On a Semantic Account of the A Priori

This post is an attempt at stating and evaluating an approach to analyzing the concept of apriority as it applies to propositions. 

Follow-up: An Account of the Analytic/Synthetic Distinction

My conception of propositions, which sees them as having an internal nature constituted by their place in the system of language and thought to which they belong, but sometimes also external projective relations to the world, is highly suggestive of an approach to analysing the a priori-a posteriori distinction.

Using 'a priori' in such a way as not to imply truth, so that a proposition can be a priori true or a priori false, we might give expression to the basic idea by saying:

A proposition is a priori iff either truth or falsity is an internal property of it.

Or, using 'a priori' like 'necessary', in such a way as to imply truth (that is, meaning what 'true a priori' means on the above usage):

A proposition is a priori iff truth is an internal property of it.

(We will stick to the first usage.)

An account of this sort is attractive from my point of view for two related reasons. Firstly, it explains the feeling that definitions or accounts of the a priori which involve considerations of a knowing subject, and what such a subject can (in some sense) do without need (in some sense) of experience (in some sense), fail to get at the heart of the matter. That is, the feeling that a proposition's being a priori or a posteriori is a matter of the nature of the proposition itself, and that the stuff about being able to know an a priori proposition independent of experience (in some elusive sense) holds as a consequence of that proposition's being a priori, rather than constituting that property.

Secondly, many philosophers are skeptical of the notion of the a priori, or of the idea that anything genuinely falls under it. But topics at the centre of the present work, such as the existence of the necessary a posteriori and the contingent a priori, involve a notion of the a priori, and furthermore, one which is held not to be vacuous. If I can provide a new account of the notion I intend here, perhaps these skeptics will be able to enter into my discussion further than they would be able or willing to otherwise.

On this account, the concepts 'a priori' and 'a posteriori' are broadly logical. They can also be called epistemological if one wishes, but there is a danger in that, since by itself it leaves one free to overlook the distinction between properties like that of being a priori, which have to do with the nature of the propositions which possess them, and blatantly epistemological properties like that of being known, that of being hard to understand, that of being easy to verify, etc., the very constitution of which involves relationships to knowers.

That said, it is of course open to anyone to stipulate that 'a priori' is to have a meaning given in terms of a knowing subject and what they can do. But I would think of the word in that usage as expressing a property the possession of which is explained by possession of the property expressed by the word as I use it - a broadly logical property. I use 'a priori' that way because I find this latter to be of more fundamental interest, but I'm not concerned to insist on or argue for such a usage. The point about a broadly logical property explaining, or having as a consequence, stuff about what a knowing subject can do is supposed to help motivate the notion or notions I want to propose, but even that is secondary. My primary concern is just to propose them and try to make them clear

What do I mean by saying that a priori propositions' truth-values are internal to them? I do not mean that a priori propositions – individuated the way we are individuating propositions here, such that external projective relations are held fixed – necessarily have the truth-values they have. (In that case, it would be difficult or impossible to allow the class of a priori truths to differ from the class of necessary truths.)

The thought is, rather: with many propositions, their internal meanings – that is, their positions in the language-system to which they belong – do not by themselves determine a truth-value; rather, this depends on their external connections to reality, and what lies on the reality end of the connections. But with the a priori propositions, there is no such dependence; internal meaning determines truth-value. Or we might use the pair of locutions 'in virtue of' and 'irrespective of': a posteriori propositions have the truth-values they have partly in virtue of what (if anything) lies on the reality end of external projective relations borne by them, whereas a priori propositions have the truth-values they have irrespective of that. We might even simply say that their internal meanings, in contrast to a posteriori propositions, have truth-values already, all by themselves.

Is Our Notion of A Priority Explicable in Terms of Twin-Earthability?

I think this idea, as explained in various ways above, and guided by our pre-existing, traditional conception of a priority, can have considerable philosophical value. It will turn out to be worthwhile, however, to see what happens if we try to explicate this notion of internality of truth-value by means of the concept of Twin Earthability. We may say:

A proposition is Twin Earthable iff in some possible situation, a proposition with the same internal meaning has a different truth-value.

