Are you reading my replies? Saying that arithmetic is “the standard model of the natural numbers” does not
“cash out” the meaning of “arithmetic” into well-defined predictions
For one thing, it doesn’t give me predictions (i.e. constraints on expectations) that we check to see who’s right.
For another, it’s not well-defined—it doesn’t tell me how I would know (as is necessary for the area of dispute) if arithmetic “exists” at this or that time. (And, of course, as you found out, it requires further specification of what counts as a model...)
(ETA: See Eliezer_Yudkowsky’s great posts on how to dissolve a question and get beyond there being One Right Answer to e.g. the vague question about a tree falling in the forest when no one’s around.)
So if you don’t see how that doesn’t count as cashing out the term and identifying the real disagreement, then I agree further discussion is pointless.
But truth be told, you’re not going to “stop there”. You going to continue on, promoting your “deep” insights, wherever you can, to people who don’t know any better, instead of doing the real epistemic labor achieving insights on the world.
Are you reading my replies? Saying that arithmetic is “the standard model of the natural numbers” does not
For one thing, it doesn’t give me predictions (i.e. constraints on expectations) that we check to see who’s right.
For another, it’s not well-defined—it doesn’t tell me how I would know (as is necessary for the area of dispute) if arithmetic “exists” at this or that time. (And, of course, as you found out, it requires further specification of what counts as a model...)
(ETA: See Eliezer_Yudkowsky’s great posts on how to dissolve a question and get beyond there being One Right Answer to e.g. the vague question about a tree falling in the forest when no one’s around.)
So if you don’t see how that doesn’t count as cashing out the term and identifying the real disagreement, then I agree further discussion is pointless.
But truth be told, you’re not going to “stop there”. You going to continue on, promoting your “deep” insights, wherever you can, to people who don’t know any better, instead of doing the real epistemic labor achieving insights on the world.