Hi Tim,
***" Dick is doing applied math and the rules of application are different than just doing math." how so Harv?***
Pure math is a formal system (e.g., based on axioms, rules of undefined terms, etc). What is not allowed in any formal system is the use of terms that refer to human psychology, epistemology, etc. These terms are applied to math, hence the term 'applied math'. Dick uses terms such as conscious, knowable, unknowable, reality, exists in reality, etc which make Dick's paper an exercise in applied math.
***is this really so bad? does his paper hinge on this statement? the statement is an argument for using mathematics. Dick's paper is not a pure mathematical work. i wondered about the statement myself, but while i don't believe it is an accurate summation of mathematics i do think it has some rational basis behind it particuarly in light of what his paper is about. certainly mathematics relates to the physical world in many ways as abstractions of features of the world such as quantities, symmetrys, spatial features and operational behaviors.***
I have no problem with using mathematics in epistemology, mathematical models have some limited usage in epistemolgy. The problem is if you are going to do such, then you have to clearly define what it is you are trying to solve in epistemology. Dick's paper moves between ontological and epistemological issues without any real regard to the entirely different enterprises that he is dealing with. To be frank, it is one confusing mesh. If you look at Frieden, he has a much better grasp on how to deal with the mathematics and application, even though he too falls stray into metaphysics without enough care.
***"This is just blatantly untrue Tim. Science uses mathematics to construct models because they are successful doing it. If science were successful using Alan's flybytheseatofyourpantsmakecommentsalongtheway type of investigation, then I imagine that Alan would be in large company. Unfortunately, scientific progress isn't achieved in such a loose and capricious fashion (otherwise I might take up physics for a profession...). Science has discovered that mathematics is helpful for developing models that have predictions that match our observations and that provide good explanations, and therefore science uses it. The philosophy behind mathematics is very contentious and divided. Even scientists disagree what mathematics is exactly, and no one has any supportable answer to the question. It can't just be definitions that should concern us, but the whole assumption that we are saying something about reality with our current understanding of math." Harv, this is almost laughable. a scientist can use mathematics any way he sees fit. and scientific progress has often been achieved in loose and capricious fashion. an example would be how the structure of benzene was discovered. it was discovered by a chemist dreaming of snakes swallowing their tales. the structure of DNA would be another example, a series of trials and errors. our antibiotics were discovered by a gross error of a scientist leaving unwashed petry dishs in a sink when he went on vacation. so not everyone is on the same page when it comes to ones opinion about what mathematics is. we all still use it and if it is used intelligently the results are often magical they are so successful. again one can embark on what ever scientific enquiry one desires and mathematics will not mind one iota if one uses it.***
The key phrase in your text here is "if it is used intelligently". It is not widely considered a scientific question to ask what mathematics is, and there certainly isn't much in the way that one can do in answering the question. However, there is a wide degree of lenience in utilizing math as you suggest. But, the argument I was responding to was this:
"Dr. Dick's use of mathematics is nothing more than any scientist might do when attacking a problem, just as his use of language and logic are acceptable vehicles in the presentation of his ideas so is mathematics. if we find his language, logic and mathematics correct then all we have to attack is his definitions. that for now i leave open to debate"
What is blatantly untrue in your statement is that Dick is using mathematics in the same manner as other scientists. Dick is saying we cannot trust our 'subconscious' (a term that he never fully defines...), and then goes about addressing epistemological questions about what we can know and what we cannot know. By what we can 'know' he is not referring to scientific knowledge, because if he were, then he wouldn't even question the reason why we must somehow provide 'proof' of knowledge that we already know. Dick is stepping outside the scientific arena altogether. This wouldn't be so bad if he provided new predictions for us to test his model, but alas, like all good pseudoscientists, he avoids any claim that he must make predictions. This is so far outside of a scientific endeavor with the mathematics making the whole endeavor just metaphysical ramblings.
This can be avoided by at least putting the work in the context of science (e.g., in terms of measurements, sampling, etc, as Frieden has done).
***i wouldn't be able to comment on this. i'm still reviewing the first chapter and have only skimmed the whole paper.***
I would suggest that if you are interested in this line of work, that you go directly to Frieden and do not pass go. Dick, as you will eventually find out, has no consistent explanation for his terms and constantly shifts back and forth in his terminology. Just try to lock him on the term 'knowable' or 'reality' for long enough to tie your shoes and you have accomplished a major feat. Frieden's work interests me, and I've already consulted epistemologists as to their opinion about it (not much as it turns out). However, at least there is obvious substance behind this mind, even though he suffers from many of the philosophical problems as Dick's work. Although, not as many since Frieden is going after epistemology whereas Dick continues to confuse epistemology and ontology. Good luck!
Harv
