"1 + 1 = 2", as has been pointed out to you before in this thread, is a matter of arbitrary choice of fundamental assumptions of a number system. Most of my working day, I assume that "1 + 1 = 10".
are made and accepted by many in this forum as if they were to be granted equal certitude; as if they were both a "matter of fact."
If you want to examine what science thinks, you must ask what scientists think, and critique science's vocabulary--not what civilians think, using sloppy civilian word usage. If you wish to use the word "fact" interchangably with "proved", I can't stop you, but I also don't need to defend science over this shortcoming. Scienctists only assign levels of confidence to theories, and any scientist who is still breathing air in this century knows that that number has been pretty heavily subject to revision and tuning over the last 2 centuries. As is common with scientific theories.
Some, including me, would argue that "1 + 1 = 2" isn't as reliable a "fact", as, say, your perception that the table in your living room exists when you are touching it. "1 + 1 = 2" is only as reliable as the proof system in which you proved it, and only assuming that you have made an appropriate mapping between the math and the field of discourse to which you wish to apply it, and, as I've pointed out, Russell and Whitehead's proof stood up for 50 years before anyone noticed it was a false proof. Can you show me the proof upon which rests your assurance that the proof system that proved 1 + 1 = 2 is itself reliable beyond question? You take proof systems as reliable, based on confidence in their repeated success, I aver that your confidence in 1 + 1 = 2 is high because of repeated observation confirmation, not because there is some magic barrier between "proof", or "fact" and "highly reliable conjecture". The scientific theory, likewise, that the earth is 4.5 billion years old is based on repeated observational confirmation of a somewhat more sophisticated, and therefore, somewhat less reliable nature. However, scientists regard that level of confidence as highly likely, and the level of reliability one assigns to a conjecture in order to be willing to call it a "fact" in casual conversation is not established by government or by AAAS committee.
If you want to say science has no business dealing in matters of fact or proof; no business seeking out, knowing, and teaching truths, then you and your hearers are subject to universe of fantasy no more grounded in science than any other source of presumed knowledge. Anything goes where fact and conjecture have an equal footing.
At bottom, conjecture is all you have. Proof is just a mathematical game. Contrary to your absurd conjecture, this does not paralyze our brains, we go right on ahead making distinctions and getting useful work done without any need of absolute certainty in order to do so. Blovating on, into paragraph after paragraph with an increasingly patronizing air toward scientists, does not improve your argument, it just makes you annoying.
At bottom, conjecture is all anyone has. My conjecture is not that conjecture paralyzes brains, but that it logically results in an "anything goes" set of postulations. Science ought to be able to operate with as much, but it is indeed strange to see science occasionally omit altogether any propsitions that might issue forth from a text several millennia old.
It is common for most people who do not live in a vaccuum to understand that some facets of objective reality are more consistent, persistent, and verifiable than others. Science too often asserts certitude when it is lacking. Bias is inherently blind to itself.
It does the heart good to see you point out that what most people call a "fact," namely "1 + 1 = 2," contains a host of assumptions behind the scenes, or denotes a set of conventions that may be outside of standard practice, of which most people are typically unaware. I tend to think lower education classes should cut to the chase, present things more easily ascertained by reason, and leave the semantic monkeyshines to the perfessers.
It also does the heart good to see certain scientists, when asked what they think about the bigger picture, to attribute an orderly universe to intelligent design.
When I am wearing my computer scientist hat, 1 + 1 = 0 usually.
When I am wearing my numerical analyst hat, 1 + 1 generally bigger than 1 but smaller than 4; depending on the size of 1.