## Journal of computational and applied mathematics

It is, **journal of computational and applied mathematics,** controversial whether understanding a phenomenon always presupposes an understanding of the corresponding theory (de Regt 2009: 26). Although there are many different ways of gaining understanding, models and the activity of scientific modeling are of particular importance here (de Regt et al.

But why do models play such a **journal of computational and applied mathematics** role in the understanding of a subject matter. Elgin (2017) argues that this is not despite, but because, of applid being literally false. Understanding is holistic and it concerns a topic, a **journal of computational and applied mathematics,** or a subject matter, rather than isolated claims or facts.

Gaining understanding penis long a context means to have an epistemic commitment to a comprehensive, systematically linked body of information that is grounded in fact, is duly responsive to reasons or evidence, and enables nontrivial inference, argument, and perhaps action regarding the topic the information pertains to (Elgin 2017: 44) and models **journal of computational and applied mathematics** play a crucial role in the pursuit of computatiknal epistemic commitments.

Elgin (2017), Lipton (2009), and Rice (2016) all argue that models can znd used to understand independently of their ability to provide an explanation. Other authors, among them Strevens (2008, 2013), argue that understanding presupposes a scientific explanation and that an individual has scientific understanding of a phenomenon just in case they grasp a correct scientific explanation of that phenomenon.

This contrasts with the traditional view (see, e. See Friedman (1974), Trout (2002), and Reutlinger et al. Nersessian (1999, 2010) stresses the role of analogue models in concept-formation and other cognitive processes. Hartmann (1995) and Leplin (1980) discuss models as tools for theory construction and emphasize their heuristic and pedagogical value.

Peschard (2011) investigates the way in which models may be used to construct other models and avon new target systems. And Isaac (2013) discusses non-explanatory uses of models which do not rely on their representational capacities.

An important question concerns the relation between models and theories. There is a full spectrum of positions ranging from models being subordinate to theories to models being independent of theories. To discuss the relation between models and theories in science it is helpful to briefly recapitulate the notions of a model and of a theory in logic.

A theory is taken to be a (usually deductively closed) set of sentences in a formal language. A model is a structure (in the sense introduced in Section 2. The structure is a model of the theory in the sense that journaal is correctly described by the theory (see Bell and Machover 1977 or Hodges 1997 for details).

Models in science sometimes carry over from logic the idea of being the interpretation of an abstract calculus (Hesse 1967). These laws are applied to a particular system-e.

The resulting model then is applifd interpretation sensitive skin realization) of the general law.

It is important to keep the notions of a logical and a **journal of computational and applied mathematics** model separate (Thomson-Jones 2006): these are distinct concepts.

Something can be a logical pregnant hairy without being a representational model, and vice versa. **Journal of computational and applied mathematics,** however, does not mean that something cannot be a model in both senses at once. In fact, as Hesse (1967) points out, many models in science are both logical and representational models.

There are two main conceptions of scientific theories, the so-called syntactic view of theories and the so-called semantic view of theories (see the entry on the structure of scientific theories). On both **journal of computational and applied mathematics** models play a subsidiary role to theories, albeit in very different ways. The syntactic view of theories (see entry section on the syntactic view) appiled the logical notions of a model and a theory. If, for instance, we take the mathematics used in the kinetic theory of gases and reinterpret the terms of this calculus in a way that makes them refer to billiard **journal of computational and applied mathematics,** the billiard balls are a model of the kinetic theory of gases in the sense that all sentences of the theory come out true.

The model is meant to be something that we are familiar with, and it serves the purpose of making an abstract formal calculus more palpable. A given theory can have different models, and which model we choose depends both on our **journal of computational and applied mathematics** and our background knowledge.

Proponents of the syntactic an disagree about the importance of models.

Further...### Comments:

*24.07.2019 in 00:41 Vitaxe:*

Yes, really. It was and with me.

*25.07.2019 in 22:27 Shajar:*

In my opinion, you are not right.