Welcome back to The Philosopher’s Lexicon. My primary goal in this series is to explore common philosophical vocabulary, hopefully transforming these words from useless jargon into meaningful terms. My secondary goal is to highlight how contentious some of these terms can be – especially those which seem obvious. These definitions will not be comprehensive by any means, so please feel free to add your own understanding of each term as we go.
This week’s entry into the lexicon is the distinction between claims that are made de dicto and claims that are made de re. Literally, a “de dicto” proposition carries its meaning in the words that are said, while a “de re” proposition carries its meaning in the thing that exists behind the words. This is most easily understood in an example. For this, most explanations turn to Quine. The Stanford Encyclopedia of Philosophy renders his example thus:
(1) Ralph believes that someone is a spy.
This could mean either of the following.
(2) Ralph believes that there are spies
(3) Someone is such that Ralph believes that he is a spy.
The first meaning (2) is what results when the initial statement (1) is taken de dicto. The meaning of the proposition is found literally within the words given, in a self-contained way. The second rendering (3) is referring to some thing out in the world that is being represented by the words in the statement, meaning that what we are looking for is not just the meaning of the words de dicto, but the meaning behind the words, de re.
There is, of course, a lot of complexity in working out this sort of ambiguity in our language with logical notation and categorical distinctions, but what is more interesting to me is how this ambiguity plays out not just in our syntax, but in our affirmation of truths, our understanding of the world, and in our beliefs.
This distinction between de dicto and de re beliefs has been on my mind recently because of a short comment made at a theological ethics talk I attended a few weeks ago. The topic of conversation (very loosely rendered) was whether (and of course, how) the morality of an act depended upon a person’s express belief in its morality de dicto, or upon the alignment of the particular act with an objective moral standard de re.
This is, of course, a fairly easy dilemma to solve if we’re operating under expressly Abrahamic assumptions. If there is an objective standard of goodness against which all acts must be measured, then clearly that standard will supersede our own human understanding and linguistic representation of it. Moving into an expressly Christian framework, if a person professes to believe in the word of Christ de dicto, but acts in a way that is contrary to all Christian teachings, the acts themselves are still immoral.
It gets a little more contentious if we shift the model around, however: if a person uses the language wrong and perhaps misunderstands the laws in their express rendering, but follows the spirit – de re – of Christ’s teachings, then she is, for many Christians, still behaving in a moral way. Of course, for many other Christians, both an express belief de dicto and a spiritual enactment of Christ’s teachings de re are important, but it’s generally clear that while de dicto belief is debatable, de re belief is not. Romans 2 gets a little tricky with the language, but drives generally at this point:
For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.) (Romans 2:12-15, NIV).
A great exemplar of the de re form of Christianity that came up in the discussion can be found in C.S. Lewis’s Narnia tale The Last Battle (spoiler alert, FYI). There is a scene where a man finds himself face to face with Aslan in the afterlife after having spent this life piously praising and praying to another God (Tash). In re, Tash is a cruel and oppressive deity, while Aslan is a good and forgiving figure, but in dicto, the man took his God Tash to be good, loving, and protective. In describing his exchange with Aslan, he says this:
Then I fell at his feet and thought, Surely this is the hour of death, for the Lion (who is worthy of all honor) will know that I have served Tash all my days and not him… But the Glorious One bent down his golden head and touched my forehead with his tongue and said, Son, thou art welcome. But I said, Alas, Lord, I am no son of thine but a servant of Tash. He answered, Child, all the service thou has done to Tash, I account as service done to me… if any man swear by Tash and keep his oath for the oath’s sake, it is by me that he has truly sworn, though he know it not, and it is I who reward him. And if any man do a cruelty in my name, then, though he says the name Aslan, it is Tash whom he serves and by Tash his deed is accepted (Lewis 204,205).
This same model remains useful if we remove it from a theological context but still maintain an objective standard de re. When it comes to mathematics, a de dicto approach would focus on notation, equations, and formulas, while a strictly de re approach would relegate mathematical language to the role of tool which merely helps us find answers. This probably seems extremely obvious, but in practice we often focus far more on the way mathematics is expressed than on the rational truths being expressed, when in truth, we really need a balance of both. In previous posts on education I’ve called this a “vocabulary-based” approach, but the de dicto/de re distinction is perhaps more precise.
A great exemplar of this distinction can be found in an anecdote from the essay “He Fixes Radios by Thinking!” from Surely You’re Joking, Mr. Feynman!:
While I was doing all this trigonometry, I didn’t like the symbols for sine, cosine, tangent, and so on. To me, “sin f” looked like s times i times n times f! So I invented another symbol, like a square root sign, that was a sigma with a long arm sticking out of it, and I put the f underneath. For the tangent it was a tau with the top of the tau extended, and for the cosine I made a kind of gamma, but it looked a little bit like the square root sign… I thought my symbols were just as good, if not better, than the regular symbols – it doesn’t make any difference what symbols you use – but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, “What the hell are those?” I realized then that if I’m going to talk to anybody else, I’ll have to use the standard symbols, so I eventually gave up my own symbols (Feynman 24).
While we can use any symbols or language we want to explain and understand principles de re, we need a common de dicto understanding for communication. Where we often run into problems, mathematically, is that we tend to treat the way that mathematics is expressed as the truth of thing – we spend our time learning nothing but mathematics de dicto and find ourselves with little to no understanding of mathematics de re. I’m sure that the same thing could be said for nearly any subject or course of study. Feynman found this to be the case even in his classes at MIT:
I often likes to play tricks on people when I was at MIT. One time, in mechanical drawing class, some joker picked up a French curve (a piece of plastic for drawing smooth curves – a curly, funny-looking thing) and said “I wonder if the curves on this thing have some special formula?”
I thought for a moment and said, “Sure they do. The curves are very special curves. Lemme show ya,” and I picked up my French curve and began to turn it slowly. “The French curve is made so that at the lowest point on each curve, no matter how you turn it, the tangent is horizontal.”
All the guys in the class were holding their French curve up at different angles, holding their pencil up to it at the lowest point and laying it along, and discovering that, sure enough, the tangent is horizontal. They were all excited by this “discovery” – even though they had already gone through a certain amount of calculus and had already “learned” that the derivative (tangent) of the minimum (lowest point) of any curve is zero (horizontal). They didn’t put two and two together. They didn’t even know what they “knew”
I don’t know what’s the matter with people: they don’t learn by understanding; they learn by some other way – by rote, or something. Their knowledge is so fragile! (Feynman 36,37).
What is clear to me in both the theological and the mathematical examples is that while the re is different, so long as we believe there is some objective external standard of truth to be found, this distinction is absolutely necessary, as collapsing the distinction tends to lead to an erosion of understanding. In religious frameworks we end up focusing on trivial contradictions and minute, seemingly arbitrary details at the expense of the general spirit or message a particular religion is attempting to prioritize. In mathematics, we focus so much on the process that we miss out on the end result. In taking the de dicto meaning of a proposition for the de re, we shift our focus from finding truth to merely affirming agreement.
Of course, if there is no re that exists outside of our representation in language and symbols, then this distinction naturally falls apart. But while I’m unwilling to stake a claim on the exact nature of what is objectively true de re, I’m committed enough to its existence to find this distinction – and this particular piece of jargon – invaluable.