Contrapositive of Some

Comments

• Kateryna Alum Member

  August 2016 984 karma

  I do not think there is a contrapositive. Some may mean all and some can mean 1 or greater.
• Kateryna Alum Member

  August 2016 984 karma

  We do know, however, that some criminals are liars. and some liars are criminals.
  
• Kateryna Alum Member

  August 2016 984 karma

  to add more, you cannot also take a contrapositive of "most" statement.
• knightalex321 Free Trial Member

  August 2016 20 karma

  No contrapositive. Some is reversible.
• quinnxzhang Member

  August 2016 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".
  
• [Deleted User] Free Trial

  August 2016 edited August 2016 107 karma

  The user and all related content has been deleted.
• quinnxzhang Member

  August 2016 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?
• Alejandro Member Inactive ⭐

  August 2016 2424 karma

  You shouldn't mark some statements as bi-conditionals!
• Alejandro Member Inactive ⭐

  August 2016 edited August 2016 2424 karma

  ...or some Bobs are tall. You can't translate that into a conditional either.
• [Deleted User] Free Trial

  August 2016 107 karma

  The user and all related content has been deleted.
• 1 Like

  quinnxzhang Member

  August 2016 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.