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Can we create a system without the law of modus ponens?


Not possible.

Modus ponens is basically to the effect that you can infer it if it follows.

Without it, you are in dry dock, inference-wise.

Of course, you can always tinker with the way it is expressed. Instead of saying

((P->Q) &P)->Q,

you can say:

-((-P or Q)&Q)&-Q)

But given that ‘P->Q’ is definitionally equivalent with ‘-P or Q’, this isn’t exactly a way to get rid of modus ponens. Same holds if you try any other work-around.

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