are not blocked by this. Curious, isn't it. Of course, in languages that deal with locatives and such through case forms, these will also violate the "is-links-same-case" rule a lot of the time.
Even if we reject the idea that prepositions are cases, we still find reason to reject "is" linking same-with-same:
Now, one could object that I am misinterpreting something - "is [noun]" and "is [prepositional phrase]" are different uses of is! But this by itself only strengthens my argument - it shows that the claim '"Is" equates. Equals should be similar."' fundamentally fails. The objection to my argument basically concedes that "is equates except when it doesn't". The rule is way too simple, and hides many important facts about is and other copulas.
How about
woe is me
mir ist kalt ('me.dat is cold', "I am (feeling) cold")
Min Gud är mig en väldig borg ("my god is me a mighty castle" - "my god is a mighty castle for me")
Further, we can show that is is not a strict equality thus:
((is) ≡ (≡)) → (the house is red) ≡ (the house ≡ red)
(the house ≡ red) ∧ (the apple ≡ red) → (the house ≡ the apple)
:= the house is the apple.
In other words, if it's true that
is equates, it follows that if the house is red, and the apple is red, the house is the apple. The point here is basically that you just can't translate '
is' into a simple logical operation. Doing so leads to bizarre conclusions, and therefore
is has to be something that is different from
≡, in such a way that is can be used to express the idea that ≡ expresses, without being the same operation. This means any "syntactical" considerations that ≡ carries may be ignored. Among these are the notion that the left and right side may be marked in different ways to show distinctions. Maybe differences in scope are marked by different cases.
Further, if is equates, the right and left side of is should be equivalent, in which case it should be acceptable to switch their order.
The house is red. / Red is the house.
Huset är rött / Rött är huset.
Both of these do work in Swedish and English, but "red" does not serve the same syntactical role as "the house" does, and thus they cannot be equivalent.
The house is red and stands by a beautiful lake.
?Red is the house and stands by a beautiful lake.
The house is red and the house stands by a beautiful lake.
*Red is the house and red stands by a beautiful lake.
We can further notice the following:
a) The captain is a woman.
b) A woman is the captain.
c) A woman the captain (indeed) is.
d) *The captain a woman (indeed) is.
Granted, some of these do sound like cheap lines in an amateur production of a story about 18th century pirates with a female at the helm. However, they are syntactically parsable with meaningful distinctions for most speakers of English: a) is unmarked or can convey some surprise, b) could convey some surprise or at the very least highlights that this is somewhat unusual, and c) affirms in some way (either positive or sarcastic) the fact.
These three acceptable utterances have pragmatic distinctions - the information structure of these three utterances are different. If "is" only equated, this would not make sense. Besides, if "is" only equated, d) should also be acceptable.
Empirical data:1. Danish
In good danish, "it is me" ('det er meg') is acceptable.
2. Russian and Polish
Since I am describing two languages, this description is a sort of average of the two - not entirely accurate for either, but close enough for government work.
In Russian and Polish, noun complements of the copula often are in the instrumental. Adjectives more often are nominative, but in some contexts, they too seem to favour (or even require) the instrumetal. Both the Russian and Polish copula are cognates to the English be/is forms. (C.f. be ~ być, быть, is ~ jest, есть.)
Further, these languages sometimes have quirky case subjects that are not nominative, for instance the Russian 'to have to', надо. With надо, the 'subject' is in the dative - yet complements of надо быть do not agree with the subject in case. Clearly быть does not "strictly" equate.
3. Finnish
In Finnish, the copula can take either nominative or partitive - the subject usually being nominative.
Sometimes, other cases are uses - e.g. the "into a role" case, the translative:
hän ei ole lääkäriksi
he/she is not "into the role of doctor" > (s)he isn't suited to be a doctor
The subject in this construction could also be in the ablative:
hänestä ei ole lääkäriksi
from him/her is not into role of doctor -> (s)he isn't "doctor material".
Much like Russian, Finnish also has verbs whose subjects are not nominative:
häne-n on pakko olla hullu
his/hers has to be mad
(s)he has to be mad
not
*häne-n on pakko olla hullu-n
his/hers has to be mad's
When stating age in years, the opposite holds: the numeral is in the genitive, but the subject in the nominative: hän on viiden - (s)he is five.
Furthermore, the Finnish copula can take partitive subjects when you make existential statements, and when specifying quantities it is mandatory:
heitä oli viisi
*he olivat viisi
*heitä oli viisiä
*heitä oli viittä
they.part were five.nom
No matter what kind of group is being quantified, the subject is partitive and the numeral is in the singular nominative - Finnish has plural nominatives and singular and plural partitives for every number so that gets a bit confusing.
Further, like many languages, Finnish does not have a separate verb for "have", but forms that meaning by using 'to be' and some kind of locative - in Finnish it's the allative, -llA, "by, at, on". "Tuomolla on kirkasta" - "by Tuomo is clear.part", "Tuomo has vodka" - linking a noun in the allative to a noun in the partitive in this particular instance!