And then:

A proposition is a priori iff it has its truth-value internally iff it is not Twin Earthable.

This seems a natural strategy, since if a proposition has its truth-value irrespective of its external connections to reality, then Twin Earthing it shouldn't be able to change that. And that is correct, but for the strategy to succeed, we also need it to be the case that Twin Earthing is unable to change a proposition's truth-value only if it has this truth-value irrespective of its external connections to reality. And certain kinds of propositions might seem like counterexamples to this, such as 'I exist', 'Language exists' (where 'language' means concrete linguistic phenomena) and 'I am uttering a sentence now' (where 'uttering' is taken to mean a spatiotemporal process).

I am indebted to discussions of Chalmers ('The Foundations of Two-Dimensional Semantics', 'Epistemic Two-Dimensional Semantics') for these examples, and for the notion of Twin Earthability (although he defines it over sentence-tokens), which Chalmers derived in turn from Putnam's famous Twin Earth thought experiment.

In Chalmers' discussion, the examples are given as counterexamples to a different sort of account of a priority, and for different reasons. Chalmers' target is a particular class of interpretations of what he calls 'The Core Thesis': 'For any sentence S, S is a priori iff S has a necessary 1-intension'. Namely, those interpretations on which intensions are regarded are 'any sort of linguistic or semantic contextual intensions'. (Chalmers goes on to argue for what he calls 'epistemic intensions'.) Chalmers is testing this account against a notion of a priority understood along traditional lines, in terms of knowledge and experience. We, on the other hand, are, at least in the first instance, testing non-Twin-Earthability against our notion of a priority as internality of truth-value. (We will eventually come back and consider how these two notions - non-Twin-Earthability and internality – might line up with a more traditional notion involving knowledge and experience.)

First, it might seem that 'Language exists' and 'I am uttering now', construed the way they are supposed to be construed, namely as implying certain spatiotemporal goings-on, do not carry their truth-values inside themselves. It might seem like they must reach out and get their truth from those spatiotemporal goings-on.

They have non-Twin-Earthability, not because they are true irrespective of what lies on the reality end of their external projective relations to reality (that isn't the case), but rather because any Twin-Earthing of them, any proposition with the same internal meaning, is sure to bear external projective relations to reality such that what lies on the reality end of these relations makes the proposition true. (They are non-Twin-Earthable for what we might call transcendental reasons: their instantiation guarantees their truth; their truth conditions are subsumed under their instantiation-conditions.)

Regarding 'I exist', we might think: this cannot be true in virtue of internal meaning, since what makes it true is that I actually exist – this proposition reaches out to me.

There are numerous unclear and discomforting things about all this, however, especially the 'I exist' case. (If we imagine 'I exist' reaching out to us, aren't we thinking of our bodies? And isn't there a way of construing 'I'-propositions such that they don't imply the existence of bodies?). We will try to address them below.

(To anticipate, since this may ease comprehension: I will end up going along with the train of thought above regarding 'Language exists' and 'I am uttering now', but rejecting it for 'I exist', provided 'I' is construed so as not to imply the existence of a body. These are very confusing topics, however, and I don't wish to be dogmatic.)

On the Peculiarity of these Examples

First, a word about the peculiarity – the weird basicness, so to speak – of these examples.

Throughout my investigation of the difficulties arising with these examples, I have been heartened but also troubled by how peculiar they are – all of them, but especially 'I exist'.

Heartened, because since this proposition ('I exist') is so peculiar, the fact that it raises confusing problems in connection with our analysis of a priority should worry us less than if a less peculiar, more worldly sort of example raised these problems. The confusing problems presumably have a lot to do with the peculiarity of 'I exist', and we know that “the first person” raises confusing problems anyway.

It might even look like this is a peculiarly philosophical proposition, what Wittgenstein might have called a pseudo-proposition, especially when we reflect that it may not even concern a body.

But – and this is why it is troubling – that wouldn't absolve us in any clear way of the need to square our account of a priority with it – it is one thing to be dismissive of certain propositions when you aren't putting forward an account of a general notion in propositional typology, but I am doing that: I'm saying that a proposition (any proposition) is a priori if it has its truth-value internally.

