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Horses have heads Symbolic Logic

  1. Feb 15, 2008 #1
    "Horses have heads" Symbolic Logic

    I was given this sentence to represent in first-order predicate calculus.
    The formula must use the following terms--horse, has, head--where:

    "horse" represents "x is a horse"
    "has" represents "x has a head"
    "head" represents "x is a head"

    Are these possibilities?
    1) (x)(horsex-->hasxhead) which means(?) "For all x, if x is a horse then x has a

    2) (x)(y)((horsex & heady)-->hasxy) which means(?) "For all x and for all y, if x is a horse and y is a head, then x has y"

    If not, how can "Horses have heads" be represented using these specification? Thank you.
  2. jcsd
  3. Feb 15, 2008 #2


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    The second is not true- a horse does not have all heads!
    2) says "every horse has every head".
    The first looks to me like a correct statement.
  4. Feb 15, 2008 #3
    Thank you. I am not positive that (1) correctly represents the sentence.

    Regarding (2): you said the formula is stating "a horse has all heads" Does it really?
    If so, I don't understand how it says that. If it's saying a single horse has all entities (which is plural) that are heads, why wouldn't it say "all horses have all heads". That is, I don't understand why it would say a single horse has multiple heads as opposed to saying multiple, i.e. all, horses have multiple, i.e. all, heads.
    I suppose i'm asking if you can explain how (2) says what you claimed; how (2) is incorrect. Thank you.
  5. Feb 16, 2008 #4


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    You said:
    Okay, here is a horse, x, standing just over that fence, and here is a head, y, between my shoulders. Does x have y? You did say "for all x and for all y".
  6. Feb 16, 2008 #5
    Just to get things straight, HORSE and HEAD are one-place predicates, and HAS is a two-place predicate, right?

    I think what you want is (Ax)[HORSEx --> (Ey)[HEADy & HASxy]].
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