Hi someguy1.
Perhaps you are missing MD's subtle point about exactly that aspect?
In trying to support his own 'stance' about the matter,
Tach himself introduced a 'real world' instance and 'procedure' for allegedly 'determining finitely' the three 'equal parts' of his circle.
So let's not use 'double standards' by unfairly now trying to disparage and disallow MD's 'real world' based arguments, hey?
Anyhow, my observations in the context so far:
- The 1/3 is an abstract 'label' for an 'abstract location' supposedly residing on an 'abstract mathematical 'number line' construct. So far so good.
- I now observe that at no stage has that alleged 'exact number' 1/3 been actually identified in reality sense. Only in the 'somewhere in there' on the line 'abstract' notion of some 'unknown location' abstractly.
- The similar 'labeling' loophole can be used in physical sense if we wanted to because we do not know the exact 'location' of some as yet 'undetected' but 'suspected' astronomical feature' we would like to identify with better precision/reality TO some actual location 'somewhere' which we may 'fix' IF we could actually compare its location to some already known feature (like the nearest real observable quasar etc) at the furthermost reach of our telescopes.
See what I am getting at when it comes to MD's argument about what the 'label' 1/3 actually MEANS in effect of actually 'identification precisely' (by location precisely with reference to nearest 'other number' which HAS been already precisely identified in reality as well as abstract number system 'line'?
In short, what I think MD is getting at is that there is NO actual location identifiable FOR that 1/3 ON the number line as such, because we cannot reference it to any other real already easily identified location of such an fraction as 1/2 etc.
MD's argument essentially (both in reality AND abstract context) that any purported 'formalized definitional' (again, whether reality or abstractly based) treatment/attempt to represent 1/3 as three actually 'equal parts' in reality is a non-sequiturright from the start. We can represent 1/2 as TWO 'equal parts', but not such 'splits' as 1/3 etc.
That is what I observe he is trying to point out.
Good luck, and enjoy your polite and dispassionate discussion, someguy1, QQ, MD, everyone!