Copernicus's post 2 above is basically my position on this.
A couple points to address, then I'm happy to drop it:
I am trying to figure out what your belief is.
I was merely defending my original point that whatever phenomenon is going on is that those two phonemes are being produced as one sound, and it is
perfectly reasonable to only represent one in a
transcription of [my dialect of] English. It was not a "theoretical" claim in any deep sense. And I stand by that: there's just one sound there, at least under some pronunciations. A "dictionary" pronounciation could certainly have two, and some careful pronunciations may also. I'm not making any claims about frequency, but based on the original question, I find that analysis (2 sounds becoming 1) plausible. If not "degemination", then make up whatever word you'd like. But I am at least suspicious that something is going on here because the two consonants are identical. Maybe it's more of a merger of two stop consonants (so that "kt" and "tk" would merge the same way). I might be wrong about that. But I'm confident in the data. I didn't intend a deep theoretical discussion, though I've read some interesting responses so I'm content with that too.
Earlier I thought you were assuming that, as a self-evident matter of fact, English has degemination at the phrasal level (self-evident in the same way that the existence of flapping is self-evident -- to any trained linguist who has familiarity with American English).
The obviousness of a phenomenon is irrelevant. However, yes, to me the elimination of one of those stops in the original phrase is pretty self evidence, just like flapping, EXCEPT that flapping is so hard-wired into my linguist brain now it's hard to think of it as anything but obvious.
Now I think that your position is that you personally have such degemination as a fast-speech process (and there may be others like you out there).
Yes. My intuitions can't speak for others, but I also don't have any intuition that I am unusual in this. It may be that I do it more, because I often speak relatively quickly, but it sounds very natural to me in what I think of as "English". The original post, as I said, seemed completely plausible. I didn't feel the need to question the observation made.
By "degemination", I mean some process (phonetic or phonological) which "shortens" identical consonant sequences to the point that they become the same as single consonants.
Sure. There's a problem with this in that it assumes a category of "consonants" [segments] within the speech representation. That seems a bit narrow to me, given that we're talking about phonetic effects, rather than basic phonology. So maybe flapping is a "real rule", while this degemination (or whatever you want to call it) is just a "phonetic effect". I don't have any claim regarding that distinction. I just think it happens. The problem regarding segmentation vs. articulation is that with articulation we can see whether it's a flap or stop based on physical properties. For "one consonant" I don't know how to test that as physical properties. Certainly the tongue would not touch twice. But that may not be enough to consider it degeminated. As I said, though, I expect English is more likely to shorten it than a geminating language. (No, I don't personally have conclusive experimental results that prove this. It's an internet forum for discussion, not a conference or journal where I'm attempting to publish my ideas and change the field.)
I think we've covered the ground regarding how to actually perform the test
Sure, we could do an experiment. But I don't think we're going to. Given that, it's irrelevant. It doesn't mean I'm wrong. It doesn't mean you're wrong. Maybe you aren't interested in discussing non-experimental, statistically significant aspects of phonology, and that's fine. But the lack of an experiment is entirely irrelevant to your argument because it means we're both equally wrong (or right)-- we don't have the data yet. So if you want to do an experiment, go ahead. As I said, I could record myself pronouncing these words. Given that positive evidence (even the very small sample size, etc.), at least it's something! Now, time to falsify it, if you wish.
I hope that you agree that it would be a rather challenging experiment, but it could be done if you constructed the right kind of stimuli, and plan to make appropriate measures
Aren't all experiments challenging? Again, this is irrelevant. I've seen a lot of clever experiments and I have no doubt this one could be done by someone who is motivated. (I'm not, mostly for reasons of time, and my main area is syntax, not phonology.) Plus, we've already seen some very plausible ideas in this thread. Doable.
I fervently hope that you agree that it would be kind of a waste of your time to do this, and that it would be actually harmful to conduct a crappy experiment.
I'm confused. What do you mean by "this"? An experiment? I thought you were suggesting one. Regardless, I'm not wasting my time with an experiment because I'm not planning to do one anyway.
Now, you've also advanced the position that most people would agree with Hypothesis 1, and this concerns me somewhat because the discussion has thereby shifted from questions of objective truth to social perception of scientific hypotheses.
