Why Should We Be Pessimistic About Antirealists and Pessimists?

The pessimistic induction over scientific theories (Poincaré in Science and hypothesis, Dover, New York, 1905/1952) holds that present theories will be overthrown as were past theories. The pessimistic induction over scientists (Stanford in Exceeding our grasp: science, history, and the problem of unconceived alternatives, Oxford University Press, Oxford, 2006) holds that present scientists cannot conceive of future theories just as past scientists could not conceive of present theories. The pessimistic induction over realists (Wray in Synthese 190(18):4321–4330, 2013) holds that present realists are wrong about present theories just as past realists were wrong about past theories. The pessimistic induction over antirealist theories (Park in Organon F 21(1):3–21, 2014) holds that the latest antirealist explanation of the success of science (Lyons in Philos Sci 70(5):891–901, 2003) has hidden problems just as its eight predecessors did. In this paper, I (1) criticize the pessimistic inductions over scientific theories, scientists, and realists, (2) introduce a pessimistic induction over antirealist theories, and then (3) construct two new pessimistic inductions. One is a pessimistic induction over antirealists according to which the author of the latest antirealist proposal cannot see hidden problems with his proposal just as his antirealist predecessors could not see hidden problems with their proposals. The other is the pessimistic induction over pessimists according to which since past pessimists have been wrong about their present scientific theories from the early twentieth century to the early twenty-first century, future pessimists will also be wrong about their present scientific theories from the early twenty-first century to the early twenty-second century.     

科学真理

一方面科学理论被普遍地认为是真理的典范;另一方面科学史告诉我们,无论多么成功的理论都逃脱不了最终被推翻的命运。这种"悲观的元归纳"表明,就其本性而论科学理论并非为一般人们所认为的那种符合论真理。关于科学理论本性的争论一直在进行中。本文在深入分析、谨慎运用相关专业资料的基础上,对"科学理论是否为真理",以及"如果是真理,它是一种什么意义上的真理"等问题进行了尽可能系统而清晰细致的讨论和论证。     

Salmon and Van Fraassen on the Existence of Unobservable Entities: A Matter of Interpretation of Probability

A careful analysis of Salmon’s Theoretical Realism and van Fraassen’s Constructive Empiricism shows that both share a common origin: the requirement of literal construal of theories inherited by the Standard View. However, despite this common starting point, Salmon and van Fraassen strongly disagree on the existence of unobservable entities. I argue that their different ontological commitment towards the existence of unobservables traces back to their different views on the interpretation of probability via different conceptions of induction. In fact, inferences to statements claiming the existence of unobservable entities are inferences to probabilistic statements, whence the crucial importance of the interpretation of probability.     

The Meaning of Life in a Developing Universe

The evolution of life on Earth has produced an organism that is beginning to model and understand its own evolution and the possible future evolution of life in the universe. These models and associated evidence show that evolution on Earth has a trajectory. The scale over which living processes are organized cooperatively has increased progressively, as has its evolvability. Recent theoretical advances raise the possibility that this trajectory is itself part of a wider developmental process. According to these theories, the developmental process has been shaped by a yet larger evolutionary dynamic that involves the reproduction of universes. This evolutionary dynamic has tuned the key parameters of the universe to increase the likelihood that life will emerge and produce outcomes that are successful in the larger process (e.g. a key outcome may be to produce life and intelligence that intentionally reproduces the universe and tunes the parameters of ‘offspring’ universes). Theory suggests that when life emerges on a planet, it moves along this trajectory of its own accord. However, at a particular point evolution will continue to advance only if organisms emerge that decide to advance the developmental process intentionally. The organisms must be prepared to make this commitment even though the ultimate nature and destination of the process is uncertain, and may forever remain unknown. Organisms that complete this transition to intentional evolution will drive the further development of life and intelligence in the universe. Humanity’s increasing understanding of the evolution of life in the universe is rapidly bringing it to the threshold of this major evolutionary transition.     

