Are capital and lowercase letters considered allographs?

Question

I got into a debate the other day with somebody over whether the capitalized and decapitalized forms of certain written words (say, Polish and polish, or China and china) could be considered homographs or not.

In my opinion, it hinges on whether capital letters and lowercase letters are considered allographs of the same grapheme or not (are "b" and "B" both ⟨b⟩?), and a quick Google showed that some sources consider them to be allographs while others deny this fact because capitalization can change meaning (as above with shine a surface and originating from Poland).

Is there a more authoritative source on this subject? Does anyone have an idea of what the general opinion on this subject is, or what people use to justify this opinion?

Answer 1

I'd suggest 'it depends' as answer. Whether or not b and B are to be considered members of the same grapheme or allographs of one single grapheme (call it /b/) is not so much a statement about reality as it is a statement about the assumptions that you built your theory on. This is exactly the same state of affairs as in phonology.

I give a simple example. In phonology, you look for minimal pairs and sound correspondences to determine whether or not two observed phones (i call them 'phonotypes') belong to one or two phonemes. Using that method, you find out that [d] and [t] belong to two distinct phonemes in German, because [de:r] and [te:r] and many other pairs are consistently kept apart. You also find out that what is written ch, [ç] and [x], should be allophones of the same phoneme (call it /x/), because of such word pairs as lachen—lächeln, 'Loch—Löcher` where [x] and [ç] are interchanged consistently, depending on the quality of the preceding vowel (it's a natural change where velar vowels go along with the velar consonant and palatal vowels with the palatal consonant).

That's all fine until someone comes up with a counterexample. There's a actually at least one minimal pair in German which does distinguish between [ç] and [x], and that's Kuhchen [ku:çən] ('small cow', diminutive of Kuh) vs. Kuchen [ku:xən] ('cake'). While you hardly in your lifetime will overhear a German speaker say Kuhchen, building diminutives with [-çən] (and [-lain]) is a demonstrably active process in German, which is used on a daily basis.

So it looks that [ç] and [x] cannot be viewed as members of the same phoneme.

Until, that is, someone comes along to point out a flaw in your analysis, and that would be the negligence of morpheme boundaries in your analysis. True, [ku:çən] and [ku:xən] do look like a minimal contrast, but only until you put back those boundaries: then, [ku:#çən] (Kuh+-chen) and [ku:xən] (single morpheme) do look different, and this difference can be understood of what is causing /x/ to come out as [ç] in the one case and as [x] in the other.

In other words, whether or not we can establish a phoneme /x/ = [ç, x] will depend not on the German language, but whether your theory does or does not take morpheme boundaries into account.

Likewise, whether b and B (and b, b, 𝒷, 𝔟, 𝕓 and so on) are 'same' or 'different' will depend on your use case. Write down MIND THE GAP on a piece of paper and stick it to the wall, everyone will thank you for the warning and understand it just as well as mind the gap; write EINSTEIN WAS WRONG in your essay, and your teacher will pick up the red pen because she thinks only Einstein was wrong is correct orthography for an essay. Write 𝖁𝖔𝖗𝖘𝖎𝖈𝖍𝖙 on a sign in Germany these days and people will find it strange, use it the same type in a newspaper masthead and people will find it customary. Use b, b, and 𝒷 interchangeably in your personal notices and it's up to you, confuse them in mathematical formulas and that important maths periodical won't publish you. Same isn't same, different isn't different.

Answer 2

Except in leet speak, they’re certainly not free homographs.

Grapheme and allograph are terms that are seemingly easy to define, hence formal definitions don’t vary much (especially if you don’t count the useless “visual phoneme” and “alias for letter/character” ones), but when it gets to actually using those terms, many scholars stretch their meaning as they seem fit.

When two text strings or graphic words consist of the same letters (language neutral), you could say they’re “equiliteral” or something. Roman letters have cased variants (and more) which are not differentiated for this. ⟨China⟩ = ⟨china⟩ = ⟨chinɑ⟩

When they consist of the same string of characters (language neutral), they’re encoded identically – “homocyphers”. ⟨China⟩ ≠ ⟨china⟩ ≠ ⟨chinɑ⟩ Characters are not cased and include punctuation.

When they use the same glyph cluster (language and script neutral), they’re visually identical – “homovisual”. ⟨China⟩ ≠ ⟨china⟩ ≠ ⟨china⟩

When they’re the same run of graphemes (script neutral), they can be considered homographs. The thing is, as mentioned above, not everyone agrees what exactly a grapheme is. Some will consider <ch> a single grapheme in English, others will not, yet others will make that decision dependent on context. Many scholars unify uppercase and lowercase variants of the same letter for graphemes, which can be a justified simplification for most written languages using the roman script (except German), because many a graphemic analyses excludes proper names for they’re too complex bearing graphotactics from times long gone and foreign languages and sentence-intial cap or graphostylistic title-case (like all-caps) can be described as systematic rules. That being said, graphemically it’s always ⟨china⟩ = ⟨chinɑ⟩ and maybe ⟨China⟩ = ⟨china⟩, but ⟨China⟩ ≠ ⟨china⟩ also occurs and sometimes ⟨China⟩ is said to be out of scope.

PS: Those terms inside quotation marks I just made up badly. I hope they help to get the idea, though.

Answer 3

Overall, I'd say it's a bit of a gray area (depending on your criteria for allographs).
On the one hand, as you've noted, capitalization can change the meaning of a word: there are, in fact, minimal pairs.

Additionally, capitalization in online conversations is often used to indicate emphasis (LIKE SO) - often capitalizing several words or sentences in succession will result in responses of "stop shouting" or similar.

On the other hand, that use of capitalization for emphasis is similar to that of bold or italicized text (though in my experience capitalization is considered the "loudest"), and I would certainly agree that "b", "b", and "b" are all allographs.