Posted on by qscrisp

I know from the bridge of how

Here's something I've been thinking about recently that has taxed my brain before: How do I know that two plus two equals four?

First of all, do I know it? It is 'common knowledge', but what if it's some sort of hallucination? If I count two on my fingers, and then count two again, and if I then count four on the same fingers (from little to forefinger), I seem to end up counting the same amount of fingers, but does this prove that two plus two equals four? The whole process can be broken down into any number of possibly discrete packets of information, and I'm not sure how they are linked. For instance, when I say, "the same amount of fingers", what does the word "same" really mean? What is the glue that sticks the concepts involved in 2+2=4 together to make the equation coherent?

Assuming that we do know two plus two equals four then, to ask the same question with a slightly different emphasis, how do we know? Do we know it by logic, or intuition?

Earlier this evening, I read the following sentence from this book:

The reader will soon notice, however, not only that various statements, for instance observations about human psychology, are artificially tacked on to the axioms, but above all that metaphysical concepts – in contrast to simple ideas of geometry, which are intuitively understood – do not become any clearer thanks to this so-called deductive method of exposition.

What struck me in this sentence was simply the passing observation that ideas in geometry are grasped "intuitively". I don't know much about geometry (as the song goes), but presumably simple mathematical ideas are grasped in the same way. Let's put it this way, if no one can really explain how we know that two plus two equals four, if we have to resort to saying that it's 'self-evident' or it 'just is', does that mean, then, it is, by definition, intuition?

Whatever the glue is that makes the equation coherent to us, I see it in verbal language, as well as mathematical. For instance:

I kicked the ball.

We have four discrete words here. How do we know what the relation between them is? What is the glue of meaning that joins "kicked" to "the ball"? It could be word order, partly, but how does word order convert itself to meaning in the mind? It could also be that we know the actuality that the words refer to and so use our experience in interpreting the words, but is this always the case?

Here's another example sentence:

In the whole history of philosophy there is no figure as lonely as Spinoza.

I can certainly feel a functioning glue here and there, particularly with words like "as", which invisibly join other words, but how do they do it? How?

I'm going to quote now from the A.C. Graham translation of Chuang-tzu, I hope he doesn't mind:

Chuang-tzu and Hui Shih were strolling on the bridge above the Hao river.

'Out swim the minnows, so free and easy,' said Chuang-tzu. 'That's how fish are happy.'

'You are not a fish. Whence do you know that the fish are happy?'

'You aren't me, whence do you know that I don't know the fish are happy?'

'We'll grant that not being you I don't know about you. You'll grant that you are not a fish, and that completes the case that you don't know the fish are happy.'

'Let's go back to where we started. When you said "Whence do you know that the fish are happy?", you asked me the question already knowing that I knew. I knew it from up above the Hao.'

I love this story, and I still haven't worked it out, but here's how it seems to me so far.

You could see this as a story about how there is union between Chuang-tzu and the fish, because we are all one being etc. etc. Certainly there are those 'overtones' to the story, but I'm not sure that's what it's really about. I almost feel like Chuang-tzu is making the remark about the fish in order to have the logical disputation that follows. Hui Shih, in asking how Chuang-tzu knows, seems to be saying, "You don't know." Chuang-tzu answers with a question. This also sounds as if he is saying, "You don't know", that is, "If I don't know that the fish are happy, then you don't know that I don't know." Hui Shi then says, "Well, the reason I don't know is because I'm not you, and you're not the fish, and that's why you don't know about them." But then Chuang-tzu says, "Let's go back to where we started." In other words, his first question could have been taken differently. What was he really asking with his first question (his reply to Hui Shih's question)? I feel like he was asking Hui Shih to look to the source of his knowing. What was the root of it. Let's assume we know something, how do we know it? What is the mechanism of knowing? Grant that you know something – for instance, that I don't know the fish are happy – don't you know it from your own experience? You experience not knowing that the fish are happy, and therefore you experience knowing that I don't know the fish are happy, too. However, that is your position relative to me. I know that the fish are happy through my experience – my position relative to them (from atop the bridge of Hao). In fact, you knew, all along, that I knew, and that was why you were asking how? How do I know? You assumed I knew, and now I am telling you. I knew in the same way you knew – relatively.

