The largest number is 6.
I counted one, two, three, four, five, six, then I stopped. So the largest number is 6.

Once I tell you that numbers are not transferable between applications then you should see that I have indeed proved, to cultured satisfaction, that the largest number is 6.

Numbers are not transferable between applications. That is, we can’t compare numbers that have arisen in different applications. So, for example, I cannot say take the number 6 and use it in this or that application. Numbers only arise in their application, theya er not preexisting. Numbers that aren’t in an application aren’t numbers, they are numerals. So a set of numbers is actually a set of numerals.

I aim to satisfy according to good, educated tastes and do not present my arguments for the pleasure of the rablle-rouser and mischief-maker.

You didn’t prove anyting. You arbitrarily defined two different applications of counting or addition (yours and mine)----which was really the same ‘application’ of numbers. And then you arbitrarily defined your largest number. This thread is hereby refuted.

It wasn’t the same application. But numbers are not transferable between applications.
So - my claim that 6 was the largest number was correct.
And your claim that seven was the largest number was correct.
Both were correct. But as the largest number they were NOT transferable - hence they were not able to be compared for largeness.

it wasn’t a puzzle, and your “solution” is incorrect. those are the same application, in the same way that the heights of two different people are the same “application,” and you can compare two peoples’ heights.