Philosophical Issues and their Implications for the Systems Architect

Many system architects select their system methodologies without explicit consideration of the philosophical perspectives that impact their decisions. This paper describes how the concepts of ontology and epistemology apply in systems science. Ontology is how we specify terms of reference for existence, allowing us to understand the theory of existence via an ‘existence framework’. Epistemology, the theory of knowledge, allows us to explore new models and theories of knowledge acquisition so the best system-based methodologies can be deployed to solve complex system problems. After introducing these concepts, the paper presents system science issues and assesses the impact of ontological, axiological and epistemological perspectives on system methodology selection, research, system design and deployment. An ontological viewpoint such as realism, as an objective view is contrasted versus nationalism, a personal perceptional view. An epistemological viewpoint is explored comparing knowledge as a product of sensory perception or rational reflection. The paper’s significant contribution is that it helps system architects understand that their philosophical views of systems science impact their system methodology choices.     

Belief Systems and Partial Spaces

One important role of belief systems is to allow us to represent information about a certain domain of inquiry. This paper presents a formal framework to accommodate such information representation. Three cognitive models to represent information are discussed: conceptual spaces (Gärdenfors in Conceptual spaces: the geometry of thought. MIT Press, Cambridge, 2000), state-spaces (van Fraassen in Quantum mechanics: an empiricist view. Clarendon Press, Oxford, 1991), and the problem spaces familiar from artificial intelligence. After indicating their weakness to deal with partial information, it is argued that an alternative, formulated in terms of partial structures (da Costa and French in Science and partial truth. Oxford University Press, New York, 2003), can be provided which not only captures the positive features of these models, but also accommodates the partiality of information ubiquitous in science and mathematics.     

The Arrow of Time and Meaning

All the attempts to find the justification of the privileged evolution of phenomena exclusively in the external world need to refer to the inescapable fact that we are living in such an asymmetric universe. This leads us to look for the origin of the “arrow of time” in the relationship between the subject and the world. The anthropic argument shows that the arrow of time is the condition of the possibility of emergence and maintenance of life in the universe. Moreover, according to Bohr’s, Poincaré’s and Watanabe’s analysis, this agreement between the earlier-later direction of entropy increase and the past-future direction of life is the very condition of the possibility for meaningful action, representation and creation. Beyond this relationship of logical necessity between the meaning process and the arrow of time the question of their possible physical connection is explored. To answer affirmatively to this question, the meaning process is modelled as an evolving tree-like structure, called “Semantic Time”, where thermodynamic irreversibility can be shown. Time is the substance I am made of. Time is a river which sweeps me along, but I am the river ; it is a tiger which destroys me, but I am the tiger ; it is a fire which consumes me, but I am the fire. – (Jorge Luis Borges)     

Friends of Wisdom?

This commentary addresses the question of the meaning of critique in relation to objectivism or dogmatism. Inspired by Kant’s critical philosophy and Husserl’s phenomenology, it defines the first in terms of conditionality, the second in terms of oppositionality. It works out an application on the basis of Salthe’s (Found Sci 15 4(6):357–367, 2010a) paper on development and evolution, where competition is criticized in oppositional, more than in conditional terms.     

On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Axiomatization and Models of Scientific Theories

In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the language of set theory itself or, more rigorously (da Costa and Chuaqui), by employing formal languages that help us in writing the postulates to define a class of structures. Both approaches are called internal, for we work within a mathematical framework, here taken to be first-order ZFC. We contrast these approaches with an external one, here discussed briefly. We argue that each one has its strong and weak points, whose discussion is relevant for the philosophical foundations of science.     

Newton’s Neo-Platonic Ontology of Space

This paper investigates Newton’s ontology of space in order to determine its commitment, if any, to both Cambridge neo-Platonism, which posits an incorporeal basis for space, and substantivalism, which regards space as a form of substance or entity. A non-substantivalist interpretation of Newton’s theory has been famously championed by Howard Stein and Robert DiSalle, among others, while both Stein and the early work of J. E. McGuire have downplayed the influence of Cambridge neo-Platonism on various aspects of Newton’s own spatial hypotheses. Both of these assertions will be shown to be problematic on various grounds, with special emphasis placed on Stein’s influential case for a non-substantivalist reading. Our analysis will strive, nonetheless, to reveal the unique or forward-looking aspects of Newton’s approach, most notably, his critical assessment of substance ontologies, that help to distinguish his theory of space from his neo-Platonic contemporaries and predecessors.     

