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# Contrapositive of Some

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in General 107 karma
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• #### Use of "except" in a personal real-world application of Bylaws - help!I live in an artist cooperative. It is stated in our Bylaws "Except for the chairperson of the committee, such committee members need not be Director…

• Alum Member
984 karma
I do not think there is a contrapositive. Some may mean all and some can mean 1 or greater.
• Alum Member
984 karma
We do know, however, that some criminals are liars. and some liars are criminals.
• Alum Member
984 karma
to add more, you cannot also take a contrapositive of "most" statement.
• Free Trial Member
20 karma
No contrapositive. Some is reversible.
• Member
edited August 2016 611 karma
Contrapositives only apply to conditional statements. An existential statement like "some criminals are politicians" has no conditional, and thus no contrapositive.
@generationhar said:
C <-> P
I recommend changing the way you diagram existential statements. The "<->" symbol commonly denotes the biconditional, which is not part of the structure of a basic existential statement.

The standard way of diagramming an existential statement is something like "some(C & P)". The conjunction is appropriate because existential statements are symmetric, i.e. "some criminals are politicians" implies "some politicians are criminals".
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edited August 2016 107 karma
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• Member
611 karma
@generationhar said:
Can't all statements be translated into conditional statements?
Certainly not. Consider an atomic proposition like "Bob is tall". Where is the conditional here?
• Member Inactive ⭐
2424 karma
You shouldn't mark some statements as bi-conditionals!
• Member Inactive ⭐
edited August 2016 2424 karma
...or some Bobs are tall. You can't translate that into a conditional either.
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• Member
edited August 2016 611 karma
@generationhar said:
If you are Bob, then you are tall.
If you are not tall, then you are not Bob.

This is not what "Bob is tall" is saying. Your conditional sentence can't even be expressed in quantifier-free predicate logics, whereas "Bob is tall" can be. This is because, in "Bob is tall", the relationship between Bob and tallness is one of predication, not implication -- "Bob is tall" isn't saying that a necessary condition for being Bob is that he's tall.

Consider also single predicate quantified sentences like "everything is red" or "something is green". Or sentences involving relations and functions, such as "2+2=4". None of these are expressed using conditionals.
@generationhar said:
It's been translated into a conditional statement. It's valid, but its soundness is questionable.
This misuses of both "valid" and "sound". Valid sentences are logical truths, but "Bob is tall" is not a logical truth, and thus is not valid. Soundness applies to arguments, not sentences (there's also another type of soundness that applies to theories, but this doesn't apply to sentences either).
@generationhar said:
All teachers are smart.
There is a conditional in this sentence. "All teachers are smart" can be expressed by something like "all(teacher → smart)". But this is a universal sentence, which is different from existential sentences, like "some teachers are smart", which don't involve conditionals.