Agreed.
In the end, the final arbiter of truth is what's out there. Even true belief such as the belief that the Higgs particle could be found if a sufficiently powerful collider were built isn't knowledge until it is confirmed empirically.
Incidentally, my working definitions for truth, fact, and knowledge are these: Truth is the quality facts possess, facts being linguistic strings that accurately map a portion of the world. Knowledge is the collection of facts. This definition ignores a priori and analytic truth, which can also be called fact and an element of knowledge, but appears to be discovered without appealing to the external world. I'm not sure that that is correct, however. I'm not sure that we could have come up with 2+2=4 with experience of combining pairs of pairs into tetrads
This discussion reminds me of a poster who calls himself a rationalist, and who has said, "Evidence is pointless,” “Evidentialism is false,” and “Empiricism is a philosophical dead end." He seems well educated and articulate, but he has somehow divorced himself from physical reality in his musings.
And surprisingly, I have seen this once before on another discussion site. The poster there has said, "Studies are not science. Neither is an experiment," "Facts need not even refer to anything real or truthful in any way," "You cannot confirm, prove, or make more legitimate any theory using supporting evidence," and "Science does not treat any observation as reliable. It doesn't use them."
Strange phenomenon. Both of these people are theists, but almost never discuss their religious beliefs. There posting is all more or less an assault on science and empiricism rather than a defense of any alternative. Both have been told that they are empiricists whether they realize it or not, a fact they demonstrate when they look before crossing the street.
This second guy would surely have accused you of committing an
argument of the stone fallacy:
"The name of this fallacy is derived from a famous incident in which Dr. Samuel Johnson claimed to disprove Bishop Berkeley's immaterialist philosophy (that there are no material objects, only minds and ideas in those minds) by kicking a large stone and asserting, 'I refute it thus.' "
The fallacy there is that Berkeley is arguing about the fundamental nature of the stone beyond perception, which is being refuted by perception. Your discussion is about whether something that can be experienced, like being able to walk an infinite number finite distances in a finite time is impossible because a mathematical illusion suggests that it should be.