Yep, Ludwig, I agree - it does contain information.

Perhaps we could say that all information has to be the truth.

Because anything that is not true has to be misinformation!

I'm sensing from the lack of response to my last two comments that:

THE TRUTH CAN HURT.

Dear Ludwig,

What do you know that you didn't know before after hearing that statement? It contains no information that I can see, but it is certainly true.

"What is truth?" is a question which implies epistemology. Truth is a word with many meanings. The questioner could have made a statement containing the word, truth, and started a discussion of its meaning in the context of that particular statement, but he didn't.

"Through a point not on a line one and only one line can be drawn not intersecting the given line."

"Through a point not on a line no lines can be drawn not intersecting the given line."

"Through a point not on a line an infinite number of lines can be drawn not intersecting the given line."

The above statements are contradictory as they are. However, there are all axiomatic embedded in the appropriate logical system. The first statement applies to Euclidean geometry, the second to spherical geometry and the third to hyperbolic geometry.

Tautologies or equivalence statements are absolute truths.

That answers the original question.

<< What do you know that you didn't know before after hearing that statement? It contains no information that I can see >>

Ah but it does contain a lot of information, david f.

It tells me that this person could be somewhat mentally or intellectually challenged! ( :>)

It tells me that they had uttered a statement that contains eight words and thirty letters!

It tells me the sex of the speaker, the presence or absence of an accent, and provides information about age and demeanour. It contains all sorts of information, not pertaining to the meaning of the statement!

Now, if we knew whether the lines in question are straight or not, and whether they are of finite lengths or not, and whether we are operating in two or three dimensions, we would know which one of your three options is the truth… in all forms of geometry, would we not?

For example, if the line was straight and of infinite length, then you could only draw one straight line of infinite length that would not intersect it… if you were operating in two dimensions only. In three dimensions, you’d have an infinite number of possible lines.

So, once you have defined the parameters, you can assert hard and fast truths. Truth is thus not a word with many meanings. It has one meaning. And it can be asserted once we are confident that we know exactly what the parameters and definitions are.

This is fun.

Surely David's grandfather's statement contains information without any absolute truths.

If he were an astronaut on the moon which has zero precipitation and therefore no possibility of rain then his comment would be nonsense, which would in turn possibly convey information about his state of mind or sense of humour. Therefore we assume he is on the surface of a planet with the possibility of rain, probably Earth.

If instead he said “Today we will either suffer catastrophic decompression from a meteor strike or we won't” then a quite different set of information is being conveyed. It is just our familiarisation with the assumptions implicit in the statement about rain that lets us think no information is being delivered.

I know this cheats a little but as an aside did any of you know before now that David's grandfather was capable of speech, or that he was still alive when David could converse with him?

Doesn't quantum physics tell us that ultimately knowledge of absolute truths are the luxury of the gods or any entity capable of seeing the future.

Even our mathematics are just a way for our species to describe the rules of the universe. Who knows how an intelligent alien race might approach the science but one imagines it would look very different to ours.