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The folllowing text is taken from a part in a book (reference below) which are about mathematical philosophy.

"... the theorem of classical logic known as the law of excluded middle: for every proposition $P$, the disjunction of $P$ and its negation, $(P ∨ ¬P)$, is true. This law is well motivated in cases where we may be ignorant of the facts of the matter, but where there are facts of the matter. For example, the exact depth of the Mariana Trench in the Pacific Ocean at its deepest point at exactly 12.00 noon GMT on the 1st of January 2011 is, unknown, I take it. But there is a fact of the matter about the depth of this trench at this time. It was, for example, either greater than 11,000 metres or it was not. Contrast this with cases where there is plausibly no fact of the matter. Many philosophers think that future contingent events are good examples of such indeterminacies. Take, for example, the height of the tallest building in the world at 12.00 noon GMT on the 1st of January 2021. According to the line of thought we’re considering here, the height of this building is not merely unknown, the relevant facts about this building’s height are not yet settled. The facts in question will be settled in 2031, but right now there is no fact of the matter about the height of this building. Accordingly, excluded middle is thought to fail here. It is not, for example, true that either this building is taller than 850 metres or not."1

I do not understand what the author means when he writes "This law is well motivated in cases where we may be ignorant of the facts of the matter, but where there are facts of the matter." (I do especially not understand what is meant by the dependent clause). Could you please help me?

1 Colyvan, Mark. (2012). An introduction to the philosophy of mathematics. Cambridge University Press. Pages 7-8.

Note This question has already been asked on MSE, but they kindly referred me to ask this question here instead.

  • In a nutshell, the world is definitely there (the facts): either an apple is red or it is not red, irrespective of our current knowledge of them: we cannot see the apple, and thus we cannot ascertain if it is red or not. – Mauro ALLEGRANZA May 6 '17 at 11:25
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There is a difference between claims being true (or false) and knowing the claim to be true (or false). For example, do you know whether at this very moment I am wearing a red shirt or not? No, you don't. But you do know that either I am wearing a red short or I do not, because one of those two claims has to be the case. That is, we are talking about a matter of fact here: If person A believes that right now I am wearing a red shirt, and person B believes that right now I am not wearing a red ahirt, then exactly one of these two people will be right, and the other one is wrong, even if they and you don not know who is right. So, in this case, we can say that R v ~R is True, even if we don't know whether R is true or not (R of course stands for 'right now I am wearing a red shirt'.)

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