Can "If" mean "since"?

Question

Here's my example: "If we all agree on the basic terms, can we do a proper agreement next week."
Can this be construed (in the proper context) as: "Since we all agree, can we etc."?
The entry for "if" in the Oxford English Dictionary (online edition) begins with:

I. Introducing a clause of condition or supposition (the protasis of a conditional sentence): On condition that; given or granted that; in (the) case that; supposing that; on the supposition that. and continues: 1. With the conditional clause or protasis in the indicative. The indicative after if implies that the speaker expresses no adverse opinion as to the truth of the statement in the clause; it is consistent with his acceptance of it.

The entry even notes that in some cases the indicative is preferred.
The Random House Dictionary similarly opens with the definition:

In case that; granting or supposing that; on condition that.

On the other hand, in logical or Boolean syntax, if is always a conditional.
But is that necessarily the case in idiomatic or everyday usage? Some might argue that there is a supposition missing in the bare if, but that is precisely my question: can if be understood as assuming the fulfilled conditional, such as in since?

TaliesinMerlin · Accepted Answer

Sure, in the sense that if can mean given that (OED entry above), if can point to a condition presently being met, in addition to a condition that might be met.
To show this, I had a little fun in the Hansard corpus for British Parliament finding examples of "if we all agree" that are based on situations where the fact isn't under dispute or hypothetical, and where one could perhaps use since without misconstruing the statement. I found a few.

Mr: Sydney Silverman: Can my right hon: Friend say why, if we all agree that these men are entitled to their pay during periods of voluntary training, the State should not pay? (9 Nov. 1948)

Mr: Levy (Elland) A good deal of what the last speaker has said is perfectly true, and I agree with him, but in the few observations I wish to make I wish to be helpful and not carpingly critical: If we all agree that the basis of Production--; and after all, this war will be won or lost by Production--; is coal, why is it that a commodity with which this country has been endowed by nature in superabundance should be the shortest of the lot? (24 March 1942)

All of these statements go beyond the use of if as a conditional because there is some presumption on the part of the speaker that the agreement is actual and not merely conditional or hypothetical. Choosing if rather than since may come across as more conciliatory or circumspect, while still meaning given that.
More obvious examples exist than the one you've thought up. Here is South Park season 3 episode 12, where a character observes a statement of fact with if rather than since:

HEY, WAIT A MINUTE. IF YOU'RE OVER THERE,THEN HOW CAN YOU BE OVER HERE ? UNLESS YOU'RE ACTUALLY A--. ( Fieldy and Jonathan ) P-P-PIRATE GHOST

Fieldy sees Jonathan. He knows where Jonathan is. Nonetheless, he uses if.

Can "If" mean "since"?

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