necessity, intentionality, internality

Here I explore a parallel between questions in the theory of intentionality and those in the theory of logical necessity.

In both fields there is a tendency to ask the typically disastrous philosophical 'what makes it the case that...?' question which, if not handled carefully, so readily leads us into spurious theorising. (It bends us towards thinking that we here must have to do with one matter which is made true by some other matter.)

In necessity we have 'What makes it the case that, in virtue of what is it is true to say that, 2+2=4?' 

In intentionality we have 'What makes it the case that this current thought is a thought about Russell?'


When considering necessity we may be pulled in either Platonist or Conventionalist directions. The Platonist says 'The mathematical statement '2+2=4' is true because it is a true description of the mathematical facts.' The Conventionalist says 'No, you got it arse-over-tit. [He got his metaphors from the gutter, but his hyphens from reading Heidegger.] Rather: the truth of '2+2=4' depends on how we carry on in maths.'

I reckon one's gotta have a bit of a tin ear to even ask and answer such odd questions. For where on earth did this talk of the truth of mathematical statements depending on something come from? Why would anyone accept that? Why would we imagine with the Platonist that mathematical statements are enough like, say, empirical propositions, to be even playing a fact-stating game? And why would we imagine with the Conventionalist that there are two things to be had - our mathematical statements on the one hand, and how we carry on in maths on the other - such that one depends on the other? 

This is why the notion of maths as made up of transformation rules is helpful. Rules, this conception reminds us, aren't true or false depending on anything. (What 'truth' means here is rather different from what it means in empirical factive discourse.) Yes, sure, it's true that certain word or symbol strings express rules - if we use them thus. However this does not mean that certain rules are themselves intelligibly said to be 'true in virtue of' anything. What it means to talk of 'truth' here just is to talk of what is said really being a rule.

So, no, thanks very much, let's not be Conventionalists or Platonists. We don't here have two things - mathematical statements and mathematical facts - which are to be related in some way. What might appear to be two separate things are in truth 'internally related', i.e. found to be of a mutual piece, in the rule itself. Contra the Platonist, the mathematical rule formulation is not something separate from, and dependent on, a 'mathematical fact' - some separate rule-designated 'underlying logical structure of the universe' to temporarily lapse into the nonsense that the Platonic fantasy encourages in us. (Rules don't designate in the 'point out' sense; they only designate in the 'stipulate' sense...) And contra the Conventionalist, the mathematical fact is not something dependent from and hanging on how we go on in maths. It is how we go on in genuine maths! (Mathematical mistakes are when we're not despite appearances doing maths. Like in chess when you don't play by the rules: that's just not playing chess!) The felt need for either Platonic Realism or Conventionalistic Idealism was a product of not questioning an underlying assumption, and of buying into the philosopher's perseverative 'what makes it the case?' game: the assumption is that there are certain e.g. mathematical goings on, on the one hand, and certain truths on the other, and that the two must be related somehow.


Philosophers sometimes raise the to-me-utterly-odd-sounding questions 'In virtue of what is my belief that James is skinny about James?' Or: 'What is the relation between my belief and James himself?' Such a question can be called the 'problem of intentionality'. Intentionality is a matter of 'aboutness'. A statement of mine is, hopefully, about something or other. The question then is about the relation between the statement and what it is about. 'What makes for particular aboutness?' is another way of putting it.

Furthermore, philosophers have sometimes debated the question of whether it is the intentionality of discourse or of thought which is primary. On the side of discourse's intentionality being derivative of that of thought, we have the fact that the very same utterance (so long as we individuate a particular utterance as a string of words rather than already in terms of its meaning) can be used in talk about two different phenomena ('I walked into the bank') - and what better than the thought which the sentence expresses to serve as the determination of its reference on one occasion rather than another? On the side of thought's intentionality being derivative of that of discourse we have the fact that (so long as you've made sure you've already swallowed something of the inner vs outer conception of mind vs behaviour) discourse can seem more worldly, thing-like, out-there, praxical, embodied, ostensively connected to the things about us, whereas thought is all in-there, invisibly hidden away, ephemeral, either immaterial or situated invisibly in the folds of the brain. So why not start with the encounterable matter of discourse and have thought's intentionality piggy backing on that?

