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If so, then I would put forth the proposition that miraculous as this conciousness might be, it still must be controlled by the logical conclusions of cause and effect.
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Oh yes - I'm in complete agreement with you here in saying that it emerges from cause and effect (deterministic) processes, (as an accidental but far reaching and fascinating bi-product) but that doesn't mean it can't transcend those things and act in unpredictable and non deterministic ways.
With those qualifications made then, I'd still say that 1+1=2, as a timeless model of the inter-relationships between abstract quantities, must be devoid of cause and effect.
I don't think logic has anything to do with cause and effect. Cause and effect must have time in order to exist. Logic as a system of abstract ideas doesn't have time. 'IF's don't 'happen' before 'THEN's any more than 'AND' s are responsible for 'NOT's. But I suspect that's not the point you were making.