Contrasting The Matrix and Descartes Meditation One

Steffaine asked:

How would you contrast the movie, The Matrix and ‘Meditation One: Of the things of which we may doubt’ by Descartes?

Answer by Geoffrey Klempner

Descartes in Meditation One works up to his case for universal doubt in several stages, but it is the last stage – the Evil Demon Hypothesis – that is the real show-stopper.


Descartes considers, and rejects, the possibility that my senses could always lead me astray. We learn about cases when we have been deceived by our senses, through the exercise of those very same senses.

But couldn’t I be dreaming now, and not realize this? This hypothesis is difficult to refute, if you allow that a ‘dream’ need not be disjointed and irrational. It is logically possible to have a coherent dream where, for example, I am in Sheffield, at my computer, writing a perfectly or at least reasonably coherent answer to Ask a Philosopher, even if such dreams occur only rarely if at all. Logical possibility is all Descartes needs.

This is the equivalent of the Matrix scenario. In reality, while I compose my answer, I am sleeping in a ‘pod’ having experiences fed directly to my brain by a super-computer.

The Matrix hypothesis is difficult to refute. But it still isn’t enough for Descartes’ purposes. Because, even on this hypothesis, certain key beliefs remain unchallenged. In particular, the belief that there exists a world of material objects in space. The existence of a physical world is one of the basic assumptions of the Matrix story.

That’s why Descartes takes the extra step of imaging a powerful, non-physical intelligence capable of producing the experience of ‘a world of material objects in space’ in me, even though in reality no such world exists. An evil demon.

But how ‘evil’ is this demon, really? Berkeley took Descartes’ argument for doubt and stood it on its head: nothing could conceivably count as proof of the existence of ‘matter’, because all we ever have is ‘experience’. All that exists, in ultimate reality, is God and ‘finite souls’ like us who have experiences that God produces in us. – When you look out at the world you are looking at the inside of God’s mind.


The three-way cake division problem

Gideon asked:

This is a puzzle. I dont know if you could describe it as philosophical.

Here’s a fair way to cut a cake into two portions, one for A and one for B. A makes the cut and B chooses. So A has a reason to make the two halves the same size, otherwise B will take the bigger slice.

The question is, can you describe a similarly fair way to cut a cake into three portions, for A, B and C ?. If A cuts and chooses, then A can deliberately cut the cake so that B gets a bigger slice. Someone gets to make a cut, or possibly the first cut. Someone gets to choose the first slice, for him or herself or for someone else, and similarly with the second slice.

You’re not allowed to spin a coin or throw dice, or do any action that involves chance.

Can this be done, without either A, B or C having possible grounds for complaint?

Answer by Craig Skinner

Yes it can.

This is an example of a Fair Division Problem. Division is fair if it is proportional (each of n sharers gets 1/nth) and envy-free (no sharer feels that another gets a bigger share than she did).

I wouldn’t describe it as a specifically philosophical problem, but fair division is crucial, for instance, to (amicable) divorce settlements or territorial divisions/treaties, and so is of interest to lawyers, politicians, and negotiators, as well as to mathematicians/logicians who think up solutions.

Sometimes we are dealing with continuous goods (divisible into arbitrarily small pieces, as with cakes); sometimes with discrete goods (indivisible, as with cats or cars) where we have to come up with a metric for comparison.

You describe a fair 2-person division for continuous goods (one divider, one chooser).

The 3-. 4-, 5,- … n-person procedure is an extension of this in which we have one divider/several choosers (Lone Divider method), or one chooser/several dividers (Lone Chooser method), as well as a more complicated Last-Diminisher method.

Here is the simplest, Lone-Divider method:

A divides cake into three pieces, X, Y and Z.

B and C each states her choice:

  Case 1. B chooses X, C chooses Y (or vice-versa).

So, B and C get their chosen slice, A gets Z

  Case 2. B and C both choose X (or Y).

So, X (or Y) is merged with say Y (or X) and B/C do a 2-person divide-and-choose on XY.

