He has also gathered very specific knowledge from special sciences, such as physical anthropology that people tend to write graffiti at or just below eye level. This expert knowledge makes Holmes sensitive to details at a crime scene at Lauriston Garden visited in A Study in Scarlet that inspectors Lestrade and Gregson have overlooked or misinterpreted. From this and other clues, he concludes that the murderer is a man, contrary to Lestrade and Gregson who suspect a woman perhaps named Rachel.
Eventually, Holmes positively identifies the culprit in part thanks to Trichinopoly ashes in his hotel room. In A Study in Scarlet , Holmes approaches the crime scene without preconceptions. By contrast, in The Adventure of Silver Blaze , Holmes initially accepted the police theory, and the narration begins with Holmes explaining to Watson that he must revise his initial assessment. The silence of the dog and its consequences is, in this context, more of a serendipitous discovery than the outcome of a systematic attention to details leading to equally systematic recall as in Lauriston Garden.
But Holmes knows of surgical procedures favored by unscrupulous racehorse handlers, which suggests an entirely new direction for his inquiry. Watson acknowledges that something is amiss with the knife, but lacks knowledge of veterinary procedures to pursue any further.
The appropriate space metaphor would be that of a warehouse where similar parts of different items would be stored in the same location. Let us turn to that property for a moment. Items stored in memory are distributed across cliques of neurons according to features those neurons as sensitive to.
For instance, the memory of the shape of the diamond of a particular deck of playing cards would be distributed across neurons coding its particular rhombus shape and neurons coding its particular shade of red. Subsequently, recalling this particular diamond would require co-activation of at least two cliques of neurons. And since those cliques of neurons would code rhombuses and shades of red associated with other memories, there would be a nonzero probability that recalling the particular red rhombus of that particular deck of cards would also trigger recall of other non-red rhombuses or other non-rhombus-shaped red things.
A distributed cam is thus an economical solution to the problem of limited storage space that Holmes complained about. A more appropriate metaphor would thus be that of memory as a library of blueprints for modular items for a 3D printer, with any given item being stored as an index of blueprints for the modules it is made of.
A distributed cam thus supports all manners of associations that may be relevant or not depending on the circumstances. In order to avoid association overload, recall is supported by an attentional mechanism called contextual focus see Gabora In a nutshell, focused attention favors associations of perceived, imagined, or recalled objects or circumstances, with memory items that share their typical features. For instance, in a state of focused attention, a chair perceived or imagined would be associated with other items of furniture with legs and seats stools, benches and backrest armchairs.
By contrast, a state of de-focused attention opens to associations with less-than-typical features, where the same chair might be associated with other objects whose shape adapts to that of some body parts. Furthermore, the relevant notion of strategy can be made mathematically precise within game theory.
Footnote 6. A strict, mathematical characterization puts strategic recall on a par with strategic deductive reasoning in non-deductive inquiry in the sense of the Strategy Theorem discussed in Sect.
More precisely, strategic recall can account for the opening of new lines of inquiry via non-analytic steps, including serendipitous ones. Genot and Jacot At the beginning of A Study in Scarlet , John Watson just returned from Afghanistan, where he spent a few months convalescing from a wound sustained in combat.
Living on a modest pension of which he intends to make the most, Watson is looking for some fellow to share a rent with. An acquaintance introduces him to Sherlock Holmes, who is looking for the same, in the chemical laboratory of a London hospital where the following interaction ensues:. Holmes reveals himself as the author and endeavors to defend his claims with an example:.
Observation with me is second nature. You appeared to be surprised when I told you, on our first meeting, that you had come from Afghanistan. I knew you came from Afghanistan. From long habit the train of thoughts ran so swiftly through my mind that I arrived at the conclusion without being conscious of intermediate steps. There were such steps, however. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair.
He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured. He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan. I then remarked that you came from Afghanistan, and you were astonished. As noted by the Hintikkas , p. We may reconstruct the above steps as a sequence of deductive steps.
