I think when you introduce the notion of absolute certainty (which is implied by the words “beyond the shadow of doubt”) we get into more tricky territory.
For example, to use the word ‘fact’ in Krishnamurti’s sense would be to say that there is a war taking place right now in Ukraine. Right? You probably wouldn’t object to that. But if I demand of this fact some kind of absolute certitude - then I run into some clear difficulties. For instance, I have never actually been to Ukraine, so I have to rely on what other people are telling me about what is going on: journalists, civilians, television news, images and reports I see on social media, etc. And it is very likely that not all that I read about or see is completely accurate. Similarly, I do not actually know what is happening in that country right this absolute second, because it is not happening right now directly in front of me.
But the fact remains, as far as I am aware, that there is violence, murder - perhaps even genocide (although this depends on how genocide is definitionally understood) - taking place in Ukraine at the moment. Only a philosopher (such as Descartes, etc) - as a philosopher - would dispute this.
There are, of course, some religious people in India who believe that the world is maya who might dispute this - they would say that the war in Ukraine is just an illusion. (And they probably go and vote for Modi!). ‘There is only Atman’. But that is up to them. Who can tell if that is in fact a fact for them, right?
Now it is interesting that Krishnamurti - following some discussions he had with David Bohm in the 1970s - began to distinguish between fact, reality, actuality, and truth.
Fact is just what we have said it to be - the obvious, conventional facts of the world: what has happened, and what is happening. We don’t know with absolute certitude that the Americans landed on the moon in 1969, but the evidence for those of us who didn’t go there personally is pretty clear (except for conspiracy nuts). So we call it a fact.
Reality - on the other hand - is anything put together by human thought: such as religious dogmas, nationalities, etc. But nature has not been put together by thought, so nature is an actuality.
And truth can only have any meaning when the mind is no longer occupied with reality (i.e. with thought). As Krishnamurti discussed with the Buddhists, only when there is a state of absolute attention does the word ‘truth’ have any meaning. And so truth - if it exists - would be the only possible place to find the absolute certitude you were talking about (because that is what ‘truth’ is by definition).
Clear? Or not clear?
The confusion comes when we take something created by thought - such as a belief - and call it a fact. It is a fact that someone has this belief (say, in Jesus Christ or Krishna), and that this belief gives them a feeling of security (serotonin in the brain, etc). But the belief is a reality not an actuality. - Do you see what I mean?
Similarly with anything created by thought - including the sense we all have (or most of us have) of being a self, a ‘me’, an ‘I’. This sense of being a self is a fact for most of us - but is it merely a reality created by thought (and so not in fact actual)?
This is how I understand it. What is your take on this?