Since the same words can be adjectives and adverbs, sentences could be constructed where the word modifies a noun and a verb:

She is and runs fast.

While others cheat, my children are and play fair.

In Yellowstone National Park, bison roam, and truly are, free.

How about "splashing is forbidden?" Splashing seems to function as either a noun or a verb.

It could be modified by an adverb to fit the verb test:

Loudly splashing is forbidden.

Or it could be modified with an adjective to fit the noun test:

That loud splashing is forbidden.

A psycholinguistic perspective

Ultimately, to address the meat of the question, I don't believe that a word can truly function as multiple parts of speech with the same meaning and parse. It's important to consider how a reader perceives the parts of the sentence.

Studies of language acquisition in young children indicate that gerunds, or words ending with -ing generally, tend to be comprehended as two separate lexical units. An example lies in a study of 15-month-olds by Toben Mintz:

Taken together, the experiments in this study demonstrate that
English-learning 15-month-olds represent the suffix -ing as a discrete
unit. Thus, although previous experiments failed to find evidence
that 15-month-olds have acquired morphosyntactic dependencies
involving -ing (Santelmann and Jusczyk, 1998), infants
may nevertheless be in the process of learning these dependencies
at this age. Specifically, having a discrete representation of an affix
allows infants to notice dependencies between that affix and other
forms.

...

The experiments reported here demonstrate
that English-learning 15-month-olds represent -ing as a
distinct form. When processing novel words that end in -ing,
they segment the suffix from the stem. This allows them to notice
morphosyntactic and morphosemantic patterns that involve that
form, and that will form a part of their acquired grammatical
knowledge

• Mintz, Toben H. "The segmentation of sub-lexical morphemes in English-learning 15-month-olds." Frontiers in Psychology
  

This conclusion is supported to varying degrees by other studies of language acquistion. See also:

• Pliatsikas, Christos; Wheeldon, Linda; Lahiri, Aditi; Hansen, Peter C. "Processing of zero-derived words in English: An fMRI investigation" Neuropsychologia 53 (2014) 47–53

By this logic, one could argue that a gerund functions as two parts of speech by virtue of being processed first as a verb and then as a noun. In the sentence, "I enjoy running," a young child processes "run" first, with "-ing" acting as a modifying unit. In this sense, it's not unlike verbs in infinitive form. "To run is fun." Here, we're comfortable calling "run" a verb and "to run" a noun clause. "Run" can still be treated as a verb -- it is free to operate on an object or be modified by an adverb. "To run races quickly is fun."

However, the case of infinitives also illustrates an important distinction between nouns and noun clauses. Even though "To run" is a noun clause, it doesn't have the same flexibility as a typical noun. It cannot be modified by an adjective or be made countable.

Given that early processing of gerunds tends to treat them as two separate lexical units, there seems to be an implication that the parsing occurs twice by young children as they learn the function of the phrase. This notion is confirmed in another notable study appraoching the question from a psycholinguistic angle:

The abstract can be found here:

• 
  "Noun or verb? Adult readers’ sensitivity to spelling cues to grammatical category in word endings." Kemp, N., Nilsson, J. & Arciuli, J. Read Writ (2009) 22: 661.

Among other things, Kemp et al. discuss the level of computation required to process phrases with ambiguous function as measured by response time, a common method in psycholinguistic research. Some passages seem highly relevant to how we mentally parse these parts of speech:

Laboratory studies confirm that having to resolve a word’s grammatical category can delay reading time, in such phrases as She saw her duck and chickens vs. She saw her duck and stumble (e.g., Boland, 1997).

The study and others cited in it also conclude that orthographic suffixes, like -ing, provide clues as to the part of speech of a word, even when used as suffixes in "fake words" where research participants were asked to identify the part of speech of made up words with differing orthographic endings. The use of segmented lexical clues to determine a part of speech parallels the earlier mentioned research related to how children process words like "splashing." It is parsed in two parts, first as a verb, but its ultimate function similar to a noun clause doesn't imply that it is in itself two parts of speech at once.

"The window was broken by John."

It doesn't seem simple to me to demonstrate that "broken" in this sentence is not simultaneously a verb and an adjective.

