Where did "on the same token" come from?

I have searched high and low, with no success, to find out why people (myself very much included) use the term “on the same token”…as in, “Blah, blah, blah, but on the same token, blah, blah, blah…” Well, I know why we use it, but where the heck did the usage come from? I will be the happiest woman alive, well, for a few minutes at least, if anyone can let me know. Thanks!

It’s by the same token, not on.

Other than that, I’ve got nothing.

“Token” used to mean evidence - in a way it still does. A public transport token, for example, is the evidence that you’ve paid to ride the train. But the sense in which it was used was broader:

My best guess is that “by the same token” might have originally meant “by the same evidence”. However, the phrase itself has a very long history. The OED gives some examples:

Notice Shakespeare, in that last reference, was able to make a pun on the multiple meanings even back in the 17th century!

Token is one of those strange words with lots of almost but not quite the same meanings. One of the meanings of “token” is something that serves as a standard proof or evidence. In fact that’s approximately the meaning used in “fare token”, for example. It’s something that serves as proof that you’ve purchased fare. That usage goes right back to the OT of the Bible where people were forever giving tokens.

So when someone says that something is “by the same token” they simply mean that it’s true by the same standard of evidence or for the same accepted argument. For example “We should be increasing production of chocolate because sales will increase as the weather cools, but by the same token we should be increasing chicken soup production”. “We should invade Iraq because the leader is a ruthless despot, but by the same token we should also invade Burma”.

I’ve also occasionally heard (and more often read) “By that token” which has essentially the same meaning and use. I’ve never heard or seen “on the same token” before.

On preview I see that Atticus has already made almost exactly the same post, with references. But dammit I’ve already typed all this so I’m posting anyway.