Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. -/- Beginning from a careful, revisionary, analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary (...) account of the nature of quantum information. Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. -/- With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. (shrink)

First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

Information theory and statistical mechanics II.

Searching for information is critical in many situations. In medicine, for instance, careful choice of a diagnostic test can help narrow down the range of plausible diseases that the patient might have. In a probabilistic framework, test selection is often modeled by assuming that people's goal is to reduce uncertainty about possible states of the world. In cognitive science, psychology, and medical decision making, Shannon entropy is the most prominent and most widely used model to formalize probabilistic uncertainty and (...) the reduction thereof. However, a variety of alternative entropy metrics (Hartley, Quadratic, Tsallis, Rényi, and more) are popular in the social and the natural sciences, computer science, and philosophy of science. Particular entropy measures have been predominant in particular research areas, and it is often an open issue whether these divergences emerge from different theoretical and practical goals or are merely due to historical accident. Cutting across disciplinary boundaries, we show that several entropy and entropy reduction measures arise as special cases in a unified formalism, the Sharma–Mittal framework. Using mathematical results, computer simulations, and analyses of published behavioral data, we discuss four key questions: How do various entropy models relate to each other? What insights can be obtained by considering diverse entropy models within a unified framework? What is the psychological plausibility of different entropy models? What new questions and insights for research on human information acquisition follow? Our work provides several new pathways for theoretical and empirical research, reconciling apparently conflicting approaches and empirical findings within a comprehensive and unified information‐theoretic formalism. (shrink)

To become more useful and efficient in sustaining the Earth's health, economics must undergo a paradigm shift in its thinking. From a humanistic perspective, humans should be the center of everything. However, from the standpoint of physics and the universe, this is not the case. As a species, having a planet among the millions in the universe where humans can survive and thrive is already a great fortune. Through this book, we also try to answer one of our long-standing questions: (...) why has economics learned so little from physics, the oldest and most rigorous academic discipline that studies nature? -/- Learning from the quantum and information theories, we also provide a new definition of value, which is expected to help economists relax assumptions and loosen established economic principles in order to change and evolve. The new definition is also expected to enable social scientists to address newly arising phenomena or events that are not accounted for by existing value systems, such as environmental crises, artificial intelligence (AI), and interdisciplinary information, more proactively and productively. (shrink)

Integrated Information Theory posits a new kind of information, which, given certain constraints, constitutes consciousness. Searle objects to IIT because its appeal to information relies on observer-relative features. This misses the point that IIT’s notion of integrated information is intrinsic, the opposite of observer-relative. Moreover, Searle overlooks the possibility that IIT could be embraced as an extension of his theory. While he insists that causal powers of the brain account for consciousness, he maintains that (...) these causal powers aren’t tied to protoplasmic material. Whatever these causal powers are, they don’t consist in mere information-processing or computation. IIT agrees, and also positively characterizes the relevant causal powers as those involved in generating integrated information. Examining the further commitments of each theory reveals that IIT renews a fundamentally ontological challenge to information-processing and computational theories of mind. (shrink)

In this paper I argue that the Integrated Information Theory of Consciousness has an underlying emergentist metaphysics, specifically of a kind that has received minimal attention and we may call functionalist emergentism. I will try to show that in this scientific theory conscious experience is a functional-role property possessed by the whole system, not by their parts, which is dependent on, but also (purportedly) causally powerful over and above, the properties of the parts. However, I will argue (...) that depicting conscious experience as a functional-role emergent property threatens the whole coherence of the theory because, by definition, functional-realizers do all the causal work associated with the instantiation of any functional-role property on any occasion. Hence, to preserve the causal power of consciousness, which, as we will see, is one of the fundamental building blocks of the theory, linked to the assertion of the very existence of consciousness, phenomenal properties should be re-thought as realizers of the relevant informationally integrated causal-roles. (shrink)

Integrated Information Theory (IIT) identifies consciousness with having a maximum amount of integrated information. But a thing’s having the maximum amount of anything cannot be intrinsic to it, for that depends on how that thing compares to certain other things. IIT’s consciousness, then, is not intrinsic. A mereological argument elaborates this consequence: IIT implies that one physical system can be conscious while a physical duplicate of it is not conscious. Thus, by a common and reasonable conception of (...) intrinsicality, IIT’s consciousness is not intrinsic. It is then argued that to avoid the implication that consciousness is not intrinsic, IIT must abandon its Exclusion Postulate, which prohibits overlapping conscious systems. Indeed, theories of consciousness that attribute consciousness to physical systems, should embrace the view that some conscious systems overlap. A discussion of the admittedly counterintuitive nature of this solution, along with some medical and neuroscientific realities that would seem to support it, is included. (shrink)