A gets Z.


Answer by Ira Allen

This is simple, as long as nobody minds odd-shaped slices.

A, B, and C are sharing a piece of cake. A makes the first cut, which cannot entirely bisect the cake; B then makes as many cuts as are necessary to produce three pieces. C chooses her piece first, A second, and B third. Because B will choose last, she is incentivized to take whatever opening cut A has made and turn it into the most equitable arrangement. If she privileges C at A’s expense, she can expect that A will get her back by leaving her with the worst piece. Because A can only make a partial cut, not entirely bisecting the cake, and because B can make as many incisions as necessary to produce a total of three pieces, there is no way for A to privilege C at B’s expense.

The one possibility that this leaves open is that B will want, for whatever reason, to put A at a disadvantage – and will not mind being similarly disadvantaged herself. Shortsighted viciousness is hard to account for in any model, though it’s arguably one of the defining features of the human.

Most puzzles of this sort rely on a principle of incomplete lines, i.e., on lines (cuts, here) that do not entirely cross from side to side of the figure (here, the cake) to be divided.


David Lewis on the logical possibility of time travel

L asked:

I am currently writing an essay on the topic of the logicality of time travel and I have been researching various philosopher’s ideas on time travel. However, I am really confused over David Lewis’ well-respected article on the ‘Paradoxes of Time Travel.’ Lewis clearly shows he believes time travel could be possible and he goes on to say that time travellers would not be able to change the past. However, he admitted that one would alter the past just by being in the past.

I am not sure if I have misread his work or if Lewis has made a contradiction. If by merely travelling back to the past an individual will cause an alteration to the past then how can time travel be possible if Lewis claims one cannot change the past? If I have understood his argument correctly (though I have probably just read it wrong), his argument appears to be logically flawed.

I was wondering, if you are familiar with his work, you would be able to explain?

Thank you!

Answer by Craig Skinner

Wouldn’t it be great to hand in an essay uncovering a logical howler by a famous philosopher!

Maybe next time.

You have misread Lewis. He doesn’t say one could ALTER or CHANGE the past, only that one could AFFECT it.

But you can be forgiven, for Lewis falls a little short, here and there, of his usual exemplary clarity. First, he doesn’t spell things out, contrasting altering/changing with affecting. Secondly, and having regard to your remark about ‘he admitted that one could alter the past just by being in the past’, his text is confusing, as follows (talking of the time traveller):

‘he changes the past from the unactualized way it would have been without him to the one and only way it actually is. To ‘change’ the past in this way,… it is enough just to be there…’

What he means here is that the TT, by being there, affects the past, has an effect on events, not that he changes it. There is no change to the past. Lewis contrasts here what ACTUALLY happens with what COULD HAVE happened had circumstances been different (eg had the TT not been there). In short he is alluding to counterfactuals and possible worlds. Of course he is a maestro in both of these fields, but I think they are a different kettle of fish from time travel.

It is a mistake to think that there could be different versions of the past, one that happened originally, and a new one when a time traveller goes back and takes a hand in events.There is only one past, it’s over, fixed, done and dusted. Any actions by time travellers have already been built in to the past. Simple example. Next month I go back to 1215 and am a signatory to the Magna Carta. This means that anybody who has studied the document in the last 800 years will have seen my signature on it. I affected the past (by being there, as a time traveller, taking part in the events, all those years ago), but I didn’t CHANGE the past.

You talk of the logicality of time travel (to the past). So here are my views on the two main alleged logical paradoxes.

The Grandfather Paradox

The fact that I am here means my grandfather wasn’t killed as a lad. But I could go back in time and shoot him, in which case I couldn’t exist. Contradiction, hence time travel impossible.

Not so. My grandfather wasn’t killed as a lad. So, if I were there as a time traveller, I didn’t succeed in killing him. Certainly, if I tried repeatedly, a series of amazing freak accidents would have occurred: the gun jams on my first try; bullets turn out to be blanks on second try; I fire at the wrong boy on my third try, etc. All very strange, but then time travel is strange so we can expect some of its implications to be strange.

