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March 27, 2005

Theories and Observation

Mathematics is often called an “exact” science, for we start from a few basic unchanging principles (axioms) and move from there. This mode of thinking is known as foundationalism. However, impure science (physics, chemistry and biology) rely on observation. To do this, they create theories. So, the central question is what exactly are theories? Why we need them? How do they connect to the truth?

All theories are inherently buried in observation (thought or actual). They begin with experimentation. This provides a range of qualitative and quantitative data. However, data on its own isn’t going to get very far. So, we put forth a model, which simply put is a collection of patterns in the data. Still, the patterns don’t explain the data, they only suggest it. A theory is the extrapolation of the model for a more general class of objects and its synthesis with other similar theories. Thus theoretical knowledge must not be provable (based on a set of axioms), but has to be consistent. This structure of knowledge is known as coherentism.

At this point, the theory is knowledge beyond experience. The outcomes suggested by a theory doesn’t need necessarily to reflect reality. This is known as the theoretical jump. Because of this, theories may provide inaccurate data - however they are not wrong. That is why you don’t disprove theories (because you can’t). This is an example of a self-saving clause. It rather cheap, really - oh well, it works. In chess, one can say that every sacrifice is only temporary, otherwise it would be called a blunder. Basically, the idea is to choose the definition which bests suits you, or draw a distinction between two synonyms (or equivalent objects) to your advantage. A theory is a definite statement, while the outcome can be probabilistic, the theory asserts itself fully.

Where do inaccuracies arise? In experimentation the inaccuracies are the “sources of (theoretical) error”. The explanation brings fault to the model - the sample are too local, the pattern is a rough estimate, circumstantial external forces, etc. However, these are just experimental irregularities. The problem usually lies in unaccounted phenomena.

Theories are definite, but developing - as soon as one finds an experiment which contradicts to the theory, the theory adapts to explain this experiment. Theoretical development is based on simplicity. There are many ways to explain a certain phenomena. Scientists seek the simplest explanation which provides most conclusions. When a theory needs too much “special case “adjustments, it is usually discarded in favour of a simpler one. Thus if theories and designed for explanation, scientific experiments are designed to develop theories by providing a better model to work on (most often scientists don’t understand what is practically going on).

So what about the theoretical jump? When a practical meaning becomes theoretical, we often apply the theory in reverse to the practice. However, by reasoning outside the system, we may come to some not so wanted conclusions. The basic, humble, simple intuitive ideas can combine to make some hard, difficult and quite counter-intuitive statements. But more on that next time.

Posted by Oleg Ivrii at March 27, 2005 06:47 PM



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