Philosophy First

Modern Science has deep roots in philosophy. Today this is mostly not visible. But there are certain situations where philosophy is popping up with all its consequences. One such situation is given when a scientist or an engineer is facing reality because he has to transform certain aspects of reality into some formalisms, especially models. Figure 3.1 shows such a situation.

Figure 3.1: Phenomenological basis of modeling process

The relationship of a human agent to empirical reality can be viewed from different points of view. The most radical view is that of philosophy, here especially the so called phenomenological approach. The primary source for reality for every human agent is the space of phenomena about which someone is conscious. As everybody learns already during childhood there are phenomena which are somehow shareable with others and those, which are primarily private. The shareable phenomena are those which are somehow connected to 'something outside', to an external world which often is called the real or the empirical world ^3.1.

Modern empirical science started when scientist decided to build scientific theories exclusively on those phenomena which can be measured. A first version of this convention is the result of a complex development between 1500 and 1750. More fine grained methodological views have been propagated during 1850 and 1970. Although there is still no completely common view of what a scientific paradigm is, there are some key elements which most scientist will accept.

1. Measurement Operation: Some repeatable operation which yields measured data independent of the observer. Representing the data in some measurement language $L_{Meas}$.
   

   $$\textbf{Measurement} : TO \times SO \longmapsto NUM \times SU$$ (3.1)

   
   
   A target object $TO$ is compared with a standard object $SO$ in a way that it is possible to associate the target object with a number $n \in NUM$ and a measurement unit $SU$ (e.g. $(5.3,m))$
2. Time: While measurement as such does not need time, to detect changes one needs some measurement of time to enable a mapping from a certain measurement into time points. This induces the concept of a clock which can generate evenly spaced ticks which can be used as basis for a measurement indexed by time points. The association between measured data and time points allows then an ordering of measured data (t,d) and (t+c,d) with $c > 0$ in the sense that $(t,d) <_{T} (t+c,d)$ or $(t+c,d) >_{T} (t,d)$ where $<_{T}$ has to be interpreted as earlier or precedes and $>_{T}$ has to be interpreted as later or succeeds.
3. Specific Relations: Some repeatable experiments to reveal specific dependencies between measured data. These dependencies can be represented as causal connections or functions.
4. Model: A single function or a collection of interdependent functions can be understood as a system with input and output. The set of all input-output measures is called the behavior of the system. Systems can be used as a model to represent certain properties of some part of measured reality. In a formal representation of a model one can describe not only the measured behavior but mostly also behavior which the system allows but has not yet been observed.
5. Validation: To evaluate the correct behavior of the system one has to compare the behavior of the model system with real inputs and outputs. These validation tests can only approach the behavior, because usually it is not possible to test all possible input-output connections.

To illustrate these ideas an example will be introduced below.