The story of the history student is another amusing example. Appalled by the carnage of the First World War, learning that it was triggered by the assassination of Archduke Ferdinand, she resolves to go back and prevent it. She studies all the archives, knows exactly where the assassin will be etc, goes back, approaches him, then trips and bumps into the assassin, who was a poor shot and would have missed, nudging his arm so that the line of fire now finds its mark. Far from preventing, she has triggered the war. Horrified, she later goes back to stop her other self from tripping, but her attempt just causes the trip, and so on.

The only way in which I could go back and kill my grandfather is if time is branching or there are parallel universes. Here I go back, kill the old boy, and the universe divides into two, one where I dont exist, the other where I came from. Alternatively my travel takes me to a parallel universe just like ours up to the time of my arrival but with a different future in that I kill the old boy and never get born in that universe (but am there as a visitor to do the killing, so no paradox). However I think we can deal with the oddities of time travel without invoking branching/parallel universes.

The Free Knowledge Paradox

Rummaging in a cupboard, I find a notebook with details of how to build a time machine. After twenty years of toil I build it, then travel back twenty years to leave the instructions in the cupboard. I am a physicist tired of failed attempts to find a theory of quantum gravity. I travel two hundred years into the future, look up the accepted theory (aha!), write it all down, return and submit it to a journal whereupon it becomes the Nobel-winning accepted theory.

Where does the knowledge come from in these cases. I dont know, but knowledge is knowledge whatever its source, one could say.

For a really strange loop how about in two hundred years physics has advanced enough for time travel and for us to make universes having laws of nature of our choice, one of us travels back 13.7 billion years and sets off the Big Bang that started our universe

Incidentally, we cant change the future either, we can only affect it. Just like the past, there is only one version.


Answer by Shaun Williamson

I am not familiar with this article by David Lewis but I am interested in the logic of time travel. If you time travel back to the 16th century then, since you didn’t exist in the 16th century you are not really travelling back to the 16th century. You are travelling back to a possible alternative 16th century. When you return to the present you are not really returning to the present you left. You are travelling back to a possible alternative present which now contains the fact that you also existed in the 16th century. The present that you left didn’t contain this fact.

I don’t know if time travel will ever be possible but the logic of time travel is perfectly consistent as long as you accept the notion of possible alternative worlds.


Answer by Geoffrey Klempner

I glanced at the article by David Lewis when I wrote my Afterword to the reprint of David Gerrold’s sci-fi time travel classic The Man Who Folded Himself but didn’t read it properly. As a result I completely missed the point that Craig has picked up on, that time travel that avoids the grandfather paradox is logically possible without positing alternative worlds.

That’s what comes from being lazy. Mea culpa. My bad.

Alternative worlds are still the only way to go if you want to have fun changing the known facts of history — such as prevending Kennedy’s assassination or the attack on the Twin Towers. But all you would be doing, as I noted in my essay, is saving Kennedy or the people in the Twin Towers in an alternative world, not the original one.

Let’s say your brand new Apple tablet which you put on the dinner table mysteriously disappears. 50 years ago a strange object (which we would today recognise as an Apple tablet) materialised in a diner in Nebraska, and was subsequently taken to Area 51 where it was studied as a possible alien artefact.

That’s how time travel works. The time traveller disappears and reappears (from their perspective) in the past. In real-time, however, the event of the time traveller materialising in the past preceded, as it must, the event of the time traveller pressing the button and disappearing.


An eight year old’s question about the external world (contd.)

Joanna asked:


I am Joanna and I am 8. My mum found this site for me because I really want to know how I can be sure that everything is actually real and that the things I can see and hear and touch and smell and taste are not just me imagining everything? And how do I know that my mum is real (even though she helped with the typing) and that I am even real? Thank you for helping me with this question because it is making it hard for me to get to sleep at night.

