Misuse as a Use of Language

This is my first post! It discusses the question of whether spoken and written languages like English could be ’logical’ by design. I will break this post up into two parts. The first one does not require a mathematical background whatsoever, whereas the second touches on the concepts of axioms, theorems and proofs.

Fallacies

The word logic as it is used in everyday parlance refers to informal logic (as opposed to formal logic , which is instead a rigorous mathematical construct). You’ve probably come across logical fallacies such as the false dilemma , which goes something like this:

Person 1: Women and trans people are in need of better mental health infrastructure.
Person 2: How can that be, when this statistic shows that it's mostly cis men who committed self harm in 2016?
Person 3: Oh yeah? What about this other statistic about trans people which clearly shows that...

Here, Persons 2 and 3 are the culprits, for insisting that only one of two alternatives can be true. This is what we mean by a false dilemma. Of course, there isn’t actually a dichotomy here; men need better mental health support systems encouraging them to process their feelings; trans people and women would benefit from policies that make it easier and safer for them to seek help. The false dilemma fallacy makes for great bipartisan politics.

Perhaps a more subtle example of a logical fallacy is one that misdirects not necessarily in its written form, but through accent or emphasis. This is the fallacy of accent , which refers to how the interpretation of a sentence can be modified by emphasizing one word over another:

Trans people are in need of better mental health infrastructure.
Trans people are in need of better mental health infrastructure.

The second sentence may be excluding the possibility that cis people need better mental health infrastructure. It suggests that, if there is a box labeled “people who need better mental health infrastructure,” then it has room only for trans people. Whatever else you might have put into that box earlier is now gone.

The Wikipedia page for the false dilemma fallacy hints at why natural (spoken and written) languages are so amenable to misinterpretation:

Our liability to commit false dilemmas may be due to the tendency to simplify reality by ordering it through either-or-statements, which is to some extent already built into our language.

Whoever wrote this sentence suggests that fallacies are built into our language.

As a bit of a sidebar, last month, my mom demonstrated a mastery of the false dilemma, using it to win an argument that we were having over something silly. I couldn’t help but marvel at how natural her suggestion seemed to me at the moment, when conveyed in the language we were conversing in – Urdu. If only we had been speaking English instead, I would have seen right through her ploy. Maybe it’s because I use English and not Urdu to reason in my daily life. I have only ever spoken Urdu to my family, and I don’t reason with my family (mostly because it’s always a losing battle). Have I been conditioned into forgoing logical thinking while talking in Urdu? Or are fallacies not only built into our language (whatever that means), but also vary in their nature and potency depending on the language and context that we’re in?

The text After Babel by George Steiner offers a possible explanation for why fallacies might be built into languages. On page $231$, he gives his perspective on how languages are shaped over time:

We speak first to ourselves, then to those nearest us in kinship and locale. We turn only gradually to the outsider, and we do so with every safeguard of obliqueness, of reservation, of conventional flatness or outright misguidance.

As human communities manufactured their languages, they did so with the express intent of obscuring any meaning to outsiders, to maintain secrecy. If anything, the ability to lie and misdirect with language has been critical to its popularization . Just as the politicians today use the false dilemma to garner support, so have those in power used logical fallacies to their advantage for thousands of years. The honest working-class person seldom wrote seminal historical texts, their language has not propagated through time quite as well. Only those with money, time, and/or inflated egos have had the luxury of writing influential texts. The punchline comes from page $224$ of Steiner:

… the uses of language for ‘alternity’, for mis-construction, for illusion and play, are the greatest of man’s tools by far.

It is certainly one of my mom’s greatest tools.

Truth is Subjective

Humans are organized into systems, communities that talk to each other in a certain language. Between two systems, languages, with all of their words, syntaxes, enunciations, and cultural connotations, can differ either slightly (Californians v. New Yorkers) or drastically (Urdu speakers v. English speakers). Can the notion of being logical differ between the two systems (and thus, their languages)?

When in the $1600$s Galileo suggested that the Earth went around the sun, he was called a heretic for contradicting with the Catholic church’s Earth-centric model of the world. It was false that the Earth went around the Sun. In a community where everyone believes in God, it is considered perfectly logical to ascribe the creation of the universe to God. There is no reason to prove it, because to a logician within this system, the theory that God created the universe is perfectly consistent with all the theories that came prior to it. Consider as another example, that most physicists do not bother to prove that time flows in one direction . They take the flow of time for granted while solving complex equations, secretly hoping that it doesn’t lead them to any contradictions down the line. We don’t actually know for sure that time flows only in one direction, but it seems to align with all the observations we’ve made so far as a species.

These are things we lay down as foundations for our worldview, and we always need to start somewhere in order to draw further inference.

It turns out that we define truth quite similarly. Once you are within a system, the truth of that system is anything that is consistent within the system. Inconsistency, i.e., contradicting with the aforementioned truths, is what is meant by being false. How was Galileo to propose his radical idea to the world, had he not the access to a language that allowed him to be logically inconsistent with what was considered true at the time?

In both mathematics and scientific deduction, contradictions are a major blow to the field, because it means that we need to upend much of the theory that we’ve been relying on. It’s like finding out that the foundation of the building you’ve been constructing so meticulously was fractured all along. Sometimes it’s exciting all the same, it just means that we need to have an open mind and accept a new idea. Albert Einstein lived through at least three such ‘major blows’ during his lifetime. The first was of his own doing, the realization that spacetime curves and contorts in ways that are impossible for humans to even visualize. The second time, he was the one who was unsettled by the Danish physicist Neils Bohr’s theory of quantum physics .

The third blow came in the $1930$s, this time aimed straight for the very foundation of mathematics as it was known at the time. It was revealed that not only is truth subjective, but that there exist statements that can neither be classified as true nor false¹. Sometimes, things we suspect are true will elude any proof. Mathematicians did not like that, the whole point of mathematics was to prove things and to be sure that we won’t run into any inconsistencies. Mathematics was the one language that was supposed to be free of this sort of ambiguity.

Prior to these revelations, mathematicians had been sleeping soundly in their mathematical beds, unaware that a man named Kurt Gödel was undoing the screws off of their bedframe. In the next post , we will see just what Gödel (and others such as Alan Turing ) had to say to the world of mathematics and logic, what any of this has to do with language, and why these findings necessitate that natural language should be logically inconsistent if we are to do anything meaningful with it.