What's Right With a Syntactic Approach to Theories and Models?

Syntactic approaches in the philosophy of science, which are based on formalizations in predicate logic, are often considered in principle inferior to semantic approaches, which are based on formalizations with the help of structures. To compare the two kinds of approach, I identify some ambiguities in common semantic accounts and explicate the concept of a structure in a way that avoids hidden references to a specific vocabulary. From there, I argue that contrary to common opinion (i) unintended models do not pose a significant problem for syntactic approaches to scientific theories, (ii) syntactic approaches can be at least as language independent as semantic ones, and (iii) in syntactic approaches, scientific theories can be as well connected to the world as in semantic ones. Based on these results, I argue that syntactic and semantic approaches fare equally well when it comes to (iv) ease of application, (iv) accommodating the use of models in the sciences, and (vi) capturing the theory-observation relation

Communication Theoretic Data Analytics

Widespread use of the Internet and social networks invokes the generation of big data, which is proving to be useful in a number of applications. To deal with explosively growing amounts of data, data analytics has emerged as a critical technology related to computing, signal processing, and information networking. In this paper, a formalism is considered in which data is modeled as a generalized social network and communication theory and information theory are thereby extended to data analytics. First, the creation of an equalizer to optimize information transfer between two data variables is considered, and financial data is used to demonstrate the advantages. Then, an information coupling approach based on information geometry is applied for dimensionality reduction, with a pattern recognition example to illustrate the effectiveness. These initial trials suggest the potential of communication theoretic data analytics for a wide range of applications.Comment: Published in IEEE Journal on Selected Areas in Communications, Jan. 201

Theories, models and structures: thirty years on

Thirty years after the conference that gave rise to The Structure of Scientific Theories, there is renewed interest in the nature of theories and models. However, certain crucial issues from thirty years ago are reprised in current discussions; specifically: whether the diversity of models in the science can be captured by some unitary account; and whether the temporal dimension of scientific practice can be represented by such an account. After reviewing recent developments we suggest that these issues can be accommodated within the partial structures formulation of the semantic or model-theoretic approach

Adaptive group testing as channel coding with feedback

Group testing is the combinatorial problem of identifying the defective items in a population by grouping items into test pools. Recently, nonadaptive group testing - where all the test pools must be decided on at the start - has been studied from an information theory point of view. Using techniques from channel coding, upper and lower bounds have been given on the number of tests required to accurately recover the defective set, even when the test outcomes can be noisy. In this paper, we give the first information theoretic result on adaptive group testing - where the outcome of previous tests can influence the makeup of future tests. We show that adaptive testing does not help much, as the number of tests required obeys the same lower bound as nonadaptive testing. Our proof uses similar techniques to the proof that feedback does not improve channel capacity.Comment: 4 pages, 1 figur

Optimal Information-Theoretic Wireless Location Verification

We develop a new Location Verification System (LVS) focussed on network-based Intelligent Transport Systems and vehicular ad hoc networks. The algorithm we develop is based on an information-theoretic framework which uses the received signal strength (RSS) from a network of base-stations and the claimed position. Based on this information we derive the optimal decision regarding the verification of the user's location. Our algorithm is optimal in the sense of maximizing the mutual information between its input and output data. Our approach is based on the practical scenario in which a non-colluding malicious user some distance from a highway optimally boosts his transmit power in an attempt to fool the LVS that he is on the highway. We develop a practical threat model for this attack scenario, and investigate in detail the performance of the LVS in terms of its input/output mutual information. We show how our LVS decision rule can be implemented straightforwardly with a performance that delivers near-optimality under realistic threat conditions, with information-theoretic optimality approached as the malicious user moves further from the highway. The practical advantages our new information-theoretic scheme delivers relative to more traditional Bayesian verification frameworks are discussed.Comment: Corrected typos and introduced new threat model

Is the dream solution to the continuum hypothesis attainable?

The dream solution of the continuum hypothesis (CH) would be a solution by which we settle the continuum hypothesis on the basis of a newly discovered fundamental principle of set theory, a missing axiom, widely regarded as true. Such a dream solution would indeed be a solution, since we would all accept the new axiom along with its consequences. In this article, however, I argue that such a dream solution to CH is unattainable. The article is adapted from and expands upon material in my article, "The set-theoretic multiverse", to appear in the Review of Symbolic Logic (see arXiv:1108.4223).Comment: This article is based upon an argument I gave during the course of a three-lecture tutorial on set-theoretic geology at the summer school "Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments", at the University of London, Birkbeck in August 201