I have discussed in another blog piece how a British man has been convicted over a joke. That alone ought to make anyone interested in freedom of speech uncomfortable. But the case of former police officer Stephen Gray raises an even more interesting question than whether an offensive joke should result in prosecution. What if, considered literally, the supposedly offensive statement is actually true?

The meme at the centre of the controversy showed bacon and contained the line: "People who eat bacon have a lower chance of marrying a 9-year-old!" Gray was prosecuted after sharing it online. According to reports of the case, the judge regarded the meme as grossly offensive and rejected the suggestion that it represented legitimate political commentary.

There is an important complication that should be acknowledged immediately. Gray reportedly explained in court that the joke referred to Muhammad and Aisha and that he intended it to raise the issue of child marriage in Muslim countries. That makes the prosecution's argument about the religious meaning of the meme considerably easier. He supplied an interpretation that the words themselves did not expressly contain.

But suppose he had said nothing.

Suppose his lawyer had simply put the meme before the court and asked the prosecution to identify precisely what factual proposition was being condemned. The words do not mention Muhammad. They do not mention Islam. They do not mention Muslims. They make a proposition about bacon eaters and the probability of marrying a nine-year-old.

That proposition is capable of empirical examination.

Indeed, if we confine the claim to contemporary Britain, the bacon part of the statement turns out to be logically redundant. A person cannot legally marry a nine-year-old in Britain. Consequently, the probability that a British bacon eater will legally marry a nine-year-old is zero. But the probability that a British vegetarian will legally marry a nine-year-old is also zero. So is the probability for someone who eats chicken, tofu, fish or nothing but lentils.

Bacon has no demonstrated causal connection with the result. It simply identifies a subset of a population in which the event in question is already legally excluded.

Consider an analogous statement: "Australians who eat Vegemite have a lower chance of legally owning slaves." The statement is true, but not because Vegemite possesses mysterious anti-slavery properties. Australians who hate Vegemite also cannot legally own slaves. The relevant explanatory variable is Australia's legal and institutional system, not breakfast spread.

This is elementary formal logic, and probability theory, but it exposes something fascinating about the bacon joke. Its literal proposition and its implied proposition are different things.

Nobody seriously thinks eating bacon biologically immunises a person against child marriage. The humour depends upon the listener recognising that bacon carries cultural associations. The reader is invited to supply what linguists and philosophers call an implicature: something communicated without being explicitly stated.

That is precisely where the case becomes interesting from a free-speech perspective.

If Gray had remained silent about his intended meaning, the prosecution would have had to move beyond the words he actually posted. It would have needed to argue that although he did not mention Islam, Muslims, Muhammad or Aisha, an ordinary reader would nevertheless understand bacon as a reference to Islam and the reference to a nine-year-old bride as an allusion to the traditional Islamic accounts of Muhammad's marriage to Aisha.

Perhaps many readers would. But notice what has happened. The legal controversy has moved away from whether the proposition expressed in words is true or false. It has become a controversy about an inferred cultural meaning.

The state is no longer merely examining what somebody said. It is examining what somebody meant, what an audience might infer, and whether that inferred meaning is sufficiently offensive to justify criminal sanction.

There is another difficulty. Child marriage is unquestionably a legitimate political subject. Britain itself has legislated against it. Governments, international organisations and human-rights groups collect statistics on child marriage and campaign for its elimination throughout the world. It would be extraordinary to maintain that child marriage becomes an illegitimate subject for political discussion merely because religious beliefs or practices enter the discussion.

The wider international version of the bacon proposition could even be tested. Take reliable international statistics on pork consumption and compare them with reliable statistics on child marriage. My expectation is that countries with high pork consumption would exhibit substantially lower rates of child marriage than many countries where pork consumption is negligible. That would not demonstrate that pork prevents child marriage. Correlation is not causation. Wealth, education, women's status, secularisation, legal institutions and numerous other variables would have to be considered.

But if such a negative correlation exists, something rather awkward follows. The joke could simultaneously be crude, culturally provocative, causally misleading and statistically correct.

Those propositions should not be confused. A statement does not become statistically false because somebody finds its implication offensive. Nor does demonstrating a statistical relationship prove the cultural explanation insinuated by the person making it. Courts should be particularly careful about keeping these questions separate when criminal liability for speech is involved.

Gray unfortunately weakened this fascinating line of defence by reportedly telling the court what he intended the meme to mean. Once he expressly connected it with Muhammad, Aisha and Muslim child marriage, there was no longer much mystery about the intended target.

But imagine the defendant who did not do that.

"Where does my statement mention Islam?" his barrister might ask.

Nowhere.

"Where does it mention Muslims?"

Nowhere.

"Can a bacon eater in Britain legally marry a nine-year-old?"

No.

"Then which factual proposition contained in the words before the court is false?"

At that point the prosecution would have to say that the problem lies not in the literal proposition but in what everyone understands the choice of bacon to imply.

That may still be enough under Britain's communications laws, depending upon the offence and the applicable legal test. Courts are entitled to consider context, implication and how communications would reasonably be understood. But as a matter of political philosophy, we have arrived somewhere uncomfortable. The criminal law is potentially punishing not an expressly stated proposition but a culturally inferred meaning attached to it.

There is a further irony. The second meme involved in Gray's case reportedly concerned adult migrants allegedly presenting themselves as children. That communication was treated differently because it was regarded as political commentary. Yet child marriage is surely political as well. Parliament legislates about it. Governments regulate it. International organisations campaign against it. Immigration can affect the enforcement problems surrounding it. The presence of a religious dimension does not magically transform a public-policy question into something beyond legitimate political criticism.

Religion has never enjoyed such immunity in a genuinely free society. Christians can be mocked over biblical morality, Catholicism over clerical abuse, fundamentalists over creationism, and religious conservatives over sexuality. That is frequently unpleasant and sometimes deliberately insulting. The answer traditionally supplied by liberal society was more speech, argument, satire and ridicule in return, not prosecution.

The bacon meme is hardly Voltaire. It is crude internet humour. But freedom of speech was never particularly necessary for observations everybody considers tasteful.

The hypothetical "bacon defence" therefore exposes something larger than one man's joke. Bacon is logically redundant to the literal proposition. Its significance exists almost entirely in the implication the audience attaches to it. Once that is understood, the question becomes much clearer.

How far should a supposedly free society permit the criminal law to punish people not simply for what they say, but for an offensive meaning that the state believes everyone knows they meant?

That is a considerably more serious question than the joke that started it.