@user170039: I don't agree with that answer.

From my point of view, it is flatly wrong.

Just because modern logicians have chosen to use a certain convention does not make it a necessity.

What you say is correct of course, but not relevant to the question, which is about the reason behind the design decisions of formal systems.

> Why is it that a conditional (or biconditional) sign is used instead to show a relation between propositions.

> any insight into the philosophy guiding the semantics of logical languages would be appreciated.

In other words, it is a question in NL (natural language). So the answer you linked to is wrong, while Rob's is both technically correct and also correct in practice. Most modern mainstream programming languages use the same equality for both booleans as well as other objects!

@user170039: There is however a good reason to treat propositions as strings separately from their truth values, namely when the logic is not classical. But similarly one has to think carefully what one means by "t=u" where "t" and "u" are terms. If the logic is not classical, this too is in general no different from a judgement about two terms (which are strings). If we favour using "=" here, it is because of pragmatic reasons and not because it has got to do with the strings being equal.

@user170039: Lol I didn't see what you wrote.

Did you want to say anything?

@user170039: Yup I just got your message.

I was trying to say that the question (even the one in the title) was about why we choose certain syntax.

Not about how it is in some particular textbook's definition of first-order logic.

In most textbooks, your answer is certainly correct, because simply by fiat the system is defined so that "t = u" is only meaningful when "t" and "u" are terms.

But precisely, it is by fiat, and that question is clearly (to me at least) asking about the reason for the fiat.

Yea.. it's not really important whether you understood the question or the answer, nor whether you agree with me. Haha!

Unless you're interested in the philosophy of mathematics or something like that.

Ah.

No wonder.

Sure

I actually am very interested in discussing and finding out what other people think.

But few people on Math SE want to talk philosophy of mathematics. =(

Do you have any particular questions in mind?

(at least as far as I can recall among those who answer frequently)

Ah I see.

Well I'm a realist, so I'm always looking to see how various formal systems capture or do not capture real world phenomena.

Sure.

Talk to you again!