The assumptions you start with can often limit the set of conclusions you are able to arrive at through logical reasoning. Computer science people were having a heck of a time attempting to adapt the binary tree - the standard for in-memory search structures - to media with large seek time, particularly disk drives. Progress was slow and fairly unproductive while the basic definition of binary tree held. Finally, somebody questioned the assumption and thought: what if we built the tree from the bottom up? And so the B-tree was born, and remains the standard in index structures to this day, with incremental improvement.
Other times, when creating, the assumptions themselves are fun to play with and observe the results. In Caia, I initially envisioned all of the major words - nouns, adjectives, and verbs - to be nouns. Nouns became adjectives when used with an attributive particle analogous to "having" (e.g. "woman having beauty" vs. "beautiful woman"). Taking an idea from Japanese, nouns became verbs by an auxiliary verb meaning more or less "do" or "make" (e.g. "make cut" vs. "cut"). Unfortunately, I ultimately concluded that verbs had to be separate, due to both practical concerns (specifically, concerns about making thoughts too long) and theoretical concerns (different nouns require different semantics, which would produce inconsistent theoretical behavior).
With another one of my languages, I took a different route, with some very interesting results. As this language is synthetic (unlike Caia, which is strongly analytic and isolating), I had quite a bit more flexibility. This language was actually modeled on the Altaic languages - Japanese, Korean, Mongolian, Turkish, etc.; as such, I suppose I can't claim that I invented this (what I'm getting to), but merely took what existed in Altaic languages and perfected it to a degree that doesn't exist in nature - at least to my knowledge.
The result is a language is which nouns, adjectives, and verbs are, in fact, all verbs; they are conjugated exactly the same, and play the same grammatical role. Even though this particular language is fictional, and I'm not expecting anybody to actually speak it, this idea might show up in other languages of mine (possibly a real one), as I find it exceptionally elegant. However, I do like to refer to "nouns" as substantives, "adjectives" as attributes, and "verbs" as actions; this is done because there are slightly differences in meaning between the noun bases in the three cases.
I explained previously that Japanese verbs had several base forms - usually distinguished by one vowel - which were then agglutinated with other things to form complex verb forms. I won't describe them again, as I use different names for the ones in my language, which might result in confusion. In my language, there are at least five different base forms of each verb: neutral, conclusive, attributive, participial, instantiative, and conjunctive (note that these names are not final, and I'm open to suggestions).
The conclusive form is the same as the Japanese conclusive: it's the main verb of the last clause in a sentence; it indicates the end of the sentence, and often has a number of suffixes indicating various details about the sentence. The attributive form is the same as one of the two uses of the Japanese attributive: it's the verb of a relative clause; adjectives are attached to nouns by forming relative clauses (e.g. "cat that is fat" vs. "fat cat"). The participial form resembles the second use of the Japanese attributive form: it is a noun referring to the act named by the verb (essentially an English gerund or participle, as in "watching FLCL makes me want to kill people"). The instantiative is unique to my language, and refers to an instance of the verb's action; for example, "a run" would be an instance of the verb "run". The conjunctive is similar to the Japanese -te form (and also includes the Japanese conjunctive base); specifically, it is used in verbs not in the last clause of a sentence (I'll come back to that). Finally, the neutral form is used in agglutination, and has something of a flexible, context-dependent meaning.
So, how exactly does this framework allow the grand unification? Let's look at an example of the specific meanings of the different bases for each word type (substantive, attribute, and action). Although I should note that not every base is necessary to unify the three; some are simply part of the bigger picture for the language.
For the substantive "human":
Conclusive form: "is [a] human"
Attributive form: "who is [a] human"
Participial: "being human"
Conjunctive: "is [a] human, and..."
For the attribute "fat":
Conclusive form: "is fat"
Attributive form: "who is fat"/"fat"
Participial form: "being fat"
Instantiative form: "fat thing/person"
Conjunctive form: "is fat, and..."
For the action "travel":
Conclusive form: "travel"
Attributive form: "who travels"
Participial form: "traveling"
Instantiative form: "journey"
Conjunctive form: "travel, and..."
Thus we are able to use identical conjugation for each type of word, treating the first two as stative verbs and the last as an active verb, in an elegant unified system. The real key to this, I think, was the separation of participial and instantiative forms. Note that not all actions have an instantiative form; it only exists where it makes sense: where something is produced or performed.
Now that I've explained how the unification works, there's just one more loose end to tie up: the meaning of the conjunctive form. This form is somewhat foreign to English speakers, because English only works this way in one of the circumstances this language uses it for (specifically, conjunction - e.g. "Murasaki is seven years old and [is] surprisingly well-spoken").
In English, when we have multiple clauses in a sentence that are related in a particular way, they are generally joined by some linker word that carries information about the relationship between the clauses; furthermore, the verbs in all clauses are conjugated normally. In Japanese, all non-main clauses are simply joined, often without any indication of what the relationship is (for matters of time, this is not that unusual; many languages lack such words); as well, the verbs in all but the main clause are deficient - they lack various things like tense, mood, politeness auxiliaries, etc. This is a matter of economy; all that stuff they stick on the verb at the end of the sentence can be rather lengthy. Thus it uses a generic verb form which in some ways resembles the -ing form of English verbs; this form indicates a conjunctive relationship between sentences (note that the literal conjunctive, as in the example a bit above, is actually indicated with a separate form in Japanese, appropriately known as the "conjunctive form/base"; what I've done is merged the two uses).
Here are some examples of things that would use this conjunctive form in Japanese. The first version is how it would be said in Japanese (note that I'm conjugating all verbs here, even though only the last one would be conjugated in Japanese); the second sentences shows how we would typically say the same thing in English.
Simultaneity: "I looked at manga and she looked at novels"/"I looked at manga while/as she looked at novels"
Coincidence: "I went shopping and ran into a friend"/"I ran into a friend when I went shopping"
Sequence: "I got a haircut, [and] went to the bank, and went to the supermarket"/"I got a haircut, went to the bank, [and] then went to the supermarket"
Consequence: "I overslept and was late for class"/"I was late for class because I overslept"
So that's all the conjunctive form is. On an interesting random note, you might notice that in none of those examples does the first version sound unnatural, and might very well be used by native English speakers in addition to the more precise second versions (though of course it would have sounded extremely strange if I had only conjugated the last verb, like Japanese does). This indicates that even in English this kind of vagueness is used; and for that matter, there are ways of indicating some of those relationships explicitly in Japanese, as well - they just aren't always used.