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This is a very deep question and I ask you to ponder at it for a while. We know from the grammar that some modal verbs are the past form of another:

PRESENT            PAST

will               would

shall              should

Question: If you had never been taught this table, and someone asked you now about their relation to each other, would you feel that should is the past of shall and would is the past of will?

closed as not constructive by user19148, Andrew Leach, tchrist, StoneyB, choster Jun 24 '13 at 4:23

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  • It feels more like a conditional than a past. 'should' really doesn't feel like it is expressing time at all but rather an alternative that might or might not happen. – Mitch Jun 23 '13 at 21:41
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    I don't think I ever have been 'taught this table', and I usually look at modals (like all other lexemes/words/polysemes/homonyms) primarily according to their distribution (the constructions in which they appear). And I didn't realise we had the grammar. Who wrote it? And do we shoot those with conflicting analyses? – Edwin Ashworth Jun 23 '13 at 22:15
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    First, we would normally say "grammar", not "the grammar", in the sentence you used. Secondly, there is no book or organisation that specifies "the grammar" or even English grammar - it follows usage and it changes over time. – TrevorD Jun 23 '13 at 22:52
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    Certainly Today he will go to the store because yesterday he said that he would go the store today is more common the construction than Today I shall go to the store because yesterday I said that I should go to the store today, but both are perfectly grammatical. – tchrist Jun 23 '13 at 22:56
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    This question, though interesting, is far too deep to be considered here. It does not ask about a linguistic matter, or even about our (Off Topic) feelings about a linguistic matter, but about our feelings about a linguistic matter under hypothetical circumstances which I am confident are counterfactual for everybody who answers on this site. That's not English, it's an exercise in creative imagination. NARQ. – StoneyB Jun 23 '13 at 23:15
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I'm not entirely sure I follow you. It would be helpful if you explained what kind of contradiction or issue you were trying to gather evidence for. My impression is that you see this table or maybe the concept that such present/future word relationships exist in English as inherently flawed.

It's hard for me to imagine the word will that means "going to" as a present tense verb. Putting that aside, the table you propose works in some contexts.

"If you show up, I will perform on stage." -> "If you had showed up, I would have performed on stage."

"I shall be there." -> "I should have been there."

There are also a whole lot of sentences for will/would, etc. for which this kind past/future translation doesn't work, and that's because English is a language where words and word phrases have multiple meanings. The table (I've never seen such a table, but...) works with some form of those words.

This is somewhat equivalent to pointing out "Light is supposed to be the opposite of heavy, but light is a noun, not an adjective!"

If you're suggesting that teaching such a table has no value: That's not a wrong opinion, but it's not the purpose of this site.

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