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"are you really saying that there is no such thing as "physical proof?" For example, it is not "proof" of my claim that a pebble is under a certain cup, to lift up the cup to show the pebble's presence?

Yes. All you have is evidence, not proof. Proof is restricted to math.

"what do you mean by "math," in your statement?"

Math is any logical construction regarding rational relationships of representations. The only reality to math is that it exists only as a mental construct. As such, it is dependent on the physical machinery of mind to exist.

"...are you really saying that math has no connection with reality? Are you really making such a claim?"

Any application of math to reality depends on the existence of evidence that the application is indeed valid.

"thus, the pebble under the cup, even if I see and touch it, has not been "proved" to exist under the cup?"

That's correct. The senses have only determined evidence. The evidence is fact, not proof.

"Suppose I state a negative proposition, "there is no pebble under the cup." I can prove that negative proposition, in a "real" situation, by simply lifting the cup to see if there is in fact no pebble there."

You can only make a true atatement once hte evidence has been uncovered. The true statement can not be made before the cup's lifted.