Gosh, you are a lot of fun.
***H: Why do you think deduction more reliable than induction? D: Because it's the position I have been taught. Mathematicians have told me that and I have never had much luck in disputing their claims. At the same time, none have done a decent job of defending induction. As I have said many times, I leave the defense of mathematics to people much more qualified than myself.***
Hmm... Through your inductive experience of learning you have come to believe that deduction is more reliable? Good thing there's induction, or else you couldn't come to that conclusion, huh?
***H: Also, anytime we define something we are imposing constraints. We may not realize it, but those constraints are necessarily inherent in a definition. D: That is exactly why I ask people to criticize my presentation. I ask, exactly what constraints have I imposed?***
You have posed the biggest constraint of all, everything you cannot possibly imagine or conceptualize as numbers is excluded.
***Defining a concept is indeed a constraint on what is referred to by that concept but the existence of that concept (together with its constraints) need not be a constraint on the universe.***
Concepts cannot be shown to exist - except in the heads of people. By conceptualizing the Universe we are constraining the Universe.
***Such a definition would allow me to say "I suspect that my feelings at this moment are time!" Is what you really meant by your example consistent with that statement? By the way, your example is exactly what I mean by a cavil: a comment with no logical content to speak of.***
I was giving an example of how a definition can limit our understanding of a concept that references something in the universe. I should have chosen a more realistic example, but then it is harder to demonstrate how a definition acts as a constraint.
***H: Either the definition is false, or there is faulty reasoning. D: How can a definition be false? If you tell me that, whenever you use a particular symbol, you intend to mean a certain thing (the essence of a definition) then I can certainly work with that idea to examine your reasoning based on that definition. Any fault I find must be in your reasoning as, if I understood your definition, there can be no fault there!***
A false definition is a definition that is inherently inconsistent in an unworkable manner. For example, bachelors are married single people is an extreme example of a false definition. A less extreme example might be 'reality is a set of numbers'.
You might ask why that is a false definition. Well, what are numbers? They are mental representations of things that exist inside the heads of people. So, reality is a set of representations of things that exist inside the heads of people. Therefore reality resides inside the heads of people. But, this collection of people is also a 'set of numbers', hence reality is a subset of reality. That is inconsistent since a set cannot be its own subset. That definition is inconsistent and unworkable - hence it qualifies as a false definition.
***If you can, go back to the "public notes" I have posted and tell me exactly where I have imposed a constraint on what may be explained through my definitions! I would just prefer that you post your comments in this thread as I suspect very strongly that they will not be to the point I am presenting at all.***
Sure, I'll make my way over there.
Warm regards, Harv