That's my best shot so far.

It's not as simple as it looks, though. Or maybe it's simpler, I'm not sure.

9 Replies to “I know from the bridge of how”

  1. I’ve been meaning to write about this for some time. Essentially, I feel that debates of this nature are moot. I mean, it matters little to me whether my existence is a hallucination, or not — the veracities of statements like this do nothing to diminish my suffering.Why does neither man consult the fish?

  2. I said perhaps the logic was flawed since to me all life would be equal and to live we must eat something that was once alive whether plant or animal. I said, in fact if we were not being hypocritical that by simply being alive we kill things. With every breath we take we may ingest insects, and walking or driving kills things big and small. So it would be impossible to obey the dictates of the religion if that was the true reason to be vegetarian. In fact, to truly follow its dictates we would have to kill ourselves.This is a significant part of the reason why I rejected Buddhism. I am actually, in practice, a vegetarian, though I don’t especially like using the word. However, I don’t really get on with the Buddhist doctrine of ‘harmlessness’. Your body kills bacteria and viruses without you even thinking about it. Merely living, uses resources that are fought for by all life. As you say, to be entirely harmless is suicide, which is, therefore, not harmless, as it harms yourself, and possibly others, too.I mean, it matters little to me whether my existence is a hallucination, or not — the veracities of statements like this do nothing to diminish my suffering.There are really no guarantees that any of these things will ‘work’, I think – I mean, the ways people try to make sense of life. I seem to be at least happier, if not entirely happy, since I read The Passion of the Western Mind back in… can’t remember the year. That might have been about 2005. No, probably earlier, I think. Must have been more like 2003 or 2004. It’s basically a history of Western philosophy. I suppose I’ve long deferred to other people’s views while retaining my own. That is, I assume they are right and I am wrong. Reading that gave me more confidence about my own views. My own feeling, which, of course, may not apply to anyone else, is that ‘knowing yourself’ may indeed diminish suffering. I don’t mean that in terms of self-knowledge of personality traits, though that helps, too, but in the sense that there is something constant to be known. I can’t put it into words, and I don’t think it can be put into words. People have been trying for a long time. I certainly don’t want to be glib and suggest that it’s easy, or that I find it easy (I certainly don’t), but I am not resigned to ‘meaningless suffering’, and there are certain avenues of investigation that I favour.Why does neither man consult the fish?This is a good question. I wonder what Chuang-tzu’s reply would have been if Hui Shih had suggested that he do this.

  3. Well, everything does depend on one’s experience, which is why words tend to be inadequate, and why they alone seldom seem to change anything. I think people basically have a way of seeing the world, and explanation comes later. I don’t think people ever really start ‘from scratch’ to find the truth, or particularly change (well, they do and they don’t). Anxieties arise in debates because there is a suggestion that differing views mean that someone is wrong and should therefore change. At least a significant portion of the suffering in this world might be relieved if we could simply accept ourselves and be unruffled by the differences of others.The difficulty in accepting oneself, of course, comes in whether you accept the part of you that can’t accept yourself. How does that work?Feel free to babble.

  4. Justin Isis writes:I feel like language just turns into poetry or something when it fails to describe the universe, since all that can really be described are human perceptions. I remember reading a book somewhere about there being a problem behind the idea of “inertia” since an object at motion tends to stay in motion…but in relation to what? Since everything in the universe is in motion anyway, there is no standard by which to judge it.I think it might have something to do with thishttp://en.wikipedia.org/wiki/GravitonAlso:http://en.wikipedia.org/wiki/Faddeev-Popov_ghosts”The Faddeev-Popov ghosts violate the spin-statistics relation, which is another reason why they are often regarded as “non-physical” particles.”Awesome”In general, anti-commuting ghosts are associated with bosonic symmetries, while commuting ghosts are associated with fermionic symmetries.”This sentence is awesome, “anti-commuting ghosts.”I feel like this language makes me want to write fiction, but a George Orwell essay or something makes me want to kill myself. “The Faddeev-Popov ghosts are sometimes referred to as “good ghosts”. The “bad ghosts” represent another, more general meaning of the word “ghost” in theoretical physics: states of negative norm — or fields with the wrong sign of the kinetic term, such as Pauli-Villars ghosts—whose existence allows the probabilities to be negative thus violating unitarity.”Man is this for real, I feel like the people making this up are so much cooler than us…

