What makes the "lazy arguments" (you have no chance, so don't bother) valid or invalid?

Question

What I am thinking of is not exactly like the Lazy argument described in Wikipedia. I am thinking of a general argument where a normative conclusion towards inaction is drawn from the knowledge of the extreme improbability or certainty that the goal of that action cannot be achieved. For example, "it is extremely improbable or almost certain that you will not be accepted into Harvard, therefore you shouldn't apply"(assuming that person is dull). Another example could be an "active" argument, such as "it is extremely unlikely that you will be attacked by a shark in Maine, therefore it is safe to swim". These type of arguments are obviously "valid" or sound (I don't know what the correct word to use would be), and I think also the person who would defer from those normative conclusions would maybe even be considered irrational.

In contrast to these, there seem to be "invalid" lazy arguments where the normative conclusion seems wrong or bizarre, for example "you shouldn't bother eating healthy, since death is inevitable" or "science is pointless, since absolute knowledge is impossible" or "you shouldn't bother preserving the species, since humans will eventually go extinct".

So My question is, why do the more practical arguments of this type have force, but the later ones seem sophistical? I was thinking maybe that the first type of arguments have actual achievable "goals" where those of the second type seem there is some sort of equivocation or confusion about what the goal is.

Answer 1

What we have here are not logical arguments, but their pragmatic replacements, cost/benefit judgement calls. But your intuition is not far off, the problem is in the basis for judgement. In practical examples that basis is clear and there is even implied quantification of cost/benefit. Applying to Harvard presumably requires a lot of effort, saving this effort produces an obvious benefit, the same with shark attacks in Maine, assuming you enjoy swimming. Obvious benefits are accompanied by minimal costs due to low probability of adverse effects.

But what exactly is the cost/benefit in "you shouldn't bother eating healthy since death is inevitable"? Saving effort on healthy eating? If so, the obvious extension is "you shouldn't bother living since death is inevitable". But if the latter is not acted upon then living is apparently recognized as having a benefit in itself, while the impact of healthy eating on that is obviously ignored in the original "judgement". Similarly, "science is pointless, since absolute knowledge is impossible" suggests that the "point" of science is "absolute knowledge". If that is the case, good call! However, usually science's goals are seen as far more modest and practical.

The difference between validity and soundness is that a sound argument also has true premises. Loosely applying it here these "arguments" are "valid" if the "point" they suggest is accepted as the basis for judgement. But once the said "point" is spelled out it becomes very hard to see how this basis is sound.

Answer 2

The "death is inevitable" conclusion is wrong, because while death is inevitable for humans, a healthy life style can increase the number of years you live, and can increase your enjoyment of these years.

So unless the healthy food is so awful that you would prefer dying young to eating that food and dying old, there is a very strong argument for living healthy.

The whole argument may also be an example of the Nirvana fallacy, where any solution to a problem is rejected unless it is perfect. So any suggestions to reduce the number of abused children would be rejected unless child abuse can be completely prevented, a burglar alarm would be rejected unless combined with automatic weapons that can keep any army away, and of course healthy food is rejected unless it makes you immortal.