'If time-travel is possible, where are all the time-travellers?'

Philosophy Of... returns, after a short leave of absence! 

Let’s assume that time travel is both logically and physically possible (contrary to the conclusions drawn in my previous post on time travel). A common objection that is raised to the prospect is really just a common-sense question: if time-travel is possible, then where are all the time-travellers? If time travel is possible, then we might expect future time-travellers to have arrived in our time. Or, more formally:

1. If time-travel is possible, then at some point in the future, humans will time-travel. 
2. If humans will time-travel, they will travel back to our time. 
3. If humans will travel back to our time, then we should have encountered them. 
4. We have not encountered any time travellers. 
5. Therefore, time travel is not possible.  

I don’t think this (the ‘future time-travellers argument’) is a very strong argument, so let’s evaluate it premise by premise. It appears that the argument is valid; that is, if all the premises are true, the conclusion cannot fail to be true (its truth logically follows from the truth of the premises). But is each premise true? I don't think so. This will be a common-sense investigation, rather than a technically philosophical one. 

Premise 1 

That humans would definitely make use of time-travel given its possibility can be easily questioned. We only have a finite time on the Earth (scientists tell us) before it is annihilated, and there doesn’t seem to me to be anything that guarantees we will have grasped time-travel by then. Perhaps it is too complicated to be grasped by humans even given 1000s of years. This certainly seems like a realistic possibility. 

Premise 2 

Let’s define ‘our time’ as the period between when human history records began and now. Even with such a general definition, this premise is also questionable. It might be, for example, that time-travel is developed, but only developed enough to allow random time-travelling, and not to specific locations in time which the future humans choose. If so, it seems perfectly possible that future humans, popping randomly into the past, never hit our time at all, and have to make do with some dinosaurs for company instead. After all, ‘our time’ thus defined is only a tiny region of the available pool space in which a time-traveller can plunge. 

Premise 3

Even if time-travellers did travel to our time, perhaps they might have reasons for not revealing themselves to us. This response is less plausible than my responses to premises 1 and 2, but nevertheless must be considered. Science fiction makes much of the fact that small changes in the past can lead to large changes in the future; perhaps it would be dangerous for future generations for time-travellers to reveal their identities to present-day folk. Maybe they were briefed about this by their leaders before setting off! 

Premise 4 

The truth of this premise depends on how we approach premise 3. It may be that if time-travellers have travelled to our time, they prefer to stay hidden. This makes it likely that some present day folk have encountered them; they just don’t know it. 

Conclusion 

Since there are good ways to challenge all four premises of the argument, I think we must conclude that this argument does not convincingly demonstrate that time travel is not possible. The discussion has strayed into the realms of science-fiction, and because of this, tongues must be kept in the vicinity of cheeks. However, there is a serious point to be made: if the above critique is reasonable, then a popular argument for the impossibility of time-travel is rebutted. This is to say nothing, of course, of the possibility of time-travel more generally. Considerations from physics may show that it cannot happen anyway. But at least if we do want to rule out the possibility of time-travel, we cannot do it by means of the ‘future time-travellers’ argument.

See also: 'Time Travel and the Grandfather Paradox.'

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.'

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 Philosophy Song

The Monty Python team approach the subject of philosophy in their typically amusing style. See also their 'philosophers' football match' - http://www.youtube.com/watch?v=ur5fGSBsfq8 .

Philosophers have beards

A couple of the 4th Century BC's greatest philosophers:

Plato

Aristotle

A couple of the 20th Century AD's greatest philosophers:

Lewis

Kripke

Ideas may advance, but beards remain in vogue.