On Feb 10, 2009, at 2:25 PM, Rich Cooper wrote: PH wrote: ---------------------------- ---------------------------- ---------------------------- Long before Strawson, linguists had observed a distinction between
obligatory and optional (AKA inner and outer) participants in the
action or state expressed by a verb. For 'give', the number of
inner or obligatory participants is 3, and there is an open-ended
number of optional relationships for the time, place, manner, etc. True, but this distinction is purely grammatical. I have to say "XX gave YY to ZZ", with all three grammatically required phrases in place (and Im not obliged similarly to say where or when or how), but Im not obliged to actually provide the information. I can say 'someone' or 'something' as a filler which satisfies the grammatical constraint without actually providing information, when the information is missing. Or I can use the passive voice and say "Mary was given a book" without saying "by XX". When sentences like these are converted to logic, the missing arguments are still missing. Its notable than if one pushes this exercise to the limit, you find the English words naming the case roles. To describe this event without mentioning John or the book, we have to say "Mary received a gift" ----------------- ------------------------ ---------------------------- ------------------------- This multi-signatured form of the statement still works with a 3-ary relation: Mary was given a book” Give( nil, Mary, book ) ^ Earlier( Give(nil, Mary, book) )
This isn't legal logical syntax, for several reasons.
First, what does 'nil' mean? In logic, this has to be a name, and hence a name of something. If 'nil' means here what it means in LISP, then this says that the empty list gave a book to Mary, which I doubt is what was intended. I presume you want to use 'nil' as a kind of blank pseudo-name which can be used to indicate that no real name is available, but this isn't a construct in any logic I've ever seen. The proper way to do this in logic is to use a quantifier:
(exists (x)( Give(x, Mary, book) ... )
but this is getting closer to the case-role form. (BTW, I notice you have permuted the order of the three arguments, thereby illustrating one of the main problems with the n-ary argument form: keeping track of which argument is supposed to be which, when there are no syntactic labels to help you remember.)
Second, more seriously, you can't make a sentence into an argument, as you do here with "GIve(nil, Mary, Book)". And even if you could, a sentence in logic denotes a truth-value (and asserting the sentence, as your first conjunct here does, asserts that this value is true.) This means that predicating a property of the sentence, as you do in the second conjunct, amounts to the assertion about the truth-value. So here you are saying that true has the property called "Earlier", which doesn't make sense. (We developed an extended logic, IKL, in which there are expressions of the form: (that (Give x Mary Book)) which contain embedded sentences, but they denote propositions, not events: it still doesn't make sense to say that a proposition is 'earlier'.)
Third, "Earlier" isn't a property. Consider: logical assertions are timeless: they aren't made "at" a time, like assertions in a tensed language. So "Earlier" doesn't make sense (earlier than when?). To convey the "pastness" of a tensed assertion in a nonindexical logic, one has to de-indexicalize it by putting times in explicitly, and then "Earlier" is a relationship between the time of assertion (the "now") and the time of the event or being described.
Someone gave mary a book Give( nil, Mary, book ) ^ Earlier( Give(nil, Mary, book) ) action John gave Mary a book Give( John, Mary, book ) ^ Earlier( Give(John, Mary, book) ) When extra modifiers are present, the form is still 3-adic with extra predicates recording the event of giving:
You miss the point. Those extra predicates have to be applied to something, and what they then say is that that thing has a certain property. If "Give" is a relation, then the form "Give(A, B, C)" has to be a sentence. And a sentence does not denote an event. In order to say the extra things, you must use a name of the event. Once you do this, the trinary form has to itself be related to the event somehow. The simple use of the same verb ("give") isnt enough to connect to a particular event.
Logic isn't just a mathematical-looking notation. It comes with a clearly defined set of semantic conditions, which have to be respected. WIthout these, it isn't saying anything. One can't just write down some stuff and declare that it means what you want it to mean. The meanings have to be built up from the meanings of the syntactic parts in a uniform, principled way, in order for it all to work as a coherent logic.
Herb gave Mary a book yesterday Give( Herb, Mary, book ) ^ Earlier( Give(Herb, Mary, book) ) ^ TimeOf( Give(Herb, Mary, book), Yesterday ) Pete gave Marsha a book in the library Give( Pete, Marsha, book) ^ Earlier( Give(Pete, Marsha, book) ) PlaceOf( Give(Pete, Marsha, book), Library) Und so wieder. The point is that the 3-adic representations can be used for all the cases you’ve mentioned.
You aren't using 3-adic relations here. Im not sure what all this means, formally, but it certainly isn't made up of 3-adic relations.
Other information is related to the action of Give( x, y, z )
If this is an action, in what sense is Give a relation? And what does it mean to assert an action?
Pat Hayes to describe the conditions under which the act took place, and the condition of x, y and z at the time of the act.
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