The Observer Effect

Founding our analysis on the Geneva-Brussels approach to the foundations of physics, we provide a clarification and classification of the key concept of observation. An entity can be observed with or without a scope. In the second case, the observation is a purely non-invasive discovery process; in the first case, it is a purely invasive process, which can involve either creation or destruction aspects. An entity can also be observed with or without a full control over the observational process. In the latter case, the observation can be described by a symmetry breaking mechanism, through which a specific deterministic observational process is selected among a number of potential ones, as explained in Aerts’ hidden measurement approach. This is what is called a product test, or product observation, whose consequences are that outcomes can only be predicted in probabilistic terms, as it is the case in typical quantum measurements. We also show that observations can be about intrinsic (stable) properties of the observed entity, or about relational (ephemeral) properties between the observer and observed entities; also, they can be about intermediate properties, neither purely classical, nor purely quantum. Our analysis allows us to propose a general conceptual characterization of quantum measurements, as observational processes involving three aspects: (1) product observations, (2) pure creation aspects and (3) ephemeral relational properties. We also discuss the important concept of non-spatiality and emphasize some of the differences and similarities between quantum and classical/relativistic observations.     

Meaning and Reference in Aristotle’s Concept of the Linguistic Sign

To Aristotle, spoken words are symbols, not of objects in the world, but of our mental experiences related to these objects. Presently there are two major strands of interpretation of Aristotle’s concept of the linguistic sign. First, there is the structuralist account offered by Coseriu (Geschichte der Sprachphilosophie. Von den Anfängen bis Rousseau, 2003 [1969], pp. 65–108) whose interpretation is reminiscent of the Saussurean sign concept. A second interpretation, offered by Lieb (in: Geckeler (Ed.) Logos Semantikos: Studia Linguistica in Honorem Eugenio Coseriu 1921–1981, 1981) and Weidemann (in: Schmitter (Ed.) Geschichte der Sprachtheorie 2. Sprachtheorien der abendländischen Antike, 1991), says that Aristotle’s concept of the linguistic sign is similar to the one presented in Ogden and Richard’s (The meaning of meaning: A study of the influence of language upon thought and of the science of symbolism, 1970 [1923]) semiotic triangle. This paper starts off with an introductory outline of the so-called phýsei-thései discussion which started during presocratic times and culminated in Plato’s Cratylus. Aristotle’s concept of the linguistic sign is to be regarded as a solution to the stalemate position reached in the Cratylus. Next, a discussion is offered of both Coseriu’s and Lieb’s analysis. We submit that Aristotle’s concept of the linguistic sign shows features of both Saussure’s and Ogden and Richards’s sign concept but that it does not exclusively predict one of the two. We argue that Aristotle’s concept of the linguistic sign is based on three different relations which together evince his teleological as well empiricist point of view: one internal (symbolic) relation and two external relations, i.e. a likeness relation and a relation katà synthéken.     

One-Mode Classification of a Three-Way Data Matrix

X is the automatic hierarchical classification of one mode (units or variables or occasions) of X on the basis of the other two. In this paper the case of OMC of units according to variables and occasions is discussed. OMC is the synthesis of a set of hierarchical classifications Delta obtained from X; e.g., the OMC of units is the consensus (synthesis) among the set of dendograms individually defined by clustering units on the basis of variables, separately for each given occasion of X. However, because Delta is often formed by a large number of classifications, it may be unrealistic that a single synthesis is representative of the entire set. In this case, subsets of similar (homegeneous) dendograms may be found in Delta so that a consensus representative of each subset may be identified. This paper proposes, PARtition and Least Squares Consensus cLassifications Analysis (PARLSCLA) of a set of r hierarchical classifications Delta. PARLSCLA identifies the best least-squares partition of Delta into m (1 <= m <= r) subsets of homogeneous dendograms and simultaneously detects the closest consensus classification (a median classification called Least Squares Consensus Dendogram (LSCD) for each subset. PARLSCLA is a generalization of the problem to find a least-squares consensus dendogram for Delta. PARLSCLA is formalized as a mixed-integer programming problem and solved with an iterative, two-step algorithm. The method proposed is applied to an empirical data set.     

Agnostic Science. Towards a Philosophy of Data Analysis

In this paper we will offer a few examples to illustrate the orientation of contemporary research in data analysis and we will investigate the corresponding role of mathematics. We argue that the modus operandi of data analysis is implicitly based on the belief that if we have collected enough and sufficiently diverse data, we will be able to answer most relevant questions concerning the phenomenon itself. This is a methodological paradigm strongly related, but not limited to, biology, and we label it the microarray paradigm. In this new framework, mathematics provides powerful techniques and general ideas which generate new computational tools. But it is missing any explicit isomorphism between a mathematical structure and the phenomenon under consideration. This methodology used in data analysis suggests the possibility of forecasting and analyzing without a structured and general understanding. This is the perspective we propose to call agnostic science, and we argue that, rather than diminishing or flattening the role of mathematics in science, the lack of isomorphisms with phenomena liberates mathematics, paradoxically making more likely the practical use of some of its most sophisticated ideas.     