That leaves the option of arguing that 'I exist' is no proposition at all, but that's not an inviting prospect. It seems dogmatic and ad hoc.

Secondly, and connected with this last point: it isn't clear that 'I exist' really is a peculiarly philosophical proposition with no practical use. Couldn't people (indeed, don't they sometimes?) assert 'I exist' in order to make someone more mindful and just toward them? And couldn't someone whose existence is in doubt, but whose supposed appearance is well-known, appear to the doubters and say 'I exist'? (Furthermore, aren't these instances of the very same (internal) proposition-meaning as Descartes tried to establish with the cogito? And that's not to say that weird, peculiarly philosophical things weren't happening there. Clearly they were.)

Accordingly, I will face up to these difficulties as best I can. I will now discuss 'I exist' and argue that it can be maintained to have its truth-value internally, when 'I' is construed so as not to imply the existence of a body. Following that, I will consider the other examples, 'Language exists' and 'I am uttering now'. (These also seem peculiar, and this seems to have to do with their being good candidate instances of Wittgenstein's remark in On Certainty (#83): The truth of certain empirical propositions belongs to our frame of reference. We will discuss this in turn.)

'I Exist'

Here is one consideration which throws doubt on the idea that 'I exist' doesn't have its truth-value internally, since it must reach out to me – i.e. a consideration which suggests that perhaps it does have its truth-value internally after all.

Suppose a computer system used by an administrator allows them to enter queries such as 'user23 space?', and the computer will tell them how much disk space user23 has left. The administrator's username is 'admin', so they can find out how much disk space they have left with 'admin space?'. But to save inputting time, a first-personal pronoun is introduced, so that the administrator and other users can enter 'I' place of their username in such queries. Let us suppose that a command involving 'I' is, under the hood, first transformed so that its occurrences of 'I' are replaced with the username of whoever is logged in (this username, we may suppose, is sitting in a particular memory location, ready for this purpose), and then passed on to be executed.

Now suppose there is a query 'loggedin?', so that the administrator can find out if user23 is logged in with 'user23 loggedin?'. When the administrator enters 'I loggedin?', the computer first looks up the username of the current user where it waits in memory (in this case 'admin'), plugs that in in place of 'I', and sends that to be executed. Suppose the system now searches a constantly updated list for the name 'admin', and returns 'Yes' if it reaches that name, 'No' if it reaches the end without finding it.

There is an obvious inefficiency here. Pointless as the 'I loggedin?' query might be in practise, if for some reason it had to be executed a trillion trillion times (say, at the whim of a rich eccentric, or for an art project), it might be worth modifying the software so that queries containing 'I' are first checked for 'loggedin?', in which case 'Yes' is immediately returned. And note that we don't need to first study the results of 'I loggedin?' working in this inefficient way – don't need to study what's on the dynamic list of users – in order to see this. We look into the system and see that it can only go one way.

It seems to me that if we think of an instance of 'I exist' as functioning like 'I loggedin?' in the unmodified computer system, we may be inclined to think that its truth-value is not internal to it, but if we think of it as functioning more like 'I loggedin?' in the modified system, we will judge that its truth-value is internal to it. On that way of thinking of it, we might say there is a tight conceptual connection, an empirically indefeasible connection, between 'I' and 'exist'. (More on conceptual connections in a future post.)

But what about the first option: thinking of 'I exist' as functioning like 'I loggedin?' in the first system? What might this come to? Well, the truly analogous procedure would be something like: when I ask myself whether I exist, I take 'I' as an abbreviation for my name, and then accordingly ask myself 'Does TH exist?', and then I use the same method I use when I consider whether someone else exists – perhaps trying to observe my body, or traces of my activity. That is plainly not how it works. But perhaps there is a half-way reasonable sort of procedure we can imagine, which contrasts with the immediate verification of 'I exist' based on a tight conceptual connection. Descartes' procedure comes to mind: I must exist, since I would have to exist in order to be thinking about whether I exist. (Perhaps there is a tight connection between 'I' and 'think.)

