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The Nature of Truth
#10
(04-18-2017, 06:00 PM)Someone else Wrote:  While I agree with the overall statement I would like to make a few nitpicks:
  • The cookie and court example are actually kind of similar: The term commonly used is "proof beyond a reasonable doubt", which notes that it is not definitively true. The term used for the grin on your brother's face and wearing a red shirt is "evidence" to support a claim. A court will typically use these terms correctly, your mother (unless she is a lawyer/judge) probably won't.
  • In science the term "proof" is rarely ever used. Scientists generally prefer (as you noted) "evidence", or typically "sufficient evidence" to "support a given theory". You can't even really prove something wrong because there is always uncertainty in your measurements, so you can find evidence against it.
  • For mathematics (including formal logic) a proof is a set of statements that, given a a set of assumptions, tries to convince others of a conclusion. Those assumptions don't necessarily have to be axioms (close to "the metal") but they are simply assumptions where, if you agree with them, you have to accept the conclusion. The funny thing to note here is the statements in the middle are never necessary for the proof to be sound, and they are essentially like comments in programming, in that they help other people follow along. Here the proof is absolutely correct, if the assumptions are.
I did use the term "proof" rather loosely in the examples. I'm aware evidence is preferable, but I do hear "experimental proof" being tossed more often (also, "experimental proof" on google has 93,700,000 results, while "experimental evidence" has 12,200,000). "Sufficient evidence" I hear a lot in a law court setting too.

I like the definition of proof that you gave. In essence, a theorem you give being contained in the system makes is all needed to make it valid with respect to the system, but the middle statements are necessary to convince a reader that it is so.
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Messages In This Thread
The Nature of Truth - by LutiChris - 04-16-2017, 04:47 PM
RE: The Nature of Truth - by MangaD - 04-16-2017, 07:48 PM
RE: The Nature of Truth - by LutiChris - 04-16-2017, 08:02 PM
RE: The Nature of Truth - by Sevendogs - 04-17-2017, 12:32 AM
RE: The Nature of Truth - by Marko - 04-17-2017, 08:51 AM
RE: The Nature of Truth - by LutiChris - 04-17-2017, 10:05 PM
RE: The Nature of Truth - by A-Man - 04-17-2017, 11:55 PM
RE: The Nature of Truth - by Som1Lse - 04-18-2017, 06:00 PM
RE: The Nature of Truth - by A-Man - 04-19-2017, 03:04 AM
RE: The Nature of Truth - by rewlf2 - 04-19-2017, 01:13 AM



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