An investigation of three-matrix permutation tests

Several methods have recently been introduced for investigating relations between three interpoint proximity matricesA, B, C, each of which furnishes a different type of distance between the same objects. Smouse, Long, and Sokal (1986) investigate the partial correlation betweenA andB conditional onC. Dow and Cheverud (1985) ask whethercorr (A, C), equalscorr (B, C). Manly (1986) investigates regression-like models for predicting one matrix as a function of others. We have investigated rejection rates of these methods when their null hypotheses are true, but data are spatially autocorrelated (SA). That is,A, andB are distance matrices from independent realizations of the same SA generating process, andC is a matrix of geographic connections. SA causes all the models to be liberal because the hypothesis of equally likely row/column permutations invoked, by all these methods, is untrue when data are SA. Consequently, we cannot unreservedly recommend the use of any of these methods with SA data. However, if SA is weak, the Smouse-Long-Sokal method, used with a conservative critical value, is unlikely to reject falsely.     

Classification Based on Depth Transvariations

Suppose y, a d-dimensional (d ≥ 1) vector, is drawn from a mixture of k (k ≥ 2) populations, given by ∏₁, ∏₂,…,∏ _k . We wish to identify the population that is the most likely source of the point y. To solve this classification problem many classification rules have been proposed in the literature. In this study, a new nonparametric classifier based on the transvariation probabilities of data depth is proposed. We compare the performance of the newly proposed nonparametric classifier with classical and maximum depth classifiers using some benchmark and simulated data sets. The authors thank the editor and referees for comments that led to an improvement of this paper. This work is partially supported by the National Science Foundation under Grant No. DMS-0604726. Published online xx, xx, xxxx.     

Self-Consistent Patterns for Symmetric Multivariate Distributions

The set of k points that optimally represent a distribution in terms of mean squared error have been called principal points (Flury 1990). Principal points are a special case of self-consistent points. Any given set of k distinct points in R ^p induce a partition of R ^p into Voronoi regions or domains of attraction according to minimal distance. A set of k points are called self-consistent for a distribution if each point equals the conditional mean of the distribution over its respective Voronoi region. For symmetric multivariate distributions, sets of self-consistent points typically form symmetric patterns. This paper investigates the optimality of different symmetric patterns of self-consistent points for symmetric multivariate distributions and in particular for the bivariate normal distribution. These results are applied to the problem of estimating principal points.     

A Spontaneous Physics Philosophy on the Concept of Ether Throughout the History of Science: Birth, Death and Revival

In the course of the history of science, some concepts have forged theoretical foundations, constituting paradigms that hold sway for substantial periods of time. Research on the history of explanations of the action of one body on another is a testament to the periodic revival of one theory in particular, namely, the theory of ether. Even after the foundation of modern Physics, the notion of ether has directly and indirectly withstood the test of time. Through a spontaneous physics philosophical analysis, this article will explore how certain aspects of the concept of ether have appeared in different branches of the history of science.     

The Construction of Chaos Theory

This paper aims at a logico-mathematical analysis of the concept of chaos from the point of view of a constructivist philosophy of physics. The idea of an internal logic of chaos theory is meant as an alternative to a realist conception of chaos. A brief historical overview of the theory of dynamical systems is provided in order to situate the philosophical problem in the context of probability theory. A finitary probabilistic account of chaos amounts to the theory of measurement in the line of a quantum-theoretical foundational perspective and the paper concludes on the non-classical internal logic of chaos theory. Finally, deterministic chaos points to a philosophy which asserts that chaotic systems are no less measurable than other physical systems where predictable and non–predictable phenomena intermingle in a constructive theory of measurement.

Problems with Peirce's Concept of Abduction

Abductive reasoning takes place in forming``hypotheses' in order to explain ``facts.' Thus, theconcept of abduction promises an understanding ofcreativity in science and learning. It raises,however, also a lot of problems. Some of them will bediscussed in this paper. After analyzing thedifference between induction and abduction (1), Ishall discuss Peirce's claim that there is a ``logic'of abduction (2). The thesis is that this claim can beunderstood, if we make a clear distinction betweeninferential elements and perceptive elements ofabductive reasoning. For Peirce, the creative act offorming explanatory hypotheses and the emergence of``new ideas' belongs exclusively to the perceptive sideof abduction. Thus, it is necessary to study the roleof perception in abductive reasoning (3). A furtherproblem is the question whether there is arelationship between abduction and Peirce's concept of``theorematic reasoning' in mathematics (4). Both formsof reasoning could be connected, because both arebased on perception. The last problem concerns therole of instincts in explaining the success ofabductive reasoning in science, and the questionwhether the concept of instinct might be replaced bymethods of inquiry (5).     

