>
>BS> A dog is an instance of function from entities to truth values
>>
>>Still does not sound right to me.
>
>That was my earlier definition, which I replaced with a
>later definition, which added the term "abstract entity"
>after "is". If you insist on doing the substitution
>you would get
>
> A dog is an instance of an abstract entity, which may be
> defined by a rule that is used for classifying entities.
>
>If you don't like my definition of _type_, please state your
>preferred version. (01)
Some terms are primitive, and we can at best provide elucidations and
examples. My elucidation of 'type' would go something like this: (02)
A type is a general entity which is instantiated by particular
entities in the way in which, for example, the type dog is
instantiated by the particular dog Fido. (03)
Even from this we get substitutability (which is an indispensable
rule for good definitions, and which your earlier definitions fail to satisfy): (04)
Fido is an instance of a type of general entity which is instanted by
particular entities. (05)
Your new definition satisfies substitutability, but it is far too
weak for our purposes. (06)
It says (07)
A type is an abstract entity, which may be defined by a rule that is
used for classifying entities. (08)
From the definitional point of view this comes down to: (09)
A type is an abstract entity (010)
since the remaining clause is, as you now phrase it, optional. (011)
For there are many sorts of abstract entities (e.g. numbers) which
are not types. (012)
>BS> Good to follow common sense, too, I think.
>
>I agree. But I don't think it's good common sense to insert
>the metalanguage of mathematics into normal English sentences. (013)
This is just the rule of substitutability. If D is a definition of A,
then any simple sentence involving A should still make sense, and
preserve its truth-value, if you replace A by D. (014)
>>Then this would mean that we would have to accept not merely
> > the statement
>>dog is_a animal
>>but also the instantiation statement
>>dog <dog, animal> animal.
>
>This substitution is not equivalent to replacing a term
>with its definition: the extension of "is_a" is not the
>definition of "is_a", and the pair "<dog, animal>" is only
>one element of the extension. (015)
We were talking about the question whether relations like is_a have
instances (in the way in which types have instances) (thus about the
question whether relations like is_a ARE types) (016)
I suggested that they do not.
You countered by saying that they do, because they have extensions,
sets of ordered pairs, so that each ordered pair would be an instance
of the corresponding relation. (017)
Thus <dog,animal> is, on the Sowa view, an instance of is_a. (018)
An instance of a relation would itself be a relation, and would
relate the corresponding terms which the relation type, of which it
is an instance, relates. (019)
Thus we would have not only (020)
dog is_a animal (021)
but also (022)
dog <dog, animal> dog (023)
The fact that the latter is nonsense is good evidence, I think, that
a relation like is_a does not have instances. (024)
>If you insist on making a meaningful substitution, you
>should replace the entire sentence "dog is_a animal"
>with the pair "<dog, animal>". (025)
Substituting a sentence with a name is not usually a good thing to do.
BS (026)
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