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Giving examples if possible, what's the difference between e.g. もっと大きい and より大きい to mean "more (than)"/"bigger (than)"? In what situations would you use もっと over より and vice versa?
For instance, why or why not would the two be interchangeable in the following sentences (example sentences from Space ALC):
危険性がより大きい
"at greater risk"それ以上である。それはもっと大きい夢である。
"It is more than that; it is a bigger dream."
I'm not a native speaker, but like Chocolate says, I think もっと simply feels more "common language", whereas より feels more fancy.
To ilustrate the range of difference, let's take your first example:
危険性がより大きい
"at greater risk"
Now, if you used もっと, I think this translation...
危険性がもっと大きい
"at (a) bigger risk"
...accurately illustrates the kind of difference between the two words. Not a huge difference, but "greater" kind of sounds more eloquent than "bigger".
I learned the word より in combination with のほう, and of course later found out that neither requires the presence of the other. However, when using もっと, a comparative meaning is implied without the use of another word. In this way, perhaps the use of より implies more of a comparative meaning than もっと(in that it sometimes makes me think of のほう, even if it is not present) . In the second example provided by the OP, when replacing the もっと with より, I think a more comparative meaning is implied thusly:
それ以上である。それはもっと大きい夢である。 "It is more than that; it is a bigger dream."
それ以上です。それより大きい夢です。 "It is more than that; it is a bigger dream (than that)."
This is just a hunch, however, and I am unsure if the second example is even grammatically correct. I removed the は and changed the verbs to make it more colloquial.
So I guess another question can be whether there is a difference between these two sentences (I wonder which is more colloquial):
それはもっと大きい夢です。
それより大きい夢です。
大きな was more natural than 大きい, but maybe that context or the ～である rather than ～です on the end makes a difference?
Conclusion of a discussion I had with ento about the restriction of usage of もっと:
Consider:
A: XとY、どちらのほうが安いですか
B: Xのほうが、Yよりもっと安いです。
もっと sounds strange in this case because it implies that Y actually is "安い" to a degree. B is comparing the cheapness of the two, when A is just comparing their prices.
Comparing the cheapness of the two is different from comparing their prices. Even though B's response satisfies what A asks, but at the same time, B slipped in a subjective judgment that X and Y are cheap.
That is to say that by using もっと, it reveals that B has a presupposition that both items are cheap, which is not necessarily the case, nor has been implied by A. So the introduction of this irrelevant presupposition makes the the use of もっと strange.
So for もっと to be used, there should be a precedent for which the "whatever-ness" you wish to express has already been established, and you wish to express more of it.
To answer "Why or why not would the two be interchangeable?", I would say changing them would change the perception of circumstances that the sentence is in:
If the sentence is 危険性がもっと大きい。, もっと would create the perception that it is already 危険性が大きい and you are expressing even more.
For それはもっと大きい夢である。 It creates the perception that the 夢 was already 大きい.