To see this, let us introduce the Simon—Newell model of problem-solving see Newell et al. In the Simon—Newell model, a problem is specified through a class of possible solutions, typically expressed in some regimented notation sequences of first-order formulas for theorem-proving applications, sequences of steps coded in algebraic chess notation for chess problems, etc.
Those possible solutions are ordered by some preference relation sometimes expressed as a utility function. A problem-solver explores that solution space, using domain-specific knowledge and heuristics to pick a starting point and select a course to navigate. The space of possible solutions is now of geographical regions around the globe divided by countries.
Still, it would exemplify the exploration of a solution space and subsequent elimination of candidate solutions captured by the Simon—Newell model. Elimination of epistemic possibilities is precisely the ancillary role that Jevons assigned to logic and probability calculus in rational inquiry. So far, we have seen that psychological associative processes involved in the discovery of solutions for a large class of problems, are amenable to formal analysis and rational reconstruction.
Similarly, a formal analysis of discovery processes must support normative judgements, in particular rankings of discovery methods as better or worse relative to how fast they converge to a solution for a given problem. This task is left unacknowledged in virtually all philosophical expositions of logical reasoning, of deductive heuristics, and of the methodology of logic and mathematics.
For this neglect the excuse is often offered that such processes of elucidations and explication cannot be systematized and subjected to rules. It may indeed be true that we cannot usually give effective rules for heuristic processes. It does not follow, however, that they cannot be discussed and evaluated, given a suitable conceptual framework. Hintikka and Hintikka , pp.
Assuming a preference for shorter proofs, a strategy with lemmas is in general preferable to a strategy without lemmas. Any language as expressive as a first-order language capable of enumerating objects would generate countably many candidate lemmas for any proof in that language. Furthermore, some candidates not only would not shorten the proof, but might delay its completion indefinitely. Thus, there can be no effective method to eliminate those candidates.
By the same token, there is no general effective method for selecting the best lemma. Footnote 7. Herbert Simon argued in much the same way as the Hintikkas, that a normative framework for discovery must be able to rank discovery strategies as better or worse and to provide with recommendations for choosing discovery strategies see Simon Taking stock in computer implementations of his model of problem-solving in Zytkow and Simon , Simon further illustrated his point with domain-specific algorithms for solving particular classes of problems, namely the discovery of empirical laws from qualitative data descriptions of chemical reactions or quantitative data descriptions of physical systems.
In both cases, the discovery algorithms can be ranked as better or worse based on how fast they converge to known empirical laws. Algorithms of that sort can solve non-deductive problems where the yes-or-no questions cannot be obtained analytically from the premises but are formulated in the same vocabulary as the premises see Genot The search space for questions grows exponentially, and heuristics that do more than re-composing the vocabulary of the premises become necessary.
We have suggested in previous sections that human memory can constrain heuristics search in the desired way, thanks to its distributive structure and how it supports associations. Indeed, the conceptual import of the Strategy Theorem is preserved in contexts where re-composition of vocabulary is insufficient, provided that heuristics for associations are available cf. Genot ; Genot and Jacot Now, and as noted earlier, associations supervene on the memory of a particular agent or, in the multi-agent scenarios discussed in Genot and Jacot , the memory of different agents.
The traditional distinction that places studies of scientific discovery outside the philosophy of science, in psychology, sociology, or history, is no longer valid in view of the existence of computer systems of discovery. It becomes both reasonable and attractive to study the schemes of discovery in the same way as the criteria of justification were studied: empirically as facts, and logically as norms. Zytkow and Simon , p. Arguably, the psychological components are part of the facts of discovery, not its logic.
Establishing them for the purpose of case studies and rational reconstructions that are the bread and butter of philosophers of science may require some speculation. The next issue is how much mileage we can get from those norms. The Hintikkas demonstrated how far deductive norms can carry us. They successfully captured the strategic role of deduction in problem-solving. Their decision-theoretic approach to strategy selection with bounded rationality collapsed eventually, but foreshadowed J.