But this is not an empirical procedure, and it doesn't involve looking out into the world. This suggests that 'I exist', despite what we might have been inclined to say (perhaps on the basis of thinking of 'I' as requiring a body), can be maintained to have its truth-value internally, and so be a priori according to the account proposed.

Here I am using notions like 'empirical procedure', and so making appealing to elements of the more traditional, pre-existing conception of a priority. This would be fishy if I were trying to fully explain those existing conceptions by means of other, independently understandable conceptions. But that's not how I think of it: traditional conceptions of a priority help explain internality of truth-value as well as vice versa. To anticipate: we will end up with two mutually supporting conceptions, giving us two angles on a single important division in propositional typology.

'Language Exists' and 'I am Uttering Now'

What about 'Language exists' and 'I am uttering now'?

Remember, it is stipulated that 'language' and 'uttering' here mean physical, spatiotemporal phenomena.

It seems to me that, so interpreted, these cases clearly do not have their truth-values internally. They do reach out and get their truth, not just their meaning, from outside language – that train of thought is one I want to go along with. (Its not applying, despite possible appearances, to 'I exist', turns on the fact that 'I exist' as construed does not imply the existence of a body.)

There are, however, superficial appearances to the contrary. When we ask ourselves 'Does language exist?' and 'Am I uttering now?', we don't actually do any “looking out into the world”, as I have, speaking figuratively, said these propositions themselves do. It seems that we just immediately, or after a moment's reflection, see that the answer is 'Yes' in both cases. Just like with 'Do I exist?'.

And yet I am insisting that there is a fundamental difference of category here. I think we can get clearer here by considering further the category that 'Language exists' and 'I am uttering now' belong to – considering, that is, what is characteristic of them as opposed to the propositions I want to call a priori?

I think this was one of the main topics, if not the main topic, of Wittgenstein's last work On Certainty. Wittgenstein was responding to Moore's work in epistemology – his 'Defence of Common Sense', wherein he claims to know he has a hand. Apparently Normal Malcolm had some role turning Wittgenstein's attention to this late in the latter's life.

The following remarks seem to characterise the peculiar class to which 'Language exists' etc. belong (I will them the 'Moorean' propositions):

83. The truth of certain empirical propositions belongs to our frame of reference.

136. When Moore says he knows such and such, he is really enumerating a lot of empirical propositions which we affirm without special testing; propositions, that is, which have a peculiar logical role in the system of our empirical propositions.

137. ... Moore's assurance that he knows... does not interest us. The propositions, however, which Moore retails as examples of such known truths are indeed interesting. Not because anyone knows their truth, or believes he knows them, but because they all have a similar role in the system of our empirical judgments.

138. We don't, for example, arrive at any of them as a result of investigation. …

Note that these Moorean propositions won't generally be non-Twin-Earthable, like 'Language exists' and 'I am uttering now' (which are clearly special in that their truth is guaranteed transcendentally, i.e. by the preconditions of formulating them). It is the combination of non-Twin-Earthability and Mooreanness which makes these cases, and their nature, require special consideration from the point of view of our account of a priority as internality of truth-value.

Wittgenstein calls the peculiar role of Moorean propositions a 'logical' role, and it is not hard to see why: that we have empirical propositions playing this role, i.e. being part of the framework which guides thought and enquiry, is part of how our practise of thought and inquiry works.

But a proposition's playing this role is not an immutable or intrinsic fact about that proposition, and that is the very thing – I want to say – which makes Moorean propositions empirical rather than a priori.

Here is a metaphor I find helpful: imagine a cluster of metal frames, some of which have two feet (I will call them 'biframes'), others of which have three ('triframes'). The biframes need support in order to stand – they are built to be able to stand or fall. The triframes can stand by themselves. At the periphery of the cluster there are both biframes and triframes, and some of the biframes are held up by bits of wood. No biframe could be supported by wood alone; but some are held up by frames and wood, others by frames alone (which may themselves be held up by wood, or by further frames held up by wood, etc.). Any biframe, if you rearranged the cluster sufficiently and removed certain bits of wood, would fall, but some may be very hard or impossible to get at. (On Certainty #255: 'What I hold fast to is not one proposition but a nest of propositions'.)

