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How would you diagram the following statement?

Only if a sandwich is complex is it tasty. Any tasty sandwich is recognized as tasty by sandwich connoisseurs. John's sandwich is complex. So John's sandwich will be recognized as tasty by sandwich connoisseurs.

I diagrammed it this way
Tasty -> Complex
Recognized as tasty -> Tasty
John's is complex
Therefore John's will be recognized as tasty

I had a friend try to diagram it and he came up with Complex -> Tasty for the first sentence, which seems incorrect given the "only if" in the first sentence.

P1: tasty sandwich --> complex
P2: tasty sandwich --> recognized
P3: John's sandwich --> complex
C: John's sandwich --> recognized

Something would have to be added or modified to properly infer the conclusion.

That's extremely helpful, thank you!

The only thing I don't get is how to determine that the second sentence should be diagrammed Tasty -> Recognized rather than Recognized -> tasty. What is the tip off?

The reason it's not the other way around is that the word any applies to the term tasty sandwich. Take the following example:
Any A is a B.
Therefore, if it is an A, then it is a B.
If B then A is a mistaken reversal.

So "any" is a sufficient condition indicator. I had either forgotten or never learned that. Thank you again!

I did want to verify, the conclusion is flawed with that argument, no?

We cant know that b/c John's sandwich is complex that it will be recognized, right?

starbury wrote:I did want to verify, the conclusion is flawed with that argument, no?

We cant know that b/c John's sandwich is complex that it will be recognized, right?

Right, it would be recognized as tasty if it were tasty.
Just because it is complex does not mean it is tasty.

gmreplay wrote:So "any" is a sufficient condition indicator. I had either forgotten or never learned that. Thank you again!

I like to remember it like this: "All" and "only" are opposites. So, if a statement says, "All A's are B's," it would be diagrammed exactly opposite to the statement, "only A's are B's." Many of my students find "all" statements to be intuitively easier than "only" statements, so I advise them to figure out how to diagram the statement as if it were an "all" statement and then reverse the relationship if it is actually an "only" statement.

JazzOne wrote:

gmreplay wrote:So "any" is a sufficient condition indicator. I had either forgotten or never learned that. Thank you again!

I like to remember it like this: "All" and "only" are opposites. So, if a statement says, "All A's are B's," it would be diagrammed exactly opposite to the statement, "only A's are B's." Many of my students find "all" statements to be intuitively easier than "only" statements, so I advise them to figure out how to diagram the statement as if it were an "all" statement and then reverse the relationship if it is actually an "only" statement.

They're not opposites - sufficient and necessary are far from opposite. Necessary = required, sufficient = enough.
(sufficient condition) ----> (necessary condition)

If = sufficient, other part of statement = necessary
Only if = necessary, other part of statement = sufficient
All = sufficient, other part of statement = necessary
Unless = necessary, negation of other part of statement = sufficient
.... and they go on

TeamBadass wrote:

JazzOne wrote:

gmreplay wrote:So "any" is a sufficient condition indicator. I had either forgotten or never learned that. Thank you again!

I like to remember it like this: "All" and "only" are opposites. So, if a statement says, "All A's are B's," it would be diagrammed exactly opposite to the statement, "only A's are B's." Many of my students find "all" statements to be intuitively easier than "only" statements, so I advise them to figure out how to diagram the statement as if it were an "all" statement and then reverse the relationship if it is actually an "only" statement.

They're not opposites - sufficient and necessary are far from opposite. Necessary = required, sufficient = enough.
(sufficient condition) ----> (necessary condition)

If = sufficient, other part of statement = necessary
Only if = necessary, other part of statement = sufficient
All = sufficient, other part of statement = necessary
Unless = necessary, negation of other part of statement = sufficient
.... and they go on

op·po·site
[op-uh-zit, -sit]
–adjective
3. being the other of two related or corresponding things: friendly with many members of the opposite sex.


This was the meaning of "opposite" I was going for. Still care to argue that necessary and sufficient conditions cannot be construed as "opposites"? I'm happy to debate the point. I just want to make sure your definition of "opposite" is not unnecessarily limited.


To further clarify, I did NOT mean the following definition of "opposite":

2. contrary or radically different in some respect common to both, as in nature, qualities, direction, result, or significance; opposed: opposite sides in a controversy; opposite directions.