The Chinese word for contradiction is maodun, which literally means ''spear-shield''.
The term has its origins in a parable of a blacksmith selling a spear and shield. He proudly claimed that the spear could cut through any shield, and that the shield could deflect any spear. When asked what would happen if someone struck his impenetrable shield with his all-piercing spear, the blacksmith had no answer.
This paradox comes to mind when we think of the impact of Peter Casey's comments about Travellers on his presidential campaign.
The paradox was that while many were quick to condemn Casey (or at least be seen to do so) for being out of kilter with public opinion, there was an underlying sense that he was tapping into a sentiment shared by more than some might care to admit.
The election result confirmed this. When Casey made his remarks, he was at 2pc in the polls, and considered leaving the contest. Ten days later, his support had surged by almost 20pc, maybe the largest electoral swing in this short a time in Irish politics.
But what does this reveal about the paradoxical nature of Irish society?
On the one hand, we offer the cead mile failte, and love to be commended for our welcoming nature. But this is generally to white middle-class tourists looking to spend their euro, dollars and sterling here.
We also like to think that we are not a racist people, and marvel at the apparent lack of racial tension in this country.
But consider our treatment of Travellers. According to the 2016 census, 80pc of them are unemployed, compared to 15pc of non-Travellers.
Almost 60pc of Travellers fail to continue education beyond primary school. The figure for non-Travellers is 20pc.
A 2010 study in UCD found that the life expectancy of male Travellers was 15 years lower than that of male non-Travellers; the difference for female Travellers was 12 years. Infant mortality rates were four times higher amongst the Travelling community, and male suicide rates were seven times higher.
The status of Travellers in Ireland is almost akin to that of the Aboriginal community in Australia. They are generally shunned by white settler folk, with the levels of interaction between the two communities embarrassingly low.
And yet this remains a great unspoken topic, where on the one hand, a public sense of political correctness demands better treatment of Travellers, but, on the other hand, few communities are willing to have a halting site in their locality.
This paradoxical treatment of an ethnic minority by a so-called tolerant society is not a one-off phenomenon, as Irish politics is riddled with contradictions.
Indeed, the presence of a wide variety of puzzles is in itself perhaps the defining puzzle of our political system.
Take the nature of Irish democracy. On the one hand, we have a strong parliamentary tradition, being one of the longest surviving democracies, having resisted the onset of different forms of totalitarianism in the 20th Century.
In spite of this proud democratic culture, the origins of the State have shaky democratic foundations.
To begin with, the Treaty that established the State in 1922 was approved by a parliament elected entirely unopposed. Even dictatorial regimes like to maintain at least a facade of electoral competition.
The self-proclaimed president of the Irish Republic, Eamon de Valera, didn't even want the Dail to discuss the Treaty in the first place, and when it voted against his wishes, de Valera and his followers rejected the Dail's legitimacy.
At the subsequent elections of June 1922, the first opportunity for the public to give its say on the Treaty, de Valera and Michael Collins attempted to silence the electorate by forming a pact. They agreed that pro- and anti-treaty candidates would not oppose each other, with TDs being returned once again without an election. In some ways, it is perhaps surprising then that such a stable regime emerged from these less than democratic roots.
Another paradoxical element of our democratic culture was the presence of a strong element of authoritarianism, the legacy of the influence of the Catholic Church. This contributed to a deferential and anti-intellectual streak, one that was particularly suspicious of any ''-ism''. Hence ideological conflict was never a feature of Irish politics, unlike most other democracies.
We like to think that Irish political culture has come a long way since then, particularly with the recent referendum votes in favour of abortion and marriage equality.
However, this too is tinged with paradoxy.
On the same day the Irish electorate was voting for marriage equality, it reinforced age discrimination by rejecting the amendment to lower the age eligibility for presidential office.
Likewise, the absence of a radical right party, an exceptional feature of Irish politics, does not necessarily imply a new-found level of egalitarianism. The Jesuit scholar, Micheal Mac Greil, who analysed prejudice in Ireland over a number of decades, found relatively high degrees of intolerance and authoritarianism, with clear majorities in favour of imposing their views on others and curbing free speech where necessary. In other words, just because there is no radical right party does not mean there are no radical right voters.
This paradoxical conservatism pervades many facets of Irish politics. The 2011 Dail election was described as an "earthquake" because of the manner in which Fianna Fail's dominance was shattered. In spite of these seismic effects, the trinity of Fianna Fail, Fine Gael and Labour remained standing, between them winning the same number of seats then as they had done at the height of the boom in 2002.
This stable party system has prevailed since the foundation of the State, despite there being few differences between the parties, despite Irish voters having one of the lowest comparative levels of attachment to parties, despite the absence of social roots that elsewhere bind voters to parties, and despite having one of the more open voting systems.
In other words, all the conditions are present for a volatile and unstable party system. But this hasn't materialised. Another paradox.
We also have no populist party, unlike most of Europe, but then the purest populist of all - the independent - proliferates.
Despite the conservative nature of the Irish electorate and the stability of our party system, there are more independents in the Dail than the combined total in all other democratic parliaments.
These are just a flavour of the many paradoxes that permeate Irish politics. They are a problem because for democracy and society to function and flourish, we need institutions that match our culture.
But with these evident paradoxes, it is not clear what institutions are fit for purpose. If we do not know our culture, how can we design an appropriate institution?
Problems arise when an irresistible force, such as the aforementioned spear, meets an unmovable object, such as the accompanying shield.
When Peter Casey makes statements about Travellers, we shift uneasily in our seats and are not sure how to respond.
Are we a liberal democratic culture that should condemn him? Are we missing a populist party to cater for such sentiment?
Where exactly do we stand in relation to minorities? What values imbue our political culture?
The truth is we don't know. But it is only through individuals such as Peter Casey raising this topic that we get closer to finding out about ourselves. So the presidential contest did have one positive consequence at least. Fancy another election, anyone?
Dr Liam Weeks is director of the MSc Government & Politics at UCC