This is equivocating between two distinct and separate definitions of "private." You are mixing these homonyms.
In the sense you're using in the quote I pulled from your comment, it means intended for or restricted to the use of a particular person, group, or class, but in the sense that it is used in Virtual Private Network, it means something else, namely not known or intended to be known publicly; secret.
> in the sense that it is used in Virtual Private Network, it means something else, namely not known or intended to be known publicly; secret.
Great. Present some evidence or stop wasting time. My evidence that it actually does not mean that is RFC2547.
RFC2547 does not support your claim... anywhere.
I'll use Webster's definitions for my evidence. Also, every explanation of what VPN is everywhere on the Internet speaks of anonymity and privacy. This means the P in VPN could only mean free from public attention, secret and NOT for the use of a particular person or group, as in private parking.
A security-conscious VPN user might want to ensure that some or all
of the packets which traverse the backbone are authenticated and/or
encrypted.
a private computer network that functions over a public network
It's a happy coincidence that you can sell a "Virtual Private Network" to endusers as a privacy-enhancing machination, given that it already contains the word "Private", even if that was meant as in private parking space, not private conversation.
One can have a private parking spot without privacy, though. Or a private pilot license.
> any transfer of data between the VPN nodes will be kept private from the Internet at large, thus the transfer is in privacy
Not if your VPN is not encrypted, which exists, although it isn't very common anymore, for obvious reasons.
The IP address "10.1.1.1" is still part of IANA's private IP address space, no matter whether it is transported in a way (say using an unecrypted tunnel over the public Internet) that provides privacy or not.