Answer by Nathan Sinclair

Hello Joanna,

Like you, lots of clever people have worried about this question. In ancient Greece there was a man who thought there was no reason to believe anything he saw or touched was real, and the story goes that his friends spent a lot of time pulling him back from walking off cliffs and in front of chariots and so on.

More recently, about 350 years ago, a French philosopher called Descartes (said: DAY-CAR) tried to work out why we should believe that what we see is real, and he thought he found the most basic truth on which everything else we know depends. This basic truth is the famous saying ‘I think therefore I am’. Even if everything you see and feel isn’t real, your sights and feelings are still real themselves, and from this basic truth Descartes thought he could give reasons to believe everything else. His argument was that since I exist something better and smarter than me must have made me, and that something must be God and God wouldn’t make me see and feel things that aren’t real. If you think this argument for God isn’t very good you are not alone. Lots of Descartes’ friends thought this argument was so bad that Descartes didn’t really mean it and secretly didn’t believe in God at all. But without a good reason to believe in God Descartes doesn’t have any reason to believe what we see and feel.

Nowadays many philosophers think the reason for believing that what you see is real is that it is the best explanation of your seeings and feelings (your experiences). If your mum existed and your eyes and ears worked that would explain why you heard your mum telling you it was time to go to bed at night, and saw her looking for you if you didn’t answer. It seems really unlikely that you would have a hallucination as complicated and as organised as what you see and feel.

I don’t think the appeal to ‘best explanation’ is much good at all, I don’t know how to judge explanations and I suspect its mainly just fitting in with what you already know. Instead lets look at two suggestions I find helpful

1) Your experiences are so complicated there has to be something behind them.

Lets try a simpler question for a moment: How do you know there is more to your computer than what you see on the screen? Well, when you close a window on your computer and then open it later the same stuff appears in it. That stuff wasn’t shown anywhere but the computer had to remember it, so wherever the computer stores that information isn’t being displayed, so the computer must have some hidden parts that aren’t shown on screen. Well maybe it just stores stuff, so there is nothing more in your computer than what is on screen at some time or other. But that can’t be right because sometimes the computer does complicated calculations. Calculations so complicated that is has to store intermediate results on the way to working out the full answer. (Something like the way you might write down part of a sum on the way to working out the final answer to a maths problem, but so complicated that there is no way the final answer can be worked without storing intermediate results along the way.)

In the same way, provided you believe that there are complex patterns in your experiences, provided you believe that when you open your eyes next you will see your hands and the room around you and so on, then you must believe in the external world (the external world is where the world writes down its intermediate answers while it works out what to show you next). To say it in a negative way, if you don’t believe in the external world then you can’t believe that the world works really hard to figure out what to show you next, the world isn’t doing really hard calculations (how fast does a ball fall, just where will rainbows appear and so on) and the complex patterns you think you see in the world really aren’t there and there is no reason to think that you will go on seeing things fall down when you let go of them, the sun rise in the east tomorrow, your mum say ‘Good Morning’ to you tomorrow and so on (your experiences are like random dots that happen to make a picture but really they are just random and the picture will get wiped out by the next lot of random dots) — No real world, no complex patterns! To say it in a positive way, if the patterns in what you see and feel are real then what you are seeing/feeling is so complicated that there must be a real world behind them where those patterns are worked out.

2) You don’t start from nothing.

The way you and Descartes set up the problem, it seems like we need something fundamental that can’t be doubted to show that the world is real (or the patterns we see are genuine patterns). Maybe if we started not believing anything there is no way we could ever learn anything. (Maybe if we were stuck at the bottom of a well with no climbing equipment we could never climb out and go buy some climbing equipment.) But that doesn’t matter because we don’t start believing nothing, we start with lots of beliefs and we change them in response to what we experience. We are not like builders building a new house on a vacant lot, we are like renovators who move into an existing house and then do it up to make it nicer. Given that you already believed in the external world what new reason is there to change your mind and reject it? This is not simply a matter of which belief got in first, but of recognising that you must start from where you are now. This doesn’t really answer your question but suggests that the question didn’t accurately reflect the real problem we face which is working out what we should believe next GIVEN what we see/feel AND what we already believe in now.

