isn't "iff" obscure?

Stream: std4

[Mac Malone]

François G. Dorais said:

That said, .mp and .mpr are pretty obscure for non-logicians

Isn't the term iff (for "if and only if") itself just about as obscure? Personally, I learned the term "iff" well after "modus ponens".

[François G. Dorais]

Mandatory xkcd: Honk! Honk!

[Kevin Buzzard]

@Mac in maths departments we never learn all this modus nonsense at all

[Mac Malone]

@Kevin Buzzard But you do learn iff? That surprises me. How does one learn the conditional and biconditional without the various modus rules?

[Patrick Massot]

Sure we learn iff.

[Mac Malone]

@Patrick Massot Interesting. I would be curious to learn how that gets cover in a pure maths context. Because apparently it is very different from Philosophy/Logic or CS.

[Kevin Buzzard]

We learn iff on day one. I literally teach my undergrads the word in the first maths lecture they ever go to as freshers, in my intro to proofs course.

[Sebastian Ullrich]

Mac, iff is standard math parlance in informal statements, even across various languages

[Patrick Massot]

Of course it is actually spelled ssi.

[Sebastian Ullrich]

It just looks extra funny in English

[Sebastian Ullrich]

Alright, that also looks funny

[Patrick Massot]

How is it in German?

[Mac Malone]

Sebastian Ullrich said:

Mac, iff is standard math parlance in informal statements, even across various languages

What does it mean in informal statements? "iff" / "if and only if" barely made sense to me as the English parallel to the biconditional even after I learned its formalization. I have no clue what it would mean informally.

[Sebastian Ullrich]

Patrick Massot said:

How is it in German?

"gdw (genau dann wenn)", it's boring

[Kyle Miller]

Mac, "P if and only if Q" is merging two sentences: "P if Q" and "P only if Q". If you want, it's "P if, and only if, Q"

But can we finally rename it to NecessaryAndSufficient?

[Mac Malone]

Kyle Miller said:

Mac, "P if and only if Q" is merging two sentences: "P if Q" and "P only if Q". If you want, it's "P if, and only if, Q"

I am aware. I mean that the correspondence between "if" and the material conditional and "only if" and its converse has never struck me as particularly intuitive (English-language-wise). Some of my concerns are well-known; others are more personal.

[Mauricio Collares]

Weirdly, "P => Q" is the "if" part of "P <=> Q" to me, not the "only if" part. I wonder if that's just me.

[Mac Malone]

@Mauricio Collares No, that is the standard interpretation. :rofl:

[Mauricio Collares]

But that's the opposite of Kyle's interpretation

[Mac Malone]

Oh, I forgot that P if Q is Q -> P whereas if P, Q is P -> Q.

[Kyle Miller]

"You can get a good croissant only if you're in France" makes sense to me

[Mac Malone]

@Kyle Miller I think my problem is that, to me, "only if" sounds inherently modal, whereas the formalization is not.

[Mac Malone]

That is, "only if" implies to me that neither of the two sides are currently true and instead talking about a future potential.

[Mac Malone]

In other words, "if you go to France, you can get a good croissant" or "if you want a good croissant, go to France".

[Kyle Miller]

That sort of thinking is exactly what math training beats out of you. There exist ways in which "if" and "only if" are used materially in normal speech, and that's the only way they're used in math. (And the converse of course isn't true: not all ways in which "if" and "only if" are used in english is material.)

[Kyle Miller]

It's a restricted technical language, and we know how it's meant to be used from exposure, and asking what a professor means by writing "iff" on the chalkboard.

[James Gallicchio]

(This is maybe the wrong thread to be arguing about math terminology...)

[Notification Bot]

27 messages were moved here from #std4 > lint structure projections by Kyle Miller.

[Mac Malone]

Kyle Miller said:

It's a restricted technical language, and we know how it's meant to be used from exposure, and asking what a professor means by writing "iff" on the chalkboard.

Personally, I do not like this, and feel this is an improper abuse of the English language. Also, I think the fact that the English conditionals do not work like this indicates something is the matter with the philosophical formalization of the classical material conditional (a view shared by a number of philosophers). However, this does not matter in math (or CS), since the whole language is constructed, which I why I prefer to use distinct symbols there.

[Kyle Miller]

Mac said:

"if you go to France, you can get a good croissant"

That's materially the converse by the way. Logically equivalent to the original one would be "if you can good croissant, then look around, you're in France!"

[Mac Malone]

Kyle Miller said:

That's materially the converse by the way.

That was kind of the point. "only if" can, to me, can intuitively mean the converse of its standard formalization.

[Kevin Buzzard]

"If you don't get down from that tree right now then I'm calling the police" implicitly means something which it doesn't logically say at all (if you do get down, then I won't). Or maybe they were saying "Iff" and I just misheard.

[Trebor Huang]

Because natural languages have this law that says usually people say the complete truth, so any violation of that suggests either you are not entirely using natural language, or you are doing somthing fishy (trying to conceal something / implying something else etc.)

[Trebor Huang]

If no matter what you do I'm calling the police anyway, then I ought to say that complete truth

[Mac Malone]

Trebor Huang said:

Because natural languages have this law that says usually people say the complete truth, so any violation of that suggests either you are not entirely using natural language, or you are doing somthing fishy

True, and this is largely what e.g. relevance logic attempts to capture. While it is natural that mathematicians do not care that much about alternative logics (due partly to being more interested in the implications of their current constructed system), I do think such logics are interesting for teasing out concepts that are naturally intuitive, but are not properly represented in classical logic.

[Bulhwi Cha]

I'm also interested in relevance logic. This SEP entry looks helpful: https://plato.stanford.edu/entries/logic-relevance.

[Chris Hughes]

I used iff instinctively with a non mathematician recently. I suspect it was understood as if.