L1.10 Lottie’s final lesson on concepts

Having warned Hipparchus of a slight delay to the tutorial, Lottie, pTravis and Masongill have pulled three chairs together in the breakfast area of the Potting Shed and are trying to agree what final questions to ask about concepts in this the last lesson. Hipparchus has told Lottie that he has to go somewhere else at the end of the lesson and so to use the time wisely. With the innocence of youth, she does not know that this is simply a white lie designed to get her to concentrate. The three ‘students’ have bits of paper with questions written on which they are trying to arrange in some sort of order.

After the previous lesson, Lottie had asked pTravis – who did study a bit of philosophy at school – when she might realise whether she’d got an answer that would satisfy her to her last question about what concepts really are. pTravis pointed, a little pretentiously, at the poster of Zhou Enlai on the wall of their den and said: “It really can be like that, in my experience. You’ll find out whether you have a plausible answer or not but with time.” Today, however, she wants clear answers to specific questions!

“Have you noticed” she says “That I’ve not really been taught much useful stuff about specific concepts, just stuff about one possible overarching framing for thinking about concepts in general?”

“But do we really speak much about concepts as such anyway?” asks Masongill.

“I caught Hipparchus sitting alone in front of the second stove, the one near his study, the other night, drinking some Armagnac and asked him whether he was teaching you what concepts are, or what it would be helpful to think they are, and he quoted Woody Allen. “Right now it's only a notion, but I think I can get the money to make it into a concept, and later turn it into an idea.” He said that the philosopher Christopher Peacoke quoted this in his book A Study of Concepts. I think he thinks that one cannot really go about talking about concepts bald-headedly. He said that Michael Dummett had said that too, and something about plumbing.”

“This isn’t really helping! What do we want to know?”

The three of them jot down some questions on a big piece of paper.

1. What are concepts for the last time?!? Are they mental? Are they in the head? Can they be shared or are they private to each thinker?
2. What about differences in concepts? Are some concepts more objective than others?
3. What about scientific concepts? Are they different from everyday ones?
4. What’s the connection between concepts and theories? Do concepts change when theories change?
5. Can concepts change (or even evolve)? Or are they immutable, abstract – perhaps Platonic? – entities that we can discover or learn about, like mathematical numbers?
6. If concepts are concepts of things, does it help to talk about concepts when one could just talk about the things?

Lottie is proud of the last one.

And so, with the list written, they all set off to beard the tutor in his lair.

***

Hipparchus reads through the list and warns his students that he will have to give short answers. This is not an ideal way to deal with philosophical problems, puzzles and issues but if they know that this is how he will reply, they can at least make a judgement about the weight to place on his answers. It will be no bad thing if they later decide they are not satisfied with his suggestions. Then, they will have to think a little for themselves.

What are concepts for the last time?!? Are they mental? Are they in the head? Can they be shared or are they private to each thinker?

“I’m not going to try to answer the first part again in isolation. On the account I have given, concepts are abstractions from thoughts. But note that ‘thought’ can mean a particular dated particular instance of someone thinking, as when someone is struck by a thought, or thinks something for the first time, at some time on some day. But it can also mean the content that is thought, what they think. Two people can share the latter. But they cannot both share the same act of thinking any more than they can share the very same itch. At most, they can try to think about the same topic at the same time and may come to the same conclusions. Thought, in the latter sense, is abstract and essentially shareable. It is the abstract calculus deployed by Davidson’s radical interpreter. And so concepts, being abstractions from those abstracta, are similarly shareable.

Now, starting from this picture suggests that the raison d’etre of thought and thus concepts is to be sharable. That is not yet to say that no thought or concepts could be private. Just because the general framework is designed to be sharable need not rule out some private thoughts. However, both Frege and Wittgenstein thought that privacy in the sense of essentially unsharable was impossible. 

Wittgenstein’s arguments turn on the idea that thinking requires some constituent successes which essential privacy threatens. Suppose, for example, one uses some internal mental act of pointing – a singular thought – to baptise a sensation as one might baptise a shade of colour, using a colour sample, for which one lacks a word. Thus one might say, in the latter case, ‘That shade!’ and in the former ‘That feeling!’. Note that such a feeling would have to be unconnected to standard ways of inducing it or natural instinctual expressions of it for fear of lapsing back into the sharable. (The name of the sensation might then be the name of whatever is caused by a pinprick and is expressed in a yelp: both parts of the shared world). For an inner baptism to serve as a demonstrative concept, however, one must be able to remember it successfully for a while. In the colour example, one’s capacity to remember can be tested, developed and assessed. Colours are part of the public shared realm. In the latter private case, there is no test. What seems to one to be an instance of the same feeling experienced again later is all one has to go on for it to count as being ‘the same’. And that shows that one cannot, here, meaningfully talk of sameness at all. As Wittgenstein says: ‘One would like to say: whatever is going to seem correct to me is correct. And that only means that here we can’t talk about ‘correct’.’ (2009 §258) Privacy of concepts fails.