Integrated information theory is a theory of consciousness that was originally formulated, and is standardly still expressed, in terms of controversial interpretations of its own ontological and epistemological basis. These form the orthodox interpretation of IIT. The orthodox epistemological interpretation is the axiomatic method, whereby IIT is ultimately derived from, justified by, and beholden to a set of phenomenological axioms. The orthodox ontological interpretation is panpsychism, according to which consciousness is fundamental, intrinsic, and pervasive. In this paper (...) it is argued that both components of the orthodox interpretation should be rejected. But IIT should not be rejected since an interpretation-neutral formulation is available. After explaining the neutral formulation, more plausible non-axiomatic epistemologies are defended. The neutral formulation is then shown to be consistent with various contemporary physicalist ontologies of consciousness, including the phenomenal concept strategy, representationalism, and even illusionism. Along the way, instructive connections between interpretations of IIT and interpretations of quantum mechanics are noted. (shrink)

– The paper explores first the postulational basis and significance of‘measures of information’in current information theory and their possible relations to physical entropy and Brillouin's‘negentropy’regarded as the negative of entropy. For some purposes, the same pattern or formal structure may be abstracted from both‘entropy’and‘information’. The paper analyzes, in the second place, the mathematical analogies which have been traced between information theory and quantum mechanics and argues that the analogies have but a limited value when (...) we come to grips with the deeper, and yet unsolved, problems of quantum theory. Lastly it is urged that the indiscriminate extensions of statistical and information‐theoretic methods, and of quantum‐mechanical analogies, e.g.‘linguistic duality’, to psycholinguistics, literary and aesthetic Gestalten, can result only in crude exaggerations. Dialectical methodology requires the continual reformulation of all scientific descriptions which have to reckon perpetually with the richness of human materials. (shrink)

Informational theories of semantic content have been recently gaining prominence in the debate on the notion of mental representation. In this paper we examine new-wave informational theories which have a special focus on cognitive science. In particular, we argue that these theories face four important difficulties: they do not fully solve the problem of error, fall prey to the wrong distality attribution problem, have serious difficulties accounting for ambiguous and redundant representations and fail to deliver a metasemantic theory of (...) representation. Furthermore, we argue that these difficulties derive from their exclusive reliance on the notion of information, so we suggest that pure informational accounts should be complemented with functional approaches. (shrink)

Integrated Information Theory (IIT) stands out as one of the most promising approaches to scientifically understand the emergence of consciousness. Even if it borrows from the phenomenology of consciousness to derive its axiomatic formulation, IIT does not initially adhere to any particular ontological position. However, its founder leans towards Panpsychism. More recently, Owen has studied the pros and cons of different ontologies as a metaphysical basis for IIT, defending a hylomorphic stance where en-grounding, en-forming relations gain the upper (...) hand in the causal narrative. This paper aims at (1) complementing Owen’s work by invoking additional arguments against physicalist IIT, both reductive and non-reductive; and (2) improving Owen’s characterization of non-physicalist causality through a “nested” version of hylomorphism that avoids the combination problem of Panpsychism. (shrink)

In this paper we review the general framework of operational probabilistic theories, along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.

Integrated information theory (IIT) starts from the essential properties of experience (axioms) and translates them into requirements that any physical system must satisfy to be conscious (postulates; see Integrated Information Theory of Consciousness: An Outline, this volume). The postulates of IIT can be seen as a list of requirements for something to exist ‘for itself’, as an intrinsic entity, and thus have relevance for ontology and metaphysics. Some implications of the theory include the divide between (...) intrinsic and extrinsic entities, the incoherence of ontological reductionism, and the intrinsic nature of meaning. (shrink)

Communication is an important feature of the living world that mainstream biology fails to adequately deal with. Applying two main disciplines can be contemplated to fill in this gap: semiotics and information theory. Semiotics is a philosophical discipline mainly concerned with meaning; applying it to life already originated in biosemiotics. Information theory is a mathematical discipline coming from engineering which has literal communication as purpose. Biosemiotics and information theory are thus concerned with distinct and (...) complementary possible meanings of the word ‘communication’. Since literal communication needs to be secured so as to enable semantics being communicated, information theory is a necessary prerequisite to biosemiotics. Moreover, heredity is a purely literal communication process of capital importance fully relevant to literal communication, hence to information theory. A short introduction to discrete information theory is proposed, which is centred on the concept of redundancy and its use in order to make sequences resilient to errors. Information theory has been an extremely active and fruitful domain of researches and the motor of the tremendous progress of communication engineering in the last decades. Its possible connections with semantics and linguistics are briefly considered. Its applications to biology are suggested especially as regards error-correcting codes which are mandatory for securing the conservation of genomes. Biology needs information theory so biologists and communication engineers should closely collaborate. (shrink)

The challenges raised in this article are not with information theory per se, but the assumptions surrounding it. Neuroscience isn't sufficiently critical about the appropriate ‘receiver’ or ‘channel’, focuses on decoding ‘parts’, and often relies on a flawed ‘veridicality’ assumption. If these problematic assumptions were questioned, information theory could be better directed to help us understand how the brain works.

