Dick,
***I have put forth an abstract interpretation of common ideas which makes the axioms of mathematics true. This makes the theorems also true with regard to the entities so interpreted. What I have shown is that my (abstract) interpretations (isomorphisms) yield as an inevitable result that "most of physics" is true!***
My understanding is that you have made a mathematical model with mathematically definable terms (e.g., reality is a set of numbers, time as an ordered set of data, etc). Once you have defined your terms and set-up the parameters of your equations, you put your variables in mathematically form and then do the math (or math modelling).
This is a different kind of abstract interpretation than what Salmon was referring to. He wasn't referring to a mathematical model.
My problem with your mathematical model is that the defined terms meld too much into philosophy (e.g., reality, time, etc) and should rather stick to more mathematical terms (e.g., lattice, configuration of the lattice, etc).
***Not by induction, but by deduction (a consequence of our definitions). Definitions which, by the way, have imposed no constraint whatsoever on the facts to be explained! Now, the fact that such a thing can be done is (in my humble opinion) quite an astounding discovery. Those who cannot see it have not looked.***
Why do you think deduction more reliable than induction? Also, anytime we define something we are imposing constraints. We may not realize it, but those constraints are necessarily inherent in a definition. For example, if I said that time is undefinable, then by definition time cannot be defined according to my definition. Any attempt to counter that statement is false according to the definition. Either the definition is false, or there is faulty reasoning. Sometimes we cannot decide which is the case. Therefore it is better not to limit reality according to our definitions and simply use definitions as a tool to predict how we think reality (nature) will act given certain scenarios. If the prediction is correct, then we have more confidence in the theory. If the prediction is false, we have less confidence in the theory. Over time we loose complete confidence of the theory (or vice versa we gain complete confidence of the theory).
***Go back to the "public notes" I have posted and tell me where I have imposed a constraint on what may be so explained! -- There is more to come!! Next step is the resolution of Yanniru's complaint in a form you all should be able to comprehend.***
I thought you didn't want me to participate in your 'public notes' discussion? You said I was cavil.
Warm regards, Harv |