Are concepts in the head? Well I have talked much of singular thoughts which contain singular concepts. And these are essentially object-dependent (whether through demonstratives or proper names). So, no, they are not constituted purely by matters internal to the head. Next!

What about differences in concepts? Are some concepts more objective than others?

“You are right to imply that I have not talked about this. Let me sketch an indirect reply. I have suggested that we should start from whole thoughts and carve out abstract conceptual structure from them. And I have rather implied the primacy of truth and falsity as measures for thoughts or judgements that something is the case. (We might also think of imperatives as expressive of thoughts, too. If so they are fulfilled or not, rather than true or false.) If what is the case is an objective matter, then any plausible account of thought had better show how once a thought is identified, its truth turns only on the objective realm.

But of course, it’s plausible to think that some judgements are not objective, are not judgements in that sense. What’s the best sport?”

“Footer, obvs!”

“Rugby, I think.”

“It is cricket. Test cricket, specifically.”

“Well we might think this an objective matter and that Lottie and Masongill are wrong and pTravis and I right. Or we might think this an expression of a mere subjective preference. We need to look to the philosophy of value judgements. Not today!

But this would feed back into the philosophy of thought or content in the nature of the articulation of thoughts. Carving out concepts of quality for sport should be seen to be a different matter to other concepts. They play a different role. In a nutshell, our concepts inherit objectivity from the best account of the thoughts in which they sit. Some concepts are of objective matters. Others may not be. Let me return to this after the next questions.

What about scientific concepts? Are they different from everyday ones?

&

What’s the connection between concepts and theories? Do concepts change when theories change?

“I regret that we have not discussed this more. Lottie: remind me to cover the philosophy of science in the autumn. I’m going to take these two sets of questions together.

In the early twentieth century, there was a dogma that scientific theories could be divided between their observational claims and their theoretical claims and that the former could be used to define the latter. This was a form of empiricism. Theoretical concepts were thus defined using observational concepts. That dogma was abandoned in the final quarter of that century. It was replaced by the idea that theories formed wholes such that theoretical concepts - or rather theory-observational concepts - are defined by reference to the totality of claims advanced by theories.

One apparent consequence of such theory holism, which replaced a distinction of theory and observation, was that changes of theories changed all the constituent concepts within theories and this suggested a worry that theories thus could not be rationally compared – that they were ‘incommensurable’ – because they comprised different theoretical (or theory-observational) languages.

Now, views such as Putnam’s account of natural kinds formed one response to that worry. Perhaps ‘gold’ refers to the same substance even as theories of gold’s nature change because the nature of the substance gold that fixes the concept of gold. If so, the concept - understood as purely referential - does not change despite the fact that what we think about gold does change. If we tether the concept referentially to the natural kind, then theory change does not change concepts. If, by contrast, we allow that what we think of gold, and hence our concept of gold, includes some of the theoretical claims we make about it – such as our knowledge of its atomic structure – then it seems that the concept does change.

But whether this shows that scientific concepts are interestingly different from non-scientific ones is hard to say. Much turns on the balance between the possibility of moments of baptism in which, in effect, demonstrative concepts can be articulated, and, by contrast, the idea that scientific concepts are often the articulations of hypothetical theoretical descriptions. 

However, linking this question back to the previous one, scientific concepts can raise the question of mind-independence in a particularly vivid manner. Do scientific concepts pick out purely objective features of the world or are they also, sometimes at least, expressions of our interests or perspectives? For example, the concept of weed is not a purely biological matter. No equivalent of Putnam’s view could apply to weeds. Weeds do not share an underlying structure. They share gardeners’ negative evaluations. By contrast, biological species do seem to be objective or natural kinds even though they too lack single essential structures. Species allow variation and its seems likely that the identity of a species depends on a kind of relative stability produced by a combination of intrinsic biological - such as genetic - and external environmental factors. They look to be a ‘homeostatic property cluster’. 

Secondary qualities may be candidates for mind-dependence. It takes a specific kind of visual system to perceive colours as some of us perceive them and hence one reaction to that is to view them, not as real properties of surfaces, but as artefacts of perceptual systems. An alternative is to think of them as genuine objective properties but comparatively shallowly embedded in natures properties. 

Such comparisons can prompt a wonder whether, in some universal way, all our concepts are in some sense expressions of our form of mind, a kind of Kantian transcendental idealism. Some take this to be the implication of Wittgenstein’s discussion of rule following. But we have no time for this topic now. Next.

Can concepts change (or even evolve)? Or are they immutable and abstract – perhaps Platonic? – entities that we can discover or learn about, like mathematical numbers?

“I detect pTravis’ wing in this question. Excellent!”

Lottie makes the universal sign for gagging.

