There are two basic approaches to the problem of induction:the empirical one, which deems that the possibility of induction depends on how theworld was made (and how it works) and the logical one, which considers the formation(and function) of language. The first is closer to being useful for induction, whilethe second is more rigorous and clearer. The purpose of this paper is to create an empiricalapproach to induction that contains the same formal exactitude as the logical approach.This requires: (a) that (...) the empirical conditions for the induction are enunciatedand (b) that the most important results already obtained from inductive logic are againdemonstrated to be valid. Here we will be dealing only with induction by elimination,namely the analysis of the experimental confutation of a theory. The result will bea rule of refutation that takes into consideration all of the empirical aspect of theexperiment and has each of the asymptotic properties which inductive logic has shown tobe characteristic of induction. (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)

The Shannon information function (H) has been extensively used in ecology as a statistic of species diversity. Yet, the use of Shannon diversity index has also been criticized, mainly because of its ambiguous ecological interpretation and because of its relatively great sensitivity to the relative abundances of species in the community. In my opinion, the major shortcoming of the traditional perspective (on the possible relation of species diversity with information theory) is that species need for an external receiver (the scientist (...) or ecologist) to exist and transmit information. Because organisms are self-catalized replicating structures that can transmit genotypic information to offspring, it should be evident that any single species has two possible states or alternatives: to be or not to be. In other words, species have no need for an external receiver since they are their own receivers. Therefore, the amount of biological information (at the species scale) in a community with one only species would be species, and not bits as in the traditional perspective. Moreover, species diversity appears to be a monotonic increasing function of (or S) when all species are equally probable (S being species richness), and not a function of as in the traditional perspective. To avoid the noted shortcoming, we could use 2H (instead of H) for calculating species diversity and species evenness (= 2H/S). However, owing to the relatively great sensitivity of H to the relative abundances of species in the community, the value of species dominance (= 1 − 2H/S) is unreasonably high when differences between dominant and subordinate species are considerable, thereby lowering the value of species evenness and diversity. This unsatisfactory behaviour is even more evident for Simpson index and related algorithms. I propose the use of other statistics for a better analysis of community structure, their relationship being: species evenness + species dominance = 1; species diversity × species uniformity = 1; and species diversity = species richness × species evenness. (shrink)

My aim in this paper is a modest one. I do not have any particular thesis to advance about the nature of entanglement, nor can I claim novelty for any of the material I shall discuss. My aim is simply to raise some questions about entanglement that spring naturally from certain developments in quantum information theory and are, I believe, worthy of serious consideration by philosophers of science. The main topics I discuss are different manifestations of quantum nonlocality, entanglement-assisted communication, (...) and entanglement thermodynamics. (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)

Cohen and Meskin 2006 recently offered a counterfactual theory of information to replace the standard probabilistic theory of information. They claim that the counterfactual theory fares better than the standard account on three grounds: first, it provides a better framework for explaining information flow properties; second, it requires a less expensive ontology; and third, because it does not refer to doxastic states of the information-receiving organism, it provides an objective basis. In this paper, I show that none of these is (...) really an advantage. Moreover, the counterfactual theory fails to satisfy one of the basic properties of information flow, namely the Conjunction principle. Thus, I conclude, there is no reason to give up the standard probabilistic theory for the counterfactual theory of information. (shrink)

A new logic of partitions has been developed that is dual to ordinary logic when the latter is interpreted as the logic of subsets of a fixed universe rather than the logic of propositions. For a finite universe, the logic of subsets gave rise to finite probability theory by assigning to each subset its relative size as a probability. The analogous construction for the dual logic of partitions gives rise to a notion of logical entropy that is precisely related to (...) Claude Shannon's entropy. In this manner, the new logic of partitions provides a logico-conceptual foundation for information-theoretic entropy or information content. (shrink)

Categorical logic has shown that modern logic is essentially the logic of subsets (or “subobjects”). In “subset logic,” predicates are modeled as subsets of a universe and a predicate applies to an individual if the individual is in the subset. Partitions are dual to subsets so there is a dual logic of partitions where a “distinction” [an ordered pair of distinct elements (u, u′) from the universe U] is dual to an “element”. A predicate modeled by a partition π on (...) U would apply to a distinction if the pair of elements was distinguished by the partition π, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered |U|2 pairs from the finite universe. That yields a notion of “logical entropy” for partitions and a “logical information theory.” The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon’s theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon’s theory based on the logical notion of “distinctions.”. (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)