Rejection is an essential part of the scholarly publishing process, acting as a filter to distinguish between robust and less credible scientific works. This study examines the advantages and limitations of the rejection mechanism through the lens of Shannon’s information theory and the theory of granular interactions thinking. We argue that while rejection helps reduce entropy and increase the likelihood of disseminating useful knowledge, the process is not devoid of subjectivity. We propose two recommendations to improve the (...) rejection mechanism: providing more informative rejection letters to guide authors and encouraging humility among editors and reviewers to minimize bias against novel ideas. These steps could enhance the efficiency of knowledge production by ensuring that valuable scientific contributions are not overlooked. (shrink)

Function refers to a broad family of concepts of varying abstractness and range of application, from a many-one mathematical relation of great generality to, for example, highly specialized roles of designed elements in complex machines such as degaussing in a television set, or contributory processes to control mechanisms in complex metabolic pathways, such as the inhibitory function of the appropriate part of the lac-operon on the production of lactase through its action on the genome in the absence of lactose. We (...) would like a language broad enough, neutral enough, but yet powerful enough to cover all such cases, and at the same time to give a framework form explanation both of the family resemblances and differences. General logic and mathematics are too abstract, but more importantly, too broad, whereas other discourses of function, such as the biological and teleological contexts, are too narrow. Information is especially suited since it is mathematically grounded, but also has a wellknown physical interpretation through the Schr dinger/Brillouin Negentropy Principle of Information, and an engineering or design interpretation through Shannon's communication theory. My main focus will be on the functions of autonomous anticipatory systems, but I will try to demonstrate both the connections between this notion of function and the others, especially to dynamical systems with a physical interpretation on the one side and intentional systems on the other. The former are based in concepts like force, energy and work, while the latter involve notions like representation, control and purpose, traditionally, at least in Modern times, on opposite sides of the Cartesian divide. In principle, information can be reduced to energy, but it has the advantage of being more flexible, and easier to apply to higher level phenomena. (shrink)

The Integrated Information Theory is a leading scientific theory of consciousness, which implies a kind of panpsychism. In this paper, I consider whether IIT is compatible with a particular kind of panpsychism, known as Russellian panpsychism, which purports to avoid the main problems of both physicalism and dualism. I will first show that if IIT were compatible with Russellian panpsychism, it would contribute to solving Russellian panpsychism’s combination problem, which threatens to show that the view does not (...) avoid the main problems of physicalism and dualism after all. I then show that the theories are not compatible as they currently stand, in view of what I call the coarse-graining problem. After I explain the coarse-graining problem, I will offer two possible solutions, each involving a small modification of IIT. Given either of these modifications, IIT and Russellian panpsychism may be fully compatible after all, and jointly enable significant progress on the mind–body problem. (shrink)

Information theory and statistical mechanics.

Although algorithmic information theory provides a measure of the information content of string of characters, problems of noise and noncomputability emerge. However, if pattern in a noisy string is recognized by reference to a set of similar strings, this article shows that a compressed algorithmic description of a noisy string is possible and illustrates this with some simple examples. The article also shows that algorithmic information theory can quantify the information in complex organized systems (...) where pattern is nested within pattern. (shrink)

A classic source for understanding the connections between information theory and physics, this text was written by one of the giants of 20th-century physics and is appropriate for upper-level undergraduates and graduate students. Topics include the principles of coding, coding problems and solutions, the analysis of signals, a summary of thermodynamics, thermal agitation and Brownian motion, and thermal noise in an electric circuit. A discussion of the negentropy principle of information introduces the author's renowned examination of Maxwell's (...) demon. Concluding chapters explore the associations between information theory, the uncertainty principle, and physical limits of observation, in addition to problems related to computing, organizing information, and inevitable errors. 1962 ed. 81 figures. 14 tables. (shrink)