“Language changes. The thoughts we express change. So the concepts that can be carved from our thoughts change. But do the concepts themselves change. Or is it – and this seems the only alternative – that we speak of different concepts. We used to speak of phlogiston. We had a concept of it wrapped up in a theory of combustion. We no longer hold that theory or speak that way. It seems sensible to me to say we still have that concept and it is helpful for historians of science. But we no longer think that it is instantiated. There is no phlogiston in the world.

One complication concerns what can be thought. Lottie, what’s the largest prime number?”

“I’ve no idea. 1001? Obviously not. I’ve no idea. I bet it’s very big! A very very big number... plus 1!”

“Not a silly idea. And it seems, Lottie, that while you were thinking of the clever idea of adding 1 to what otherwise might be a divisible ‘round’ number, you were thinking of ‘the largest prime number’ and its properties. But it can be proved that there cannot be such a number. So can we have such a concept? We can have the concept of a prime number. We can have the concept of a larger prime number. But can we have the concept of the largest prime number?”

“Can’t we use the Theory of Descriptions – as for the present King of France? Might it not be just an un-instanced concept, like phlogiston?”

“Try to think whether you can separate the conjuncts in this new case. But akin to the risk to a singular thought of uninstantiation, we need to think of the two roles of concepts. They carve out the rational stance of a thinker to the world. And they are an aspect of how thought can successfully reach out to the world.

Let me gesture at the issue another way. Thomas à Kempis said that man proposes and God disposes. We can think of a conceptually articulable judgement as like that. Once we have made a judgement the world may or may not be in accord with it and thus it may or may not be true. This suggests that the conceptual realm, the realm of thought, is independent of the world and simply measures it. But we have already noted that names do not have such independence. Whatever the generality in the concept of Frege – however Frege himself might have varied and still been Frege – the fortunes of that name turn on the actual existence of Frege. And there is more. Even a ruler used to measure, for example, pTravis’s fine pipe is itself a part of the world, an object used with a particular technique. And that technique is the technique it is because of a certain uniformity in application. As Wittgenstein says: 

§242. It is not only agreement in definitions, but also (odd as it may sound) agreement in judgements that is required for communication by means of language. This seems to abolish logic, but does not do so. – It is one thing to describe methods of measurement, and another to obtain and state results of measurement. But what we call “measuring” is in part determined by a certain constancy in results of measurement.

So we should balance our tendency to think of concepts as abstract entities in a Platonic realm with awareness of their grounding in practices and judgements. 

On the other hand, and please think about this afterwards, conventionalists in philosophy deny Platonism and think that formal systems such as the rules governing arithmetic are established by convention only. They answer only to our decisions, to nothing other than our convenience. And indeed conventions abound such as for setting the mundane names of abstract concepts. But once one has set up conventions – set up the rules of the game – some things seem to follow. Now, does what follows also have to be established piecemeal by convention? If I set up the symbols for the positive integers such as 2 and 7 and for the plus function and perhaps explain the latter, do I also have to set up a new convention for every addition? And if not, why not?

You will notice that I have not answered the original question.

If concepts are concepts of things, does it help to talk about concepts when one could just talk about the things?

“We began this two week series of lessons because Lottie thought it funny that I talked about ‘the concept of justice’. I could just have talked about justice. And there had better be an obvious route from the concept of justice to justice in at least some cases. Concepts are ways of thinking about aspects of the world.

But why speak of concepts at all? Let me end with two suggestions. The first is that, while it may be a term of art, it helps in the philosophy of thought and language to think about thinking. It serves to label that element of a thought that is sometimes also the meaning of a word. It is a way to articulate the nature of someone’s rationality given that, as we saw in the distinction between sense and reference, what someone thinks and what is the case can be different things even when what they think is the truth. But as the Generality Constraint claims, thought as a whole seems to have a structure. Different thoughts can be related by subsidiary aspects. And to think about that, we need to think about concepts.

But there is another reason which applies to the doing of philosophy when one is not primarily engaged in interpreting others but trying to get clear on ideas. Wittgenstein expresses a related idea but puts it in the register of what words mean and even how they are used. Still, this is a manifesto for philosophers to attend to concepts even if few do what might be called ‘the philosophy of concepts’. Taking about concepts rather than of what they are concepts is called ‘semantic ascent’.

§370. One ought to ask, not what images are or what goes on when one imagines something, but how the word “imagination” is used. But that does not mean that I want to talk only about words. For the question of what imagination essentially is, is as much about the word “imagination” as my question. And I am only saying that this question is not to be clarified a neither for the person who does the imagining, nor for anyone else a by pointing; nor yet by a description of some process. The first question also asks for the clarification of a word; but it makes us expect a wrong kind of answer.
§371. Essence is expressed in grammar. (Wittgenstein 2009)

With this, Hipparchus lapses into silence and his students are happy to let him be. pTravis presses a bottle of hard liquor into his hand - whisky not cognac as it is still quite a while before noon – and they slip out of his study.