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On October 5, the Third Research Seminar of the Project team was held in a closed non-public format

Frege's triangle, Pierce's quadrangle, DDI approach, representations and scientific research intersubjectivity in the report on the past Third Methodological Workshop of the Project Team for the development and use of computer simulations in science, industries and business.

On October 5, the Third Research Seminar of the Project team was held in a closed non-public format

By October 5th, through a series of discussions and research, the Project Working Group has come to the fundamental foundations of studying the nature of modelling and computer simulations. For this reason, there is an urgent need in identifying theoretical foundations and methodological tools to reveal modelling foundations.

A post-graduate student of the Moscow State University of M.V. Lomonosov, Faculty of Philosophy, and the Project researcher - Mikhail Voloshin, who from the very start of the Project showed motivation to solve the indicated problems with the help of his own developments in this non-trivial research area, volunteered to conduct the seminar.

Frege's triangle

The talk began with an analysis of Frege’s ion of a sign - otherwise known as Frege’s semantic triangle.

In Frege's works Sense and Meaning (Über Sinn und Bedeutung, 1892), Function and Concept (Funktion und Begriff, 1891), Concept and Object (Über Begriff und Gegenstand, 1892), Thought (Der Gedanke, 1918), the foundation for the logic of predicates started. This will be actively applied in modern times, especially in those areas where the traditional Aristotelian logic of syllogisms is less effective.

Like many ingenious discoveries, Frege’s triangle was discovered by accident and was not originally the author's goal. 

                                                  Picture 1. Frege's triangle

This is where Mikhail Voloshin's interesting line of reasoning begins. It should lead to understanding the epistemological foundations of models used in science and computer simulations specifics that are used both in science and in solving engineering, industrial and business problems.

Frege supplements a two-part sign model (signifier-signified) with a third element - the sign meaning. Mikhail Voloshin examines here an analytical toolkit for parsing computer simulations as a complex mechanism for generating new knowledge about the target system.

Pierce's quadrangle

Next, the Pierce quadrangle was analysed. Here, a sign (representation) is something that replaces someone or something in any relation or under some name. Peirce supplements Frege's triangle with a fourth element - an interpreter: a sign is a sign of something only in the context of its use by a certain subject. Signs do not constitute a certain class of objects among others. Everything may be a sign.

Accordingly, if we take a model for a sign, then everything can be a model. 

                    Picture 2. Pierce’s quadrangle.


Three main approaches

There is a generally accepted classification of various approaches to philosophical study of scientific modelling. They are divided into a syntactic approach (model is an interpretation of a theory represented by formal calculus), semantic (a model is defined as a structure on a set, and a theory is a hierarchy of such models), and a pragmatic approach (a model is an autonomous level in the structure of scientific knowledge, mediating the theoretical and empirical content of knowledge, but not reducible to them). Mikhail Voloshin gives preference to the pragmatic paradigm when building a general methodology for the development and use of simulations.

The pragmatic approach supporters distinguish an intermediate epistemological level between the traditional theoretical and empirical levels. Each of these levels can “live its own life,” as far as the intermediate model level. Models are autonomous from theory and experience since they are constructed with the involvement of partial elements of both, but the choice of these elements - and possibly some additional considerations - for example, aesthetic ones - this choice depends on the intentions of the subject who creates and uses the model. The model is a model of the target system only for someone who intends to use it that way. (Morrison M. Models as autonomous agents // Models as mediators: perspectives on natural and social science. Eds. Morrison M., Morgan M. – NY: Cambridge University Press, 1999. – pp. 38-65).


What Mary Hesse pointed out in the 60s was that a significant function of models is the communicative function: the model must ensure the intersubjectivity of scientific knowledge; that means to be understandable for those who use it and for those who wants to use its results. Then the ways of representing the simulation results take on special significance (Hesse M. Models and analogies in science. – University of Notre Dame Press, 1970)


 One of the specific features of computer simulations is that they provide us with new ways of representing the process and the result of modelling ( for example, visual).



There is an approach to the analysis of simulations formulated by Hughes and known as the DDI-approach (denotation, demonstration, interpretation).

The process of scientific cognition using models is divided into three stages:

1) picking a certain system as a model for another (denotation),

2) working with simulation (demonstration),

3) transferring the simulation results back to the target system (interpretation).


                         Picture 3. DDI-approach.


The interesting part is that the scientific subject is a significant participant in all the three stages, which is consistent with the pragmatic approach in general. (Hughes R.I.G. The Ising model, computer simulation, and universal physics // Models as mediators: perspectives on natural and social science. Eds. Morrison M., Morgan M. – NY: Cambridge University Press, 1999. – pp. 97-145).


Epistemic opacity

Some philosophers (such as Paul Humphreys) point out specific issues that arise when using computer simulations, and distinguish them from other types of simulations.

The key one is “epistemic opacity” of the simulation process: a scientist using a computer model often does not know exactly what kind of computational processes takes place in a computer.

In this regard, a project was even proposed for a "non-anthropocentric epistemology" of simulations, which includes computers as equal actors in the simulation process. (Humphreys P. The philosophical novelty of computer simulation methods // Synthese. – Vol. 169 (3), 2009. – pp. 615-626.)

Mikhail Voloshin offered his criticism of this discussion: knowledge inaccessible to one scientist may be available to another, and we can talk about the distribution of this knowledge in the scientific community in general. Therefore, although opacity exists for the individual subject, the "collective" subject of scientific activity has mechanisms to overcome it. This once again points of the fundamentally intersubjective simulations’ nature.