Both arise and rise are irregular verbs.
When an opportunity, problem, or new state of affairs arises, it begins to exist. This is the most common meaning of arise.
He promised to help Rufus if the occasion arose.
A serious problem has arisen.
The feeling of hope arose from the people.
When something rises, it moves upwards.
The sun rises in the morning.
Clouds of birds rose from the tree-tops.
When someone who is sitting rises, they stand up. You can also use rise to say that someone gets out of bed in the morning.
Cambridge Dictionary also lists rise for "to begin to oppose or fight a bad government or ruler":
The people rose (up) against the oppressor/tyrant/dictator.
Please visit here to see other meanings listed for rise which all are connected with moving upward.
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You can find both words in most of dictionaries. As a physicist I would not use the word "dimension" in a daily life. For me, this is a mathematical term designated to a property of space. The noun "size" refers to geometrical properties of objects that surrounds us. Below are some daily meanings of the noun "dimension" from dictionary.com.
a. measurement in length, width, and thickness.
b. scope; importance: the dimensions of a problem.
Best Answer
Semantically, there is no real difference between the two constructions, and they can be used interchangeably. I agree with you that "should" has become the far more common construction.
Even back to the Old English (and earlier Proto-Germanic), the words carry a nearly identical sense of obligation. As such, I'd be hard pressed to articulate even a minor connotative difference between the two forms in modern usage.