Can information theory be used to understand neural signaling? Yes, but assumptions have to be made about the nature of that signaling. The traditional view is that the individual neural spike is an all-or-none phenomenon, which allows neural spikes to be viewed as discrete, binary pulses, similar in kind to the signals in digital computers. Under this assumption, the tools of information theory can be used to derive results about the properties of neural signals. However, new (...) results from neuroscience demonstrate that the precise shape of the individual spike can be functionally significant, thus violating the assumption that spikes can always be treated as a binary pulse. Instead, spikes must sometimes be viewed as a continuous signal. Fortunately, information-theoretic tools exist for the study of continuous signals; unfortunately, their use in the continuous domain is very different from their use in the discrete domain, and not always well understood. Researchers interested in making precise claims about the nature of the information used, stored, and processed in neural systems must pay careful attention to these differences. (shrink)

There is a new theory of information based on logic. The definition of Shannon entropy as well as the notions on joint, conditional, and mutual entropy as defined by Shannon can all be derived by a uniform transformation from the corresponding formulas of logical information theory. Information is first defined in terms of sets of distinctions without using any probability measure. When a probability measure is introduced, the logical entropies are simply the values of the (...) probability measure on the sets of distinctions. The compound notions of joint, conditional, and mutual entropies are obtained as the values of the measure, respectively, on the union, difference, and intersection of the sets of distinctions. These compound notions of logical entropy satisfy the usual Venn diagram relationships since they are values of a measure. The uniform transformation into the formulas for Shannon entropy is linear so it explains the long-noted fact that the Shannon formulas satisfy the Venn diagram relations--as an analogy or mnemonic--since Shannon entropy is not a measure on a given set. What is the logic that gives rise to logical information theory? Partitions are dual to subsets, and the logic of partitions was recently developed in a dual/parallel relationship to the Boolean logic of subsets. Boole developed logical probability theory as the normalized counting measure on subsets. Similarly the normalized counting measure on partitions is logical entropy--when the partitions are represented as the set of distinctions that is the complement to the equivalence relation for the partition. In this manner, logical information theory provides the set-theoretic and measure-theoretic foundations for information theory. The Shannon theory is then derived by the transformation that replaces the counting of distinctions with the counting of the number of binary partitions it takes, on average, to make the same distinctions by uniquely encoding the distinct elements--which is why the Shannon theory perfectly dovetails into coding and communications theory. (shrink)

We present a critical discussion of the claim (most forcefully propounded by Chaitin) that algorithmic information theory sheds new light on Godel's first incompleteness theorem.

Integrated Information Theory (IIT) stands out as one of the most promising theories for dealing with the hard problem of consciousness. Founded on five axioms derived from phenomenology, IIT seeks for the physical substrate of consciousness that complies with such axioms according to the criterion of maximally integrated information (Φ). Eventually, IIT identifies phenomenal consciousness with maximal Φ or, what is the same thing, with the strongest cause-effect power in the system. Among the scholars critical of this (...) theory, some point to the so-called Intrinsicality Problem (IP), namely that consciousness cannot be an intrinsic property of the system because maximal Φ crucially depends on the possible existence of bigger values of Φ if the initial system is appropriately linked to or embedded in larger systems. Although proposals in the recent literature aim to solve the IP by going beyond reductionism and physicalism, none of them tackle the real issue, i.e., the insufficiency of IIT’s causal-metaphysical structure. This papers endeavors to provide a solution to the IP in IIT within a hylomorphist ontology that includes formal causation. Complementing IIT with formal causation provides the theory with a criterion of individuation that solves the IP and, by relaxing identification between maximal Φ and consciousness, it lends a more robust metaphysical structure. To wit, maximal Φ is a necessary but not sufficient condition for the existence of consciousness. (shrink)

In this paper, I discuss how information theory has been used in the study of animal communication, as well as how these uses are justified. Biologists justify their use of Shannon’s information measures by the work they do in allowing for comparisons between different organisms and because they measure a quantity that is purported to be important for natural selection. I argue that there are problems with both sorts of justification. To make these difficulties clear, I focus (...) on the use of Shannon’s information measures to quantify the amount of information transmitted by the fire ant’s odor trail and the honeybee’s waggle dance. Both of these systems are relatively simple and well understood, and the application of Shannon’s information measure to these systems initially seemed very promising and relatively straightforward. They are therefore particularly suitable for revealing the benefits and difficulties of applying Shannon’s information measures to biological systems in general, and animal communication systems in particular. (shrink)

Simple hypotheses are intrinsically attractive, and, for this reason, need to be formulated with utmost precision if they are to be testable. Unfortunately, it is hard to see how Phillips & Singer's hypothesis might be unambiguously refuted. Despite this, the authors have provided much evidence consistent with the hypothesis, and have proposed a natural and powerful extension for information theoretic approaches to learning.

