Is "+" a two-place predicate?

Question

In Volume I of Fundamentals of Mathematics, Edited by H. Behnke, F. Bachmann, K. Fladt, W. Süss and H. Kunle, it is stated that "[T]he function sign '+' is a two-place predicate".

To me, a predicate is a statement which takes one or more arguments (subjects) and evaluates to either true or false. The authors have been careful not to restrict the discussion to so-called "classical logic". So, perhaps there is some alternate mathematical universe in which "1+1" has a truth value. But I know of none.

I don't believe the authors give a concrete definition of the term predicate, so I'm kind of at a loss for a means of assessing the validity or reliability of this assertion.

The principal author of the chapter in question is Hans Hermes, so I am not wont to blithely dismiss its content.

Is it generally accepted that a function symbol such as "+" is a predicate?

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Edit to add: in computer programming "1+1" often does have a truth value. Namely "true". But in that context "0+0" is false.

Answer 1

You are right; it is not usual to call + a predicate.

Either the book you're quoting is using very nonstandard terminology, or it's a typo.

Answer 2

Suppose that + is a predicate. Then it takes two truth values and returns a truth value (note that I didn't say true or false, I'm NOT assuming conventional two-valued logic). Now, the context consists of conventional arithmetic, so let's suppose the natural numbers instead of the integers (the integers end up worse to try to make '+' into a predicate). It sounds reasonable to me to say that 0 could represent the most false proposition. But, since there does not exist a greatest natural number, every single instance of +(x, y) yields a truth value which is less than some other truth value. Consequently, there is no greatest truth value. That wholly flies in the face of conventional multi-valued and infinite-valued logic where there exists a greatest truth value, and at least sometimes or maybe always it gets supposed there exists a greatest truth value in classical logic also.

So, at the very least, I don't see how someone could plausibly maintain '+' as a predicate. It either leads to a paradox of there not existing a greatest truth value and there existing a greatest truth value, or it needs such a radical concept of logic that it seems difficult to see how it could work.