not all otters are non-authors

ampm
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not all otters are non-authors

Postby ampm » Thu Jan 10, 2013 10:22 pm

I am wondering on a plausible diagramming scheme for this statement.

What I've come up with is that this statement is equivalent to: 'some otters are authors'. However, on the actual exam, these statements will most likely trip people up so for diagramming purposes how would you guys diagram?

Not all otters are non-authors: O -> (/(/(A)) or O -> S -> A.

I would think this takes a pattern form where if you have a statement: Not all A are/do/{verb} B = A -> S -> (/({verb} B)).


Similarly, if we have a statement like 'all dodos are not quotable' is this equivalent to:

1. not all dodos are quotable = 'some dodos are not quotable' so: dodo -> S -> (/(Quotable))

OR

2. if you're a dodo, you're not quotable: D -> (/(Quotable))

Any thoughts?

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ScottRiqui
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Re: not all otters are non-authors

Postby ScottRiqui » Thu Jan 10, 2013 10:28 pm

ampm wrote:
Similarly, if we have a statement like 'all dodos are not quotable' is this equivalent to:

1. not all dodos are quotable = 'some dodos are not quotable' so: dodo -> S -> (/(Quotable))

OR

2. if you're a dodo, you're not quotable: D -> (/(Quotable))

Any thoughts?


I would read it as equivalent to (2), associating "all" with "dodos".

ampm
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Joined: Fri Dec 09, 2011 4:02 pm

Re: not all otters are non-authors

Postby ampm » Fri Jan 11, 2013 11:24 am

ScottRiqui wrote:
ampm wrote:
Similarly, if we have a statement like 'all dodos are not quotable' is this equivalent to:

1. not all dodos are quotable = 'some dodos are not quotable' so: dodo -> S -> (/(Quotable))

OR

2. if you're a dodo, you're not quotable: D -> (/(Quotable))

Any thoughts?


I would read it as equivalent to (2), associating "all" with "dodos".


I would feel like saying 'All dodos are not quotable' is same as stating 'not all dodos are quotable' which is stating that some dodos are not quotable.

By saying not all dodos are quotable, we don't know how many dodos are not quotable but we can conclusively say that some dodos are not quotable.

The other possibilities:

1. We don't know whether any dodos are in fact quotable so we can't state:
All dodos are not quotable nor All dodos are quotable.

2. Also, because we don't know about the quotability of dodos (none of them could be quotable), we can't even say:
some dodos ARE quotable.

We only know that not all dodos are quotable so we can only say:

some dodos are not quotable.

Does this seem reasonable?

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TripTrip
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Re: not all otters are non-authors

Postby TripTrip » Fri Jan 11, 2013 11:45 am

ampm wrote:What I've come up with is that this statement is equivalent to: 'some otters are authors'. However, on the actual exam, these statements will most likely trip people up so for diagramming purposes how would you guys diagram?

O=Otters
a=state of being an author

∃Oa


ampm wrote:Similarly, if we have a statement like 'all dodos are not quotable' is this equivalent to:

1. not all dodos are quotable = 'some dodos are not quotable' so: dodo -> S -> (/(Quotable))

OR

2. if you're a dodo, you're not quotable: D -> (/(Quotable))

Any thoughts?

D=dodos
q=state of being quotable

All dodos are not quotable: ∀D-q
Not all dodos are quotable: -∀Dq

Two VERY different statements.



ampm wrote:I would feel like saying 'All dodos are not quotable' is same as stating 'not all dodos are quotable' which is stating that some dodos are not quotable.
Not at all.

ampm wrote:By saying not all dodos are quotable, we don't know how many dodos are not quotable but we can conclusively say that some dodos are not quotable.
If you're saying "not all dodos are quotable," yes. If you're saying "all dodos are not quotable" then we do indeed know that there is no dodo that is quotable, because each and every dodo is not quotable.

ampm wrote:1. We don't know whether any dodos are in fact quotable so we can't state:
All dodos are not quotable nor All dodos are quotable.
I don't know what you're talking about anymore If you know "All dodos are not quotable" then you also know "All dodos are not quotable."

ampm wrote:2. Also, because we don't know about the quotability of dodos (none of them could be quotable), we can't even say:
some dodos ARE quotable.
Your conclusion is technically true, but only because we know that no dodos are quotable.

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TripTrip
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Re: not all otters are non-authors

Postby TripTrip » Fri Jan 11, 2013 5:11 pm

I suppose I should have prefaced: the things that you are trying to diagram require quantifier logic. If you are not well versed in predicate logic, you would probably be better off not diagramming this stuff.

ampm
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Re: not all otters are non-authors

Postby ampm » Fri Jan 11, 2013 11:52 pm

TripTrip wrote:I suppose I should have prefaced: the things that you are trying to diagram require quantifier logic. If you are not well versed in predicate logic, you would probably be better off not diagramming this stuff.


Hm so that makes sense.

I guess the way I was pronouncing the sentence in my head, by putting the inflection on different parts of the word, had me confused between pts 1 and 2.

On the LSAT, I guess I'll interpret it straight and say 'All dodos are not quotable' = D -> ~q.

I'm familiar with the notation you used but not to the point where I would use that on the actual exam. Is that your way of doing things?

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TripTrip
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Re: not all otters are non-authors

Postby TripTrip » Sat Jan 12, 2013 12:46 am

The only time I would diagram like that is on an LR question looking for similar structure. Those trip me up if I don't diagram them out completely. Otherwise I avoid quantifier logic on the test because it takes too long.

(D -> -q) is close enough, as long as you remember what it means. :)




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