If we are looking to semantics capable of generating non-trivial non-flat preferences over questions, some cognitive semantics is most likely our best bet. For instance, Charles J.
Also, and quite obviously, cognitive semantics is by design sensitive to bounds on cognitive resources and has the means to express them. Switching to cognitive semantics would have definite advantages for capturing interrogative strategies. Let us briefly suggest two of them which are really two sides of the same coin. The first advantage of cognitive semantics over model-theoretic semantics is its fine-grained interpretation for parts of discourse substantives, adjectives and verbs that accounts for relations of neighborhood and evocation for instance, how watchdog and thief could evoke barking.
Contrast with model-theoretic semantics, with its coarse-grained semantic structures lumping parts of discourse as predicates, and its need for ad hoc conditional clauses to express their relations.
The second and closely related advantage is the straightforward relation between evocation and recall, and thus between conceptual and neurological levels of description. This relation supports the unification of semantic and associative components of interrogation strategy selection. We hypothesized that this mapping would yield further constraints on strategies. Uchii in personal communication. Uchii later expanded his arguments in two electronic essays Uchii , Jevons implemented his logical alphabet in a mechanical computer in the s, and used it to formalize reasoning by elimination of possibilities, a method often used by Sherlock Holmes.
A problem is deductive if, and only if, some answer to Q is entailed by K , that is, if it is not possible to interpret all the elements of K as true and at least one of the answers to Q as false. Hence, a problem is non-deductive iff it requires an extension of K. For the formally minded reader: some questioning strategies can fall short of providing enough information to entail an answer to the big question.
Given the semi-decidability of first-order logic, some of these unconclusive strategies can be infinite i. Thus, the standard means for strategic reasoning from utilities elimination of dominated strategies would require the elimination of infinite strategies.
This would be tantamount to solving the Halting Problem, which is uncomputable by Turing machines, and formally equivalent to the decision problem for first-order logic for a detailed formal argument, see Genot ; Genot and Jacot For the formally-minded: results presented in Hintikka et al. For alternative proofs for the results in Hintikka et al. Merton credited Charles S.
For the formally-minded: assuming the game-theoretic form of sequential decision problems as a sequential 1-player game vs Nature , contextual focus under volitional control can be mathematically described as strategic in the game-theoretic sense. Specifically, recall from a distributed cam is a probabilistic process recalling an item carries a probability for recalling others. A strategy assigning to positions where a decision-maker has to make a move, a lottery between possible moves, is called a behavioral strategy.
And since different lotteries characterize different behavioral strategies, switching contextual focus is tantamount to a change in strategy selection. With J. For the formally-minded: the Strategy Theorem expresses a normative claim, namely, that the best discovery strategies for a class of non-deductive problems Holmesian problems expressible in a first-order language parallel the best deductive strategies for a class of deductive problems the deductive transformation of the non-deductive problems, cf.
However, due to the semi-decidability of first-order logic, there can be no effective method to transform a non-deductive problem into a deductive one some candidate transformations where the premise set is still too weak to entail the desired conclusion may generate infinite proof attempts, and eliminating them would be tantamount to solving the Halting Problem.
Hence, we are in a situation where normative claims are possible even in the absence of effective rules. Knows nothing of practical gardening. Knowledge of geology: practical, but limited. Tells at a glance different soils from each other. After walks has shown me splashes upon his trousers, and told me by their colour and consistence in what part of London he had received them. Knowledge of chemistry: profound Anatomy: accurate, but unsystematic. You can also search for this author in PubMed Google Scholar.
Reprints and Permissions. Beaman, P. Sherlock Holmes's skills as a philosopher? Nature , Download citation. They have to rely on reasoning. It is through reasoning that they find out what they want to know. Sherlock Holmes is aware that he engages in a special form of reasoning—special when compared to the kind we ordinarily do. He cals it reasoning backwards. In solving a problem of this sort, the grand thing is to be able to reason backwards. That is a very useful accomplishment, and a very easy one, but people do not practise it much.
In the everyday affairs of life it is more useful to reason forward, and so the other comes to be neglected.
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