Mapping a *Definition* with Lawgic, Two Scenarios

benjipants

A stimulus says "A poem is any work of art that exploits some of the musical characteristics of language." (PT27 Sect.1 Q20) I would map that statement with lawgic as follows:

Expl Musical Char of Lang & Work of Art ----> Poem

or Work of Art that Exploits Musical Char of Lang ----> Poem


Now, what if the stimulus said "A poem is a work of art that exploits some of the musical characteristics of language"?

Seems like it should be obvious, but it's not (to me anyway). Is it a bi-conditional?

If something is a poem, then it's a thing that is a work of art that exploits the musical characteristics of language. So Poem ---> WA that EMCL.

Then let's say we come across this mysterious thing that is a work of art that exploits some of the musical characteristics of language. What's that called? Is it necessarily a poem? (WA that EMCL ---> Poem?)

PS: Not sure any of this matters.

Cant Get Right

“Any” is inclusive so that anything which possesses those properties is necessarily a poem. I’m not sure “a” implies that. It may reverse the necessary/sufficient relationship, but I think this may get into some existential translating. In formal logic, beyond what I think you’d ever need for LSAT, I think the “a” version would be translated: “There exists an x such that x is both a poem and a work of art that exploits some of the musical characteristics of language.”

For the purposes of the LSAT though, I wouldn’t worry too much about mapping out this type of statement.

runiggyrun

The first one is a biconditional and the second one is a conditional (just as you both describe it).
The first one combines the two indicators "is" (necessary) and "any" (sufficient) referring to the same construct "work of art that exploits the musical character etc.". When both a sufficient and a necessary indicator apply to the same construct, you get a biconditional.

Shortened to a letter argument 'cause I'm lazy:

A is any (B that is C) breaks down into

A is a (B that is C)
+
Any (B that is C) is A.

Which gives us
A <--> B that is C
OR
A <-->B+C

The second one doesn't have the ANY so it's a simple use of the "is" necessary indicator
A is a (B that is C)
A-->(B that is C)
A--> B+C
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Analogous example:
Biconditional: A [mother] is any [woman that has children]
[Woman that has children] is referenced by both the "is" (necessary) and "any" (sufficient) indicators.

A [mother] is a [woman that has children]
Any [woman that has children] is a [mother]

[Woman] AND [has children] <--> [mother]
You can't have any mothers that are not women or that don't have children.
You can't have any women that have children that are not mothers.

Simple conditional: A mother is a woman that has children.
[Mother] --> [woman] AND [has children].

You can't have any mothers that are not women or don't have children, but the reverse isn't necessarily true. Maybe there are some women that have children that are not mothers because they abandoned their children in a dumpster and therefore shouldn't be considered mothers.
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The relevant lessons on the use of Any and Is as logical indicators are here:
https://7sage.com/lesson/basic-translation-group-1
https://7sage.com/lesson/miscellaneous-logical-indicators

benjipants

Looks like I came to the right place! Thank you both!!