Материал: искусственный интеллект

Contents

viii Contents

Probability and Beyond

Density Hypercubes, Higher Order Interference and Hyper-decoherence:

A Categorical Approach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Stefano Gogioso and Carlo Maria Scandolo

Information Retrieval

Investigating Non-classical Correlations Between Decision

Fused Multi-modal Documents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

Dimitris Gkoumas, Sagar Uprety, and Dawei Song

Investigating Bell Inequalities for Multidimensional Relevance

Judgments in Information Retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Sagar Uprety, Dimitris Gkoumas, and Dawei Song

Short Paper

An Update on Updating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

Bart Jacobs

Fundamentals

Why Should We Use Quantum Theory?

The Case of Human Sciences

Michel Bitbol(B)

CNRS, Archives Husserl, Ecole Normale Sup´erieure, 45, rue d’Ulm, 75005 Paris, France michel.bitbol@ens.fr

1 Introduction

Why is quantum theory so universal? Why does it apply to so many situations beyond the field of microphysics? To answer such questions, we can find inspiration from a remarkable reflection of the French philosopher of Science Jean Cavaill`es about probabilities: “If any physical law is nothing else than a gamble for action, the scandal of probabilities ceases: far from being an inadequate substitute for our power to know, probabilities must be seen as the paradigm and the foundation of all scientific activity” [6]. Accordingly, if quantum laws are understood as a gamble for action, the “scandal” of their probabilistic status ceases. The careful analysis of the structure of probabilistic valuations based on state vectors in a Hilbert space is capable of profoundly transforming our view of quantum mechanics. It can help us to suspend the relationship of distrust (not to say of distance and strangeness) that we have maintained with this theory since its creation, and to change it into a feeling of proximity and trust. It can help us see quantum mechanics, not as an anomaly in the space of physical theories, but rather as their deepest archetype.

From this decidedly probabilistic standpoint, the application of quantum theory to many cases in the human sciences is no longer a coincidence, but a necessity. That it is a necessity becomes clear as soon as one understands two things: (i) that quantum theory formalizes a broad class of activities of knowledge rather than the objects of such knowledge; and (ii) that there is an isomorphism between certain situations of knowledge typical of the human sciences, and most situations of knowledge in microphysics. To put things shortly, both the human sciences and microphysics deal with situations in which knowing is not tantamount to observing, but rather to intervening and participating. As soon as we realize that quantum theory is above all a generalized probabilistic valuation for situations of knowledge in which intervention and participation are insurmountable, its universality and its applicability to such cases as decisionmaking, case-sensitive categorization and behavior in situations of uncertainty, becomes almost trivial.

By contrast, the purely pragmatic justification that is usually provided for applying quantum theories to the human sciences looks shy and contrived. The standard name for this application is “quantum model”: quantum model of decision, quantum model of perception, quantum model of meaning ascription etc.

c Springer Nature Switzerland AG 2019

B. Coecke and A. Lambert-Mogiliansky (Eds.): QI 2018, LNCS 11690, pp. 3–21, 2019. https://doi.org/10.1007/978-3-030-35895-2_1

4M. Bitbol

And the best reason one then finds for the (“surprising”) validity of such models is that quantum theories are “rich” and that “A richer expression scheme comes with a greater modeling power” [27].

This looks weak yet reasonable. But is the status of “model” ascribed to quantum theoretical accounts of human processes credible ? First of all, what about this word “model”, that mostly refers to restrictive uses of a theory aiming at making sense of some particular experimental situations ? Remind that “model” is a word derived from the latin ‘modulus’, ‘a small measure’. Its primary semantic content is therefore a likeness made to scale. But what if, as Heisenberg and several other creators of quantum mechanics suspected, quantum theory is no image, and no likeness, of anything ? What if quantum theory does not resemble its object in any way, but only formalizes gambles about the reactions of any object whatsoever when it is put in a certain class of situations of knowledge [11] ? What if, as Richard Healey pointed out, “quantum theory makes a radical break with previous physics not because of the weirdness of the physical behavior it represents, but ... (because) quantum theory is simply not in the business of representing what happens in the physical world” [15] ? Then, the very idea of quantum models representing some human processes is undermined. But conversely, the fact that quantum theory can indeed be applied to human sciences makes a non-representationalist interpretation of quantum mechanics much more compelling.

2 On the Human Science/Natural Science Issue

There are some philosophical reasons to this persistent resistance to quantum theoretical approaches of the human sciences. Those who resist sometimes fear that the desire to formulate quantum theories of human processes stems from an old thesis proposed by Otto Neurath around 1930 under the name of “Physicalism”. The latter thesis amounts to a quest for the general unity of science under the exclusive authority of physics promoted “queen of sciences”. But the search for the unity of the sciences by their absorption in physics understood as universal knowledge may well imply a reductionist act of faith, with the basic assumption that only the things described by physics are real, and that all the rest, especially the individual and social processes that concern the human sciences, is only an epiphenomenon. John Searle expressed this conflation of physicalism and reductionism thus: “That,” he said, “is the raw structure of our ontology. We live in a world made entirely of physical particles in fields of forces. Some of them are organized into systems (...). Now the question is: how can social facts be justified within this ontology?” [26]. Here, physics reveals ontology; ontology holds the ultimate truth about the world; and every other science, including social and mental sciences, must conform to it.

This way of relating quantum mechanics to the human sciences certainly represents a possibility for thought, but it is not the only one, and not even the most interesting. Another philosophical approach may lead us to identify a deeper relationship between the two families of sciences. This is the approach,