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unique instance of an effect

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One way an instance of an effect can seem unique is that it appears to change without cause. That unexplained change demonstrates the existence of some factor not presently accounted for or the lack of something you were counting on.  As a child, I noticed that after turning off a CRT, I could see a thick layer of dust that had been interfering with my enjoyment.  So I started to collect and lift it off with my finger when I noticed that the clumps of dust would dance across the screen.  This amused me greatly and served as my first experiment in electrostatics.  When I found that other materials would ruin my fun by causing the dust to fall uselessly to the ground, I realized that the dust had lost something I was counting on.

Another way an instance can seem unique is that it deviates from the expected course. What deviates from the expected course either involves something you didn't expect or lacks something you expected.  As a child, I noticed a spider with an extra "foot" coming out of one its legs.  Some time later, I noticed a young spider with the same extra "foot".  I later identified that trait as "mutation".

Yet another way an instance can seem unique is that it does not obviously share a Conceptual Common Denominator with anything presently known. This demonstrates that the cause differs significantly from what is familiar.  For a long time, I didn't see a common denominator between liquid water and boiling water.  I would have to learn about phase transition and statistical mechanics for that.

In all three cases, some (comparatively) unique instance depended on peculiar circumstances which I had to discover and identify in conceptual terms.

Can we formulate a general rule of causal inference?  Can we say that what seems unique MUST involve or lack something we haven't thought of?  Is that really what "unique" objectively means? 

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