde6 Kb7 5 h5 Black has a queen for two knights and a pawn, normally a winning advantage for the side with the queen.
The computer's verdict on this position is that Black should be able to force a win. Here is the key trapping position, reduced to its bare elements. D 13 The Black queen can make 8 moves in all, but they will all lead to her capture. It is very difficult to programme a computer to disregard this complex - at each move the computer will calculate these 8 possibilities, and their further ramifications, including over twenty possible replies by the White knights and the king.
The possible variations multiply up to such an extent that they exceed even the computer's capacity for calculating billions of different positions.
The human player thinks differently. He, or she, can conceptualise the array on the right-hand side of the board as a semi-permanent object. The trapping piece-complex is treated as a stable unit. It can be imagined as a separate object, one that does not affect the play. If the complex is treated in this way, it then becomes easier to ignore it when calculating the main lines, and analysing the best play for both sides. This results in White winning a crucial pawn on the queen side, so as to reach a won ending.
The central variation continues: It is only near the final stages, after around 10 or so moves, that the computer begins to assess the position correctly, as a win for White.
Firstly, with respect to the differences between the way that humans and computers think, the fact that humans 12 For discussion of this endgame study, see Josten The future possible moves within the piece complex are, as it were, "suspended" and removed from consideration by the player, at least on a temporary basis.
Secondly, it is a phenomenologically important fact that the structure which is treated by the player as a relatively stable object is a complex spatial structure. This structure can be interpreted as a high-level property of the chess game, and illustrated by a concrete arrangement of pieces on a board, but its essence is nevertheless something abstract and formal.
At the basic level, each piece is understood in terms of its spatial role. Players also exercise the imagination in further ways, in thinking through tactical sequences and assessing strategical possibilities, and in recognising larger structures, piece groupings that have different degrees of permanence and complexity.
In playing chess the player is dealing with what is at one level something purely mathematical: an abstract spatial structure governed by formally specifiable rules. Such structures are represented, for greater convenience, by arbitrarily chosen shapes on a board with a certain spatial configuration. The arrangements of pieces on the board have phenomenological significance, and carry emotional charge.
Although its essential aspects are purely formal, a chess position is seen as being richly meaningful. It is, of course, arguable that this constitutes a further dimension in which humans and computers differ. These considerations about the way we grasp chess positions have important implications for epistemology. It is not only in playing chess and similar games that these two features of consciousness are combined.
The structure of visual consciousness that is manifested in the case of seeing chess positions tells us something important about the general nature of perception. How we should analyse what goes on when a person plays chess has relevance to current philosophical disputes concerning the proper way to analyse the perceptual relation.
The game of chess provides a model of our perceptual engagement with physical reality. In the concluding section of this paper I shall explain why this is so. Much recent philosophy of perception has involved increasingly convoluted attempts to defend forms of Direct Realism otherwise known as Disjunctivism. The subject is immediately aware of intrinsic properties belonging to the external physical object perceived. An irreducible experiential relation connects the external object perceived with the subject's perceptual consciousness.
It can appear to fit in with some of our common-sense convictions about our perceptual contact with the world. However, it faces two formidable objections. Firstly, there is the causal-scientific argument, developed by Valberg and Robinson. This turns on the point that both hallucinatory experiences, and also veridical experiences, are generated by exactly the same kinds of proximal brain states.
Such states are sufficient, as the hallucinatory case indicates, to produce an experience as of an external world. The argument offers a good reason for holding that veridical experiences are inner states, which, like hallucinatory experiences, supervene solely upon the proximal brain state that is causally linked to the distal object perceived.
It therefore follows that in seeing an object, I am immediately aware of the qualitative component of my inner experience - a phenomenal state of the same ontological kind that occurs in hallucination. What is an "irreducibly experiential relation"? What kind of relation connects the subject's conscious experience to a mind-independent object?
How does it fit into the natural world? It is difficult to spell out the Direct Realist theory in any clear way, so as to explicate the direct non-causal relation that is supposed hold between the subject and the specific object he, or she, perceives.
Without any positive account, there are no grounds to which the Direct Realist can appeal in order to specify which particular object is perceptually linked to the 14 Disjunctivism in its modern form stems principally from papers by Snowdon and McDowell So Direct Realism becomes parasitic upon the causal account.
There is no irreducible real relation connecting a subject's conscious experience with any mind-independent physical item, which can make that very item phenomenally present in experience. The phenomenal redness that I am immediately aware of, when for example I stare at a juggling ball, supervenes on my brain state alone, and is an item logically distinct from that ball, ontologically in the same category as the green after-image I will experience a moment later when I look away from the red ball onto a white surface.
