Regarding your question 1 :
- To prevent something from happening, why do we
usually search for a cause that is a NC? Both prevention and production of something need the SC, because NCs do not reveal the entire 'picture'.
This appears to be backwards to me. A SC captures one reason for a consequent, but not necessarily the only reason for a consequent. Suppose you wish to know if a number is even. A sufficient condition for evenness is divisibility by 4, but obviously this is not a necessary condition for evenness. An NC for evenness would be divisibility by 2, and this does "capture the whole picture".
In the quoted text, Hurley states : "scientists try to isolate a necessary condition or group of necessary conditions that, if removed, will eliminate the smog". Let's suppose: their efforts have succeeded and they have identified the, say, 10 chemicals that cause smog. (For now, let's ignore your point about the difficulty in detecting chemical10.) Then, quasi-formally we have :
- smog = (chem1 ∨ chem2 ∨ ... ∨ chem10)
- ¬smog = (¬chem1 ∧ ¬chem2 ∧ ... ∧ ¬chem10)
Some of your confusion may arise from the fact that the disjunctive statement for smog (ie 3) is both a NC and a SC for smog since we are assuming that scientists have identified all of the chemical components of smog. Suppose that 'smog' were not defined by 3, but instead by the statement
- An SC for smog = chem1 ∨ chem7.
Then 5 is not a NC for smog since we can still have smog if there is no chem1 or chem7 present - e.g., just chem3 is present in the air. In other words, a SC is sufficient to cause a consequent, but it is not the only way to cause a consequent.
If we wish to eliminate smog, then 4 (the conjunctive statement for ¬smog) tells us that we must necessarily eliminate each of the 10 chemicals. Again, this is both a NC and a SC for no smog since we are assuming that scientists have succeeded in identifying all of the chemical constituents of smog. Suppose that ¬smog were not defined by 4, but instead by the statement
- ¬smog = ¬chem4 ∧ ¬chem8.
Then 6 is a NC for not having any smog, but 6 is not a SC since other problem chemicals may be present. The Argument Form of 6 is the 'mirror opposite' of the Argument Form of 5 (the subgroup of the disjunctive statement illustrated in the previous paragraph). Beware that I use 'mirror opposite' to describe the relation between NC and SC in the two examples, not to the formal content of 5 and 6 (since 5 and 6 are not the negations of each other): ie, 5 is a SC but not a NC, while 6 is a NC but not a SC, hence 'mirror opposite'. The use of 'mirror opposite' is probably not the best choice of words since it is perhaps too strong in this context.
The reason I have bolded try in the text quoted from Hurley is that this may be why you question the case "but Chemical 10 is fatal but hardly detectable". If scientists have not succeeded in identifying all of the constituents of smog, or are unable to detect all of the constitutents, then establishing NCs and SCs are more selective. Assuming other unknown or undetectable chemicals are required and not listed, the disjunctive statement for smog would become SC but not NC, while the conjunctive statement for ¬smog would become NC but not SC.