It's one of Prime Minister Justin Trudeau's favourite turns of phrase: "Canada's strength comes from our diversity." In his official statement after the alleged terrorist attack in Edmonton he invoked it, and whether the occasion is celebratory, tragic or anything in between, he never misses an opportunity to say that diversity is our strength. He's made it his brand identity, because the line's a political winner.

But it misses something about what makes our society strong, and what Islamist-inspired terrorists, fascists on the right and so-called anti-fascists on the left all seek to destroy.

By race, religion, language, sexuality, lifestyle and ethnicity, Canadians are visibly diverse. You see it every time we walk down the street. But that diversity of appearance hides a deeper and more powerful unity of purpose and desire. Beneath the visible differences, there's our common humanity, and our shared hopes for our lives in this country. What we share is what makes Canada possible.

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There are those who aim to set us against one another, using religious or racial difference – our diversity – as a spark for conflict. But Canadians of all races and faiths are largely united in a desire to live in a country of peace, order, good government and equality before the law, and in wanting to ensure that Canada remains a place where people of many origins and beliefs can be neighbours without fearing one another. Much of the rest of the world is not like that, and most Canadians oppose anyone who seeks to undermine this rare thing we have.

Canada's diversity is a fact. Canada's unity as a liberal, democratic society, built on a diverse population, is an act.

On Sunday, only hours after someone allegedly inspired by the so-called Islamic State launched a terrorist attack in Edmonton, the New Democratic Party elected Jagmeet Singh as its leader, marking the first time that a member of a visible minority has been at the head of a major national party. The events are related, in that they represent two possible futures: one where points of difference are points of hatred and deadly conflict, and one where what we share transcends differences in how we look, what we wear and how we pray.

Mr. Singh's leadership is being taken as a symbol of Canada's changing demography – and that changing demography is a fact. But the ability of a group of voters who mostly do not practise Mr. Singh's religion or share his background to nevertheless choose him as their representative? That is the kind of act that makes this country possible.

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And Mr. Singh, for all that is different about him compared to previous leaders, was elected because of all that he has in common with his fellow, non-Sikh Canadians. He did not run for NDP leader in order to turn Canada into – to quote the famous heckler who ironically helped him win – an Islamic state, or a Sikh state. NDP voters of all faiths – and none – could vote for him because he espoused a vision of a shared Canada.

There are, of course, people who have other ideas about this country. We saw them staging small but noisy protests in several parts of Canada last weekend: People on the far right, who oppose immigration by certain groups, and people who call themselves anti-fascists, but who tend to behave like fascists.

Neither group likes Canada the way it is. The former wants to focus on those superficial things, like skin colour and religion, and keep out those who aren't of their kind. The antifas, for their part, have a history of opposing the things that make Canada liveable: democracy, tolerance and the rule of law. The people in black hoodies with their faces covered gained prominence during Toronto's G20 protests; their idea of political speech involved smashing windows and spray-painting slogans.

Both of these groups know that their level of popular support is almost nil, which is why they feed off one another. When fascists and anti-fascists meet to protest and counterprotest, their hatred hides the fact that they are really a mutual admiration society. They have to be, because nobody else likes them much.

But the more they succeed in capturing our attention, the more anti-democratic radicals of the left have a hope of positioning themselves as the answer to the rise of the anti-democratic far right, and vice versa. As for anyone inspired by Islamic State, their only hope is that acts of random terror will provoke a backlash against innocent Canadians who just happen to share the same faith or ethnicity as a terrorist, which will eventually lead to our society becoming polarized along religious lines.

We can focus on differences as the measure of what makes us who we are, or we can celebrate differences while recognizing that what makes our society possible is all that we share. It's our choice.