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. The Rosen modeling relation

The two systems are related via the encoding and decoding arrows. Encoding is the

process of measurement: it is the assignment of a formal label (such as a number) to a natural

phenomenon. Decoding is prediction: it is taking what we generate via the inferential

machinery of the formal system into representations of expected phenomena. Additionally,

the arrows for inference and causality represent the entailment structures of their respective

systems.

The modeling relation provides us with a way of ascertaining congruence between the

natural system, N, and the formal system or model, F. What determines successful

congruence is that the diagram, as a whole, commutes. That is, the numbered arrows meet the

condition: (1) = (2) + (3) + (4). This means that our measurements (2), when run through the

inferential machinery (3) of our model, will generate predictions (4), which will agree (when

verified) with the actual phenomena (1) occurring in N. It bears mentioning that any encoding

from N to F is an abstraction and if the modeling relation holds, then F is a model of N. If all

four conditions of the modeling relation do not hold, then F is merely a description of N

under a specific condition.

The importance of this distinction between model and description is that it goes to the

very heart of Zack Kopplin’s argument. “Science” is about models and their use. Description

has its place, but teaching schoolchildren representations and descriptions is

teaching

them science and the scientific method. Traditional definitions of the scientific method tend

define it as “a method of procedure that has characterized natural science since the 17th

century, consisting in systematic observation, measurement, and experiment, and the

formulation, testing, and modification of hypotheses” (As retrieved from Google in May

2014). Or take the Union of Concerned Scientists’ (2007) definition:

“A scientific hypothesis must be testable and falsifiable. That is to say, a hypothesis

must make predictions that can be compared to the real world and determined to be

either true or false, and there must be some imaginable evidence that could disprove

it. If an idea makes no predictions, makes predictions that cannot be unambiguously

interpreted as either success or failure, or makes predictions that cannot be checked

out even in principle, then it is not science.”

The scientific method and related definitions of “science” are science as a model, where, as in

the Rosen definition, the model can be used to make predictions, and there exists a mapping

between the model and the “observed natural system.”

Faye (2006) conceptualizes realism as follows:

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