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Dadadarren, I appreciate the reply. I happen to be a double halfer (triple halfer!) myself. I do not support the thirder arguments, but I am trying to extract the insights you bring to the debate. You seem to agree that 'ambiguous' or 'unspecified' reference has something to do with the problems in these questions. But is this problem distinct from your claim that 'First and Third Person Perspectives' get mixed up/conflated, or is it the same problem?
From a first-person perspective, Today has at least two different meanings. Today might mean "primitively understood' as 'this day' or 'the day I am in now' that is known primitively and only from a first person experience. But Today might also mean (starting from 1st person) that heterophenomenologically shared specific day (e.g. Sunday, or 5/12/2019). You might say "Today is a busy day for me" which mostly implies the former first person perspective. Or you may ask a cowoker: "What day is Today?", where Today is both your first person experience "This day for me", but also implies a third-person shared reference class that your coworker will pick from. There is no ambiguous reference in these propositions, even though the latter example 'mixes' both first and third person perspectives. This is why it seems that ambiguous reference generates the confusion more so than mixing perspectives.
Anyway, I am a double halfer, but I have a specific argument that purposely mixes both perspectives (first and third) that argues for the halfer position:
MIRROR ARGUMENT:
HEADS=the fair coin lands on Heads
MUH = HEADS and you wake on Monday (temporally uncentered)
MCH = HEADS and it is Monday (temporally centered)
Then:
(M1) P(MUH)=P(HEADS)=1/2
Now imagine contemplating the following credences (probabilities) during an awakening:
(M2) P(MCH|MUH)=1, or in words, the credence this is a Monday awakening and Heads, given you wake on Monday and Heads, is one.
(M3) P(MUH|MCH)=1, the credence you wake on Monday and Heads, given this is a Monday awakening and Heads, is one.
(M4) Therefor: P(MUH)=P(MCH)=P(HEADS)=1/2 , where P(MUH)=P(MCH) follows from (M2), (M3), and the definition of conditional probability.
See below for full paper.
http://philsci-archive.pitt.edu/15911/
I also argue that an infinitely repeated Sleeping Beauty Problem will give the 1/3 solution, and that this does not conflict with the double halfer position.
Marc
With regard to your clone example, you say:
--After waking up I argue the question of "The probability of me being the clone/original" is invalid.
Perhaps the question is invalid, but only because you specified the question poorly to begin with. You say there are two individuals, but don't specify who is asking the questions. Who is it who is "waking up", and who asks the question "The probability of me being the clone/original?" Are both clones waking up and asking the same question? If your question applies to both clones at the same time, then it is entirely appropriate to say: whatever clone you are talking about, the probability is 1/2. If the question applies only to a specific clone, then in the question you must specify which clone is asking the probability question. But you never specified who was asking the question. Just because you use the word 'me', it doesn't mean you are referring to a specific first person entity (e.g. the person writing this response, or you, or whoever). Your reference to 'me' is fundamentally ambiguous, and that is why the question is invalid--not because you mix first and third person perspectives.
I read your paper. I think your insight revolves around the following invalid question: "What is the probability that I am me." I have no idea how to answer this questions, but it is not problematic because of mixing perspectives. It's problematic because of ambiguous reference. But this question is completely different in character than "What is the probability that today is Monday?". That question is not problematic at all. "Today is Monday" is a benign proposition that is either true or false, and easily confirmed or denied.