Participles

Participles are one of the classic areas of dispute about part-of-speech categories. I’m not qualified to give a summary of the overall state of linguistic opinion about this area, but my impression as an amateur is that the analysis of participles is still somewhat unsettled.

I'm using Björn Lundquist's "The Category of Participles" (2013) as an important source for this answer.

In general, participles behave in some ways like adjectives, and in some ways like verbs. Lundquist quotes a definition from David Crystal (1991):

Participle: "a word derived from a verb and used as an adjective" (2)

There is another quote from Lundquist that I think is relevant:

Classifying participles as adjectives is quite pointless unless we have a theory about (lexical) categories. (6)

Overall, I think a truly satisfying answer to this question will have to be more theoretical than I can manage.

“Participial adjectives” are definitely adjectives, but they also are at least related to verbs

One type of participial words are so much like adjectives that, as far as I can tell, everyone agrees that they are adjectives. These are the “non-eventive” participles/participial adjectives.

It’s actually a bit difficult for me to think of ways in which non-eventive participles in English could be considered verbs, and I can’t recall encountering any explicit arguments in support of this position, so I won’t attempt to give much support for this. Here are just a few random ideas:

• Most obviously, they are are generally built on roots that have indisputably verbal uses: “broken” has the same root as “breaks” in “The glass breaks.”




• They can sort of take subjects, in “by” phrases or in compounds.

These arguments are kind of weak, I know, but participial adjectives are clearly more similar to verbs than most adjectives are.

Eventive participles are as far as I know classified as verbs by mainstream grammar, but it is difficult to find a definite test that distinguishes them from adjectives

It seems to me to be possible to make stronger arguments that eventive participles, which in mainstream linguistic analysis are often regarded as “verbal” participles because of the grammatical properties that they share with verbs, partake of the nature of adjectives. Lundquist in fact argues that all passive participles, both stative/resultive and eventive, are adjectives. As far as I can tell, he doesn't classify them as being simultaneously adjectives and verbs any more than nominalizations are simultaneously nouns and verbs. But if there are strong arguments for both "participles are verbs" and "participles are adjectives", saying that they can be both seems like an obvious possible conclusion (although that solution obviously is not without complications of its own).

General ways in which participles are more like adjectives than verbs: Lundquist notes morphology and distribution. Most of the morphological points are more relevant to languages with more inflection than English (e.g. gender agreement, like in Romance languages) but there are still some possible arguments from morphology.

• Like adjectives, but unlike finite verb forms, participles are invariant for
  grammatical number and person.




• In English, at least, participles cannot inflect for absolute tense in the way that finite verbs obligatorily do. The verb in “they run” is clearly present tense, while “They ran” is past tense. But the so-called “present participle” in a phrase like “the running team members” can be used in either past or present absolute tense contexts. It’s true that it has a kind of relative-tense component, in that it refers to people who were/are/will be running at the time the narration is dealing with, but this is a different type of tense from what we see in English finite verb forms.

Distribution: Eventive participles have very similar distribution to adjectives (as I said, this point is made by Lundquist). E.g. when used predicatively, there must be a linking verb like the copula "to be". Participles seem to be able to be coordinated with adjectives e.g. "I was nervous as hell and sweating bullets" (Beasts, Bullets, and Blood, by Christiaan). Participle and adjective phrases both can be used attributively; while some recognize a distinction in possible position (that adjectives may precede nouns, and participles cannot) this isn't a clear defining factor of adjectives, because there are words like asleep and awake that are commonly classified as adjectives but that cannot be used attributively at all, and other things aside from adjectives can come before nouns (e.g. articles, quantifiers, attributive noun phrases).

Candidate tests for differentiating adjectives and eventive participles all seem to have some flaws

There are some apparent ways in which eventive participles differ from the typical adjective. However, I don’t know of anything that eventive participles do that no adjectives do; there are a number of “weird” adjectives that show one or another of the grammatical traits usually associated with participles.

Direct Objects: participles can have them, but so can some adjectives

One of the typical ways in which participles seem to differ from adjectives is that eventive participles may (but not all do) take direct objects.