But to note this point is not to deny the fact that perception is also, in an important sense, direct. As Kant emphasised, there is a further component in experience, which comprises the exercise of low-level classificatory concepts. These concepts arise, without inference, in perceptual takings normally focused directly upon external objects and their features surface or otherwise. The reddish shape I am non-conceptually aware of prompts me to see the object in front of me directly as a juggling ball.
The Causal Theory continues to meet with resistance. One objection to it interweaves semantical considerations about the content of experience with phenomenological considerations about the meaningfulness of our experience of objects.
The charge is that the Causal Theory is unable to give a satisfactory account of how we come to have any kind of awareness of properties belonging to mind-independent objects, an awareness that forms the basis of our understanding of a rich and complex objective reality. Part of the answer to this objection involves spelling out the structural realist conception of physical objects that, from a scientific perspective, is naturally allied with the Causal Theory. According to this conception, the intrinsic properties of objects are ultimately all primary qualities, qualities whose nature is essentially spatial.
According to the form of structural realism originally outlined by Russell, the monadic properties that belong to a macroscopic object at a higher level of explanation are ontologically reducible. They can be accounted for in terms of spatial and causal relations between the micro-objects that constitute the higher-level 17 This argument is spelled out more fully my , Ch.
These need not necessarily relate to the same entity. What we understand, when we grasp the objective nature of an object, is something that can, in principle, be accounted for by reference to complexes of spatial structures connecting micro- objects, and the way that they causally interconnect. What we take to be the sensible qualities of objects in the world - the familiar colours, sounds, smells, tastes and feel of objects present to conscious experience - turn out to be states of our own minds, which we project onto the structures that we perceive.
By interpreting our perceptual grasp of the world along these structural realist lines, we can defend the Causal Theory against the charge that it is unable to explain how experiences have empirical content relating to an objective world.
Nevertheless, this appeal to our grasp of the essential spatial structure of the physical world does not exhaust the issues raised by the objection. There is a further dimension to the problem. The worry is that, on the structural realist account, we cannot do adequate justice to the phenomenology of our perceptual experience. This deeper worry arises because, according to the Causal Theory, external physical objects can only be conceived of in austere formal terms, stripped of their intrinsic properties.
The objection is that we are left with something that is only, at best, a grasp of a bare structure. Allegedly, this understanding fails to match up to our everyday grasp of the kinds of objects we encounter in perception. On the structural realist view, the notion of a physical object ends up as thin and attenuated. Yet the world that we engage with in our ordinary activities seems to be the very opposite of this. It is a world that is rich and complex, full of value and meaning.
We encounter perceptually a multiplicity of complex natures, higher-level monadic properties, powers and norms. However, from what has emerged about the way that we see chess positions, it should be clear that there is a good reply available to the Causal Theorist.
As the examples from chess indicate, seeing or otherwise perceiving anything is always a complex affair. The way that we see chess positions is, to a large extent, indicative of how we see things in general. One component of visual experience - the sensory aspect of perceptual consciousness - involves something qualitative being immediately presented to the subject: an array of shapes and colours.
Experiences have a 21 See Russell The patterns of pieces and squares presented in experience, when the player looks at the pieces on the board, need to be distinguished from the objects that are the focus of the chess player's higher-level cognitive attention, in which the pieces are taken to be related to each other according to formal rules that determine their potential moves.
As we have noted, what the chess player sees, in the more inclusive sense, are abstract objects. In a strict sense, such objects are grasped in spatial terms, by virtue of the potential relations that the individual units bear to each other.
However, as the example of chess also shows, an essentially spatial grasp of an entity is compatible with that entity having a further level of meaningfulness for us. As has been argued above, chess structures can have a meaningfulness which goes beyond the merely formal. We perceive chess positions as containing relatively stable complexes of pieces, which can be considered, at least temporarily, as larger-scale unified objects.
A chess player sees part of the board as a well-defended king's position, or a strong centre, a blocked pawn chain, and so on. We also noted that, despite the abstract formal nature of chess, pieces and piece-complexes are often conceived in value-laden terms, and they can take on a rich emotional significance.
Parallel considerations apply to our perception of physical objects in general. Webone marked it as to-read Sep 17, Paul Cannon gaprjndashvili it May 26, For example with the waiting move 5.
Mini skills 1 day ago. Rf4 scoops our pawn. Bereolos rated it really liked it Jun 26, Donald marked it as to-read Mar 30, Feb 05, Emilio rated it really liked it Recommends it for: Finally, I found the cool 1. Candy Cane Classic 18 hours ago. Loaded with chess puzzles and succint insights. Technique in Chess. Pawn Power in Chess.
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