# A Thought on Distinguishing Pure from Empirical Notions

In the past posts I described a Matrix (person in a vat) scenario with a twist.

Neo’s body which is identical with my body is put in a vat. His sensory organs are connected to random generators. By pure chance it happens so that Neo’s sensory organs are affected in exactly the same way as my sensory organs are affected through my life.

After some number of years, Neo is disconnected from those random generators, and is “returned to real world”.

I want here to propose that the scenario is interesting in the sense that it can help us make a distinction between two groups of concepts (or notions).

In the first group we have things like individual entities, for example people I met in my life, and also natural kinds which I become aware in the world.

While Neo, when he comes out of the Matrix will seem to know all those people and natural kinds, we are aware that he has never in his life seen them, or became aware of them. I compared this to a situation where some fictional character happens to be described with exact properties that some real person has. Even this might be the case, the fictional character won’t be that real person, and only given this distinction can the sentence “the real person has all the same properties as that fictional character” make sense. Same goes for fictional natural kinds, which by pure chance happen to have same properties as a real natural kind. So, whatever Neo is thinking about while in the pure-chance-Matrix, it isn’t those individuals, nor it is those natural kinds. I’m not sure if the name is good, but we might call those “empirical notions”.

In the other group are things like numbers, math theorems, and concepts like THING, CHANGE, MOVEMENT and so on. It seems to me that if Neo while in Matrix thinks about numbers, or thinks about proof of some math theorem, there is no distinction to be made as the distinction we made for individuals and natural kinds. There is no reason to say to Neo “We have a Pythagorean theorem, and it has the same properties as the theorem you thought you know by the name of ‘Pythagorean theorem’, but which was not a real theorem!”. At least I can’t see what we could mean by saying such thing.

So, in general the criteria would be this: pure notions are those things of which we are aware and of which Neo can be aware too while in the pure-chance-Matrix. Empirical notions are those of which we are aware, but of which Neo can’t be aware.

I guess this is not something that will be readily accepted, but given that (by pure chance) someone accepts this, there is an interesting question – which of our notions are pure, and which are empirical?

There is a list of notions which I’m not sure where to put. Take for example artifacts – can Neo be aware of notion of chairs while in pure-chance-Matrix? From one side I’m inclined to think – yes, mostly on the base that someone in the history did thought of chairs, even before any chair was made – namely the first person that invented chairs. So, any relation to actual chairs doesn’t seem required in order to have a notion of chairs. Also, it seems normal to say that there is a possibility for two societies to have chairs, even they were never in any contact with each other. (E.g. if we go to another planet, can’t we find that they have chairs too?) But from other side, chairs are real phenomenon in the world, they have actual history – there are facts about chairs, and surely whatever a pure notion is, there can’t be facts about it? I guess we could think of chairs in terms of possibility – that is in terms as the inventor of chairs thought of them, but also think in terms of actualized possibilities – that would be the phenomenon of chairs. So, in both cases it would be about a possibility, just in one case we would have actualized possibility. We could then say that Neo can be aware of possibility-for-chairs, but not of actual-chairs.

## 5 thoughts on “A Thought on Distinguishing Pure from Empirical Notions”

1. This is actually identical to Davidson’s swampman, isn’t it? (It’s interesting he later regretted bring up swampman at all) Admittedly it’s inverted since Davidson has the man created from scratch with no historical connecton to things while you have his history being falsified.

I’d reject that we couldn’t still talk about the Pythagorean theorem since what is causally connected to Neo with that theorem isn’t any external thing but a set of pure possibilities. The alternative is an anti-realist one but there so long as the theorems are created in someone’s mind then we have math. It’s just that Neo thought what he knew what the Pythagorean Theorem of Pythagoras while he really knew the Pythagorean Theorem of virtual Pythagoras. (And this is actually interesting since Pythagoras didn’t really invent the Pythagorean Theorem so this line of reasoning actually applies to everyone)

2. The point is that we can know structure independent of knowing things. I’m actually reading Davidson here and I think this may be something his externalism rejects simply because he doesn’t accept scholastic realism. (That is the idea that structures or generals have a reality independent of any particular mind) Thus (if I’m reading him right – and heaven knows I’ve read him wrong enough times to be cautious) Davidson is a nominalist who would say our knowledge is always caused by things.

The problem with the nominalist and mathematics is legion. Even if one adopts math as a kind of language or at least game about symbolic manipulation I think we can talk about knowing the rules but the rules would be of a different game with identical rules.

I don’t think this a small thing, by the way. I consider it fairly likely that somewhere in the universe is at least one other sentient species. Presumably they learned math. Now if we take math as a kind of game or language and not as a feature of the structure of reality then the externalist is committed to the claim that we and our alien friends don’t both know the same mathematics.

But so what? Both math1 and math2 are structurally identical so we can deal with this without difficulty. If one finds this counter-intuitive (as I admit I do) then one can simply say that there are real generals in the universe. (This needn’t commit one to a Goedel styled mathematical platonism – there are other ways of dealing with universals such as Armstrong’s or Peirce’s approaches)

3. I think it is (re swampman), but it seems that this scenario is less problematic, as it doesn’t depend on the mind-body issue. It requires just to allow the possibility of illusion.

You are mentioning the wide/narrow distinction, and I’m thinking that this empirical/pure distinction is nothing but the wide/narrow distinction combined with belief that the ‘narrow content’ isn’t actually narrow, but that is in some way real (be it Platonism, or the Pierce’s approach you mention). As you I’m having trouble with the idea that those notions exist in minds only.

I think you have it right when you say “Even if one adopts math as a kind of language or at least game about symbolic manipulation I think we can talk about […] different game with identical rules.”, and that would explain why even if we look at the math as language game, we and aliens can have (one and the same) math. I do believe that there is more to math than just language game, but I think your comment shows that even for those who don’t believe that, the math is shown as something which is more universal than a particular/actual practice of math.

I still think that framing the issue in terms of possibilities seems most intuitive and commonsense, and I would like to point to this on the example with the idea of math as a language game. We could then say that the possibility of math as a specific language game existed even before in any society this kind of language game was developed, or really independent on the fact if such society ever existed in the history of the universe. Then Neo can be aware of this possibility (even he would be wrong to count it as actualized in the illusion), and when he gets into the world, he sees a real actualization of that possibility. And really, I think this is crucial for *inventing* or *creativity* – one should be able to think of some things as possible, even they are not actualized. I think we should be able to say that the creator was thinking of whatever he ends up creating, even his creation doesn’t yet exist. In same way, I think, if the human mind is supposed to have some role in the establishing of new practices (be them language games or something else), it is helpful to think of it becoming aware of possibility of those practices and language games, and only them acting in order to actualize those practices.