The location model for mixtures of categorical and continuous variables

Recent research into graphical association models has focussed interest on the conditional Gaussian distribution for analyzing mixtures of categorical and continuous variables. A special case of such models, utilizing the homogeneous conditional Gaussian distribution, has in fact been known since 1961 as the location model, and for the past 30 years has provided a basis for the multivariate analysis of mixed categorical and continuous variables. Extensive development of this model took place throughout the 1970’s and 1980’s in the context of discrimination and classification, and comprehensive methodology is now available for such analysis of mixed variables. This paper surveys these developments and summarizes current capabilities in the area. Topics include distances between groups, discriminant analysis, error rates and their estimation, model and feature selection, and the handling of missing data.     

Understanding Pluralism in Climate Modeling

To study Earth’s climate, scientists now use a variety of computer simulation models. These models disagree in some of their assumptions about the climate system, yet they are used together as complementary resources for investigating future climatic change. This paper examines and defends this use of incompatible models. I argue that climate model pluralism results both from uncertainty concerning how to best represent the climate system and from difficulties faced in evaluating the relative merits of complex models. I describe how incompatible climate models are used together in ‘multi-model ensembles’ and explain why this practice is reasonable, given scientists’ inability to identify a ‘best’ model for predicting future climate. Finally, I characterize climate model pluralism as involving both an ontic competitive pluralism and a pragmatic integrative pluralism.     

The Argument(s) for Universal Gravitation

In this paper an analysis of Newton’s argument for universal gravitation is provided. In the past, the complexity of the argument has not been fully appreciated. Recent authors like George E. Smith and William L. Harper have done a far better job. Nevertheless, a thorough account of the argument is still lacking. Both authors seem to stress the importance of only one methodological component. Smith stresses the procedure of approximative deductions backed-up by the laws of motion. Harper stresses “systematic dependencies” between theoretical parameters and phenomena. I will argue that Newton used a variety of different inferential strategies: causal parsimony considerations, deductions, demonstrative inductions, abductions and thought-experiments. Each of these strategies is part of Newton’s famous argument.     

Inventing Electric Potential

Investigations with electrometers in the 1770s led Volta to envision mobile charge in electrical conductors as a compressible fluid. A pressure-like condition in this fluid, which Volta described as the fluid’s “effort to push itself out” of its conducting container, was the causal agent that makes the fluid move. In this paper I discuss Volta’s use of analogy and imagery in model building, and compare with a successful contemporary conceptual approach to introducing ideas about electric potential in instruction. The concept that today is called “electric potential” was defined mathematically by Poisson in 1811. It was understood after about 1850 to predict the same results in conducting matter as Volta’s pressure-like concept—and to predict electrostatic effects in the exterior space where Volta’s concept had nothing to say. Complete quantification in addition to greater generality made the mathematical concept a superior research tool for scientists. However, its spreading use in instruction has marginalized approaches to model building based on the analogy and imagery resources that students bring into the classroom. Data from pre and post testing in high schools show greater conceptual and confidence gains using the new conceptual approach than using conventional instruction. This provides evidence for reviving Volta’s compressible fluid model as an intuitive foundation which can then be modified to include electrostatic distant action. Volta tried to modify his compressible fluid model to include distant action, using imagery borrowed from distant heating by a flame. This project remained incomplete, because he did not envision an external field mediating the heating. However, pursuing Volta’s strategy of model modification to completion now enables students taught with the new conceptual approach to add distant action to an initial compressible fluid model. I suggest that a partial correspondence to the evolving model sequence that works for beginning students can help illuminate Volta’s use of intermediate explanatory models.

On the Performance of Simulated Annealing for Large-Scale L2 Unidimensional Scaling

In this research note, I present a modified version of G. De Soete, L. Hubert, and P. Arabie’s (1988) simulated annealing approach for the problem of L₂ unidimensional scaling via maximization of the Defays criterion. The modifications include efficient storage and computation methods that facilitate rapid evaluation of trial solutions. The results of two experimental studies indicate that the enhanced simulated annealing algorithm is competitive with A. Murillo, J.F. Vera, and W.J. Heiser’s (2005) recently published pertsaus2 procedure in terms of solution quality and computation time. Both Fortran and MatLab versions of this modified simulated annealing implementation are available from the author.     

