How do numbers relate to reality?

The other day at work I was thinking about numbers and how they relate to reality.

I don’t think there is any natural relation between numbers and reality; I believe we first create or discover categories in reality and then associate these categories with numbers.

For example: we create the category “leaf” and then we can make statements like “There are 146 leafs on that tree.”

A more scientific example would be the noticing of certain features of objects such as weight. We could then pick a certain amount of a certain element or object and designate that to be a unit of weight.

This designation is arbitrary. There may be reasons given for choosing this particular amount of this particular element such as how it makes it easier to combine with the measurements of other features of objects such as volume or something.

Still though the designation would be arbitrary because why choose to have a certain amount of space as a unit of volume? It could be said because it makes it easier to relate to other units of measurement; but then we’re back with the question “Why choose that specific something to be the unit for the measurement of that feature?”

But I have gone somewhat off track.

So numbers act as a very useful means for mapping out reality. Science is dealing solely with that part of reality that can be mapped out with numbers; that can be quantified and measured.

The problem is that science has increasingly become religious; especially in its public projection. It tries to say to us that all that exists is what is measurable. That is to say that anything that can’t be talked about in terms of number doesn’t exist.

I believe this is making the mistake of confusing the map with the territory.

There are different kinds of maps all of which are designed with a different purpose in mind.

There are maps that map the varying altitudes of a terrain designed for use by mountaineers and pilots; but they don’t indicate the colour of the terrain, the nature of the terrain and so on.

I think the claim that all that exists is measurable is the same as the claim that all a terrain is, is differences in altitude.


I don’t ascribe to any belief.

Or rather a more accurate articulation of my position is that I neither belief nor disbelief anything. I pretend to believe something for a bit to have a little play around with it.

You know explore the world through that lens. Then when I grow bored of that perspective I pretend to belief something else and so on.

I created a game as a means of doing this. I call it the “If-Then-Or-If-Then” game.

For example: if proposition A is true then propositions B,C,D,E are true and propositions F,G,H,I are not true.

Or if Proposition A is not true then propositions B,C,D,E are not true and propositions F,G,H,I are true.

Which has led me to the question: “How do I get from proposition A being true to proposition B being true?”

I mean it seems self-evident but that’s not an answer that’s just another way of saying “I don’t know”.

I think this is the problem that the logical positivists hit against.

Of course we are using the rules we’ve noticed in experience to make these leaps. But as Hume shows we can discover that A causes B but we cannot discover why A causes B.

When ever we think we have discovered why A causes B we have just produced an answer that has the same problem. We just come up with another A causes B which requires an explanation as much as the original A causes B.

I think it’s because language is relational and any explanation of any relation is just another – often more complex – relation or set of relations that require as much explanation as what they are meant to be explaining.

It’s a bit like that skittles advert where everything the guy touches turns into loads of skittles except when he touches a skittle it turns into loads of skittles as well.

It’s funny to think that concept through! He’d end up surrounded by a constantly expanding sphere of skittles. He’d fall to the centre of the earth, the earth would eventually explode scattering skittles everywhere and there’d be this poor man left at the centre of it all with nothing to do but eat skittles. Ha Ha.

Really all we can do is describe relations.

We cannot explain them.

But that’s fine because all we need to do in order to act upon the world is describe the relations. Language is just a tool that enables us to interact with our environment.

The problem of induction

I am very interested in the questions “What questions can we answer?” and “How do we go about answering these questions?”

Recently I thought I had simmered it down to just one question: “What would happen if I did this?” The method: “Try it and see.”

Of course here I am articulating the question and method in a rather flippant manner.

The more appropriate (let us say) articulation of the question would be: “If this set of conditions were to arise what set of conditions would follow?”.

The method would be the empirical scientific method.

More recently I have realized that all this method gives us is a history of what has happened when certain conditions were met in the past.

The process of experimentation flows so rapidly from the present to the past that it only tells of what has gone before.

The information we avail ourselves of via the scientific method furnishes us with a history upon the basis of which we make a bet. The probability of this bet paying up in the future approaches – but never reaches – certainty the more times it has occurred in the past.

This is nothing but Hume’s problem of induction. It delimits the realms within which science can operate.