"Él tiene una enfermedad del corazón."
Traducción:He has a heart disease.
In English, it can be "he has a heart disease." Or it can be "he has heart disease." In English, "disease" is a count noun.
I believe that "heart disease" is an example of a noun that can be both count, and non-count, depending on circumstances.
Sure, some people somewhere have undoubtedly uttered "a heart disease" (among other potential reasons, non-countable nouns still usually have countable uses: "two literatures" meaning "two types / schools of literature"), but let's remember the audience of this course: non-native speakers, beginner English learners at that. They need to concentrate on general, common usage. In the Corpus of Contemporary American English plain "heart disease" beats "a heart disease" by a factor of 450:1 (and it would be a good deal more than that if one eliminated irrelevant occurrences like "a heart disease patient"). For comparison "disease" beats "a disease" by only 23:1. Clearly, there is something different happening between "heart disease" and "disease."
Correspondingly, the link you've provided lists "heart disease" as a non-count noun, which is self-evidently true the overwhelming majority of the time. The Oxford Dictionary agrees, explicitly listing "heart disease" as an example of a mass noun:
Just yesterday, my mother was talking about heart disease and some different kinds of heart diseases. One of her friends has a heart disease.
A search on Google for "a heart disease" had 16,100,000 results. That is considerably more than "some." "Heart diseases" has 11,300,000 results
"Heart disease", in general, may be used more frequently than "a heart disease," but my point still stands. I don't think 16 million uses makes the term uncommonly used.
"Heart disease" is one kind of "disease". It is a more specific concept that than "diseases in general". But there are various, more specifically designated, types of "heart disease."
Here is an article on "heart disease" and "heart diseases" http://www.healthline.com/health/heart-disease/types#overview1
This article specifically lists six forms (types) of heart disease, that is, six heart diseases. It states that there are also other types; that there are other heart diseases.
See also this article: http://www.mayoclinic.org/diseases-conditions/heart-disease/basics/definition/con-20034056. It says that "heart disease" is a "umbrella" term under which are several more specific forms of heart disease. As it notes, many heart diseases can be prevented or treated.
The definition of a "count noun" is a noun, specific examples of of which one can count. By that definition, "heart disease" is/ can be a count noun.
Non-count nouns have no plural form. As I said previously, As used in the articles I reference, "disease" is count noun-- it can be used in plural, and in the singular. "So is "heart disease".
By the way, note that I stated that I "believe" it (disease) might be an example of a noun which could be both "count" and "non-count." (But I did not assert that as definite, because I did not research that.)
Of course this (Duolingo) is for people learning English. That is why I make comments-- to help people learn English. As a person who teaches writing in English to college students, and as an editor of professional journals (in English), I am fairly knowledgeable about, and competent in, English.
And since my university has a good international program, and I have had many students from Spain, and Mexico (and other Spanish-speaking countries), I have known, and helped, with their English, many native Spanish speakers.
Why deny English learners the opportunity to learn that, in the correct context, "a disease" or "disease" (in general) can both be appropriately used? Especially on a topic as important to people as "heart disease" (of which there are several forms, that is, several types/kinds of heart diseases.).
From where I sit the links you are posting keep making my point: "heart disease" is overwhelmingly used in a non-countable manner. How does the second one begin? "Heart disease describes a range of conditions that affect your heart." Yep, just like I said "heart condition" is a standard countable alternative.
If you'd actually looked at those purported 16 million matches for "a heart disease" you'd see a good chunk of them, well, aren't really. What's on the first page? "a heart disease risk"; "a heart disease-related event"; "a heart disease risk factor" — clearly all entirely irrelevant.
If you want to believe the editors of the Oxford Dictionary mark "heart disease" as a mass noun with no actual basis just to confuse people, then I guess that's your prerogative. Native Spanish speakers won't have any trouble coming up with "a heart disease"; it's a word-by-word translation of what comes naturally to them. What they need to be taught in order to most authentically imitate native speech is the overwhelming non-countability of this common term, which is a linguistic aspect actually different from Spanish.
It would appear this is simply (unsurprisingly, given that this whole conversation started based on my observation that the word-by-word translation into English isn't very natural) a topic where the two languages differ thoroughly as to definiteness and countability: http://context.reverso.net/translation/english-spanish/have+heart+disease http://context.reverso.net/translation/english-spanish/has+heart+disease
SaraGalesa es correcto.
For mor: see this. http://www.differencebetween.info/difference-between-illness-and-disease
Según Google Ngrams, "heart disease" es aproximadamente 3000 veces más común. Supongo que nunca en mi vida haya oído "heart illness". Para mí estos dos hechos serían suficiente para decir que no hay razón particular para aceptarlo. No obstante, no es algún tipo de violación clara de las reglas del idioma inglés y se pueden encontrar unos ejemplos en Google (aunque "heart disease" tiene 600 veces más), entonces otros podrían tener una opinión diferente.
Lee la explicación arriba de Sara Galesa, es banstante más clara. "Porque lo dice más gente" no me parece una explicación aunque es un buen indicativo. Hay expresiones que pueden decirse solo en un país o en una región y no en el resto de países y no por eso son incorrectas.
No sé quién programa el sitio, pero seguramente no domina ni el Español ni el Inglés, seguramente programa lo que le indican poner sin discusión, pues en ocasiones las traducciones tienden a lo literal y otras a como seria la aplicación del idioma sobre la frase para que sea entendida en el contexto de su propia gramática. Es una pena porque eso hace que se repitan los ejercicios para reforzar lo que probablemente se vuelva un vicio al hablar o una mala acepción. Como dato curioso me llama la atención que los ejemplos en Inglés tienden a los que hablan de violencia y en Alemán a los de comida...