Radiation causes cancer.
This statement is true, false, and somewhere in between depending on your understanding of the verb "to cause".
As an introduction, in the most stringent sense of the idea that Aristotle, Thomas Aquinas and Paul Hume used to define "cause", the above is a false statement. Not everyone who develops cancer is exposed to intense amounts of radiation. In another sense of the word, the above statement is entirely true, Radiation exposure can be a contributing factor to whether or not one develops certain kinds of cancer. Finally, there is the more common sense of the word "cause" that we utilize in the English speaking world in which we would all agree with that statement.
You can learn about how radiation from sources like Radon, UV light and Nuclear Fallout have been found to contribute to cancers such as Lung, Skin, and Leukemia here, if you so choose.
Long ago, a chain of thinkers from Aristotle to more modern brainiacs tinkered with the notion of what it means for one thing to "cause" another. They developed some wonderfully specific criteria that have helped guide research in physics for some time. However, the strict causality that works great with questions of physics turned out to be far too inflexible to apply to other fields, where many many factors are at play that may not be possible to isolate to a standard that would satisfy Aristotle, Hume, or Newton. As such we have roughly three, often overlapping, ideas that we may be expressing when we say "X causes Y". Most Formal Logic textbooks and such will break it down into several clauses as follows:
Necessary: Condition B cannot occur without A, meaning that for every instance of B, there will be an observed instance of related A. Rain cannot happen without moisture in the air, for example. Moisture is Necessary for rain.
Sufficient: Condition A will ALWAYS be followed by B. For every instance of condition A, B will certainly occur. Heating liquid water at one atmosphere of air pressure is sufficient bring it to a boil.
Contribution: Condition A will, absent other factors, lead to more of B. Drought conditions during growing season will cause lower crop yields. There are a number of situations that could make this not occur for each and every type of crop and farm that exists, and many other factors can come into play (irrigation, GM crops, expanding acreage, etc...) but it is generally true that drought contributes to poor crop yeilds.
In physics, computing, and pure abstract logic, we see many instances of the necessary and sufficient clause. Thousands of tests can be done on a sample to get certainty of causality for a phenomenon regarding it being necessary, sufficient, or both to measurements like 0.9999 certain. If/Then statements, flowcharts and such are great examples of cause it its purest form.
But when talking about environments with more variables we cannot control, in messy real world situations involving things like people, or (gasp!) groups of people, we tend to utilize the Contribution concept of causality.
On some level, if you have grown up and been educated in the West (or most of the world at this point) you have internalized this if not learned it formally. When someone on Facebook links to a headline stating "Exposure to violent images causes violence", short for a study concluding something like "Repeated exposure to violent images throughout childhood correlates to increased violent behavior." and someone inevitably comments "I watched murder porn all day every day as a kid and I turned out fine..." or "Cavemen killed each other, and they never had murder porn..." we tend to feel something is wrong with that. Violent imagery is neither necessary nor sufficient to predict all instances of violent behavior, but in two similar groups, the group with the higher exposure is likely to engage in more violence.
Too often people stating Contribution levels of causality are met with disagreement from those who demand Necessary or Sufficient levels of causality before they will consider the premise. People and groups of people are too complex to expose to the kind of rigor that would "prove" causality at that level. For decades the assertion that "Smoking causes lung cancer" was held back by demands for the kind of causality and statistical certainty that simply does not exist when examining contributory impacts on things as complicated as living organisms. For an example, here is a paragraph from "Freedom-of-Choice.com" that argues smoking does not cause lung cancer:
"Smoking is but one factor that can increase the incidence of lung cancer. Over 20% of all lung cancers occur in nonsmokers.1 Smoking by itself can not cause lung cancer. The process of developing cancer is complex and multifactorial. It involves genetics, the immune system, cellular irritation, DNA alteration, dose and duration of exposure, and much more.2 Some of the known risk factors include genetics, asbestos exposure, sex, HIV status, vitamin deficiency, diet, pollution, shipbuilding and even just plain old being lazy.2 When some of these factors are combined they can have a synergistic effect, but none of these risk factors are directly and independently responsible for "causing" lung cancer!"
What made me feel the need to write this was an discussion I was having with a friend of mine about the availability of firearms and homicides. Some states and nations who have systems in place to limit access to firearms (especially for those with criminal histories or mental illness) show lower rates of firearm deaths than other places. There are many, many, other factors (population density, age distribution, poverty, efficacy of a mental health system, even climate and geography) to consider, but using all 50 states as a sample, states with looser gun laws tend to have more gun fatalities, with the correlation being found to be (r^2 = 0.42) which is a rather high correlation with social science studies with a sample size of 50. The study does a great job of reiterating "Correlation alone is not causation" and including case studies (like my home state of Missouri) where specific loosening of firearms related laws (like we had in 2007 eliminating our State's universal background checks) specifically contributed to specific murders. Laws are, of course, only one part of availability - firearms are sold illegally and stolen all the time.
It's a good study, but available in PDF form because academics are allergic to plain html for some reason - you can check it out here
Of course, as with smoking and smoking-related-illnesses, some argue that only "necessary and sufficient" can be taken into account when talking about this particular item. If humanity were as lab-controllable as chemical samples, we could likely do that. 99.999% certainty would be wonderful when discussing when we have to make hard choices about what we do in our society, but we are unique and complicated creatures and that isn't going to happen any time soon.
Making good social decisions saves lives and makes our lives better. This often requires utilizing the Contribution level of causality and ascertaining what level of contribution. Physician John Snow in 1854 saved many, many, lives by showing statistics linking exposure to fecal water to contracting cholera. Not EVERY incidence of cholera came from contaminated water (one baby seemed to get it from an infected diaper) so it wasn't a necessary condition, and not everyone who drank the contaminated water displayed cholera symptoms, so it wasn't sufficient. But is WAS contributory to cholera and by decreasing the flow of shit-water into people's mouths, he saved many lives. His story is an interesting read.
When talking about groups of people, the contributory level of causality is generally what we mean when we say "X causes Y". More people understanding this would raise our level of discourse.
*Note 1*I would love to shrink this to a more terse piece as a witty answer to every variation of "Well, I drank shit water and I didn't get sick" that would leave the reader with an understanding of Necessary, Sufficient, and Contributory... but that will have to come another time.
*Note 2* Wikipedia actually has a pretty great starting out point for the history of the concept of Causality, from Aristotle to the Modern Day.