Strange loops

In 'The Barber Paradox' and 'The Pinocchio Paradox', I gave examples of self-reference paradoxes. Douglas Hofstadter, in 'Godel, Escher, Bach' introduces the notion of a 'strange loop', saying:

'The "Strange Loop" phenomenon occurs whenever, by moving upwards (or downwards) through the levels of a hierarchical system, we unexpectedly find ourselves back where we started.' (GEB, p.10).

'Strange-loopiness' is best expressed in the paradoxes mentioned above, but it also crops up elsewhere, Hofstadter points out, in art and music. Here are some more examples:

1. The next sentence is false
2. The previous sentence is true

In this developed version of 'The Liar Paradox', consideration of each sentence in turn seems to send us in a logical loop. The truth of the first sentence depends on the falsity of the second, which entails the falsity of the first, which depends on the truth of the second, and so on ad infinitum.

So too with Escher's impossible waterfall:

And the rather more famous never-ending staircase:

Hofstadter gives a musical example: a particular Bach canon, which modulates upwards by one key at a time, seemingly getting further and further away from its original key, until finally, it suddenly ends up back where it started, in its original key.

The common feature to all these 'strange loops' is the notion of moving through a hierarchical system, step by step, and but always ending up back where one started, on the first level of the system, and thus inviting an infinite loop. Some philosophers have suggested that time could exhibit the same sort of 'strange loopiness', though this is a notion that is rather hard to conceptualize. Hofstadter himself applies the notion to human consciousness, in an original and inventive attempt to explain why conscious experience seems so radically different from everything else the human mind has been able to comprehend; developed from 'Godel, Escher, Bach', his work on this crazy theory is called, appropriately, 'I Am A Strange Loop.'

Mary and the black and white room

Is there 'something-it-is-like' to see red, over and above the
 physical facts about red? The Mary story suggests that there is.

Imagine a scientist named 'Mary.' She lives 200 years in the future, at a time when physics has finally explained everything it can about the physical universe. Mary is an expert in her field, and knows every truth there is to be known about the physical world.

Furthermore,  Mary has lived in a black and white room all her life, and has never seen anything coloured. In this room, she has gained all her scientific knowledge from birth, and conducted all the experiments and discoveries that have made her famous. She knows everything there is to know about the world through science; in particular, she knows all there is to know about the workings of the human brain, including how it forms beliefs, how humans perceive redness, and all the rest.

Mary steps out of her black and white room and immediately apprehends the world in all its colour; the first thing she sees is a red rose. Mary, despite having a grasp on every single piece of scientific knowledge in the world, has learned something new on stepping out of the room: she has learned what it is like to see the colour red.

What is this story supposed to prove? What does it actually prove? Philosophers have been debating this ever since Frank Jackson published a paper in which he introduced the example. Mary represents the perfect scientist, and the totality of the knowledge of all physical facts about the world. Yet as she apprehends colour for the first time, she learns a new fact about the world which she did not know before: what it is like to see the colour red. Before she left her room, Mary knew all scientific, physical facts about how a human being sees an red object, and how the light reflects off that object and into the eye of the human being, creating a red sensation. However, nothing she knew from this position of total expertise could have told her what it is actually like to see a red object from the first-person perspective; she had to leave the room and actually see a red object to grasp this.

The example attempts to show that once all the physical facts are in, some things are left unexplained. All the physical facts about colour do not entail the facts about what it is like to experience colour; and thus we cannot explain what it is like to see colour purely in terms of physical facts. The example is not specific to colour: Jackson generalises it to all conscious experience. Mary can be re-cast as knowing all the facts about rough objects, and how they are felt to be rough; but only when she leaves her perfectly smooth room can she know what it is like to feel a rough object. The example applies to what it is like to see colour, hear sound, touch objects, or taste. In a nutshell, the heart of human conscious experience; in philosophical terms, 'Qualia.'

