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[gepr]

Although I really like and agree with Nick's answer, his is a little dense. So I'll try for something more pedestrian.

Your math concepts are the result of many iterations between the measurement of marks on paper and the evolving concepts in your physiology. From your first sight of some math markings on paper or a chalkboard, you took measure of those markings and the words spoken or written by teachers or in books. You eventually made good use of your generic computer and abstracted out the core concepts, the patterns of glucose consumption, that allow you to recapitulate the markings, even if the language or other parts of the context has changed.

As such, the concepts and the marks on the paper are mutually referent. Without the markings, your concepts are ungrounded, meaningless. Without the patterns of glucose consumption, the markings are ungrounded, meaningless.


On April 23, 2017 10:32:13 AM PDT, Frank Wimberly <wimberly3 at gmail.com> wrote:
>So it's easy to substitute the word 'conceptual' for the word 'mental'
>whenever I talk to you (or Nick).
>
>I'm curious.  My qualifying exam in real analysis consisted of 10
>questions
>(stimuli, inputs?) like "State and prove the Heine-Borel Theorem". The
>successful response was a written version of a valid proof.  I hadn't
>memorized the proofs but I had memorized conceptualizations of them.
>How
>does that fit?  Would the referents​ be the proofs in the text or as
>presented in class?
>
>I passed.
>
>Frank
>
>Frank Wimberly
>Phone (505) 670-9918
>
>On Apr 23, 2017 10:00 AM, "┣glen┫" <gepropella at gmail.com> wrote:
>
>>
>> I've made this same point 10s of times and I've clearly failed.  I'll
>try
>> one last time and then take my failure with me.
>>
>> When you assert that there's a dividing line between rigorous and
>> whimsical mental models, what are you saying?  It makes no sense to
>me,
>> whatsoever.  Rigor means something like detailed, accurate, complete,
>etc.
>> Even whimsical implies something active, real, behavioral, physical. 
>In
>> other words, neither word belongs next to "mental".  When you string
>> together mutually contradictory words like "rigorous mental model" or
>> "whimsical mental model", your contradiction prevents a predictable
>> inference.
>>
>> At least the word "concept" allows one to talk coherently about the
>> abstraction process (abstraction from the environment in which the
>brain is
>> embedded).  It preserves something about the origins of the things,
>the
>> concepts.  When you talk of "mental models", then you're left talking
>about
>> things like "mental constructs" or whatever functional unit of mind
>you
>> have to carve out, register, as it were.  What in the heck is a
>"mental
>> construct"?  Where did it come from?  What's the difference between a
>> mental construct and, say, a physical construct?  What _is_ a "mental
>> model"?  How does it differ from any other "mental" thing?  Is there
>a
>> difference between a "mental foot" and a "mental book"?  What if my
>"mental
>> books" are peach colored clumps of "mental flesh" with 10 "mental
>toes"?
>> It's ridiculous.  Contrast that with the terms "conceptual foot" or
>> "conceptual book".
>>
>> So, in the end, I simply disagree.  The term "conceptual" does much
>to
>> illuminate.
>>
>>
>> On 04/22/2017 08:35 PM, Vladimyr wrote:
>> > there exists a dividing line between rigorous and whimsical mental
>models
>> >
>> > that the term “conceptual” does little to illuminate.
>>
>> --
>> ␦glen?
>>
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-- 
⛧glen⛧