Logic -- explain converse / reverse / inverse / etc. as simpy as possible

http://www.jimloy.com/logic/converse.htm

* statement: if p then q
* converse: if q then p
* inverse: if not p then not q
* contrapositive: if not q then not p

If a statement is true, the contrapositive is also logically true. Likewise, when the converse is true, the inverse is also logically true.

I'm glad I did a last-minute googling check because I was about to tell you completely the wrong thing.

Well that was simple and easy.

Hooray!

i love this stuff

thought this was another shoe thread

i wld wear inverses

now explain 'baseball boots' as simply as possible

they'd have y'know a decent insole
xpost
no

If a statement is true, then its contrapositive is true.
If a statement's contrapositive is true, the the statement is true.
If a statement is not true, then its contrapositive is not true.
If a statement's contrapositive is not true, then the statement is not true.

kudos

If a statement is true, then you can't tell whether its converse is true.
If you can't tell whether a statement's converse is true, then the statement is true.

Similarly,

If a statement is true, then you can't tell whether its inverse is true.
If a statement is false, then you can tell whether its inverse is true.

If you can't tell whether a statement's converse is true, then the statement is true.

Wait, really?

No. This is why you have to be careful of converses and inverses -- they seem like they should logically follow, and sometimes they end up with true statements, but they do not logically follow.

Contrapositives, as noted above, do logically follow.

proof through uncertainty

It's nice to know I'm not the only Formal Logic geek on ILX.

(If you didn't notice, the second statement there about converses is the converse of the first, and the second statement about inverses is the inverse of the first, and they both end up with false statements. Although putting the contrapositive statement through the converse, inverse, and contrapositive moves all lead to true statements.)

Am I the only one that is shocked and suprised when people don't think that this stuff is fascinating and fun?

I once convinced a friend of mine in college to take formal logic to fulfill her math requirement. She doesn't talk to me now :(

Proofs were the reason I loved high school geometry. I made a perfect grade in that class, and people thought I was a freakshow. Come on! This stuff is easy!

taking a proofs class is the only thing I've remotely enjoyed about computer science undergrad so far :/

<i>Am I the only one that is shocked and suprised when people don't think that this stuff is fascinating and fun?</i>
No! And boy do some people LOATHE this stuff, it turns out

but we didn't talk about formal logic, that was grade school

xpost

And boy do some people LOATHE this stuff, it turns out

Come with me, come to the land of batshit rightwing cartoonists

What sort of grade school do you go to, dude?

xpost

What sort of grade school do did you go to, dude?

WHEN TYPOS TURN INTO UNINTENTIONAL INSULTS, PART 74.

I get really frustrated in math class when we skip the proofs.

I think this is very interesting in the abstract, but if I had to be tested on it, I would fail horribly.

Proofs... god, no no no.

we had to take a formal logic class as part of my writing/journalism first year undergrad - half the people almost failed, a bunch did fine, and a handful were like 100% (xpost to braggin 2007). i kept my textbook and friends were like wtf throw that out and i was like no way + u can't deal with logic anyway as if i'm listening to u?!

I thought philosophy was just about shooting the shit before I took a 'logic' class in college. I did well but couldn't say I liked it. I need illustrative examples, variables trigger my mathphobia something awful.

The only thing that got me through my Philosophy major was taking as many logic courses as I could.

It's nice to know I'm not the only Formal Logic geek on ILX.

I studied mathematical logic in grad school for 5 years. 5 soul-destroying years.

I still like logic, though. The philosophical kind, that is.

a problem for truth-conditional semantics (I can't make any sense of this when lexical semantics is not taken into account. I'm not sure I know what I'm talking about.)

statement: not(p) or q
converse: not(q) or p
inverse: p or not(q)
contrapositive: q or not(p)

p: I am late.
q: I am early.
statement: I am not late or I am early. (If I am late, I am early.)
converse: I am not early or I am late. (If I am early, I am late.)
inverse: I am late or I am not early. (If I am late, I am not early.)
contrapositive: I am early or I am not late. (If I am early, I am not late.)

I'm not following you - could you explain that?

The inverse of "If I am late, I am early" would be "If I am not late, I am not early," btw, and the contrapositive would be "If I am not early, I am not late," so that might be where you're going wrong. But I still don't understand the whole thing..

not(p) or q

that's not a statement. You have to state something, at the very least.

Ok, that's what I thought. I never actually took a formal logic course and learned most of this stuff from teaching LSAT classes, so I thought maybe I was missing something.

If you start with a negative, your results will always be negative.

I started my Philosophy course dreading logic, ended up getting full marks (though in our course you're not allowed to get above 80, so I could've got anywhere between that and 100% - highly unlikely to be the latter). Was actually pissed off that joint honours meant I couldn't take any further logic classes.

Truth-functional propositional logic is a mere starting point in a subject that's incredibly, impossibly rich. Besides regular predicate logic, there's also intuitionistic logic, wherein ¬¬p → p is not valid, and modal logic, which gives meaning to terms like "necessary", "possible", and "implies". Plus many variants, most of which are studied as "philosophical logic".

"Mathematical logic", on the other hand, doesn't stray into such odd territories, but instead, tends to concern itself with more semantical matters, such as models, extensions of the set-theoretical world in which mathematics is often cast, and the nature of the upper semi-lattice that is the recursive structure of subsets of natural numbers.

I prefer the former world, after experiencing too much of the latter. There are far more open questions, and the applications are much more interesting: Mathematical logic has virtually zero applications outside of itself, while philosophical logic at least is of interest to philosophers of other subjects.

While driving home from the grocery store tonight, I caught a snippet of of an interview on the BBC-via-NPR in which an expert on food technology claimed "in today's economy, logic is making more sense than ever." Just thought y'all should know.

https://billwadge.wordpress.com/2015/09/30/i-deduce-you-are-studying-logic/