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Given:

Proof-of-concept technologies, although important, are less valuable than they would be if they were supported by careful experiments that identify key attributes of the design or principles that span applications.

Is the sentence above logically equivalent to

If proof-of-concept technologies, although important, were supported by careful experiments that identify key attributes of the design or principles that span applications, then proof-of-concept technologies would be more valuable.

As well as its contrapositive,

If proof of concept technologies,although important, were less valuable, then proof of concept technologies were not supported by careful experiments that identify key attributes of the design or principles that span applications.

??

closed as off-topic by Jason Bassford, Chappo, Lambie, JJJ, Phil Sweet Jun 19 at 1:33

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  • In the contrapositive, technologies were not supported should be technologies would not be supported. Other than that, they're correct both logically and grammatically. – John Lawler Jun 15 at 21:20
  • On the most natural reading (2) is not logically equivalent to (1), because you have moved although important inside the if clause - hence (1) asserts that proof-of-concept technologies are important but (2) does not. You can read it as a suppletive element outside the if clause though. (1) is not equivalent to / does not imply (3) any more than my house would be more valuable if it had a swimming pool implies if my house was more valuable it would have a swimming pool. IOW, what was a sufficient condition in (1) has become a necessary condition in (3). – Minty Jun 16 at 1:14
  • "Questions about English without research, although important, are less valuable than they would be if supported by research." Answer: No statement without "if" can be logically equivalent to ones with "if". And am sure that is true in your mother tongue as well. So please be more careful in posting your questions. – Lambie Jun 17 at 21:01
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Your contrapositive is incomprehensible, and the other two examples, though just about comprehensible, require the reader to do far more work than you can reasonably expect.

Abandon these sentences and think how you would explain what you mean if you forbidden to use any words with more than three syllables.

I think that you mean to say "Proof-of-concept is OK as far as it goes, but to be of real value it is necessary to show how the concept could be applied in practice".

-1

You ask a question about logical implications rather than grammar. Perhaps logic us a sort of grammar, though, the grammar of thought. So I shall respond first about the logic of what the sentence is saying. I shall take it in chunks, not always in the same order as that in which the sentence you are asking about is written.

  1. ..., although important, ...

The word although is concessive. It is equivalent to "even if". So it is saying that what follows in some way contradicts what you would expect, granted that the writer agrees that it is important. So Proof-of-concept technologies are not as important as they might be (under, presumably, certain conditions). So the use of although serves in the sentence as a sign post, warning us that what we have just read is about to be contradicted or undermined in some way. We already know that we are going to be told that the value of these technologies are in some part deficient. It is a powerful device.

So what are those conditions said to be?

  1. They would be more valuable if "they were supported by careful experiments that identify key attributes or principles that span applications" (NB **I am using angled **

This is a straightforward remote conditional, with modal verbs. In logic, we are used to seeing the relationship put the other way round:

2a If they were supported by careful experiments, <then> they would be more valuable.

It is a straight instance of straight entailment: "P entails Q" (where P and Q are statements), therefore if we know P is true, then we are allowed to assume Q is also true. This move in logic is known as modus ponens. But a second entailment also follows. If Q is false, then P must be false. And this modus tollendi. So if careful supporting experiments are not ** carried out, these technologies are **not important . This move from 'if P then Q' to if not-Q then not-P used to be called by the Latin term modus tolle

And here is the rub. I turns out the be necessary to supply the bits in angled brackets to make the syllogism work. These are, nevertheless nothing more than clarifying insertions.

This writer, however, has chosen to write the statement in reverse, as it were. He says that the proof-of-concept technologies

are less valuable than they could be if they were supported by careful experiments etc...

So, by modus tollens,

If these technologies are not supported by careful experiments, then they are not less valuable than they could be.

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