Frames correspond to propositions. Their standing corresponds to truth or belief. Wood corresponds to experience, empirical confirmation. Triframes correspond to a priori propositions, biframes to empirical propositions.

The biframes which stand without being in contact with wood, i.e. which are supported by other frames, correspond roughly to Moorean propositions: the special category of empirical propositions with which we are concerned, and with which Moore and Wittgenstein were concerned. Or perhaps better: out of these standing biframes not in direct contact with wood, some are more robust than others with respect to the removal of bits of wood. Some might fall right away if you remove a single bit of wood near them, and perhaps we should not count them in this category (depending on how exactly we project the metaphor). Likewise perhaps those which would fall if a small number of easily identifiable bits of wood were removed. Then, the biframes which correspond to propositions of this special category – 'Language exists', 'I have a hand' etc. – are those which don't clearly depend on any particular bits of wood.

These special biframes are no mere epiphenomena, however: they belong to our 'frame of reference'. So in a sense they are foundations:

401. I want to say: propositions of the form of empirical propositions, and not only propositions of logic, form the foundation of all operating with thoughts (with language). ...

But this is then squared with, for example, the metaphor of biframes, with this brilliant remark:

248. I have arrived at the rock bottom of my convictions. And one might almost say that these foundation-walls are carried by the whole house.

In other words: don't be mislead by a “bottom-up” metaphor into thinking that Moorean propositions are not themselves supported, in a diffuse way, by non-Moorean empirical propositions. The image of the cluster of metal frames (or Wittgenstein's 'nest') helps avoid this: we do not imagine the cluster extending high into the air, but rather getting denser and covering a wider area.

And what's the difference between these and what we call a priori propositions? In our frame metaphor, the correlates of a priori propositions – triframes – stand by construction. Here is what Wittgenstein says about the difference:

655. The mathematical proposition has, as it were officially, been given the stamp of incontestability. I. e.: "Dispute about other things; this is immovable - it is a hinge on which your dispute can turn."

656. And one can not say that of the proposition that I am called L. W. Nor of the proposition that such-and-such people have calculated such-and-such a problem correctly.

657. The propositions of mathematics might be said to be fossilized. - The proposition "I am called...." is not. …

Putting this 'fossilization' talk from On Certainty together with the bits of wood from the metal frame metaphor above, we might say: bits of wood supporting biframes can petrify and become part of the frames themselves. (But that is not a plausible story about the actual origin of each a priori proposition taken individually. Perhaps it is plausible, however, that when we enter new regions of the a priori, so to speak, we often do so in this way. Or that, when humankind apprehended a priori propositions initially, we got there in this way. But this is all by the by.)

But in this case, fresh wood may still grow in the same area. And this sheds light on a distinct metaphor from Wittgenstein's Remarks on the Foundations of Mathematics which helped inspire the one about metal frames above: A mathematical proposition stands on four feet; it is over-determined.

This isn't the same metaphor, but I wager that these four feet do not all correspond to the same sort of thing: one of them can be distinguished as the 'fresh wood' alluded to above: for example, nothing can refute '7 + 5 = 12', it is not held hostage to experience (as we can see from the standard, convincing critiques of Mill's view that arithmetical propositions are empirical generalizations), and yet!: experience bears it out in some sense. We put seven and five things together, and we usually find we have twelve. Or better: our experience is such that this proposition is useful, is possible even (i.e. is something we can grasp, use, instantiate).

Another Angle on the Difference Between Moorean and A Priori Propositions

Another angle from which to see the difference between Moorean propositions and a priori propositions, in particular 'I exist' as we construed it in the previous section, is with a thought experiment involving experiences radically different from those most of us have had. Suppose everything went black and all bodily (kinaesthetic) sensation ceased, and a voice, claiming to be a demon, or some kind of scientist, but not belonging to the world of our experience, announced that space, or everything in it, has been destroyed, so that there is no language (construed as spatiotemporal occurrences) and no uttering (construed likewise).

If this happened to me, I would be unable to refute this. Or at least, no immediate knock-down objection would come to mind; the most near-to-hand strategy for refuting it would probably involve appeal to a belief in psycho-physical parallelism, which the demon would gainsay. I wouldn't know what to think.