However, this is not a bright line for distinguishing participles from adjectives because many linguists recognize some types of transitive adjectives. See this Language Log post by Geoff Pullum: New transitive adjectives. “Worth” is the classic example, and the post additionally mentions “underweight,” “overweight”, “long” and “short” as adjectives that may take NP complements.

(Non) Gradability: a feature of all eventive participles, but also of some adjectives

One big thing that seems to set eventive participles apart from a “typical” adjective is the pretty much absolute grammatical impossibility of using eventive participles in a number of constructions that require “gradable” adjectives.

• No eventive participle can take the superlative suffix "-er" or comparative suffix "-est", although this is not conclusive since there are plenty of adjectives that don't take these suffixes either, and the phonological structure of participles (most are more than one syllable) actually means it would be expected even if they are adjectives that they would not take these suffixes.



• 
  

  It seems that eventive participles can sometimes be acceptably modified by the comparative adverb "more" ("more sinned against than sinning", "more telling him than asking him", "the song was more shouted than sung") but this is also sometimes possible, at least colloquially, for verbs ("I guess we more cried, than talked." - "7 MONTHS BUT WHO’S COUNTING? I AM. I ALWAYS WILL BE." - Rockstar Ronan tumblr).

  
  
  

  I can't think of an example of a clearly eventive participle modified by the superlative adverb "most".

  
  



• The adverb “very”, which normally can modify adjectives and adverbs but not finite verb forms, also doesn't seem acceptable before eventive participles. We cannot say things like “*He is very writing a book”.




• Lundquist cites a paper "Matushansky, O. 2002. Tipping the scales: the syntax of scalarity in the complement of seem. Syntax 5.3: 219–276." that argues that gradability is also the origin of another restriction on the distribution of eventive participles: they cannot come after certain verbs such as "seem".

This prohibition is much more absolute than it is for most supposedly “ungradable” adjectives, like “perfect” or “unique”, which can in fact be used gradably because of the phenomenon of “coercion”, specifically “scalarity coercion”: basically, gradable use implies that these words should be interpreted as having a gradable meaning, even if their usual definitions are not gradable (Lundquist 4, citing Matushansky 2002).

However, there are some adjectives that seem as resistant, or at least nearly as resistant, to scalarity coercion as unambiguously eventive participles.

• 
  

  the word "former", which I think needs to be classified as an adjective.

  
  
  

  
  

  
  
  • The former president, A former tennis champion
  
  
  • *The very former president, *A very former tennis champion
  
  

  
  

  
  
  

  It’s true “former” is a weird adjective, since it was formed as a comparative of “foremost”/obsolete “form(e)”. However, I don’t think it can be considered a comparative in modern English (for one thing, it can form a -ly adverb “formerly”, which I don’t think is usual for comparative adjectives).

  
  


• 
  

  Some pre-posed participial adjectives:
  
  *a very running experiment
  
  *a very sleeping child
  
  *a very falling tile

  
  
  

  These are generally classified as adjectives because of their position preceding the noun. But we can see that they cannot be modified by “very”. This shows that adjectives can fail the “very” test. (An alternative viewpoint that also seems consistent to me would be to reject the classification of these words as adjectives. For an example of that perspective, see BillJ's answer to Mari-Lou's "running" question or "Another look at participles and adjectives in the English DP", by Tibor Laczkó (2001).)

  
  


• 
  

  Certain adjectives are hard to use with "seem" in certain contexts. The following example is reproduced in Lundquist (4):

  
  
  

  
  

  (12) a. This music seems nice/*choral.
  
  b. This problem seems insoluble/*mathematical.
  (from Matushansky 2002)

  
  

  
  
  

  People may have different acceptability judgements of the sentences above, but it’s at least evidence that adjectives don’t always pass the gradability tests that eventive participles always fail.

  
  

Even if it turns out that no other types of adjectives are quite as ungradable as participles, it’s not clear why gradability should be considered a defining feature of adjectives.

Summary: I think it is hard to identify syntactic tests that are completely sufficient for distinguishing participles from adjectives. On the other hand, "eventive participles" clearly also act like verbs in some respects and appear to be part of verbs' inflectional paradigms (which I think is relevant for part-of-speech classifications in some theories of grammar). Because of this, I do think the idea that these words are both adjectives and verbs has some intuitive appeal. However, a serious theory of part-of-speech classification needs to be based on a deeper level of analysis that I unfortunately cannot explain, because I am not sufficiently familiar with the science of syntax.