4. Many languages in Africa
In Africa, many languages have copulas whose "complements" syntactically and formally actually are objects. (NB: in many of these languages, nouns do not have case, but ~case is conveyed by a verb marked that agrees in gender with the noun.)
5. Swedish
But wait a moment, I stated previously that Swedish takes the nominative? Well, even Swedish raises some objections to the "is equates" model! I will use English word-for-word translations to make it easier for non-Swedish readers to keep up. I am not making statements about English grammar in this section.
Reflexives - "I am myself" - "jag är mig själv" - is perfectly accepted by the standard grammars. "Jag är jag" is also possible, but has slightly different connotations. All reflexives in Swedish are accusative.
In the third person, though, "He wants to be he" means something entirely different from "he wants to be himself". "He wants to be he" requires the two "he" pronouns to have different referents, and signifies that the first wants to become the second. "He wants to be himself", " does not state that two different referents are one, it states that he wants to be (back to) his (usual) self. Thus, to express the notion that he wants to be his own self, the rules require one to use the accusative reflexive.
I have further tried finding rules for the construction "let me be me" in Swedish. In English, it seems the is equates rule actually "seems" to be applied here (or rather, most people probably go for "be me" anyway, and those who think is equates think that's why it should be me there. The underlying mechanisms are indistinguishable from the regular speaker in this case). I feel like "vara jag" (= be I) is more natural in this context, in which case the is equates principle fails in the somewhat unusual other direction: an accusative notional subject with a nominative complement!
6. English
I am not going to point to the actual fact that the overwhelming majority seem to be entirely okay with "it is me". The examples I want to attract attention to are syntactically a bit more complicated.
Would you want to be me?
I found very few examples (in fact none) of this with the complement in the nominative. I am pretty sure some instances of this must be the result of equates-believers - certainly someone who believes it should be "it is I" must have written a sentence with "would ... want to be [personal pronoun]". I may not have searched diligently enough, but this at least indicates that for most people, the intuitive case to use with the copula is the accusative even if they believe that they use the equating strategy.
One step further, we find
606 000g it is hard to be me
0g it is hard to be I
The numeral followed by a superscript g stands for number of google hits.
We could of course also look at the syntax of equating - it should require "it would be hard for him to be me" to become "it would be hard for him to be for me", since "for me" is the PP that is equated with the complement of the copula.
One nice thing to note about the above example is that either we posit some ethereal subject that has a hard time being me, or we posit that to be in it doesn't equate anything with me. Again, "is equates" fails.
My conclusion from these examples is that the natural case for complements in English indeed is the accusative. Using the nominative is a learned affectation that fails for almost everyone whenever the syntax has the tiniest complication. Luckily, most situations with complications involve a noun in the accusative, and so the "accusative is right" and "equal case is right" become indistinguishable in most of those situations. Luckily, a few constructions do exist that show that it's more likely that the "accusative is right" rule is more fundamental to English grammar.
An improved model
It is in fact easy to posit a model that accounts for the syntactical and semantic behavior of the copula without having to resort to the principle I set out to argue against. In addition, the principle I set out to argue against leads to bizarre conclusions, and does not fit with actual empirical evidence.
One of the roles of the copula is simply to signify that the subject is being described by an element that is syntactically subordinate to the copula. This element's case (and sometimes the case of the subject as well) can be controlled by the copula or by syntactic and semantic factors. Other particles and elements may also inform us of the function of the copula (e.g. "There ..." in English turning it into an existential quantifier). The copula can be used to tell of ownership ("is John's"), membership in a group ("is one of us", "is one of the best cooks", "is a freemason"), age ("on viiden"), quantity ("heitä on viisi"), adjectival properties ("the house is red"), location ("I'm inside", "honey, I'm home"), existence, and further serve as an auxiliary (future tense with imperfective infinitives in Russian, obligation with genitive subjects and participles in Finnish, ....)
The advantages of this model is that it's actually applicable to actual real existing languages. It won't fail as soon as you attempt to apply it to Finnish or Russian or honest-to-God English. It also is applicable even to a language that actually completely maintains case equality, or to a language that always requires the complement to be nominative.
Granted, unlike the "is equates" model, the only prediction we can get out of this model is that 'languages will vary'. But, if we assume an empirical approach, it's better if our model makes general but true predictions than if it fails arguably even for the language it attempts to describe, but certainly for a multitude of other languages as well. "Is equates" was an acceptable hypothesis, but once it's proven wrong, we shouldn't use it anymore except for the conclusions we could reach by investigating it.
Conclusion
We can see that the argument that was presented as a logical cause of a grammatical rule is based in a flawed understanding of both logic and language. This is not unusual.
In Swedish, it is "it is I", but not because it's logical - it is thus because that's how Swedish works. In English, it's unstable. Flawed logical arguments should not be used to tar one of the two alternatives as bad or illogical - doing that would actually be illogical. The linguistic intuitions of the speaker community should be the basis for this. It would be a sad day indeed if crappy logic were given a victory just because it looks scientific. It would basically be conceding the victory to pseudoscience and pseudologic.