How does listing out a large list of personal definitions, alongside what an LLM supplies, help in formulating an argument?
It seems like it will make it more difficult, instead of easier, to get even a convincing outline down if you use any definitions other than the widely accepted ones as recorded in major dictionaries, such as the OED, Merriam-Webster, etc...
I don’t want to discourage you but wrangling this such that even a coherent, falsifiable, non self-contradictory, sketch of an outline emerges, seems really unlikely.
what do you want, then? typically one defines terms in a logical argument. shall I rename the terms to “variable 1” and “variable 2″ to make it less ambiguous..? I could reduce word count significantly but it seems like you wanted me to expand on what I’d said previously, so I wrote some overviews of the moving parts I see and asked an llm to give specifics that can be checked for.
Weighing in here because this is a suboptimality I’ve often encountered when speaking with math oriented interlocutors (including my past self):
The issue here is an engineering problem, not a proof problem. Human minds tend to require lots of cognitive resources to take provisional definitions for things that have either no definition or drastically different definitions in their minds outside this specific context.
Structuring your argument as a series of definitions is fine when making a proof in a mathematical language, since comprehensibility is not a terminal goal, and (since each inferential step can be trusted and easily verified as such) not a high-priority instrumental goal either.
But when you’re trying to accurately convey a concept and it’s associated grounding into someone else’s mind, it’s best to minimize both the per-moment attempted deviation from their existing mentality (to maximize the chance that they both can and will maintain focus on your communications) and the total attempted deviation (to minimize the chance that the accumulated cognitive costs will lead them to (rightly!) prioritize more efficient sources of data).
This gives us a balance between the above two elements and the third element of making the the listener’s mind be as close as possible to the conveyed concept. The efforts of all involved to maintain this balance is key to any successful educational effort or productive argumentative communication.
PS: If you’re familiar with math education, you may recognize some of it’s flaws/inefficiencies as being grounded in the lack of the above balance, by the way. I’m not an expert on the subject, so I won’t speak to that.
To use more standard definitions in order to not make things more difficult for yourself?
Your free to ignore this ‘want’ of course, and use your own personal definitions for a bunch of concepts, but I’m not going to be able to help you along, nor likely will any other passing reader, since only you would know what’s what.
I mean, outside of labeling the parts of what I’m trying to describe, what is it you want out of a description? what is the datatype of “argument” that you want—evidence? logical derivation from an already shared evidence base? it seems to me that we can just erase away the names of the definitions I gave, and then what I gave is… both of those things. so I’m trying to figure out what it’s missing that you want to see, other than “fewer unnecessary words such as new names of terms”.
I mean, outside of labeling the parts of what I’m trying to describe, what is it you want out of a description?
Can you explain what this means?
Assuming it’s just asking for what the request was, then; the outline of a potentially convincing argument.
what is the datatype of “argument” that you want—evidence?
It’s unclear what ‘datatype of “argument”’ means either, you can see already how difficult it is to have substantial discussions if one party could potentially use words with differing meanings and/or custom terminology.
But I’ll assume ‘datatype of “argument”’ just means ‘type of argument’, otherwise you’ll have to explain it too.
If so, you are free to pursue any line that seems promising.
It could be a statistical analysis, it could be a purely formal logical derivation, it could be inferences, induction, etc...
I’ll stick to answering just the first two questions to keep the comment chain easily readable.
How does listing out a large list of personal definitions, alongside what an LLM supplies, help in formulating an argument?
It seems like it will make it more difficult, instead of easier, to get even a convincing outline down if you use any definitions other than the widely accepted ones as recorded in major dictionaries, such as the OED, Merriam-Webster, etc...
I don’t want to discourage you but wrangling this such that even a coherent, falsifiable, non self-contradictory, sketch of an outline emerges, seems really unlikely.
what do you want, then? typically one defines terms in a logical argument. shall I rename the terms to “variable 1” and “variable 2″ to make it less ambiguous..? I could reduce word count significantly but it seems like you wanted me to expand on what I’d said previously, so I wrote some overviews of the moving parts I see and asked an llm to give specifics that can be checked for.
Weighing in here because this is a suboptimality I’ve often encountered when speaking with math oriented interlocutors (including my past self):
The issue here is an engineering problem, not a proof problem. Human minds tend to require lots of cognitive resources to take provisional definitions for things that have either no definition or drastically different definitions in their minds outside this specific context.
Structuring your argument as a series of definitions is fine when making a proof in a mathematical language, since comprehensibility is not a terminal goal, and (since each inferential step can be trusted and easily verified as such) not a high-priority instrumental goal either.
But when you’re trying to accurately convey a concept and it’s associated grounding into someone else’s mind, it’s best to minimize both the per-moment attempted deviation from their existing mentality (to maximize the chance that they both can and will maintain focus on your communications) and the total attempted deviation (to minimize the chance that the accumulated cognitive costs will lead them to (rightly!) prioritize more efficient sources of data).
This gives us a balance between the above two elements and the third element of making the the listener’s mind be as close as possible to the conveyed concept. The efforts of all involved to maintain this balance is key to any successful educational effort or productive argumentative communication.
PS: If you’re familiar with math education, you may recognize some of it’s flaws/inefficiencies as being grounded in the lack of the above balance, by the way. I’m not an expert on the subject, so I won’t speak to that.
To use more standard definitions in order to not make things more difficult for yourself?
Your free to ignore this ‘want’ of course, and use your own personal definitions for a bunch of concepts, but I’m not going to be able to help you along, nor likely will any other passing reader, since only you would know what’s what.
I mean, outside of labeling the parts of what I’m trying to describe, what is it you want out of a description? what is the datatype of “argument” that you want—evidence? logical derivation from an already shared evidence base? it seems to me that we can just erase away the names of the definitions I gave, and then what I gave is… both of those things. so I’m trying to figure out what it’s missing that you want to see, other than “fewer unnecessary words such as new names of terms”.
Can you explain what this means?
Assuming it’s just asking for what the request was, then; the outline of a potentially convincing argument.
It’s unclear what ‘datatype of “argument”’ means either, you can see already how difficult it is to have substantial discussions if one party could potentially use words with differing meanings and/or custom terminology.
But I’ll assume ‘datatype of “argument”’ just means ‘type of argument’, otherwise you’ll have to explain it too.
If so, you are free to pursue any line that seems promising.
It could be a statistical analysis, it could be a purely formal logical derivation, it could be inferences, induction, etc...
I’ll stick to answering just the first two questions to keep the comment chain easily readable.