Yes

There are constructions called zeugmas (after Greek ζεῦγμα, 'a yoking') where a word or phrase is intentionally made to apply to two or more others in a sentence despite functioning differently for each. The horde of words in English that can function as various parts of speech mean that zeugmas can be created where a single word simultaneously acts as two separate parts of speech.

@DavePhD had a particularly nice one in his reply

She is and runs fast.^{[adj.; adv.]}

that could also be reworked into the still stranger

She is but stands fast.^{[adj.; adv.]}

The doubled, incompatible, but grammatically functional senses of the word—usually requiring a double-take to figure out—are the appeal of the rhetorical device. It's simple enough to create such expressions using -ing words:

He is and likes running.^{[v.; n.]}

They are and enjoy knitting.^{[v.; n.]}

although anything creative is likely to be rather awkward:

He's being and is a hit.^{[v.; n.]}

He was, has, and eats standing.^{[v.; n.; adv.]}

and No

If you consider the doubled parts of speech in those zeugmas irrelevant because they're different 'meanings'... well, as Mr Yeats pointed out in his post, nouns and verbs are definitionally different "meanings". A noun used as a verb may intend act as (a) ~ ("man/crew/staff"), act like (a) ~ ("cat/horse/slut/fool around"), make (a) ~ ("sound/peep/bridge"), use (a) ~ ("hammer/canvass/google"), provide (a) ~ ("water/house/board"), &c. A verb used as a noun may intend an instance of ~ ("a run/try/fuck") or several instances of ~ ("a beat/pulse/record"), something that ~ ("a shoot/hit/fuck"), &c. They'll all be slightly different as a matter of course.

If you exclude any such form of doubled meaning, the only form of word that could work as a verb and noun simultaneously would be verbal forms.

It [sic] isn’t also a noun in either of them. Just because running bulls is the subject of sentence 1 doesn’t mean that running is a noun; it can’t be a noun or it wouldn’t be able to take a direct object like is happening there. Only transitive verbs take direct objects; nouns never do.

If you peremptorily define your opponents' contention out of existence, of course, it is impossible for them, me, or anyone else to continue to argue their case.

and Maybe

You can rest there and be content that everyone who disagrees with you is making some form of a category error. Ambiguity between adj. and adv. senses of participles could be dealt with by similar definitional adjustments, like Aml's "adjectives-being-used-adverbially" in his reply to DavidPhD's post.

I'd think it should be unsettling that you're just shifting definitions out from under your opponents. It certainly seems odd you'd put up a 500 point bounty just to hear how right you are. The actual definition of noun

A word used as the name or designation of a person, place, or thing; the class or category of such words...

and verb

That part of speech by which an assertion is made, or which serves to connect a subject with a predicate.

don't remotely support your contention that there is a magical bright line between the "noun" in "I like eating" and the "verb-in-a-noun-phrase" in "I like eating bacon". In fact, they don't support the idea that either "eating" is a verb at all, let alone universally.

The essential nature of the gerund in Latin—and, by extension for many grammarians, its -ing equivalents in English—is that it is a noun which retains the verb-like regimen (taking adverbs, objects, &c.) of its origin. RaceYouAnytime says as much both with his examples and his research describing the way generic English learners intuitively approach this structure. Aml claims to agree with you completely, but still understood your "running" as a noun with an object. Both historically (Latin and Old English's grammatical suffixes make verbals' noun status much more emphatic) and popularly, that's exactly how gerunds are approached.

You can absolutely define away your opponents' points. It doesn't really make them 'wrong' in any meaningful sense, though. You've just redefined 'noun' and 'verb' into something they and most other English speakers don't intend. You shouldn't expect such arguments to be convincing to them or anyone who doesn't share your specialized definition of these terms.

It's not that I think you're wrong on the basis of modern linguistic processing. It's just that no one is 'right' here. You're using a separate definition of noun and verb from theirs and you're just talking past each other. Buy 'em a beer and change the subject. They can suffer in the Hell of Poor Grammatical Understanding in the afterlife of your choosing.

