Can "particularly" mean the opposite of "especially"?

Question

The common wording of the quote is:

All generalizations are false, including this one.

But can it be phrased like so?

All generalizations are false, particularly this one.

Meaning that there's nothing special about this generalization, that this generalization is not an exception.

Or let's say that there's some general rule, and a particular case X. Can I use "particularly" to mean that there's nothing special about X, that the general rule applies to X as well?

My idea that "particularly" is used when something is a particular case of something more general. And that that can be for 2 reasons: a) because X is somehow special, b) because there's nothing special about X. But I can't find the proof in dictionaries that the b) meaning is valid.

I looked in dictionaries, specifically Merriam-Webster, Collins, and Cambridge. But at least they weren't specific enough for me to tell if the usage I have in mind is valid. The closest I could get is probably the third meaning in Merriam-Webster.

UPD Okay, maybe "the opposite of" was a bit far-fetched, because mentioning something is already making it somewhat special. But given that, you can either make it "worse" (by meaning that there's more to it) or "better" ("I chose it, but that's about it"). In the "worst" case, what you've chosen is really special (especially). In the "best" case, the choice was arbitrary (for example).

And there's probably the middle case: "You will most likely think that the case X is not an exception, but in case you do, I'm explicitly saying that it's not." It might be because the speaker is overly cautious (says it just in case). Or because they expected X to be an exception, but it turned out that it's not, and they want to share their experience (make sure those who will follow to not repeat the same mistake, but it's not like otherwise most will).

I don't have good examples at the moment. But if I had, they'd probably be rather technical.

You might say that in the middle case one would use "even if X.". But that sounds like a stronger version of the meaning I have in mind. The speaker expects the listener to make the mistake or to be surprised: "You will most likely think that the case X is an exception, but don't be fooled, it's not."

Answer 1

This would not be wise.

• All generalizations are false, particularly this one.

has the default sense

• All generalizations are false, and especially this one.

In fact, Cambridge Academic Content Dictionary only lists this sense:

particularly: very or very much; especially:

• We’re particularly interested in hearing from people who are fluent in both Spanish and English.

The sense you want can be conveyed using 'in particular', though the 'especially' sense still competes strongly:

5. In particular [synonym of 'for example']

'In particular' helps point out a specific example.

[LanguageTool]

The words below represent different parts of speech and are not synonyms (so they cannot [always] be used interchangeably). They have similar meanings, but make sure to double-check that the particular word you select fits grammatically within your sentence.

• ILLUSTRATION

thus; for example; for instance; namely; to illustrate; in other words; in particular; specifically; such as.

[USF Education undergraduate academic success center ... transitions]

• All generalizations are false – and in particular, this one [is].

Disambiguating fully, but getting clunkier,

• All generalizations are false – and to particularise, this one [is].

Answer 2

Can I use...

You can do whatever you like. Whether any one else will take the meaning as what you want it to mean is another matter.

Particular has a standard meaning, which is what you have found in dictionaries: that the description applies to an instance which is singled out for attention. If there is nothing special about that instance, why single it out? To do so indicates it merits special attention.

This is why you cannot find evidence that particularly is used to show there's nothing special about a particular instance. [Did you see what I did there?]

Your example sentence is actually rather good, but it doesn't mean what you want it to mean:

All generalizations are false, particularly this one.

It's drawing attention to the particular generalisation that all generalisations are false. It's an example of paradox, "An apparently self-contradictory statement" [OED]