is the referent of "One Metre" a length, or is it a stick, or is it a process?
I say it is a length. — Banno
Is this an adequate reading? — StreetlightX
The confusion arises when we take a C1 comparison and substitute in a C2 comparison without noticing that the scope of the discussion has changed. — fdrake
I also think you're right that Witty's presentation of the issue is confusing because he doesn't make this narrow application clear, and it can come across as a general purpose statement about the Paris meter as such. But a close reading will dispel any such reading I think. — StreetlightX
In this language-game it is not something that is represented, but is a means of representation.—And just this goes for an element in language-game (48) when we name it by uttering the word "R": this gives this object a role in our language-game; it is now a means of representation.
W's extension of the standard metre example to the word/name "R" here could indicate that the preparation/use distinction applies to all names in our language... I think? — Luke
The key thing, it seems to me, is bound up with what it means to compare an item in our game of measuring with the meter stick. If we grant that a comparison takes place between distinct elements, then it is inappropriate to measure the meter stick with itself. If we constrain 'comparison' to mean 'must be done between distinct units in the language game, one of which is the meter stick itself', then applying the meter stick to itself is not a comparison in the sense of comparison at work in the language game. But I believe it is a comparison in the broader language game of length measurement, standardisation and unit ascription.
The comparison which occurs between the meter stick and itself is not a comparison in sense C1, but it is nevertheless a comparison of length/extension.
It is required that a length is the same as itself as a constitutive rule of of the broader length comparison language game, because the game operates on its items as token length representations rather than as actual objects for measurement. Precisely, then, comparisons in this broader game are comparisons of lengths relative to lengths and not lengths relative to the meter stick. Call this comparison sense C2.
So in terms of C1 comparisons, the meter stick can't be held up to itself - this is not an appropriate move in the language game, but in terms of C2 comparisons it absolutely is; C2 comparisons operate on lengths.
What is "a comparison in sense C1"? What type of comparison is being made in the C1 sense if it is not a comparison of length/extension? — Luke
The Paris metre represents the word "metre", but there is still a need to signify which aspect of it represents "metre"? — Metaphysician Undercover
Are you saying that 'token length representations' are abstract units of measurement? Therefore, C2 comparisons are not made relative to the metre stick, but to the metre unit? — Luke
Are you saying that C2 comparisons involve the use of the metre unit, and so here comparisons can be made between the metre unit and the metre stick? — Luke
The issue we're discussing arises, then, when we interpret the meter stick as an thing to be measured using itself; the problem being, how can it make sense to say that the meter stick is a meter long when we're using comparison to the meter stick to measure? The alleged problem with this is that the length of the meter stick will always be a the length of the meter stick, so it's not appropriate to say we measure any length using it in the game of measuring using the meter stick as a standard.
Once we've set the stage for the units of a dimension, we can largely forget that the units are there. — fdrake
we'd still have the ability to quantify rotation even without triangles. — fdrake
I imagine this step of abstraction is similar to the one going from '1 meter' to 'length 1' (like C1 to C2 in my previous post). — fdrake
I think he's using the example to illustrate what can happen when we pay insufficient attention to the prerequisites for our language use; even maybe how asking a question in the wrong context; or a poorly formulated question; leads to batshit insanity. — fdrake
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