If Mary really does learn a new fact about the world when she leaves her room, then it follows that what she knew before leaving the room (every physical fact about the world) was not enough to explain some other fact: it follows that there are non-physical facts, facts about conscious experience that are not entailed by physical facts. This suggestion has profound implications for how we think about conscious experience and its place in the physical world: physicalism / materialism is false.


David Chalmers lays out the argument in clear, simple terms:

1. Mary knows all the physical facts
2. Mary does not know all the facts
3. Therefore, the physical facts do not exhaust all the facts.

See also: Zombies, and the Explanatory Gap.

What is knowledge?

If knowledge isn't Justified True Belief, then what the hell is it?

Philosophers like to analyze concepts; that is, to take a concept and give conditions necessary and sufficient for that concept. For example, an analysis of ‘talking bullshit’ might go something like:

• A person p is talking bullshit if and only if a) p says that a statement is true or false, and b) p does not know whether that statement is actually true or false, and c) p is indifferent to the truth or falsity of that statement. (Or something similar).

We can draw from this analysis that all it is to talk bullshit is to fulfill conditions a, b and c in the analysis. That is just what ‘to talk bullshit’ means in everyday language.

More interestingly, philosophers like to discuss knowledge, which has a few more strings attached. Ever since Plato, the widely-accepted analysis of knowledge in philosophy was the following:

• A person p knows a proposition x if and only if a) p believes x, and b) p is justified in believing x, and c) x is true.

That, it was thought, is all it means to know something. If I know that I had breakfast this morning, all that means is that I have a ‘justified true belief’ that I had breakfast this morning. All it is to know that I had breakfast this morning is to fulfill conditions a, b and c in the above analysis, concerning breakfast.


However, Edmund Gettier, a little known American philosopher, wrote a 3 page article in which he demolished this long-held analysis of knowledge with such force that the ‘justified true belief’ model was instantly discredited by the philosophical community. He came up with an example to show that there are cases where a person could have a justified true belief, yet still they would not have knowledge in those cases:

“Suppose that Smith and Jones have applied for a certain job. And suppose that Smith has strong evidence for the following claim:

a. Jones is the man who will get the job, and Jones has ten coins in his pocket.

Smith's evidence for (a) might be that the president of the company assured him that Jones would in the end be selected, and that he, Smith, had counted the coins in Jones's pocket ten minutes ago. Proposition (a) entails:

b. The man who will get the job has ten coins in his pocket.

Let us suppose that Smith sees the entailment from (a) to (b), and accepts (b) on the grounds of (a), for which he has strong evidence. In this case, Smith is clearly justified in believing that (b) is true.” 

(Gettier, 'Is Justified True Belief Knowledge?'. Analysis 23 (1963), 121-123.)

However, as it turns out, Smith gets the job; the president has a sudden change of heart and decides to hire him instead of Jones. Furthermore, Smith too has ten coins in his pocket, which he had previously deposited there but had forgotten about.

What then, shall we say about this case? Well, Smith had a justified true belief that ‘the man who will get the job has ten coins in his pocket.’ It was true, as it turned out. Smith was justified in his belief as well, since he had it on good authority that a man with ten coins in his pocket would get the job (Jones). However, do we really want to say that Smith knew that ‘the man who will get the job has ten coins in his pocket?’. No, because his ‘knowledge’ turned out to be accidental. Therefore, knowledge is not justified true belief after all. Knowledge cannot be accidental - there must be something added to the analysis to rule out such accidental cases. As of 2012, philosophers are still looking for the answer.

Rarely in philosophy are there any really significant developments or widespread changes in thought. However in this case, it is undeniable that Gettier instigated one. Having published his paper in 1963, he has proceeded to sit back looking justifiably smug ever since, and as such has never published anything else, though he retains his status as Professor of Philosophy at the University of Massachusetts. Papers published: 1. Philosophical revolutions set in place: 1. That’s not a bad success rate.

The 'Pinocchio paradox'

As usual, Philosoraptor makes an intriguing point. It's a type of self-reference paradox; a variant of the 'liar' paradox.

