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Mike S., On 13/09/2012 20:32:
> On Wed, Sep 12, 2012 at 6:22 PM, And Rosta <and.rosta@hidden.email <mailto:and.rosta@hidden.email>> wrote:
> It's based on a type-A ontology, in which there is no inherent distinction between categories and individuals. If you have what looks at first glance like an individual but then peer closely at it, it can be seen as a category with multiple instances. Conversely, if you have what at first looks like a category with multiple instances, but look at it myopically, you can't see the differences between the instances, and it looks like one individual.
>
> Is it correct to say then that you would deny a formal connection in
> the language definition between your myopic singularization of "cat"
> and individual cats, but rather include that information in the
> Encyclopedia entry for "cat"?
I don't know if it would even be in the encyclopedia entry. I suppose the entry would include criteria for deciding whether something is one cat or multiple cats, so to that extent I answer Yes.
>
> That type-A ontology is to me and Jorge the most natural one, but to Martin, to John C, to John Woldemar, and probably to most folk schooled in logic (or even in common sense?) it isn't, so I reached the conclusion that a loglang should be ontologically neutral, either by not saying anything in its formal rules that necessitates specific ontological premises or by having an array of parallel mechanisms that cater to a range of different ontological proclivities.
>
> Does it make a huge difference? In Montague's program the model has several distinct domains, among them a domain of truth values Ds (s for sentence value), a domain of individual entities De, a domain of worlds Dw and a domain of time indices Dt. However, I believe a type-A model is obtained from a Montagovian model by permitting the union of those domains: Ds + De + Dw + Dt would approximate your model (assuming "+" is the union operator). Likewise, the reverse can be obtained by defining a handful of predicates that build the Montagovian domains, Ds(x) "x is a sentence value", De "x is an individual entity", etc.
>
The problem I see in this is how to define "is an individual". The truth values, worlds and time indices don't seem to be a problem; they have their places in the taxonomy of types.
> Of course, Montague was trying to formalize a fragment of English, which gives his discrete domains one clear purpose not as urgently needed in Xorban, as English syntactic categories are typed in the following way:
> - e and s are types
> - if a and b are types, then a/b is a type
> - if a is a type then a/w is a type (this is an intension)
>
> Xorban's minimalistic production rules seem to diminish the importance of defining syntactic categories in such manner. Nevertheless, to address what seems "natural" to me, I will admit that I bristle a bit at the idea of treating sentence value "true" as being in the same category as the individual slice of pizza that I had for lunch last week. Predicates are functions that range over truth values and only truth values, and if everything is founded on predicates, then that would appear to effectively make truth values privileged in any model you cook up, regardless of what, say, worlds or events are.
>
I take your point. But one needn't agree that predicates are functions that range over truth values. But if that's how you model them, then it makes sense that truth values would have a privileged status.
,, And.