The lesson from the discussion of necessity was that debates about what comes first can be a function of a split conception of a phenomenon that traduces the grammar of necessity. We find this too in discussions of the relation of rules to instances of rule-following. We have those (call them Rule Platonists) who think that the relation between some rule-following behaviour and the rule which this behaviour follows is one of a determination of behaviour by a prior rule. And we have those (call them Communitarians on Constructivists) who think of the relation in the reverse: the content of the rule is given by what the people do who say they are following it. A lovely set of options: either buy into mythical entities and mythical guidance by them, or risk evaporating normativity itself by losing the possibility of distinguishing between apt and inapt goings on, by acquiescing in the sea of human floundering. Where did we go wrong? Ah, yes, it was in the underlying assumption that we have two separate phenomena to be related, rules and rule-following, such that we can ask the philosopher's beloved 'what makes it the case?' question: 'What makes it the case that going on thus and so is going on in accord with the rule?' Ditch that schizoid assumption and then we lose the question. We already identify the relevant behaviour as the 'following of this rule'  and the rule is the prescription to 'here go on thus'.

So, too, with intentionality. Ditch the assumption that when we have to do with a successful thought about Russell what we have are two separate phenomena - a thought, and a Russell - and then we don't need to answer a question about how two separate phenomena are related. 'Well, wait a minute, are you telling me that Russell isn't separate from a thought?' No - don't be daft. The point is rather that the thought about Russell is not identifiable otherwise. It is, one might say, always-already about him.  In order to successfully ask a 'what makes it the case?' question it must at least be possible for it not to be the case. That is why there's even a point to saying what in truth does here make for it being the case. But with regards intentionality there really is no such possibility here being canvassed. It is not as if we can identify the relevant thought otherwise. And this isn't because of any contingent difficulty. Rather: the thought itself is that relation to that object, and is not some inner object waiting to be related (by causality, by functional role, by evolution, by God) to the object. (A lovely upshot of all of this is we no longer have to trouble with the cognitive scientific project of linking thought to world through codifying rules in neural states which then cause the behavioural interactions which are the rules' followings - since the marvellous thing is that thought being always-already related to world we can all just go home.)

This is the problem we get into when philosophers describe beliefs and thoughts as representations. Because pictures, diagrams, and literary sketches represent, have an independent existence from what they represent, and stand in a relation (successful, unsuccessful etc.) to what they represent, we somehow imagine that thoughts and beliefs may too. But, no, to think or believe is already to stand in the relation in question. It is not to possess some entity in your mind which may then be in a representational relation to the belief or thought's object. The relation of person to object which relation constitutes the having of the thought is an internal relation. My thought about Russell is not an entity in my mind which is related - in virtue of something or other, but what? - to Russell. It is rather already my relation to Russell himself. The only relation we have to do with is between me and Russell, not between my thought and Russell - my thought is not a relatum but itself the relevant relation between me and he.


The concept of internal relations is one which Wittgenstein took over from the idealists. We have to handle it carefully. When we say that grammatical rules and grammatical rule followings, thoughts and their objects, expressions and the feelings they express, a command and obeying it, the white disc inside this symbol and the black line that provides its circumference O, etc. are 'internally related' it can still sound all too much like we have two things, it's just that they are related through their concepts - perhaps in virtue of the descriptions they fall under. But, well, that's not our situation. We rather have a bad question that sets things up for us to answer as if we had to please relate two phenomena - when we don't. We rather have a Russell and then someone's cognitive relation to a Russell. We have a smile of happiness: the happiness is expressed in the smile as the rule is expressed in the rule following. The happiness, the rule, the thought, the white disc: they do not have their life elsewhere than in the smiling, following, intentional object, and black ring we're considering.

The upshot I perceive, at any rate, is that we don't answer our 'what makes it the case...?' questions by citing the internal relation. Our talk of the internal relation is instead part of our metaphilosophical story as to why we don't need to, why we shouldn't, why the question is a puzzlement that arises only when we're in the grip of a schizoid fantasy. The talk of internal relations, handled sensitively, is our relinquishing of this fantasy, and our regaining of a non-alienated relation to our worlds. In this non-alienated vision, rules or norms and thoughts and feelings are no longer hived off from activity and expression, but live in them as, say, an object's length reposes in the object's substance. Now we have a life-with-language; now we are in our expressions; now living and thinking rediscover their originary unity. 


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