I apologise for the confusion. I did try to make clear that this wasn't about whether evidence was 'good' or not, but rather whether it could be called evidence at all.
Not to put too fine a point on it, my answer to that is "yes, of course it can be considered evidence." For me, that's the easy part. The more serious considerations are "evidence for what?" and "of what quality is the evidence for that conclusion?".
I agree, however in seeking an inference to explain the observation, it can't be helped to speculate 'if X exists, then this observation would also occur'. The cherry picking occurs when only supportive observations are selected in favour of X and contrary observations are ignored.
No argument.
I've started to give up on the term skeptic, as I can't define it. It becomes something of a Scottsman fallacy when you try to sort people into being a skeptic or pseudoskeptic. What I was more referring to is self-proclaimed skeptics - I wonder sometimes if there is a correlation between such knee-jerk reactions and how loudly somebody advertises their skepticism.
A matter of personal taste, perhaps. "Skepticism" to me is the epistemological position that claims or assertions of knowledge must be testable and supported by hard evidence, and that knowledge is conditional, not absolute, and therefore subject to evolution and refinement based upon the amount and kind of evidence available.
"Psuedoskeptics" do exist, but I find that term so vastly overused by the woo-woo crowd that in many contexts it is all but meaningless.
No need to apologise.

I wouldn't have put it up if not seeking good criticism of my point and my articulation of it. I know many might find the question pedantic, however I have a great interest in precisely how science language is used amongst a demographic.
I am also interested in language usage. I have seen many arguments derailed to the '◊◊◊◊ YOU TOO!' stage when one party was simply insisting on coherent definitions fo key terms, and the other was convinced they were dodging the real issues with "semantic games."
Semantics are important: they are how we communicate. When we do. ;-)
I'm not sure why you make the distinction of claiming that it's safe to say one can make a claim that an unexplained phenomenon might exist, yet that unexplained pheomenon could not possibly be a fairy.
Because the first is a simple acknowledgement of anomalous data -- or evidence, if you will -- whereas the other represents an
interpretation of that data. Once one begins interpreting data one is no longer a neutral observer. At some point, of course, interpretation has to occur, but if it is brought in prematurely it can bias the collection of additional data -- e.g., instead of simply collecting additional data and examining it to see what sort of patterns may emerge, one begins seaching specifically for data supporting the observation of fairies. When data is selected to fit a pre-supposed pattern, other explanatory patterns may be easily overlooked.
I might interject my own argument here for a moment and move my own goal posts intentionally, if I may - I recognise now that the example I used has a large problem. Fairies aren't a model in themselves explaining a flying humanoid; there is no single, straight forward criteria explaining what one means. Indeed, it's probably one of the biggest holes many paranormalists and faithers fall into (definining their model with any precision).
Oh yes, for sure.
I once spent considerable time debating a woman on a "paranormal" list who claimed that she had attained SPIRITUAL POWERS through her acceptance of HIGHER CONSCIOUSNESS (she liked to intersperse her text heavily with all-caps, rather like a religious tract). It took months of constant prodding and wading through mystical obfuscation that would have made a Zen master blush to get her to actually state what any of these alleged "powers" actually enabled her to
do.
When she finally did describe one of them (basically remote viewing), I proposed a simple demonstration/test -- at which point she spent another month redifining the alleged power as everything from astral projection to physical teleportation via a "hyperdimension". Basically she invalidated any test I proposed by saying that particular test could only test {fill in 'spiritual power' of your choice}, whereas what
she could do was really {fill in different 'spiritual power' of your choice}, etc., etc. yadda, yadda.
The one that always cracks me up is the mystic who says -- usually repeatedly -- that what they are trying to convey can't be presented in words, nevertheless, they then procede to fill hundreds of megabytes of webspace and/or thousands of pages of physical text talking about it.
Again, I'm assuming you have more particle physics experience than I do. Would it not be possible (if unlikely) to see the results of a particle collision and witness, say, two particles where your maths initially only counted for one? Have there never been moments in science history where an unexpected observation with no immediately recognisable relationship to accepted models has resulted in the support of a weaker model?