The Intentionality of Formal Systems

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand.     

Schwinger and the Ontology of Quantum Field Theory

An epistemological interpretation of quantum mechanics hinges on the claim that the distinctive features of quantum mechanics can be derived from some distinctive features of an observational basis. Old and new variations of this theme are listed. The program has a limited success in non-relativistic quantum mechanics. The crucial issue is how far it can be extended to quantum field theory without introducing significant ontological postulates. A C*-formulation covers algebraic quantum field theory, but not the standard model. Julian Schwinger’s anabatic methodology extended a strict measurement-based formulation of quantum mechanics through field theory. His extension also excluded the quark hypothesis and the standard model. Quarks and local gauge invariance are postulates that go beyond the limits of an epistemological interpretation of quantum mechanics. The ontological significance ascribed to these advances depends on the role accorded ontology.

Model-Based and Manipulative Abduction in Science

What I call theoretical abduction (sentential and model-based)certainly illustrates much of what is important in abductive reasoning, especially the objective of selecting and creating a set of hypotheses that are able to dispense good (preferred) explanations of data, but fails to account for many cases of explanation occurring in science or in everyday reasoning when the exploitation of the environment is crucial. The concept of manipulative abduction is devoted to capture the role of action in many interesting situations: action provides otherwise unavailable information that enables the agent to solve problems by starting and performing a suitable abductive process of generation or selection of hypotheses. Many external things, usually inert from the epistemological point of view, can be transformed into what I callepistemic mediators, which are illustrated in the last part of the paper, together with an analysis of the related notions of ``perceptual and inceptual rehearsal' and of ``external representation'.     

Games as formal tools versus games as explanations in logic and science

This paper addresses the theoretical notion of a game as it arisesacross scientific inquiries, exploring its uses as a technical andformal asset in logic and science versus an explanatory mechanism. Whilegames comprise a widely used method in a broad intellectual realm(including, but not limited to, philosophy, logic, mathematics,cognitive science, artificial intelligence, computation, linguistics,physics, economics), each discipline advocates its own methodology and aunified understanding is lacking. In the first part of this paper, anumber of game theories in formal studies are critically surveyed. Inthe second part, the doctrine of games as explanations for logic isassessed, and the relevance of a conceptual analysis of games tocognition discussed. It is suggested that the notion of evolution playsa part in the game-theoretic concept of meaning.     

Steps from Erratic Projects towards Structured Programs in Research

Currently, research is mostly organized in research projects intended to provide results within a limited period of time. Here, small teams of scientists erratically define single scientific studies, write a proposal, and send it to the refereeing board. In case of a funding, the study is carried out and the results are published. To optimize the research and reduce the respective costs and/or raise the outcome, multiple research projects should be organized within a comprehensive research program. A meta-model (paradigm) can help comprise (a) the representation of the state-of-the-art decision knowledge, (b) the adding of new research questions, (c) the performing of trials to answer these questions, and (d) the revision of the current model. It will be discussed how to structure studies within research programs and these within one super-program.

Abduction as a Logic and Methodology of Discovery: the Importance of Strategies

There are various ``classical' argumentsagainst abduction as a logic of discovery,especially that (1) abduction is too weak amode of inference to be of any use, and (2) inbasic formulation of abduction the hypothesisis already presupposed to be known, so it isnot the way hypotheses are discovered in thefirst place. In this paper I argue, bybringing forth the idea of strategies,that these counter-arguments are weaker thanmay appear. The concept of strategiessuggests, inter alia, that many inferentialmoves are taken into account at the same time.This is especially important in abductivereasoning, which is basically a very weak modeof inference. The importance of strategicthinking can already be seen in Charles S.Peirce's early treatments of the topic, and N.R.Hanson's later writings on abductionalthough they did not use the concept of``strategies.' On the whole, I am arguing thatthe focus should be more on methodologicalprocesses, and not only on validityconsiderations, which have dominated thediscussion about abduction.     

de Broglie Waves as the “Bridge of Becoming” Between Quantum Theory and Relativity

It is hypothesized that de Broglie’s ‘matter waves’ provide a dynamical basis for Minkowski spacetime in an antisubstantivalist or relational account. The relativity of simultaneity is seen as an effect of the de Broglie oscillation together with a basic relativity postulate, while the dispersion relation from finite rest mass gives rise to the differentiation of spatial and temporal axes. Thus spacetime is seen as not fundamental, but rather as emergent from the quantum level. A result by Solov’ev which demonstrates that time is not an applicable concept at the quantum level is adduced in support of this claim. Finally, it is noted that de Broglie waves can be seen as the “bridge of becoming” discussed by (2005).