Peace all,
I wanted to comment on the example given about a day being from sunrise to sunset and the rebuttal. Just sharing my thoughts inspired by the example.
When we say the word "day," we need to be sure that both the sender and receiver of the information agree on the definition of the word "day"... once that agreement has been made, then the description about what a day is can be determined as fact or not.
Granted you do not know if anyone is experiencing what you are experiencing exactly, but when I point at a thing and tell you this is a "bottle" for the sake of communication you will agree even if you call it something else. That way any time you hear me say "bottle," you will call up the image of the thing I pointed to, i don't know if you see the bottle as i do, but when i say bottle, you know the thing i am referring to. This is how we all learn language no?
Back to the example. If day is defined as from sunrise to sunset, and this is what has been agreed upon for the English language to represent the actual perceivable event of the sun rising and setting, then it is a fact that a "day" is sunrise till sunset. If someone come along and says a day is 598948539 years, then clearly he is not using the word to refer to the even that i am talking about when i say day... thus, clarification on my part would be made as to what I call day.
Math and Science use languages to communicate observable and experienced events. Without agreeing on the language used in math or science or physics, etc... there would be no way to verbally communicate mathematical principles.
Given this is written forum, words are the dominant means of communicating (aside form pics and vids), so I would say that once defintions have been decided upon, then we can go into dealing with facts. You understand this sentence due to the agreed meaning of the words (as in the English language) I am using to explain my point. To verify that you understand you can ask questions to be sure that we agree on the definition and context of my words...
This is why gestalts like periodic tables and dictionaries are created... and the efficiency of these gestalts are tested everyday in conversation and chemical experiments.
I truly hope that i delivered my message across clearly...?