If, on the other hand, the voice told me that I no longer exist, it would be totally different: I would steadfastly deny that, and nothing the demon could say to me would shake my belief that I exist. We will come back to this in a moment, when we consider how the conceptions of internality of truth-value and non-Twin-Earthability line up with the traditional conception of a priority.

To summarize our conclusions so far:

'I exist' is a priori (i.e. has its truth-value internally) and non-Twin-Earthable.

'Language exists' and 'I am uttering' are a posteriori and non-Twin-Earthable.

This is when we construe 'I' as not implying the existence of a body, and 'language' and 'uttering' as meaning spatiotemporal phenomena. If we construe 'I' bodily, 'I exist' falls in line with the other two. Conversely, if we construe 'language' and 'uttering' as not necessarily being spatiotemporal, 'Language exists' and 'I am uttering now' may be argued to fall in line with 'I exist'.

So, we appear to have two different notions here, with different extensions, both of which can be legitimate parts of our typology of propositions: internality of truth-value, and non-Twin-Earthability. We shall continue to reserve the term 'a priori' for the notion of internality of truth value. All a priori propositions are non-Twin-Earthable, but not the other way around.

Are All Non-Twin-Earthable A Posteriori Propositions Moorean?

The above discussion of propositions which are non-Twin-Earthable yet a posteriori focused on Moorean propositions – propositions it is hard or impossible to doubt, and which play a peculiar logical role in our thought and language which Wittgenstein tried to describe in On Certainty – such as 'Language exists' and 'I am uttering now'. Their being like that makes it important to distinguish them from a priori propositions, since our traffic with them resembles our traffic with certain a priori propositions in striking ways: we don't have to look out into the world of experience to verify them.

The question now arises: are all the propositions which are non-Twin-Earthable yet a posteriori like that? That is, are they all Moorean?

The answer, and this seems quite definite, is no: take, for example, the conjunction 'Language exists and first-order logic is undecidable'. Adding the second conjunct leaves non-Twin-Earthability unaffected, since it is a priori, but destroys Mooreanness. (Or, if you think it's Moorean that first-order logic is undecidable, pick some less basic a priori fact from the formal sciences.)

Comparison with the Traditional Conception

How do these two notions – non-Twin-Earthability, and determination of truth-value by internal meaning alone (which latter is what we have been using 'apriority'/'a priori' for), line up with the traditional conception of a priori truths as those which can be known without recourse to experience?

Our choice of terminology above has probably given the game away: the a priori propositions (those whose truth-values are internal to them) just are those whose truth-values can be known a priori in the traditional sense, i.e. without recourse to experience. And, since the non-Twin-Earthable propositions outrun those whose truth-values are internal to them (the a priori propositions, on our usage), they also outrun the propositions which are traditionally a priori.

I will not embark on an extensive discussion of the traditional idea, but will be quite rough and ready with it.

To repeat: non-Twin-Earthable propositions are not all traditionally-apriori, but the a priori (on our usage) propositions just are the traditionally-a priori ones. I regard the first part of that suggestion as more certain, and more robust with respect to different precisifications of traditional-apriority, than the second; .

The non-Twin-Earthable propositions which are not traditionally-apriori are the 'transcendent' ones: those whose concrete instantiation ensures their truth: as we just saw, these include both Moorean propositions such as 'Language exists' and 'I am uttering now', but also more complicated, non-obvious transcendental propositions. They give information concerning what goes on in space and time, and no propositions traditionally regarded a priori do that (perhaps an exception must be made for the most extreme Liebnizian rationalism, but even he distinguished between truths grounded by the principle of non-contradiction and those grounded by the principle of sufficient reason).

The case of 'I am uttering now' seems particularly clear: when we know that, we are clearly relying on experience: in the most straightforward case, the very experience of uttering. It could conceivably fail to come off.

A more complicated case could be imagined where some antecedent condition is empirically and reliably connected with me uttering 'I am uttering now', I might observe the condition and be said to know the proposition already, i.e. not by means of my experience of uttering it.