Oh, certainly. In your first example, if something were empirically observed from a particle collision that wasn't predicted by the mathematical model for that collision -- that is, if it were observed many times -- then the mathematical model would be called into question. In that sort of situation the mathematical model
is the hypothesis, or at least a part of it. If observation consistently fails to support the hypothesis, then the hypothesis is either refined or scrapped, as need be.
If that's what you've been saying, I have no disagreement there.
I initially had a different impression of what you were trying to convey, which seemed to be along the lines of just proposing an "explanation" out of whole cloth, and
then going out to see if it was supported by evidence.
The difference is that between a physicist observing that things dropped fall to the ground, asking why, proposing a model, and testing it -- and an alchemist deciding that there
must be a way to turn lead into gold, and then going off on a quest for the Philosopher's Stone. It's the difference between seeking an explanation for an observation, and seeking an observation to fit an imagined explanation.
This seems somewhat chicken and egg, then. Remember, I'm not qualifying it as good evidence - just defining the observation as 'evidence' or 'not evidence'. If you have no pre-existing evidence at all for a model, then there is going to have to be a first observation which inspires the speculation. Indeed, we both agree it would be far from sufficient to accept the model, but it still must be considered evidence in order for it to accumulate.
If you had no pre-existing evidence at all for a model why would you have the model at all?
I can see the chicken-and-egg potential, but I'm not sure our minds generally work that simplistically. Did people invent demons first and then decide that the Earth had to be flat so there would be a place for the demons to live, over the edge? Or did they decide that the Earth was flat, and
something had to exist over the edge, therefore they peopled that place with demons?
The truth is that both demons and the flat Earth were invented to explain
other observations, and the two just happened to get slapped together at some point.
Not at all.

I remind you I'm not a particle physicist, so could be butchering their craft big time.
I'm not a particle physicist, either, though I did spend some time studying the subject.
I'm picturing a possibly fantasy situation where a particle is smashed, numbers are crunched, particles counted and something comes up amiss, leading in itself to then speculating if an anomalous result is a new phenomena. Of course chances are low, but I would find such a situation (if even possible) where such a speculation is not even considered to be somewhat against how science works.
That kind of speculation goes on all the time. It's speculation about an observed phenomenon: "we expected two gamma rays with energy 'X', but we got two gamma rays with energy 'X-(1x10^-19)' ... I wonder where the missing energy went?"
I'm not in 100% agreement with your view that at the time, there was the sentiment that the existing theory left a great deal of the process unexplained. While particle physics isn't my field, science history is - and it was far from black and white in terms of any acceptance of the necessity for novel explanations. Many at the time felt fermentation was merely a chemical reaction, and the presence of replicating life forms was coincidence. For many, there was no need to ask how it started (you do have to bear in mind that reductionism as we understand it today wasn't a strong driving force behind discoveries in the past. People were satisfied with 'it just is'. Mind you, many of the greatest discoveries were made by vitalists and the like who were happy with such answers).
Well, I partly agree. I didn't say that there "was the sentiment" that the existing theory of fermentation left a great deal of theprocess unexplained -- the fact is that the existing theory
did leave a great deal of the process unexplained. It was inevitible that sooner or later
some people would notice this fact, and wonder about a more complete explanation.
For that matter, it can be justly said that there wasn't much concern amongst the general populace in 1905 about the photoelectric effect, and even most scientists and engineers were not greatly perturbed by the fact that Newtonian machanics permitted mass to accelerate to infinite velocity. Yet Einstein's papers on the photoelectric effect and special relativity changed the course of science in the century following their publication, and ultimately engendered whole new branches of science.
Einstein happened to be one of those who "noticed" that additional explanation was necessary. Pertinent to our discussion, what he noticed was that existing hypotheses didn't fully explain existing observations in certain areas of exploration, so he proposed new hypotheses.
No, I owe you a big thanks for the criticisms, even if we ultimately agree. While I might be 'right' overall (by populat agreement), I still like to clarify my personal understanding of the details.
I wasn't intending to criticize so much as discuss. I don't by any means claim to have a lockdown on "the Truth" -- I leave that to the obfuscatory mystics.
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