Science

When wondering whether a phenomenon A causes a phenomenon B, people often ask whether phenomenon A is necessary and sufficient to produce the phenomenon B. That got me thinking whether a phenomenon A can ever be proven to be a necessary condition for phenomenon B. According to modal logic, a proposition "p" is necessary if, and only if, not "p" is not possible. So, if we can demonstrate that in the absence of A, B is not possible, we would be demonstrating that A is necessary for the occurrence of B. My question is: Can it ever be proven that something is not possible? How?

Comments

You’ve stumbled on one of the most important andenduring topics in philosophy, as well as onto the central question: What isthe nature of the necessity in causal relationships? Philosophers agree that untilthe work of David Hume, many philosophers took held that the necessity of aneffect, given its cause, is logical necessity. If the cause is present, then itis logically impossible that its effect must follow. If I let my keys drop froma height of one foot, then the keys mustfall. But you rightly note, as Hume did, that the necessity claim means thatit’s logically impossible for the keys not to drop, and you well ask: How do we determine logical impossibility? Hume argued that the testfor logical impossibility is inconceivability: Can we conceive or imagine thekeys not dropping? Sure – we can imaginethat the keys remain suspended, or that they “fly” left, right, or up. So it ispossible that the effect will not follow, and whatever necessity there is whena cause brings about its effect, it is not logical necessity. For an excellent start on this issue,including the historical and philosophical background, see the Hume entry in the Stanford Encyclopedia of Philosophy.

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