L1.9 Lottie’s ninth lesson on concepts
The next day, Lottie surprises her tutor by being in his study before him. She has skipped breakfast while he has been delayed at it by the Chairman of the Potting Shed Committee, in effect ‘the boss’ and so, in effect, his boss. Hipparchus is a very private hippo whose past career remains something of a mystery to all but the Chairman and his own sister, Lois, who also lives here. Having left all that behind very suddenly, he is wary and resistant to the idea of answering to someone. But Alcock seems instinctively to understand this, has only made two demands of him and has left it entirely up to him how he carries them both out. One task is teaching Lottie. Today, he wanted to know how that was going. Hipparchus thinks he detected some pleasure from Alcock that he had heard that some of the younger grownups also wanted to attend some of the lessons.
Who would have thought that they would have spent two whole weeks on the nature of concepts? Hipparchus is grateful for the freedom to follow where the demands of education might lead.
But Lottie realised last night in her bunk that she still cannot answer a fundamental question about concepts even after 8 days of lessons. So she rushes in now.
“I want you to tell me what a concept is. No ifs and no buts. Tell me! If you cannot, then teachers are rubbish! I sort of get what you mean when you say they are abstract. And I sort of see why you like bloody pTravis’ bloody ruler and millimetre example – bloody pTravis! – but I don’t know where that gets us. What… is… a concept?!?”
Today ignoring a tone which on other days would deserve a reprimand, Hipparchus begins: “I had hoped that what I’d said up until now was enough to answer that. And yes, I do like pTravis’s example. That young fellow has a fine mind!”
Lottie looks a little nauseated but her tutor continues.
The intentional stance
“I think I mentioned that Daniel Dennett has a similar idea to Davidson’s for how to ‘naturalise’ – or fit into nature – meaning. He contrasts three explanatory stances we can take to the world. There is the ‘physical stance’ in which prediction and explanation is a matter of subsuming things under natural laws. There’s the ‘design stance’, in which we predict that designed objects will function as they are designed to: you might predict when your alarm clock will ring by where the alarm hand is pointing without knowing any of the underlying physics. And we can predict ‘intentional systems’ using the ‘intentional stance’ which deploys a rational calculus concerning what rational subjects ought to think and how they ought to reason. Dennett thus aims to shed light on what is ‘measured’ through our systems of measurement.
There are some complications. It turns out that he has to think that not deploying the intentional stance would lead to ignorance of real features of the world even if, say, Martian neurologists were able to make exact predictions of our future actions – I should really say our movements! – just using the physical stance (via an exact neurology). So it is not a strategy without some ‘conceptual’ costs. The conceptual realm is not reduced to anything more basic nor somehow shown not really to exist, to be an artefact of ‘measurement’.”
“I think you’re playing for time! What are concepts?”
“Very well. Here’s a succinct answer. A concept is the ontological shadow of a rule.”
A concept is the ontological shadow of a rule
“Oh! I didn’t see that coming.”
“Only someone who admired Wittgenstein’s philosophy would say this. Wittgenstein spends more than one hundred paragraphs of his great book – the Philosophical Investigations – discussing what it is to follow a rule. One element of this concerns the worry that being able to follow a rule, for example adding 2 or making judgements of what is red, is an ability that one can demonstrate over time, into an indefinite future. But also, one can come to understand it in a flash. What sort of mental state could one get into in a flash but which would lead to making the correct judgements in the future? I hope you see the connection back to Fodor and Millikan. Causal mechanisms won’t do. But equally, any mental symbol, or formula or pictures won’t be enough on its own because you would also need to know how to apply or interpret it.
Wittgenstein concludes that understanding a rule is a basic – in the sense that nothing more fundamental can explain it – ability. ‘In the beginning was the act’ as he quotes from Goethe.
The ‘plus 2’ rule goes beyond all the additions of 2 that numerate creatures like us have ever made. It is of unlimited application. We could never exhaust our mastery of it. We could always give more examples of it. And yet… we can grasp this rule.”
“But surely that’s just because we grasp some sort of formula or pattern?”
“Any such formula or pattern would have to be applied to each new instance. Think of the new instances as like our thought about ‘the next visitor to the Potting Shed’. We do not yet have that specific instance in mind. We cannot have a singular thought about it. We cannot name it! So we always encounter it de novo”
Something begins to fizz in Lottie’s mind. It seems she is standing on some kind of precipice of thought.
“But if a formula or pattern or anything like that won’t work, what makes what I do when I next add 2 to something right? Who is to say? Why cannot I just say what I like? Surely this is a get out of gaol for all my future maths exams?!?”
“Very good. It can seem that way. But do you really think I have nothing to say about why wrong answers are wrong? It is true that my explanations will run out. You might be a particularly stupid axolotl who cannot be taught maths. But in fact, what is possible in the sublunary realm is possible. I can teach you maths. You can understand or even just brutely ‘acquire’ the rules. And part of what you acquire, which will guide your shopping lists for the rest of your life, is the concept of adding 2. The concept is the ontological shadow of this - or other - rules. We ‘thingify’ our ongoing rule-guided actions.
This series of discussions began because last week you said ‘concept shmoncept’ when we were discussing justice. What is the concept of justice? Well, in part at least, it is the intellectual practice of thinking about and assessing legal judgements, the interactions of subjects, and the functioning of civic society such as this Potting Shed community. The concept of justice is the ‘shape’ of our considered responses to a range of related questions of how to think and act. The idea of ‘concept’ crystallises our judgements into something thing-like which is sometimes a helpful way to talk. It is an abstraction from the articulation of our judgements into subsidiary elements. We say that this and that is just. In so doing, we spell out a conception of justice. But as I said nearly two weeks ago: it is important to start from whole thoughts or whole judgements. A concept is an abstraction from that.”
Hipparchus implies, by turning back to his bookcases, that the lesson is over. In truth, Lottie feels a little bludgeoned by it. Has she the answer to her question? Or has she merely picked up merely a slogan? It is too soon to tell.