Discussion on Poppers and Sober’s View of Simplicity
Popper’s theory of simplicity is directly derived from his Falsification theory. To illustrate this we can say that; it is true that Popper decreed that the more falsifiable a theory was; the better the theory is, and the better it will be received. If this is true; it is then is stated that the degree that a theory is falsifiable should track the degree to which a theory is simple; so if this were to be true should then prefer the theories that are highly simple (and falsifiability).
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So if we were to place this I’m a real life scientific setting we could say that; i) parrots are feathery or ii) all birds are feathery. Now according to Popper ii) would be a better theory in terms of falsifiability and in terms of simplicity, as; it is falsified by more types of findings, could be falsified by any sighting of a non feathery bird; and it is more simple as a parrot is less simple, as it is much more specific, than birds in general.
In terms of the merits of Popper’s theory, in a perfect Popperian world this theory of simplicity would make life for scientists quite easy – as it is a part of his theory of falsification. Further more his description and application of simplicity makes a great deal of sense, in terms of relation to parts of falsification which are part of the modern scientific process, as complicated and convoluted are usually quite difficult to debunk (falsify).
However, take this illustration of a mathematical equation representing a scientific theory, adapted from Post (1969); we have theory a), which represents a linear relationship: y = 1. 5 – 2x; whilst according to theory b) y = 1. 5 – 2x + 0. 3×2. Now according to Poppers falsifiability criteria of determining simplicity; the two theories of are equally as simple (since each can only be falsified by one occurrence). This leads to an automatic counter-intuitive result, which leaves the theory high and dry, as they are clearly not at the same level of simplicity.
Sober’s view on simplicity goes something like the following; instead of, unlike most who have tackled simplicity, relating simplicity to the correctness of a given theory, sober makes an attempt to relate simplicity to the informativeness of a theory. So what this essentially means for the premise of a simplicistic theory, is that simplicity should be concerned with how much information a theory or phenomena gives us in relation to how many laws, or premises, we begin with.
To illustrate this better it may be more prudent to discuss Sober’s theory in relation to inputs & outputs; therefor simpler theories would produce more outputs in relation to the inputs. Furthermore, a more specific definition of Sober’s argument is that the simplest theory may be the most informative one. Sober’s theory, to me, is quite bold – and, excuse the pun, a very simple way of determining the simplicity of a scientific theory.
Unlike Popper and Quinean philosophy, Sober theory seems to give simplictity a greater level of importance, as science is all about gaining information – which this theory draws it wisdom from. However, the theory runs into problems quite early on. One major problem concerning Sober’s theory is that he tries to relate simplicity on a wider ontological level; which leaves me wondering; if we were use the theory that gives the most information, even if it was false, we would be in the position of having to accept it, and then gaining useless knowledge.
If we were to assume that the problems that each theory faces never occurred, the theoretical virtue of Sober’s simplicity, is that simplicity is directly influenced by the amount of information a theory has put into it, and outputted from it. Poppers theoretical virtue is the simplest theory is better, as a simple theory is easier to debunk and increases its falsifiability (as it doesn’t possess any ad hoc escape routes).
Personally I am more greatly drawn towards Sober’s take on simplicity, as science is directly concern with the pursuit of knowledge, meaning that his criteria which determines whether a theory if simple or not is more logical. I feel that Popper, whilst does a good job of keeping the his theories in unity, necessarily approach the problem correctly – whilst falsification seems to a vital piece of good scientific methodology, I can’t quite see the connect between it and simplicity.