On Sep 6, 6:34Â pm, galathaea
gmail.com> wrote:> On Sep 6, 6:03 pm, Tegiri Nenashi
gmail.com> wrote:
>>> On Sep 6, 3:31 pm, galathaea
gmail.com> wrote:>>> if i understand what you mean by lambda quantifier
>>> (as in the standard form on which eval's work through application
>>> Â e.g. lambda calculus lambdas
>>> Â Â with their well known universal properties)
>>> then i would expect the exponential to be the corresponding operation
>>> in other words
>>> Â given a objects X and Y
>>> a function f from X to Y is an element of the exponential object
>
>>> Â Â Â Â Â Â Â Â X
>>>  f elementOf  Y
>
>>> and the evaluation at an element of X is given by
>
>>> Â Â Â Â Â X
>>> Â eval: Y Â x X Â --> Â Y
>
>>> (such that a variety of commutative diagrams obtain)
Could you please be more specific what algebraic structure you have in
mind? Specifically, what are the elements ("element of" prompts that
perhaps sets)? Given two sets X and Y, they define the set of
functions X->Y; is that the operation you suggested?
If my interpretation is wrong, may I ask for amn example? In the
analogies that I brought in the root message I could, for example,
explain how universal quantifier works on domain of three elements
x={1,2,3}, that is how we do conjunction P(1) ^ P(2) then amend the
expression to (P(1) ^ P(2)) ^ P(3) this is how Ax.P(x) becomes a
proposition. Can you draw a similar venue for lambda abstraction?
>> In binary form -- exp(x,y) --
>> exponentiation is not associative, that would also disqualify it.
>
> why do you think an operation must be associative?
Because all the other analogies (sum, product, and predicate logic
quantifiers) have this property?
