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Frank Waaldijk 《Foundations of Science》2005,10(3):249-324
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. 相似文献
3.
András Kertész 《Foundations of Science》2012,17(1):91-108
Chomsky’s principle of epistemological tolerance says that in theoretical linguistics contradictions between the data and
the hypotheses may be temporarily tolerated in order to protect the explanatory power of the theory. The paper raises the
following problem: What kinds of contradictions may be tolerated between the data and the hypotheses in theoretical linguistics?
First a model of paraconsistent logic is introduced which differentiates between week and strong contradiction. As a second
step, a case study is carried out which exemplifies that the principle of epistemological tolerance may be interpreted as
the tolerance of week contradiction. The third step of the argumentation focuses on another case study which exemplifies that
the principle of epistemological tolerance must not be interpreted as the tolerance of strong contradiction. The reason for
the latter insight is the unreliability and the uncertainty of introspective data. From this finding the author draws the
conclusion that it is the integration of different data types that may lead to the improvement of current theoretical linguistics
and that the integration of different data types requires a novel methodology which, for the time being, is not available. 相似文献
4.
Bert Mosselmans 《Foundations of Science》2005,10(3):325-345
This paper explores the relationship of time and value in the history of economics, using the contributions of Girard, Achterhuis,
Kula and Mirowski. In the ‘anthropometric stage’ time and value are intertwined: value and time are not abstract concepts,
but they express a concrete process which incorporates the social positions of individuals. In the ‘lineamentric stage’ the
concepts of time and value remain cyclical, but they receive an abstract character. The economy reproduces itself cyclically,
because the origin of value – human labour – reproduces itself in each production period. In the ‘syndetic stage’ the cyclical
conception of the economy is abandoned through the perception of a non-reproductive system. Time and value are detached from
each other, and linear time enters economic theory as an analytical tool. The labour theory of value is replaced by external
denominants of value: utility and external scarcity 相似文献
5.
Understanding Pluralism in Climate Modeling 总被引:1,自引:0,他引:1
W. S. Parker 《Foundations of Science》2006,11(4):349-368
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. 相似文献
6.
Diderik Batens 《Foundations of Science》1998,3(2):259-283
The paper highlights the import of the paraconsistent movement, list some motivations for its origin, and distinguishes some
stands with respect to para-consistency. It then discusses some sources of inconsistency that are specific for worldviews,
and the import of the paraconsistent turn for the worldviews enterprise.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
Liane Gabora 《Foundations of Science》1998,3(2):395-428
In order to become aware of inconsistencies, one must first construe of the world in a way that reflects its consistencies.
This paper begins with a tentative model for how a set of discrete memories transforms into an interconnected worldview, wherein
relationships between memories are forged by way of abstractions. Inconsistencies prompt the invention of new abstractions.
In regions of the conceptual network where inconsistencies abound, a cognitive analog of simulated annealing is in order;
there is a willingness to question previous assumptions - to ‘loosen’ conceptual relationships - so as to let new concepts
percolate through the worldview and exert the needed revolutionary effect. In so doing there is a risk of assimilating dangerous
concepts. Repression arrests the process by which dangerous thoughts infiltrate the conceptual network, and deception blocks
thoughts that have already been assimilated. These forms of self-initiated worldview inconsistency may evoke feelings of fragmentation
at the level of the individual or the society.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
8.
Jan t Broekaer 《Foundations of Science》1998,3(2):235-258
In the work of the late Belgian philosopher, logician and freethinker Leo Apostel (1924–1995) the concept of ‘world view’
is extensively developed. From the diverse research of Apostel, I gather and examine the constituents of a world view and
their relationships. I propose to understand it as a pluralist and open, rationalised ontology of the ‘world whole’, comprising
knowledge systems, valuative ethical systems and concomitant action guiding systems, to a large extent reflecting insight
in the exact sciences. The prolific and scattered opus of Apostel renders my account of encompassing world views approximate
and incomplete. It merely outlines the intrinsically unfinished project and presents a recent development. This development
mainly involves our approach to the phenomenon of emergence from a quantum theoretical perspective.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
Development (and Evolution) of the Universe 总被引:2,自引:2,他引:0
Stanley N. Salthe 《Foundations of Science》2010,15(4):357-367
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. 相似文献
10.
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. 相似文献
11.
The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters
at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application.
The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse
and used to characterise the general laws of a theory. In classical mechanics, for example, we select position and momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified
elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions
of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed,
how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions
of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the
process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising
and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation
involved in scientific- model construction, and argue why it provides an explication of the construction of models of the
nuclear structure. 相似文献
12.