Objects and Processes in Mathematical Practice

In this paper it is argued that the fundamental difference of the formal and the informal position in the philosophy of mathematics results from the collision of an object and a process centric perspective towards mathematics. This collision can be overcome by means of dialectical analysis, which shows that both perspectives essentially depend on each other. This is illustrated by the example of mathematical proof and its formal and informal nature. A short overview of the employed materialist dialectical approach is given that rationalises mathematical development as a process of model production. It aims at placing more emphasis on the application aspects of mathematical results. Moreover, it is shown how such production realises subjective capacities as well as objective conditions, where the latter are mediated by mathematical formalism. The approach is further sustained by Polanyi’s theory of problem solving and Stegmaier’s philosophy of orientation. In particular, the tool and application perspective illuminates which role computer-based proofs can play in mathematics.     

Comparison tests for dendrograms: A comparative evaluation

Classifications are generally pictured in the form of hierarchical trees, also called dendrograms. A dendrogram is the graphical representation of an ultrametric (=cophenetic) matrix; so dendrograms can be compared to one another by comparing their cophenetic matrices. Three methods used in testing the correlation between matrices corresponding to dendrograms are evaluated. The three permutational procedures make use of different aspects of the information to compare dendrograms: the Mantel procedure permutes label positions only; the binary tree methods randomize the topology as well; the double-permutation procedure is based on all the information included in a dendrogram, that is: topology, label positions, and cluster heights. Theoretical and empirical investigations of these methods are carried out to evaluate their relative performance. Simulations show that the Mantel test is too conservative when applied to the comparison of dendrograms; the methods of binary tree comparisons do slightly better; only the doublepermutation test provides unbiased type I error. Les arbres utilisés pour illustrés les groupements sont généralement représentés sous la forme de classifications hiérarchiques ou dendrogrammes. Un dendrogramme représente graphiquement l’information contenue dans la matrice ultramétrique (=cophénétique) correspondant à la classification. Dès ultramétriques correspondantes. Nous comparons trois méthodes permettant d’évaluer la signification statistique du coefficient de correlation mesuré entre deux matrices ultramétriques. Ces trois tests par permutations tiennent compte d’aspects différents pour comparer des dendrogrammes: le test de Mantel permute les feuilles de l’arbre, les méthodes pour arbres binaires permutent les feuilles et la topologie, alors que la procédure à double permutation permute les feuilles, la topologie et les niveaux de fusion des dendrogrammes comparés. L’efficacité relative des trois méthodes est évaluée empiriquement et théoriquement. Nos résultats suggèrent l’utilisation préférentielle du test à double permutation pour la comparaison de dendrogrammes: le test de Mantel s’avère trop conservateur, tandis que les méthodes pour arbres binaires ne sont pas toujours adéquates.

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This work was supported by NSERC grant no. A7738 to Pierre Legendre and by a NSERC scholarship to F.-J. Lapointe.     

The Constructive Realist Account of Science and Its Application to Ilya Prigogine’s Conception of Laws of Nature

Sciences are often regarded as providing the best, or, ideally, exact, knowledge of the world, especially in providing laws of nature. Ilya Prigogine, who was awarded the Nobel Prize for his theory of non-equilibrium chemical processes—this being also an important attempt to bridge the gap between exact and non-exact sciences [mentioned in the Presentation Speech by Professor Stig Claesson (nobelprize.org, The Nobel Prize in Chemistry 1977)]—has had this ideal in mind when trying to formulate a new kind of science. Philosophers of science distinguish theory and reality, examining relations between these two. Nancy Cartwright’s distinction of fundamental and phenomenological laws, Rein Vihalemm’s conception of the peculiarity of the exact sciences, and Ronald Giere’s account of models in science and science as a set of models are deployed in this article to criticise the common view of science and analyse Ilya Prigogine’s view in particular. We will conclude that on a more abstract, philosophical level, Prigogine’s understanding of science doesn’t differ from the common understanding.