  5. Robin Davies writes:Chapter 10 of David Deutsch’s The Fabric Of Reality is called The Nature Of Mathematics and covers some of your initial points. I wouldn’t dare to summarise the chapter because it’s quite long and involved but it seems that mathematicians have been trying for quite a while to prove that mathematics provides absolute, infallible truth but have failed. Deutsch says “our knowledge of mathematical truth depends on, and is no more reliable than, our knowledge of the physical world.” Some mathematicians, called intuitionists, say that the only reliable truths in maths are the unchallengeably self-evident ones. So, for example, they believe in the reality of the finite natural numbers but deny the existence of infinite sets. Deutsch thinks this is worthless and is another form of solipsism. Elsewhere in the book he argues that solipsism, far from being a world-view stripped to its essentials, is actually just realism disguised and weighed down by additional unnecessary assumptions.It may indeed be hard to see why we should “feel” that two plus two equals four but there is so much riding on the consequences of that concept (i.e. most of the built or manufactured environment, our concept of time, etc. etc.) that to deny it seems like a more direct form of solipsism, i.e similar to expressing disbelief in reality itself. This attitude can’t be disproved but it seems to be an intellectual dead end.Hmmm… what if two plus two didn’t always equal four and sometimes equalled three in particular places for a few microseconds? Maybe that’s why my computer keeps crashing…

  7. Of course then we have the sticky subject of change. Change tends to be the Boogie Man.I seem to recall a Lovecraft quote that runs:”What we hate is simply change itself.”I can’t find it with Google, though.But I think life is so very grey.My life is certainly very grey.And I gave it some real thought in the shower. I do my best pondering there. I realized then my terrifying rage had kept me alive and safe on many occasions.Yes, I think this is very true. By which I mean, I can think of the equivalent realisation in my own life. Even times when I have been called my own worst enemy, actually, the motivation of that enemy that is myself has been something like self-protection and so on. Even if you can see the behaviour itself isn’t helping (though it might help), if you recognise what the motivations were, you can avoid spiralling into self-blame and so on… maybe.We are all uniqueI’m not.Sorry. I’ve always wanted to say that, and you have very kindly provided me the opportunity.I remember reading a book somewhere about there being a problem behind the idea of “inertia” since an object at motion tends to stay in motion…but in relation to what? Since everything in the universe is in motion anyway, there is no standard by which to judge it.I’ve actually been reading in this area recently, but don’t dare say anything about it. I tried recounting what I had read on the phone to someone recently, and realised I couldn’t.Man is this for real, I feel like the people making this up are so much cooler than us…Yes, well, this is precisely why we need to invent a new language. Chapter 10 of David Deutsch’s The Fabric Of Reality is called The Nature Of Mathematics and covers some of your initial points.I was fairly sure that I couldn’t have been breaking any new ground.Deutsch says “our knowledge of mathematical truth depends on, and is no more reliable than, our knowledge of the physical world.”Interesting. In terms of easy mental categories I’m filing this for now with Aristotle and William of Ockham.Elsewhere in the book he argues that solipsism, far from being a world-view stripped to its essentials, is actually just realism disguised and weighed down by additional unnecessary assumptions.I’m interested in the idea of solipsism, but one does tend to assume there are other people one is talking to. Of course, solipsism and immaterialism are not necessarily the same. That is, the former is narrower than the latter. This attitude can’t be disproved but it seems to be an intellectual dead end.Just thinking about this. I’m not sure why it would be a dead end. If there is only one reality then there’s not much choice left to us. Pointing out the cracks in that ‘reality’ could lead us to feel that, actually, there is more choice. One thing I’ve been thinking about recently is the idea of people who get stuck on the ‘anything’ phase. An ‘enlightened’ person has no self and sees all as illusion. ‘Anything’ is possible. But it could be that to maintain the ‘anything’ position prevents one ever from becoming ‘something’. In this sense, it could be a dead end. But then ‘something’ can become a dead-end, too, if one believes that that is all there is. So, maybe there has to be a balance, or something, or both attitudes can be seen as tools for navigating through life.

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