F. Gonzalez Asenjo 《Foundations of Science》1998,3(2):429-465
Antinomicity is not necessarily dependent on negation; there is a more general conception of antinomicity based on the fundamental
idea of opposition. To study this fact is indispensable to show first that truth and falsity are independent of assertion
and negation. Then it can be seen that antinomies can be found everywhere, and that some single categories are in intrinsic
opposition with themselves while others are opposed to one another in pairs. An antinomic ‘manifesto’ concludes the work.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
In agglomerative hierarchical clustering, pair-group methods suffer from a problem of non-uniqueness when two or more distances
between different clusters coincide during the amalgamation process. The traditional approach for solving this drawback has
been to take any arbitrary criterion in order to break ties between distances, which results in different hierarchical classifications
depending on the criterion followed. In this article we propose a variable-group algorithm that consists in grouping more
than two clusters at the same time when ties occur. We give a tree representation for the results of the algorithm, which
we call a multidendrogram, as well as a generalization of the Lance andWilliams’ formula which enables the implementation of the algorithm in a recursive
way.
The authors thank A. Arenas for discussion and helpful comments. This work was partially supported by DGES of the Spanish
Government Project No. FIS2006–13321–C02–02 and by a grant of Universitat Rovira i Virgili. 相似文献
14.
Pierre Uzan 《Foundations of Science》2007,12(2):109-137
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) 相似文献
15.
The issue of determining “the right number of clusters” in K-Means has attracted considerable interest, especially in the
recent years. Cluster intermix appears to be a factor most affecting the clustering results. This paper proposes an experimental
setting for comparison of different approaches at data generated from Gaussian clusters with the controlled parameters of
between- and within-cluster spread to model cluster intermix. The setting allows for evaluating the centroid recovery on par
with conventional evaluation of the cluster recovery. The subjects of our interest are two versions of the “intelligent” K-Means method, ik-Means, that find the “right” number of clusters by extracting “anomalous patterns” from the data one-by-one. We compare them
with seven other methods, including Hartigan’s rule, averaged Silhouette width and Gap statistic, under different between-
and within-cluster spread-shape conditions. There are several consistent patterns in the results of our experiments, such
as that the right K is reproduced best by Hartigan’s rule – but not clusters or their centroids. This leads us to propose an adjusted version
of iK-Means, which performs well in the current experiment setting. 相似文献
16.
Pierre Uzan 《Foundations of Science》2010,15(1):1-28
This paper suggests an epistemic interpretation of Belnap’s branching space-times theory based on Everett’s relative state
formulation of the measurement operation in quantum mechanics. The informational branching models of the universe are evolving
structures defined from a partial ordering relation on the set of memory states of the impersonal observer. The totally ordered
set of their information contents defines a linear “time” scale to which the decoherent alternative histories of the informational
universe can be referred—which is quite necessary for assigning them a probability distribution. The “historical” state of
a physical system is represented in an appropriate extended Hilbert space and an algebra of multi-branch operators is developed.
An age operator computes the informational depth of historical states and its standard deviation can be used to provide a
universal information/energy uncertainty relation. An information operator computes the encoding complexity of historical
states, the rate of change of its average value accounting for the process of correlation destruction inherent to the branching
dynamics. In the informational branching models of the universe, the asymmetry of phenomena in nature appears as a mere consequence
of the subject’s activity of measuring, which defines the flow of time-information. 相似文献
17.
Karin Verelst 《Foundations of Science》2008,13(3-4):347-370
In this paper I investigate the relation between physics and metaphysics in Plato’s participation theory. I show that the logic shoring up Plato’s metaphysics in paraconsistent, as had been suggested already by Graham Priest. The transformation of the paradoxical One-and-Many of the pre-Socratics into a paraconsistent Great-and-Small bridges the abyss between archaic rationality and the world of classical logic based ultimately on the principle of contradiction. Indeed, language is an organ of perception, not simply a means of communication. J. Jaynes, Origin of Consciousness 相似文献
18.
在劳丹之后,科学哲学似乎沉闷了一段时间,但现在终于出现了一种新的尝试,一种新型的科学哲学。从次协调逻辑的视角来解读,作为科学哲学中心问题的合理性、进步、真理三者统一于协调。科学的直接目标是增强理论的协调力,间接目标是真理。科学是在理论与理论之间的冲突与协调运用中发展的。冲突是科学进步的动力,没有冲突就没有进步。进步在于理论协调力的不断增强。合理性在于协调性,协调是进步的理想状态,是间接逼近真理的手段。一个理论被称为真理,是因为它具有较大的协调力。因此,合理性标准、理论进步标准、真理标准三者实际上可以统一于一个标准,即协调力标准。这就是次协调逻辑的哲学精神,也是协调合理性模式的精髓或本质。 相似文献
19.
We argue that abduction does not work in isolation from other inference mechanisms and illustrate this through an inference
scheme designed to evaluate multiple hypotheses. We use game theory to relate the abductive system to actions that produce
new information. To enable evaluation of the implications of this approach we have implemented the procedures used to calculate
the impact of new information in a computer model. Experiments with this model display a number of features of collective
belief-revision leading to consensus-formation, such as the influence of bias and prejudice. The scheme of inferential calculations
invokes a Peircian concept of ‘belief’ as the propensity to choose a particular course of action.
相似文献
T. R. AddisEmail: |
20.
Towards a Hierarchical Definition of Life,the Organism,and Death 总被引:3,自引:3,他引:0
Gerard A. J. M. Jagers op Akkerhuis 《Foundations of Science》2010,15(3):245-262
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. 相似文献