ONLY in Formal Logic Diagramming

[mcwoodhill]

I understand that for conditional relationship, Only if A then B means B arrows A

But for formal logic relationship, this diagram seems to be a reverse:

The only A are B, paraphrase it and it sounds like all a is b to me. That means the diagram is A arrows B

Is it correct? I read through the Logic Bible and it says for some occasions this does happen. Wondering if it is an iron rule for formal logic diagramming.

Thanks in advance.

[James Finch]

HI MC,

Conditional reasoning is a form of formal logic, and "only" is a trigger word for a necessary condition of a conditional relationship, while "all" is a trigger word for a sufficient condition. Essentially they create opposite relationships between variables: if only A are B, then all B are A, while if all A are B, then only B are A.

If you have a situation where only A does/is B, then we only can make a definitive statement if we know that something is either B or not A. So the logical link is still:
B A and A B.

Consider the common axiom "Only the good die young." What can we glean from this phrase? That if you die young, you must be good, and if you're not good you won't die young. But we can't reverse that relationship and assume that all good people die young, or that if you're good you won't die young. It creates the same logical relationship as saying that "All the people that die young are good."

Hope this helps!

[mcwoodhill]

It helps a lot, thanks.

I presume formal logic is different from conditional because they are taught by different chapters of the Reasoning Bible.

Now it's way more clear for me.