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.     

The Future of Life and What it Means for Humanity

Vidal’s (Found Sci, 2010) and Rottiers’s (Found Sci, 2010) commentaries on my (2010) paper raised a number of important issues about the possible future trajectory of evolution and its implications for humanity. My response emphasizes that despite the inherent uncertainty involved in extrapolating the trajectory of evolution into the far future, the possibilities it reveals nonetheless have significant strategic implications for what we do with our lives here and now, individually and collectively. One important implication is the replacement of postmodern scepticism and relativism with an evolutionary grand narrative that can guide humanity to participate successfully in the future evolution of life in the universe.     

Must Complex Systems Theory Be Materialistic?

So far, the sciences of complexity have received less attention from philosophers than from scientists. Responding to Salthe’s (Found Sci 15, 4(6):357–367, 2010a) model of evolution, I focus on its metaphysical implications, asking whether the implications of his canonical developmental trajectory (CDT) must be materialistic as his reading proposes.     

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.     

On the Nature of Initial Conditions and Fundamental Parameters in Physics and Cosmology

The cosmological theory of the author, discussed in (Greben in Found Sci 15(2):153–176, 2010), has a number of implications for the interpretation of initial conditions and the fine-tuning problem as discussed by Vidal (Found Sci 15(4):375–393, 2010a).     

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.

Participating in the Meaning of Life, a Contributor’s Critique

The aim of this contribution is to critically examine the metaphysical presuppositions that prevail in (Stewart in Found Sci 15(4):395–409, 2010a) answer to the question “are we in the midst of a developmental process?” as expressed in his statement “that humanity has discovered the trajectory of past evolution and can see how it is likely to continue in the future”.     

Development (and Evolution) of the Universe

I distinguish Nature from the World. I also distinguish development from evolution. Development is progressive change and can be modeled as part of Nature, using a specification hierarchy. I have proposed a ‘canonical developmental trajectory’ of dissipative structures with the stages defined thermodynamically and informationally. I consider some thermodynamic aspects of the Big Bang, leading to a proposal for reviving final cause. This model imposes a ‘hylozooic’ kind of interpretation upon Nature, as all emergent features at higher levels would have been vaguely and episodically present primitively in the lower integrative levels, and were stabilized materially with the developmental emergence of new levels. The specification hierarchy’s form is that of a tree, with its trunk in its lowest level, and so this hierarchy is appropriate for modeling an expanding system like the Universe. It is consistent with this model of differentiation during Big Bang development to view emerging branch tips as having been entrained by multiple finalities because of the top-down integration of the various levels of organization by the higher levels.     

Scale Relativity: an Extended Paradigm for Physics and Biology?

With scale relativity theory, Laurent Nottale has provided a powerful conceptual and mathematical framework with numerous validated predictions that has fundamental implications and applications for all sciences. We discuss how this extended framework reviewed in Nottale (Found Sci 152 (3):101–152, 2010a) may help facilitating integration across multiple size and time frames in systems biology, and the development of a scale relative biology with increased explanatory power.     

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 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)     

Coherence of Our Best Scientific Theories

Putnam in Realism in mathematics and Elsewhere, Cambridge University Press, Cambridge (1975) infers from the success of a scientific theory to its approximate truth and the reference of its key term. Laudan in Philos Sci 49:19–49 (1981) objects that some past theories were successful, and yet their key terms did not refer, so they were not even approximately true. Kitcher in The advancement of science, Oxford University Press, New York (1993) replies that the past theories are approximately true because their working posits are true, although their idle posits are false. In contrast, I argue that successful theories which cohere with each other are approximately true, and that their key terms refer. My position is immune to Laudan’s counterexamples to Putnam’s inference and yields a solution to a problem with Kitcher’s position.     

Towards a Hierarchical Definition of Life,the Organism,and Death

Despite hundreds of definitions, no consensus exists on a definition of life or on the closely related and problematic definitions of the organism and death. These problems retard practical and theoretical development in, for example, exobiology, artificial life, biology and evolution. This paper suggests improving this situation by basing definitions on a theory of a generalized particle hierarchy. This theory uses the common denominator of the “operator” for a unified ranking of both particles and organisms, from elementary particles to animals with brains. Accordingly, this ranking is called “the operator hierarchy”. This hierarchy allows life to be defined as: matter with the configuration of an operator, and that possesses a complexity equal to, or even higher than the cellular operator. Living is then synonymous with the dynamics of such operators and the word organism refers to a select group of operators that fit the definition of life. The minimum condition defining an organism is its existence as an operator, construction thus being more essential than metabolism, growth or reproduction. In the operator hierarchy, every organism is associated with a specific closure, for example, the nucleus in eukaryotes. This allows death to be defined as: the state in which an organism has lost its closure following irreversible deterioration of its organization. The generality of the operator hierarchy also offers a context to discuss “life as we do not know it”. The paper ends with testing the definition’s practical value with a range of examples.     

The Foundational Role of Ergodic Theory

The foundation of statistical mechanics and the explanation of the success of its methods rest on the fact that the theoretical values of physical quantities (phase averages) may be compared with the results of experimental measurements (infinite time averages). In the 1930s, this problem, called the ergodic problem, was dealt with by ergodic theory that tried to resolve the problem by making reference above all to considerations of a dynamic nature. In the present paper, this solution will be analyzed first, highlighting the fact that its very general nature does not duly consider the specificities of the systems of statistical mechanics. Second, Khinchin’s approach will be presented, that starting with more specific assumptions about the nature of systems, achieves an asymptotic version of the result obtained with ergodic theory. Third, the statistical meaning of Khinchin’s approach will be analyzed and a comparison between this and the point of view of ergodic theory is proposed. It will be demonstrated that the difference consists principally of two different perspectives on the ergodic problem: that of ergodic theory puts the state of equilibrium at the center, while Khinchin’s attempts to generalize the result to non-equilibrium states.     

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 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.     

n-Way Metrics

We study a family of n-way metrics that generalize the usual two-way metric. The n-way metrics are totally symmetric maps from E ⁿ into \mathbbR _{\geqslant 0} {\mathbb{R}_{ \geqslant 0}} . The three-way metrics introduced by Joly and Le Calvé (1995) and Heiser and Bennani (1997) and the n-way metrics studied in Deza and Rosenberg (2000) belong to this family. It is shown how the n-way metrics and n-way distance measures are related to (n − 1)-way metrics, respectively, (n − 1)-way distance measures.     

PARAMAP vs. Isomap: A Comparison of Two Nonlinear Mapping Algorithms

Dimensionality reduction techniques are used for representing higher dimensional data by a more parsimonious and meaningful lower dimensional structure. In this paper we will study two such approaches, namely Carroll’s Parametric Mapping (abbreviated PARAMAP) (Shepard and Carroll, 1966) and Tenenbaum’s Isometric Mapping (abbreviated Isomap) (Tenenbaum, de Silva, and Langford, 2000). The former relies on iterative minimization of a cost function while the latter applies classical MDS after a preprocessing step involving the use of a shortest path algorithm to define approximate geodesic distances. We will develop a measure of congruence based on preservation of local structure between the input data and the mapped low dimensional embedding, and compare the different approaches on various sets of data, including points located on the surface of a sphere, some data called the "Swiss Roll data", and truncated spheres.