The integrated information theory is a promising theory of consciousness. However, there are several problems with IIT's axioms and postulates. Moreover, IIT entails that some twodimensional grids of identical logic gates have more consciousness than humans. Many have found this prediction to be implausible, and as will be argued here, this prediction also exacerbates the so-called 'hard problem of consciousness'. Recently, it has been argued that if we treat the phenomenological aspects of consciousness as an illusion, we (...) can avoid the hard problem altogether by replacing it with the more tractable illusion problem: the problem of explaining how introspection systematically misrepresents experiences as having phenomenology. IIT is intended to be a theory of the phenomenological aspects of consciousness. However, it is possible to reformulate the axioms and postulates of IIT consistently with illusionism. Here it is argued that the resulting theory -- illusionist integrated information theory -- removes several problems for IIT including the hard problem and the logic gate problem, and also enables meaningful progress for illusionists on solving the illusion problem. (shrink)

This paper presents Integrated Information Theory (IIT) 4.0. IIT aims to account for the properties of experience in physical (operational) terms. It identifies the essential properties of experience (axioms), infers the necessary and sufficient properties that its substrate must satisfy (postulates), and expresses them in mathematical terms. In principle, the postulates can be applied to any system of units in a state to determine whether it is conscious, to what degree, and in what way. IIT offers a parsimonious (...) explanation of empirical evidence, makes testable predictions, and permits inferences and extrapolations. IIT 4.0 incorporates several developments of the past ten years, including a more accurate translation of axioms into postulates and mathematical expressions, the introduction of a unique measure of intrinsic information that is consistent with the postulates, and an explicit assessment of causal relations. By fully unfolding a system's irreducible cause-effect power, the distinctions and relations specified by a substrate can account for the quality of experience. (shrink)

Information theory offers a measure of "mutual information" which provides an appropriate measure of tracking efficiency for the naturalistic epistemologist. The statistical entropy on which it is based is arguably the best way of characterizing the uncertainty associated with the behavior of a system, and it is ontologically neutral. Though not appropriate for the naturalization of meaning, mutual information can serve as a measure of epistemic success independent of semantic maps and payoff structures. While not containing (...) payoffs as terms, mutual information places both upper and lower bounds on payoffs. This constitutes a non-trivial relationship to utility. (shrink)

This paper is a criticism of full-information theories of welfare. Such theories unsuccessfully attempt to accommodate an internalist intuition (that one's good depends in some way on one's desires or hypothetical desire) with a rationalist intuition (that only fully-informed desires are relevant to one's good).

In this paper, we examine the causal framework within which integrated information theory of consciousness makes it claims. We argue that, in its current formulation, IIT is threatened by the causal exclusion problem. Some proponents of IIT have attempted to thwart the causal exclusion problem by arguing that IIT has the resources to demonstrate genuine causal emergence at macro scales. In contrast, we argue that their proposed solution to the problem is damagingly circular as a result of inter-defining (...) information and causation. As a solution, we propose that IIT should adopt the specific interventionist causal framework that we offer and show how IIT can harness this interventionist framework to avoid the causal exclusion problem. We demonstrate how our argument remains fully compatible with the methodology, empirical data, and conceptual aims of the theory. (shrink)

Intelligent design advocate William Dembski has introduced a measure of information called “complex specified information”, or CSI. He claims that CSI is a reliable marker of design by intelligent agents. He puts forth a “Law of Conservation of Information” which states that chance and natural laws are incapable of generating CSI. In particular, CSI cannot be generated by evolutionary computation. Dembski asserts that CSI is present in intelligent causes and in the flagellum of Escherichia coli, and concludes (...) that neither have natural explanations. In this paper, we examine Dembski’s claims, point out significant errors in his reasoning, and conclude that there is no reason to accept his assertions. (shrink)

The causal and simulation theories are often presented as very distinct views about declarative memory, their major difference lying on the causal condition. The causal theory states that remembering involves an accurate representation causally connected to an earlier experience. In the simulation theory, remembering involves an accurate representation generated by a reliable memory process. I investigate how to construe detailed versions of these theories that correctly classify memory errors as misremembering or confabulation. Neither causalists nor simulationists have paid (...) attention to memory-conjunction errors, which is unfortunate because both theories have problems with these cases. The source of the difficulty is the background assumption that an act of remembering has one target. I fix these theories for those cases. The resulting versions are closely related when implemented using tools of information theory, differing only on how memory transmits information about the past. The implementation provides us with insights about the distinction between confabulatory and non-confabulatory memory, where memory-conjunction errors have a privileged position. (shrink)