I am not referring to could as a past tense of can
What is the difference between the following sentences?
You should do it.
You could do it.
closed as general reference by MετάEd, Daniel, tchrist, Matt Эллен♦, JSBձոգչ Dec 4 '12 at 19:47
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The short answer is should implies either moral stricture or recommendation (it is desirable that you do it, either morally, or for your personal benefit). You should not swear. You should eat regularly.
The could form normally means you're being informed (or reminded) it is possible for you to do it, without necessarily implying anything about whether the speaker cares what you do, or whether it's beneficial to anyone. You could have banana flavour. You could be called up for jury service.
However, there is a standard 'idiomatic' usage wherein You could do it means exactly the same as You should do it.
Some would say that in that idiomatic usage, the word could actually amplifies the command (or criticism, for failing to have already done something). Using could in this way often implies a degree of exasperation on the part of the speaker; often meaning that the person being addressed is simply lazy (because he hasn't done whatever is being spoken of).
LATER: Here's one context where they don't mean the same. Suppose your car won't start, and a friend is standing next to you while you have the bonnet up trying to figure out what to do.
You should clean the spark plug leads implies that your friend thinks it's quite likely doing this will fix your problem, whereas
You could top up the oil implies your friend doesn't really know if that will do any good, but he thinks it might (and implies that he's probably not a motor mechanic!)
"You should do it" means that it would be to your advantage if you do it.
"You could do it" means that you are able to do it, or that you may or may not do it but that the choice is yours and there is no advantage either way.
Should is used to indicate obligation, duty, or correctness, typically when criticizing someone's action; it also used to give advices.
Could is used to express possibilities.
Could is the simple past tense of can. Can implies possibility.
Should is the simple past tense of shall. Shall implies obligation or compulsion, arising either from moral duty or simple expediency. This verb contrasts with will (and would, its simple past), which expresses desire or purpose, but without certain intent or outcome.
Each of these words is also used to add a sense of conditionality or something like the subjunctive found in the romance languages but now largely defunct in modern American English (only affecting conjugation in the 3rd person singular).
So could, ultimately, expresses a possibility, perhaps merely conditional. Should expresses an obligation but with a somewhat softened effect compared with shall, which is also largely archaic in modern American English.
Presuming each describes a present scenario:
You should do it, means "You have some degree of compulsion to do it, arising from a duty, obligation, or best interest." People often speak this way meaning only, "I think it would be best for you," and people are sometimes irked to be spoken to so.
You could do it, means "You have the ability to do it," and might also carry the sense that there are contrary reasons for not doing it.
As ways of expressing the opinion that one's listener or reader should do it, the first is stronger than the second, and stops just short of being a command. The second, by contrast, states only the possibility, and pulls back even to the point of being merely an observation.