Forwarded on behalf of Brent Meeker: > On 24-Jul-05, you wrote: > > > Brent Meeker writes: > >> Here's my $0.02. We can only base our knowledge on our experience > >> and we don't experience *reality*, we just have certain > >> experiences and we create a model that describes them and > >> predicts them. Using this model to predict or describe usually > >> involves some calculations and interpretation of the calculation > >> in terms of the model. The relation of the model to reality, if > >> it's a good one, is it gives us the right answer, i.e. it > >> predicts accurately. Their are other criteria for a good model > >> too, such as fitting in with other models we have; but prediction > >> is the main standard. > > > > This makes sense but you need another element as well. This shows up > > most explicitly in Bayesian reasoning models, but it is implicit in > > others as well. That is the assumption of priors. > > > > When you observe evidence and construct your models, you need some > > basis for choosing one model over another. In general, you can create > > an infinite number of possible models to match any finite amount of > > evidence. It's even worse when you consider that the evidence is noisy > > and ambiguous. This choice requires prior assumptions, independent of the > > evidence, about which models are inherently more likely to be true or not. > > In practice we use coherence with other theories to guide out choice. With > that kind of constraint we may have trouble finding even one candidate > theory. We begin with an intuitive physics that is hardwired into us by > evolution. And that includes mathematics and logic. Ther's an excellent > little book on this, "The Evolution of Reason" by Cooper. > > > > > > This implies that at some level, mathematics and logic has to come before > > reality. That is the only way we can have prior beliefs about the models. > > Whether it is the specific Universal Priori (1/2^n) that I have been > > describing or some other one, you can't get away without having one. > > > >> So in my view, mathematics and theorems > >> about computer science are just models too, albeit more abstract > >> ones. Persis Diaconsis says, "Statistics is just the physics of > >> numbers." I have a similar view of all mathematics, e.g. > >> arithmetic is just the physics of counting. > > > > I don't think this works, for the reasons I have just explained. > > Mathematics and logic are more than models of reality. They are > > pre-existent and guide us in evaluating the many possible models of > > reality which exist. > > I'd say they are *less* than models of reality. They are just consistency > conditions on our models of reality. They are attempts to avoid talking > nonsense. But note that not too long ago all the weirdness of quantum > mechanics and relativity would have been regarded as contrary to logic. > > > Brent Meeker

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