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Nick: > I now see why And judges loi as redundant to substance/individual: > individuals are things quantified by natural numbers, masses are > things quantified by [0,1]. Or, I would say following discussion with Lojbab, by "PA in every PA arbitrarily delimited but equal bits of". > But collectives are also things > quantified by [0,1]: you have half a collective, even though you also > have 2 ppl out of the collective. And you certainly can have pisu'o a > collective You can have half of pretty much anything -- an apple, say. Anything -- substance, collective, individual -- can have fractions. 'fractional quantifiers' do not in and of themselves entail that the quantificand is substance. Rather, 'fractional quantifiers' when applied to substance fractionally-quantify over bits of the substance. > I think the deal is > > for n \elem N* (0, 1, 2, 3...) > for q \elem [0,1] > > lo broda = n lo broda (n people) > loi broda = q lo broda (e.g. 1/2 the group of people; 1/2 the goo of a person) > q lo broda =def q loi pa lo broda > (1/2 of an individual is by definition half the substance of that > individual: fractional quantification of individuals forces a > substance interpretation. Not a collective interpretation: an > individual of broda cannot consist of a collective of broda) I'm not clear whether you are proposing that this should be so, or whether you are describing what you take to be the case in current SL. I'd prefer it if you were doing the former, but if you are doing the latter then it is hard to see how you reach these conclusions. Could you be clearer about this? Then I can comment properly. > I'm petering out here, but the point is: > the lo/loi distinction is wholly redundant to the piro/ro > distinction, but signals it in the absence of overt quantification: Do you intend your interpretation of the piro/ro distinction to be a stipulation or simply something already present in SL? I think the meaning of piro is insufficiently clear and must be stipulated by BF, but I'm wondering if you were assuming this. > it indicates the potential domain of quantification > The outer quantifiers when omitted have default values, which are > either defeasible or not. I suspect they are defeasible. Lojbab and I agreed today that it is consistent with CLL to say that the outer quantifiers when omitted are simply absent, though a quantifier may be glorked from context if logic or context demands it. > But in > formally speaking of lojbanmasses, we must supply them; we leave > omitting them until we get to speakability There is no need to have a quantifier for "the substance of all broda" or "the collective of all broda". > Both collectives and substances are quantified by piro. So loi isn't > freed up at all to do collective work, if loi indicates "this is > fractionally quantified" It turns out that according to CLL the default quantifiers are merely best-guesses about what would be glorked from context. As such, the guesses may simply be wrong, rather than constituting any sort of prescription. This could mean that loi is not fractionally quantified. > An explicit outer quantifier forces a conversion from lo to loi or loi to lo > > The matrix (omitting forced conversions) is: > > OUTER GADRI INNER > ro lo ro Individual > piro loi ro Collective > piroi loi tu'o Substance > ro lo tu'o Substance individuated (Substance -> Individual) I don't understand what the last of these is. > loi tu'o and lo tu'o both indicate substance. lo tu'o heads to > countable amounts of substances (re lo pisu'o djacu; pa lo piro > djacu), loi tu'o presumably to generic substances What is the difference between a countable substance and an individual? > I'm sure there are holes in this you told me about 2 months ago that > I didn't get. Remind me what they are To repeat what I said above, it would be helpful if you could flag which bits are stuff you are proposing should become part of the prescription regardless of what the current prescription says. Without knowing this, I can't comment. --And.