The first premise isn't actually a contradiction — Michael
And from a contradiction, anything and everything follows. This is the principle of explosion.
That is to say, "1. A -> not-A" is impossible; when the impossible can happen, anything can happen. — unenlightened
Except perhaps in your first citation above:here is no cite, no source, no reference that says such a thing. — TonesInDeepFreeze
and (a->~a) doesn't "hold.""if a conditional holds... — TonesInDeepFreeze
Obviously the universe is the result of God accidentally contradicting Himself by making a mistake, which He cannot do, being infallible. Explains everything!
ABSTRACT This paper attempts to make intelligible the logic contained in the Diamond
Sutra. This `logic’ is called the `logic of not’. It is stated in a propositional form: `A is not A, therefore it is A’. Since this formulation is contradictory or paradoxical when it is read in light of Aristotelean logic, one might dismiss it as nonsensical. In order to show that it is neither nonsensical nor meaningless, the paper will articulate the philosophical reasons why the Sutra makes its position in this contradictory form. The thesis to be presented is that as long as one understands the `logic of not’ from a dualistic, either-or egological standpoint, it remains contradictory, but in order to properly understand it, one must effect a perspectival shift from the dualistic, egological stance to a non-dualistic, non-egological stance. This thesis is advanced with a broader concern in mind: to reexamine how the self understands itself, how it understands others, and how it understands its intra-ecological relationship with nature.
my definition of MP — Hanover
this is a definitional debate — Hanover
An odd lot we are. — Hanover
"If A is true, then A is false" is a necessarily false statement. — Hanover
The OP uses propositional logic. In propositional logic, the argument is valid. — Banno
here is no cite, no source, no reference that says such a thing.
— TonesInDeepFreeze
Except perhaps in your first citation above:
"if a conditional holds...
— TonesInDeepFreeze
and (a->~a) doesn't "hold." — tim wood
It seems folk think A → ~A is a contradiction. It isn't. — Banno
Only line 1 is not, ~A. It's A→~A. — Banno
Yep.But (A->~A) & A is a contradiction. — Srap Tasmaner
Well for a start you would no longer be dealing with a complete version of propositional calculus...Would there be any harm in requiring that the conditional in a modus ponens have fresh variables on the right hand side? — Srap Tasmaner
Too often this is an excuse for poor logic.But around here we're more interested in the practical use of logic, — Srap Tasmaner
Modus ponendo ponens is the principle that, if a conditional holds and also its antecedent, then its consequent holds." (Beginning Logic - Lemmon)
Perhaps your argument is based on taking that to mean this?:
If a conditional holds and also its antecedent, then modus ponedo ponens is the principle that then its consequent holds. — TonesInDeepFreeze
A is a formula.
~A is a formula.
Modus ponens is the principle that for any formulas P and Q, if P and P-> Q, then Q.
So, one instance of modus ponens is: if A and A -> ~A, then ~A. — TonesInDeepFreeze
There is no governing body in what to call it. — Hanover
there are exactly zero citations so far found where someone other than us has analyzed whether the OP case belongs in mp. — Hanover
Where we have found debate over invalid mp formulations on the web — Hanover
I see no evidence supporting your usage. — Hanover
The OP is not a problematic example of mp. It's not mp at all. — Hanover
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