fom
Posts:
1,969
Registered:
12/4/12


Re: Matheology S 224
Posted:
Apr 14, 2013 5:38 PM


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 "AntiInference" rules is:
 From Fx one shall _not_ infer Ex.

It does not matter what your "new logic" is.
Firstorder 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 firstorder logic definitely makes it not firstorder 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 secondorder 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 secondorder 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"