The possible paradox can be phrased as follows: 

Pinocchio says 'My nose will now grow.' There are two possibilities:

1. Pinocchio's nose grows; therefore he is telling the truth. However, if so, his nose does not grow, since it only grows when he tells a lie.
2. Pinoccho's nose does not grow; therefore he is lying. However, if so, his nose will grow, since his nose grows when he tells a lie.

Thus, we have a seemingly possible utterance which must lead to one of two self-contradictory outcomes.

Pinocchio is defined as 'a being whose nose grows if and only if he utters a lie'. We might object that a statement such as 'my nose will now grow' can never be a lie, since it is impossible to tell a lie about a future event. Thus, Philosoraptor's question can be easily answered - nothing happens when Pinocchio says this. Additionally, if Pinocchio himself is confused by the supposed paradox, then he is unlikely to be able to lie either way, since lying is just reporting a known falsehood about a situation as the truth!

We can enforce the paradox by re-defining Pinocchio as 'a being whose nose grows whenever he utters a falsehood.' Since uttering a falsehood need not be lying, the 'problem' remains. Now we must consider if statements about future events have a truth value when uttered in the present; many philosophers argue that they do not, since determinism about future events may not hold. I personally have no idea on this one.

The supposed passage of time

Time seems to pass - at least, that’s what plenty of people (some philosophers included) seem to think. However, on reflection, it’s pretty baffling what this claim is supposed to amount to. Taking it literally, we might suppose that time flows literally like a river, with moments passing by like water passing from one section of the river to the next.

'The Persistence of Memory' by Salvador Dali

However, if this is the way in which time flows, it makes sense to ask the question ‘how fast does time flow?’ The problem is, we cannot answer this question without talking nonsense. A river, let’s say, flows at x cubic liters per second - there’s nothing problematic about this observation. In the case of time, the only answer we can give to the question is ‘one second per second.’ But this is not a proper rate at all - it doesn’t tell us anything about the rate of time’s flow, since it is trivially true. It reduces to 1/1, which is not a rate; it’s just ‘1’. We are none the wiser.

We should therefore look to describe the passage of time in some other, perhaps metaphorical, sense. But to do this, we need to get a grip of what exactly we mean by the claim that ‘time passes.‘ Talk of events zooming out of the future, past us through the present, and into the past is all well and good, but seems pretty vague when considered in any depth. We see objects moving about, changing position - and ‘watching the world go by’ just means watching lots of these objects move about. But that this should indicate a great sweeping movement of all spatial events into the past seems unclear. 


Everyday talk about time’s passage seems puzzling from a philosophical perspective because the notion seems so ill-defined. However, we still think it’s true to say that ‘world war two happened’, and that ‘Fidel Castro will die’ (eventually). Descriptions of past and future events seem to require the passage of time, for what else could it mean for an event to become past if not to recede into the past, replaced by a moment that was once future?


There’s a strong case for arguing that time does not flow at all - that events are just laid out in a big static block, called ‘space-time.’ On this view, time is just like space - one dimension of this four-dimensional block of reality. If the universe is ‘static’ in this way (and most physicists already think that it is), then there is no reason to suppose a passage of time exists at all. Rather, time’s passage is a subjective illusion in our consciousness. A good analogy is one of a reel of film, which though giving the illusion of real motion, is just a series of still images all following each other. Life is similarly a series of stages, ‘sped up’ to look like passage in the minds of conscious observers. 

The proponent of this view, which I think is probably true, must give an account of what it means to say that time passes. Various theories have been proposed concerning the inner workings of the human mind, and how it might produce a sensation of passage, which does not exist in reality. However, for me, the biggest conceptual task in thinking about this view is the notion that time is like space. As noted, this is uncontroversial in physics, but radical in everyday talk about the world. It takes a bit of getting one’s head around. Still; think about what it means to say that 'time passes'; and if, like me, you are puzzled by the notion, then a static universe without real passage starts to make much more sense.

(More posts to follow on this view, sometimes loosely labelled ‘The B-theory’, or ‘four-dimensionalism.’)