Recent suggestions to supply quantum mechanics (QM) with realistic foundations by reformulating it in light of quantum information theory (QIT) are examined and are found wanting by pointing to a basic conceptual problem that QIT itself ignores, namely, the measurement problem. Since one cannot ignore the measurement problem and at the same time pretend to be a realist, as they stand, the suggestions to reformulate QM in light of QIT are nothing but instrumentalism in disguise.

The distinction between explanation and prediction has received much attention in recent literature, but the equally important distinction between explanation and description (or between prediction and description) remains blurred. This latter distinction is particularly important in the social sciences, where probabilistic models (or theories) often play dual roles as explanatory and descriptive devices. The distinction between explanation (or prediction) and description is explicated in the present paper in terms of information theory. The explanatory (or predictive) power of a probabilistic model (...) is identified with information taken from (or transmitted by) the environment (e.g., the independent, experimentally manipulated variables), while the descriptive power of a model reflects additional information taken from (or transmitted by) the data. Although information is usually transmitted by the data in the process of estimating parameters, it turns out that the number of free parameters is not a reliable index of transmitted information. Thus, the common practice of treating parameters as degrees-of-freedom in testing probabilistic models is questionable. Finally, this information-theoretic analysis of explanation, prediction, and description suggests ways of resolving some recent controversies surrounding the pragmatic aspects of explanation and the so-called structural identity thesis. (shrink)

In earlier work we proposed an account of information grounded in counterfactual conditionals rather than probabilities, and argued that it might serve philosophical needs that more familiar probabilistic alternatives do not. Demir [2008] and Scarantino [2008] criticize the counterfactual approach by contending that its alleged advantages are illusory and that it fails to secure attractive desiderata. In this paper we defend the counterfactual account from these criticisms, and suggest that it remains a useful account of information.

Quantum information theory has given rise to a renewed interest in, and a new perspective on, the old issue of understanding the ways in which quantum mechanics differs from classical mechanics. The task of distinguishing between quantum and classical theory is facilitated by neutral frameworks that embrace both classical and quantum theory. In this paper, I discuss two approaches to this endeavour, the algebraic approach, and the convex set approach, with an eye to the strengths of each, and the relations (...) between the two. I end with a discussion of one particular model, the toy theory devised by Rob Spekkens, which, with minor modifications, fits neatly within the convex sets framework, and which displays in an elegant manner some of the similarities and differences between classical and quantum theories. The conclusion suggested by this investigation is that Schrödinger was right to find the essential difference between classical and quantum theory in their handling of composite systems, though Schrödinger's contention that it is entanglement that is the distinctive feature of quantum mechanics needs to be modified. (shrink)

Algorithmic information theory, or the theory of Kolmogorov complexity, has become an extraordinarily popular theory, and this is no doubt due, in some part, to the fame of Chaitin’s incompleteness results arising from this field. Actually, there are two rather different results by Chaitin: the earlier one concerns the finite limit of the provability of complexity (see Chaitin, 1974a, 1974b, 1975a); and the later is related to random reals and the halting probability (see Chaitin, 1986, 1987a, 1987b, 1988, 1989.

clusions are only probably correct. On the other hand, algorithmic information theory provides a precise mathematical definition of the notion of random or patternless sequence. In this paper we shall describe conditions under which if the sequence of coin tosses in the Solovay– Strassen and Miller–Rabin algorithms is replaced by a sequence of heads and tails that is of maximal algorithmic information content, i.e., has maximal algorithmic randomness, then one obtains an error-free test for primality. These results are only of (...) theoretical interest, since it is a manifestation of the G¨ odel incompleteness phenomenon that it is impossible to “certify” a sequence to be random by means of a proof, even though most sequences have this property. Thus by using certified random sequences one can in principle, but not in practice, convert probabilistic tests for primality into deterministic ones. (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.