fom
Posts:
1,968
Registered:
12/4/12
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Re: Matheology S 224
Posted:
Apr 14, 2013 5:38 PM
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On 4/14/2013 3:33 PM, Nam Nguyen wrote:
> On 14/04/2013 1:05 PM, fom wrote:
>
>
>> So much for any claims concerning "standard FOL".
>
> Why don't you read my post there carefully.
>
>
Why don't you read what the paradigm of first
order logic is carefully?
This is what you presented:
- Ix <-> ~Fx /\ Fx <-> ~Ix
- Ix -> Ex.
And of one of the new "Anti-Inference" rules is:
- From Fx one shall _not_ infer Ex.
--------------------------------------------
It does not matter what your "new logic" is.
First-order logic has a paradigm. If a quantifier
can be true of any singular term t, then it will
be true of
Ex(x=t)
Now, you could think of how one might define
predicates to express what you have called
quantifiers. But, adding quantifiers to
first-order logic definitely makes it not
first-order logic.
And, for what this is worth, you will probably
have difficulty with those particular
predicates. They look as if they would have
to be second-order logic.
There is a simple schema for "There are exactly
n denotations". A "finiteness" predicate would
seem to have to quantify over that schema in order
to find one that is satisfied.
I have no difficulty thinking about second-order
logic. But, it is not first order logic.
--------------------------------------------
I had been sympathetic toward seeing what you
had been trying to do. I just figured that I
might be of some assistance to clean it up. I
have been flamed before without anyone trying
to help. It is not fun.
But all you really want to do is win arguments.
Worse yet, you start arguments to win arguments,
and, then, you only win in so far as it is in
your own mind.
http://en.wikipedia.org/wiki/Doxastic_logic#Types_of_reasoners
see "conceited reasoner"
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