For myself, as a side note, looking at both sides from the outside, I don't see the analytical benefit in calling "eating" a verb-in-a-one-word-noun-phrase instead of just treating it as a noun and saying verbal nouns can take objects. That approach seems less complicated in analytic languages and simply correct in synthetic ones.

To be really pedantic, the definition of a verb (for instance) is different from the definition of a noun, even if the same word is used, so at one level your intuition is correct.

As a practical matter, a given word can have all four uses, and the good old ubiquitous "fuck" does this quite nicely.

1) n. "Sometimes the fu*king you get isn't worth the f**king you get." (Meaning that some sexual relationships aren't worth the emotional price you wind up paying.)

2) v. "After f**king her all night he could barely see straight the next day."

3) adj. "What a f**king nightmare!"

4) adv. "Are you f**king serious?"

From my experience, it strikes me that words which would ordinarily be (or be like) two parts of speech have been separated into different categories, thus creating "new" parts of speech. If I'm not incorrect, gerunds and verbal nouns might fit this category.

I love fishing.

Is fishing a gerund or a participle? I just feel lovely while I fish, because I love to fish.

I run holding scissors

Am I holding the scissors or are the scissors holding me? Physics will have told you that forces create counter forces. Hence, I run scissors that are in a hold, even if that's not the common interpretation.

Edit: Point in case, it's not "the fishing", and neither "to fish", which would be the respective definite noun or non-finite verb forms. One easy way out is to simply label such use as a different lexical category. Alternatively, the fact that the gerund form wasn't used with an article could be explained either by its verb characteristics, which doesn't make sense to me when it's the subject, or by the omission of the indefinite article as it's also observed in "I love fish". However, I think the latter form is overly simplistic, because it doesn't give much to go on, but that's a different topic (links to relevant questions elude me at the moment).

My personal take is that even "I fish" is ambiguous to a degree, because the verb is a verbalization (?) of the stronger noun. I find the difference between the noun and the nominalization of the verbalization of a noun (gerund) quite bizarre. The point is, if in "I love fishing" the common noun is not entailed, e.g. because the fish is not the ultimate goal of the action, than the word is misused. Still, it surely retains the meaning of a verb. So I can only conclude that if you want a clean separation of verbs and nouns, constructions like this would have to be avoided.

After all, "I " to say "I am called " sounds rather primitive, but it sure works in the right context. This is difficult to pinpoint because English is neither a pure analytic language nor purely synthetic.

I noticed a similar confusion in physics and programming. A number literal can be understood as a constant function without any arguments. A function f can be used as variable of it's results, e.g. the Time is introduced as variable parameter but can be an operator in higher physics.

1. Running [of] bulls is easy. 'Running' is here a gerund, not a verb. It is a type of noun, as is an infinitive (cf. "To run bulls is easy.")




2. [The] running bulls are dangerous. 'Running' is here an adjective at the surface level, but at a deeper level it is a verb (cf. "The bulls that are running are dangerous.")

When looking at a particular level, each 'word' has one and only one 'POS'; unless you consider ambiguous samples, where more than one POS is possible (but each interpretation still uses only one POS per word).

The very strange word galore must be seen as a quantifier. But it also has descriptive force: one wouldn't say 'There were mutilated corpses galore strewn across the field of battle'. So in 'There were pavilions galore covering the Crusaders' camp', 'galore' means 'many' 'colourful and splendid' [pavilions] and must also be in the adjective class.

Dictionaries are moving 'galore' from the adjective class to the determiner, but, while this shows progress, it is an inadequate corrective. Though they don't mention the 'splendour/attractive array' or the 'happy abundance' ('There were toffee apples galore') requirement, every example I've found demands this. 'There were pebbles galore on the beach' says a lot more than 'There were a lot of pebbles on the beach'.

I humbly submit.

These answers are quite expert, which I am not. - How's that? expert is both an adjective and a noun.

I've wondered about this question also. And it seems to me that coordinating conjunctions play a dual role, they seem to function as both pronouns and conjunctions at the same time.

The man, who is wearing a funny hat, is the chef. - who refers to
the subject noun antecedent, and it also functions as a conjunction for the
subordinate clause.