July 18, 2018
As the dust settles over the wreckage left by President Trump’s visit to Europe, two things have caught my attention. The first concerns his attitude to the allies of the US, in the form of NATO and members of the EU. He gave everyone a hard time but I noticed – perhaps I am alone in this view – that the UK and Germany were subjected to more vitriol than other countries. Could it be that both have women as head of government? Does Mr Trump feel uncomfortable in the presence of Angela Merkel and Theresa May so that he has to be aggressive until he thinks they know their place?
The second point concerns the role of logic in rational thinking. Mr Trump’s lack of concern for truth and his repeated contradictory statements are dangerous. Here’s why I think that.
The law of contradiction states that contradictory propositions cannot both be true at the same time. If p is a proposition, its contradiction is not-p; the law says that p and not-p cannot both be true. Here’s a somewhat tongue-in cheek example of what happens if we admit contradictions.
We first need to define the inclusive or function, which I will write as OR. If p and q are propositions, p OR q is true if either p, q or both are true. To put it another way, p OR q is false if and only if both p and q are false. Obviously, if we first establish that p is true, then p OR q must be true even if we don’t know whether or not q is true. However, suppose we now admit that not-p can also be true, i.e. p is false. Since we have just shown that p OR q is true, then q must be true if p is false.
To make the point more clearly, suppose p is ‘Trump supports NATO’ and q is ‘Theresa May is the Pope’. In that case, p OR q becomes ‘Trump supports NATO’ OR ‘Theresa May is the Pope’. Suppose that Trump does indeed support NATO, then ‘Trump supports NATO’ OR ‘Theresa May is the Pope’ is true. Now, suppose that ‘Trump supports NATO’ is false. In this case, ‘Theresa May is the Pope’ is true because we have just shown that ‘Trump supports NATO’ OR ‘Theresa May is the Pope’ is true. This follows from allowing that ‘Trump supports NATO’ is simultaneously true and false, i.e. we have allowed a contradiction.
This example seems frivolous but it is a deadly serious point. The law of contradiction is of fundamental importance. If we admit that p can be both true and false, or, in our example, ‘Trump supports NATO’ is both true and false, anything can be proved. When we admit that contradictions are acceptable, and take a cavalier attitude to truth, rational discussion becomes impossible. We enter a world where truth becomes a matter of opinion or some kind of social construct, a world of ‘alternative facts’ and ‘fake news’. In a darker vein, we may enter the kind of world described by Orwell in 1984 where ‘War is peace’, ‘The best books… are those that tell you what you know already’ and ‘If you want to keep a secret, you must also hide it from yourself’.
The physicist Alan Sokal, who teaches at UCL and is a professor at New York University, mounted a brilliant attack on the facts as a matter of opinion viewpoint, along with wilful obscurity among other things, when he wrote a spoof article called ‘Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity’. In spite of the paper being nonsense, a well-known intellectual journal published it. In a paper he later published in Lingua Franca as part of the follow-up, he stated that
‘…anyone who believes that the laws of physics are mere social conventions is invited to try transgressing those conventions from the windows of my apartment (I live on the twenty-first floor)’.
A final thought: perhaps the first woman to become Pope will take the title Pope Theresa the First. Who knows? The name has a long religious history, albeit with a slightly different spelling.
Notes and sources
 For a detailed explanation, see https://en.wikipedia.org/wiki/Law_of_noncontradiction
 Bertrand Russell proved that he was the Pope using contradiction as the basis – hence my choice of the elevation of Theresa May.pbye