Definition talk:Biconditional

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No, I don't think merging the "iff" page into the "Material Equivalence" page is appropriate.

"Iff" as defined here is merely to indicate that it is a shorthand for "if and only if". It is used in the context of a natural language description of a mathematical concept. We do not want to send the (possibly) casual reader into a great long digression into logic when all we want to do is point out that no, "iff" is not a spelling mistake.

The initial reason for having such a link in the first place was because some misguided well-meaning person started going through replacing instances of "iff" with "if". So as to stop this, I put that page in place saying "iff means if and only if, and if you want to learn more, check out the page on Material Equivalence". Sometimes all you want is a one-line definition.

If I'm over-ruled, so be it. But please do not be swayed by how Wikipedia does it. This is NOT Wikipedia. --prime mover 00:36, 11 March 2011 (CST)

I agree with prime mover on this one. We don't want to make it harder for a novice to follow a proof than it has to be, and for most people a simple page explaining iff means if and only if will make more sense than a page of formal logic and truth tables. And it really isn't that much work to click the link from iff to material equivalence if you want to learn more. --Alec (talk) 01:34, 11 March 2011 (CST)

I agree. --Joe (talk) 10:27, 11 March 2011 (CST)

Good points...perhaps I will revert those edits. JamesMazur2 (talk) 07:31, 11 March 2011 (CST)

Thx James - good man. --prime mover 13:28, 11 March 2011 (CST)

Primitive Symbol?

Both 1996: H. Jerome Keisler: Mathematical Logic and Computability and Givant's book refer to $\iff$ as a primitive symbol. Anyone know why? It seems unnecessary. My intuition is that it's for the same reason that $\implies$ is primitive even though it can be expressed in terms of $\neg$ and $\lor$. But the relationship implied in the latter things is less obvious than the relationship between $\iff$ with $\implies$ and $\land$, so I'm not sure. --GFauxPas 12:34, 15 June 2012 (EDT)

Convenience. As you say, you can dispose of all symbols except $\land$ and $\neg$ if you want. You can go even further and just use Definition:NAND or Definition:NOR if you like.
On the page on Definition:Language of Propositional Logic: "... there is more than one way to define propositional logic as a formal system." And again: "The signs of the alphabet of L0 usually include (but may be a subset of) the following:" etc.
The plan is (in due course) to implement the work of who worked on minimising the axioms of PropLog; all good stuff, but for an accessible approach to the subject, more primitive symbols are to a certain extent better than less. And as we are specifically following (more or less) published accounts of the subject, it is prudent to present the axioms (more or less) like they do. --prime mover 12:52, 15 June 2012 (EDT)