Untrue. Scientific "truth" does not exist. There is only the sharing of knowledge (via publication, etc.) and the conventionalization of that knowledge (through, for example, teaching in classes and what is accepted in mainstream theories and presented in textbooks). While there may philosophically be a "real truth" out there, science, as a field, does not have a way of identifying it. All we can do is talk to one another and decide among the various theories regarding which, after all of the evidence is presented, is most acceptable. We might be right. We might be wrong. But it's eventually subjective and interpretive, not objective. Hypothesis testing is great, but still there are infinitely many possibilities by definition.
So the way the field works is exactly what I described, except that in a more formal situation (again, remember, this is an internet forum, and it would be absurd to have an expectation of cutting edge experimental results with every post, I'm sure you agree), then we would have some data to back it up and argue our point so others agree.
An example of this is the requirement for a 5% of "by chance" statistical results. (That is p<.05.) This is
entirely conventional and has no objective truth to it. It's a good guess, and we are ok with it, but that's an opinion, not a fact.
Where we may disagree is that I would like taking a guess (in the end everything is a guess, just some better or with more evidence than others), rather than having no guess at all. You're welcome to falsify it. That's science.
So in the end, your posts are going off topic rather than actually addressing the point. If all you wish to say is "we don't have experimental data that proves any of this", then I certainly agree.
Surely you have nothing better to do this summer (hah!)
I wish. Dissertation is taking all of my time

I've had numerous intuitions about phonetic properties of my speech and have been surprised to look at the measured phonetic reality, so you may develop new intuitions.
This is interesting! But wouldn't you say that most of the time you're more right than wrong? I have not even come close to suggestion intuitions should replace actual experiments. That would be absurd. But given that we don't have experimental results, my observations/intuitions aren't better than nothing?
Although I didn't lay out the reasoning, my claim that Modern Hebrew is more likely than English to have actual neutralization is based on the (uncontroversial) fact that MH has active synchronic phonological processes avoiding geminates.
Right, I think I hinted at that in my reply. It may be true. But I don't see how we can KNOW that English does not, when English does not have such cases to test (except across word boundaries, which we're apparently considering to be less than optimal test cases). In a theory like Optimality Theory, some effect (whatever it may be) would be inherent in the ordering of constraints. In some other theory, perhaps this would be undetermined. But merely speculating doesn't do much here, given your own reasoning.
(I am interested in that you brought up historical degemination in MH, though, so thanks for that. I'm fairly familiar with Arabic, less Hebrew, and I didn't know that MH was degeminating/ed, so I looked up a few things about that.)
One argument to be made here is poverty of the stimulus: so again, depending on the theory, children may simply have no such rules because the context never comes up.
As an odd example here, I've encountered a situation where Spanish speakers produce word-final voiceless stops. (This was in an artificial grammar experiment where, oddly enough, there was no such input, but by mixing up aspects of Spanish and aspects of the artificial grammar, they arrived at a midpoint with word-final voiceless stops once in a while.) They did this enough that I noticed a pattern: for some reason, they seemed to be aspirating word-final [t]. Of course it might be due to having heard me speak in English (but are they really that aware of aspiration? I don't know), or it might be a natural grammatical property of Spanish that (non-existent) word-final voiceless stops are aspirated. I wouldn't claim my data proves anything, but it does make me curious and very open to the idea that languages may have "rules" (or "emergent effects" or whatever you want to call them) for situations that actually never come up. Another argument in support of it is that not all new sounds are as difficult to learn. Our grammars are complicated, and I think it would be underestimating their complexity to assume they don't have any more properties than the absolute minimum.
My argument does crucially rely on the distinction between actively eliminated strings, which directly motivate a thing in the grammar (rule, or package of constraint rankings, depending on your meta-theory)
The rules themselves (and your argument) also depends on a meta-theory. I have a feeling you are working within one, implicitly, which is why we seem to disagree more than we need to, when I'm speaking (to the greatest extent possible) about data rather than theory, trying to remain theory neutral since I have no particular theoretical claims at this time.
but not every historical fact has a corresponding object in the grammar of a language, for instance, the phonological relationship between "father" and "paternal" is not part of the grammar of English.
Indeed not, and that's immaterial here. Diachrony may inform synchronic study, but it can't determine grammar rules.
Now this post has become longer than I intended, but, anyway, that's where I'm coming from with this.