But hold on: is that right? It might be thought that there is a mistake here, similar to the mistake that would be made by saying that the way we know our own intentions is by observation and empirical correlation (cf. Wittgenstein's Remarks on the Philosophy of Psychology). We may just know that we intend to utter, not by observing ourselves, and know that our intention will be carried out, and then utter 'I am uttering now' knowingly. But in that case we may say: very well, but you are still drawing on past experience in knowing that your intention will be carried out. Furthermore, we can maintain high standards of knowledge and say: you don't really know you're uttering now until you experience it (hear it, see it, feel it etc.), because something could go wrong with your attempt at uttering – your larynx could disappear, for example.

So, not all non-Twin-Earthable propositions are traditionally a priori: 'I am uttering now' is the former but not the latter.

Does the converse hold? Are all traditionally a priori propositions non-Twin-Earthable? I say Yes, but I will not bother arguing this directly, since it falls out from the other things I am arguing: that the a priori propositions are just the traditionally a priori propositions, and all a priori propositions are non-Twin-Earthable.

One challenge to the idea that the a priori propositions – i.e. those whose truth-values are determined by their internal meanings alone – just are the traditionally a priori propositions is that already troublesome proposition, 'I exist'. Above, we made a case for saying that – provided the 'I' is construed in such as way as not to require the existence of a body – this proposition is a priori: its internal meaning determines its truth-value. And our intuitive considerations in favour of that were not unrelated to the traditional conception of apriority: we spoke of 'looking out into the world', 'looking into the language-system', and reasoning.

I think we should follow through with this, and say that 'I exist' (on our “bodiless” construal of it) is traditionally a priori: you can know it without recourse to experience.

However, there is an opposing line of thought here. We see it, for example, in Chalmers. Chalmers' idea about 'I exist' is that we know it via introspection, which is a kind of experience. But we may want a narrower concept of experience which this doesn't fall under.

It is admitted by Chalmers that it is 'somewhat controversial' that 'I exists' can only be known on the basis of experience. 'I am uttering now', on the other hand, Chalmers regards as a clear case of something that can only be known the basis of experience.

I propose to go along with this, and say that 'Language exists' and 'I am uttering now', construed so that they give information about spatiotemporal goings-on, is neither traditionally a priori nor a priori in our internality sense.

It is clear that 'Language exists' and 'I am uttering now', construed the way they are supposed to be construed, give information about particular contents of space and time – and that makes us feel that in some sense, surely, these can only be known on the basis of experience. But it seems there is a conceptual gap between 'I exist' and 'I occupy space and time' (or anything else which says something about the contents of space and time) – otherwise Descartes' recovery of his old beliefs would have been considerably easier.

(Here we come upon an interesting difference between space and time. Kant's calling time 'the form of the internal sense' and space 'the form of the external sense' is suggestive of it, so perhaps he comments on it somewhere. Roughly: while perhaps I could be taken out of the “time-space” I was in and put into another one, so that there is no fact about whether I am presently earlier or later than my birth in external time (in the sense of Lewis's distinction between personal and external time), but I cannot imagine not being in any time-space at all. If everything went dark and all bodily sensation ceased, and I heard a voice telling me I have been taken out of space, I would be unable to refute this. Or at least, no immediate knock-down objection would come to mind; the most near-to-hand strategy for refuting it would probably involve appeal to a belief in psycho-physical parallelism, which could only be founded on experience. If the voice, on the other hand, told me I had been deprived of all temporal locatedness and relations, I would immediately be able to see that this was in some important sense wrong. We might say that spatial locatedness is a posteriori, temporal locatedness (in some sense, at least – i.e. Lewis's personal time) a priori.)

Another major source of potential difficulty for my thesis that the traditionally a priori propositions just are the a priori ones in our internality sense, perhaps the most fundamental source of difficulty, is the synthetic a priori; substantial a priori truths which don't seem to be “true in virtue of meaning” in the sense that 'A priori propositions are those whose truth-values are internal to them', for example, is in this discussion (since we stipulated that we would use 'a priori' for internality of truth-value).

To begin to meet this difficulty, we must give an account of the analytic-synthetic distinction. I will make a start on this in the next post.