Here’s a paired response you can hold on to for when an opponent claims that the infinite magnitude of a wildly improbable extinction risk means that it must be acted on:
Our opponents have claimed that the magnitude of an extinction risk is infinite and therefore we should take action to avoid it no matter how unlikely it is to happen. We’ve got two responses: first, mathematical abuse of the concept of infinite leads to absurdity and second that extinction risks aren’t even infinite.
First, in The Restaurant at the End of the Universe (1980), Douglas Adams demonstrates how the notion of “infinite” breaks mathematical logic:
The Universe — some information to help you live in it:
1. AREA: Infinite
The Hitchhiker’s Guide to the Galaxy offers this definition of the word “Infinite.”
Infinite: Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real “wow, that’s big,” time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by colossal multiplied by staggeringly huge is the sort of concept we’re trying to get across here.
2: IMPORTS: None.
It is impossible to import things into an infinite area, there being no outside to import things in from.
3: EXPORTS: None.
4: POPULATION: None.
It is known that there are an infinite number of worlds, simply because there is an infinite amount of space for them to be in. However, not every one of them is inhabited. Therefore, there must be a finite number of inhabited worlds. Any finite number divided by infinity is as near to nothing as makes no odds, so the average population of all the planets in the Universe can be said to be zero. From this is follows that the population of the whole Universe is also zero, and that any people you may meet from time to time are merely the products of a deranged imagination.
So, according to Adams, since nobody — inclusive of our opponents — are statistically real we don’t have to try to save them. Or, for a more simple analytic, our opponents’ abuse of the notion of “infinite risk” makes all risks — plausible and otherwise — functionally equivalent and if they can’t solve for every way you can think of to die — like “rampaging herd of zombie wombats” — then they’ve got no actual solvency and should lose, RFD: rampaging herd of zombie wombats.
But secondly, extinction really isn’t all that bad. Earth has gone through several mass extinctions. Wikipedia summarizes (ref 3/23/2014):
In a landmark paper published in 1982, Jack Sepkoski and David M. Raup identified five mass extinctions. They were originally identified as outliers to a general trend of decreasing extinction rates during the Phanerozoic, but as more stringent statistical tests have been applied to the accumulating data, the “Big Five” cannot be so clearly defined, but rather appear to represent the largest (or some of the largest) of a relatively smooth continuum of extinction events.
- Cretaceous–Paleogene extinction event (End Cretaceous, K-T extinction, or K-Pg extinction): 66 Ma at the Cretaceous.Maastrichtian-Paleogene.Danian transition interval. The K–T event is now officially called the Cretaceous–Paleogene (or K–Pg) extinction event in place of Cretaceous-Tertiary. About 17% of all families, 50% of all genera and 75% of all species became extinct. In the seas it reduced the percentage of sessile animals to about 33%. The majority of non-avian dinosaurs became extinct during that time. The boundary event was severe with a significant amount of variability in the rate of extinction between and among different clades. Mammals and birds emerged as dominant land vertebrates in the age of new life.
- Triassic–Jurassic extinction event (End Triassic): 200 Ma at the Triassic-Jurassic transition. About 23% of all families, 48% of all genera (20% of marine families and 55% of marine genera) and 70% to 75% of all species went extinct. Most non-dinosaurian archosaurs, most therapsids, and most of the large amphibians were eliminated, leaving dinosaurs with little terrestrial competition. Non-dinosaurian archosaurs continued to dominate aquatic environments, while non-archosaurian diapsids continued to dominate marine environments. The Temnospondyl lineage of large amphibians also survived until the Cretaceous in Australia (e.g., Koolasuchus).
- Permian–Triassic extinction event (End Permian): 251 Ma at the Permian-Triassic transition. Earth’s largest extinction killed 57% of all families, 83% of all genera and 90% to 96% of all species. (53% of marine families, 84% of marine genera, about 96% of all marine species and an estimated 70% of land species, including insects. The evidence of plants is less clear, but new taxa became dominant after the extinction. The “Great Dying” had enormous evolutionary significance: on land, it ended the primacy of mammal-like reptiles. The recovery of vertebrates took 30 million years, but the vacant niches created the opportunity for archosaurs to become ascendant. In the seas, the percentage of animals that were sessile dropped from 67% to 50%. The whole late Permian was a difficult time for at least marine life, even before the “Great Dying”.
- Late Devonian extinction: 375–360 Ma near the Devonian-Carboniferous transition. At the end of the Frasnian Age in the later part(s) of the Devonian Period, a prolonged series of extinctions eliminated about 19% of all families, 50% of all genera and 70% of all species. This extinction event lasted perhaps as long as 20 M[illion years]a, and there is evidence for a series of extinction pulses within this period.
- Ordovician–Silurian extinction event (End Ordovician or O-S): 450–440 Ma at the Ordovician-Silurian transition. Two events occurred that killed off 27% of all families, 57% of all genera and 60% to 70% of all species. Together they are ranked by many scientists as the second largest of the five major extinctions in Earth’s history in terms of percentage of genera that went extinct.
Despite the popularization of these five events, there is no fine line separating them from other extinction events; indeed, using different methods of calculating an extinction’s impact can lead to other events featuring in the top five.
None of these extinction events actually killed everything and all of them together helped make it possible for us to be here today. Point is that extinction is hardly the infinite risk they’ve hyperbolized it to so don’t trust their self-serving ability to assess risk or make a cost-benefit analysis, and even if extinction were just that bad the variety of ways to die that they can’t solve for means that there’s not a logical reason to vote for them.
Cut card here.
At this point, you may want to run a Politics of Fear critique on your opponents’ rhetoric claiming that their irrational hyperbolic fear-mongering makes them bad people whose policy suggestions should always be considered doubtful. Hold their infinite claim, indict them on it, refuse to trust any different evidence that they offer. Extend it with something like “Our opponents have clearly demonstrated that they can’t even cherry-pick good evidence to make their point so why should we trust any of the evidence they present? Dismiss the remainder of their position with prejudice and we can be done here” if you think your judge is tired and annoyed enough to want to be done with the round, doubly so if you’ve given them an independent voter for your side.
If your opponents beg and plead on 1% chance of solvency, then run a counterplan of sending them to a Gambler’s Anonymous 12-step program because if solvency is unlikely then they need to come back with a better plan, not foolishly squander time and resources on a plan they admit is unlikely to work. (Note: this applies to chance of solvency, not partial solvency. I’m a big fan of partial solvency if it’s honestly admitted, which is usually isn’t, because a great many teenagers prefer melodrama to nuance — and that’s really the root cause on why I’m writing this, isn’t it?)
Please note that the one thing you can’t do here is say the word “infinite” in any other context, like “infinite prep time” on a block of idiotic stock topicality cards that end with “fairness and education” that you shouldn’t be reading anyway. Doing so is a double turn on the absurdity indict and will either get it or you dropped, and rightly so: if you can’t bother to think about what you’re saying, then what makes you think the judge should bother thinking about it either?
Additionally, please be aware that the universe is not simply infinite; scientists estimate that there are up to 1082 particles in it from which all stars and planets and whatnot gets constructed. The purpose of the Adams (1980) card is to prove that math concepts can be abused, not actually prove anything about the universe, thus even if your opponents can disprove the astrophysics of it, the math is still technically as plausible as anything they might claim.