[FOM] ARE THERE CONTINGENT LOGICAL TRUTHS?

[laureano luna]

This post just means to ask for help.
 
I propose the following (usual) definitions:
 
1. A truth is contingent whenever its negation has a model.
2. For any sentence "p" and any model "M", M satisfies not-p whenever it does not satisfy p.
 
Add to these definitions the classical excluded middle for formal logic:  every sentence (closed well-formed formula) is either true or false.
 
Henkin´s semantics shows there are general non-standard models in which some sentences, that under classical excluded middle are second order logical truths, are not satisfied (since those models make SOL semantically complete, which it can´t be under classical excluded middle). 
 
According to 2. those models satisfy the negations of some second order logical truths.
 
According to 1. those logical truths (whose negations have a model) are contingent.
 
So, there must be some contingent second order logical truths.
 
What is wrong above?
 
Laureano Luna Cabañero.

		
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