Philosophy of Modeling: Neglected Pages of History

The work done in the philosophy of modeling by Vaihinger (1876), Craik (1943), Rosenblueth and Wiener (1945), Apostel (1960), Minsky (1965), Klaus (1966) and Stachowiak (1973) is still almost completely neglected in the mainstream literature. However, this work seems to contain original ideas worth to be discussed. For example, the idea that diverse functions of models can be better structured as follows: in fact, models perform only a single function – they are replacing their target systems, but for different purposes. Another example: the idea that all of cognition is cognition in models or by means of models. Even perception, reflexes and instincts (animal and human) can be best analyzed as modeling. The paper presents an analysis of the above-mentioned work

Explanation and Understanding in a Model-Based Model of Cognition

This article is an experiment. Consider a minimalist model of cognition (models, means of model-building and history of their evolution). In this model, explanation could be defined as a means allowing to advance: production of models and means of model-building (thus, yielding 1st class understanding), exploration and use of them (2nd class), and/or teaching (3rd class). At minimum, 3rd class understanding is necessary for an explanation to be respected

Philosophy of Modeling: Some Neglected Pages of History

The work done in the philosophy of modeling by Vaihinger (1876), Craik (1943), Rosenblueth and Wiener (1945), Apostel (1960), Minsky (1965), Klaus (1966) and Stachowiak (1973) is still almost completely neglected in the mainstream literature. However, this work seems to contain original ideas worth to be discussed. For example, the idea that diverse functions of models can be better structured as follows: in fact, models perform only a single function – they are replacing their target systems, but for different purposes. Another example: the idea that all of cognition is cognition in models or by means of models. Even perception, reflexes and instincts (animal and human) can be best analyzed as modeling. The paper presents an analysis of the above-mentioned work

Truth Demystified

For further development, see Karlis Podnieks in ResearchGate. How could we recognize truth, if we only have models, means of model-building, and the history of their evolution? Where is the truth in the cloud of models – with so many of them already gone with the wind? We can define truths as more or less persistent invariants of successful evolution of models and means of model-building. What is true, will not change in the future (for some time, at least). This approach to truth could be named demystified realism (or, demystified theory of truth) – the kind of realism based on a minimum of metaphysical assumptions. (“Robotic realism” also would be appropriate, but the term is occupied already.

Philosophy of Modeling: Some Neglected Pages of History

The work done in the philosophy of modeling by Vaihinger (1876), Craik (1943), Rosenblueth and Wiener (1945), Apostel (1960), Minsky (1965), Klaus (1966) and Stachowiak (1973) is still almost completely neglected in the mainstream literature. However, this work seems to contain original ideas worth to be discussed. For example, the idea that diverse functions of models can be better structured as follows: in fact, models perform only a single function – they are replacing their target systems, but for different purposes. Another example: the idea that all of cognition is cognition in models or by means of models. Even perception, reflexes and instincts (animal and human) can be best analyzed as modeling. The paper presents an analysis of the above-mentioned work

Platonism, intuition and the nature of mathematics

Platonism is an essential aspect of mathematical method. Mathematicians are learned ability " t o   l i v e " in the "world" of mathematical concepts. Here we have the main source of the creative power of mathematics, and of its surprising efficiency in natural sciences and technique. In this way, "living" (sometimes - for many years) in the "world"of their concepts and models, mathematicians are learned to draw a maximum of conclusions from a minimum of premises. Fixed system of basic principles is the distinguishing property of every mathematical theory. Mathematical model of some natural process or technical device is essentially a  f i x e d  m o d e l  which can be investigated independently of its "original"

Fourteen Arguments in Favour of a Formalist Philosophy of Real Mathematics

The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have not yet been used or were neglected in past discussions

Теорема Гёделя о неполноте

Published as: К. М. Подниекс. Теорема Гёделя о неполноте. "Математика XX века. Взгляд из Петербурга", МЦНМО, 2010, стр. 170-174.Если оценивать открытия ХХ века по их влиянию на образ научного мышления, то открытие Курта Гёделя следует (по значению) приравнять к открытию принципов теории относительности и квантовой механики

MDA: correctness of model transformations. Which models are schemas?

How to determine, is a proposed model transformation correct, or not? In general, the answer may depend on the model semantics. Of course, a model transformation is “correct”, if we can extend it to a “correct” instance data transformation. Where should model semantics be defined? Assume, model syntax and semantics are defined in the same meta-model. Then, how to separate syntax from semantics? The answer could be the definition of model schemas proposed in the paper