These are the things that let me sleep at night and not worry if my children are real or if they are going to be there when I get up in the morning, I hope they help you too.


Experiencing a ‘temporary epiphany’

Alex asked:

‘Temporary Epiphany’ is what I call it when it happens, as I am unsure if there is a word for it. Sometimes when I am puzzling over the vast expanse of the universe or the amazing probability of human existence, I will be overcome with a sudden extraordinary understanding of the subject, unable to translate the feeling into words, it quickly subsides and I can no longer remember what it was I had just ‘seen’ in any great detail.

Has this ‘phenomenon’ ever come up in your studies? I wish to understand more about this subject but I have searched without prevail.

Answer by Shaun Williamson

It is wrong to call this a temporary epiphany. There is a great difference between ‘understanding something’ and ‘feeling that you understand something’. You shouldn’t confuse these two things.

Intense feelings of understanding life and the universe are quite familiar to people who take recreational drugs or to people who consume large amounts of alcohol. They may be interesting as feelings but they should be compared with dreams and fantasies and not confused with reality or real understanding.


On a proposed argument for theism

James asked:

A friend proposed the following argument (which he asserts is a syllogism) as evidence for Theism.

1. Time has not been found to be a solid, liquid, or gas. Neither is it a form of radiation or energy.

2. It is absolutely necessary for the world to have come into existence and its continued existence as we know it.

3. Insofar as time possesses qualities unlike any other phenomena and shares qualities with the Christian conception of a deity it is positive evidence that believing in such a God is a reasonable proposition.

The author of that argument claims to be an expert in science, philosophy, and logic. We agreed to consult an expert.

Please feel free to be blatantly honest and direct in your critique. No need to mince words.

Please note, we’re not arguing whether or not it is reasonable to believe in God. Only about the validity and soundness of this argument.

Answer by Jürgen Lawrenz

In order to qualify as a syllogism, your 3 points would have to put at least one proposition that is universally accepted. Point 1 in this argument is merely a negative and consequently does not qualify unless you wish to prove a negative as the outcome. Further it is inadmissible since it is incomplete – for the negative to hold you would have include all possible arguments of what ‘time is not’.

Next, Point 2 is already questionable: Not everyone, neither scientists nor philosophers, are agreed that the universe had to come into existence. It is entirely possible that the universe is just a brute fact and eternal in the sense of cycling infinitely through various states of existence. The steady state conception of the universe is a case in point.

Further: It cannot be demonstrated scientifically that the universe as we understand it is ‘all there is’. What we know of it may well be just a little corner of activity and heat. You should consider in this context that being able to detect energy is our sole means of establishing the existence of something. If there is no energy, then we are reduced to guessing – in other words to intellectual games.

It follows that Point 3 is an untenable conclusion from the incomplete negativity of Point 1. Whether time does possess any qualities at all is merely a debating point and wholly dependent on the cosmological paradigm that one or the other speculant espouses. Hence it cannot be said to share any qualities whatever with ‘God’ – and I note here that your ‘syllogism’ makes no effort to define what the term ‘God’ represents – as if it was self-understood. The Christian conception itself is not a single one, but a variety and depends on the theological particulars of the various creeds.

Philosophers have warned us repeatedly: Logic can prove things that exist, but not confer existence on matters that exist in logic alone. But your proposition is neither a logical chain nor even a plausible succession of propositions. Hence your syllogism fails on every count.


Answer by Stuart Burns

The easiest way to critique this argument is to address each clause in turn.

1) I think get your point — you are listing all of the known possibilities that you think time might be categorized as. But your premise is flawed because you left out ‘plasma’, and also ‘geometric property of space-time’. There may be other ‘obvious’ categories that should be included, but I can’t think of them off the top.

2) I do not agree that it is necessary that the world came into existence. To assume such is to preclude the possibility that the world has always existed (ie. is infinitely old). And I cannot figure out what role the clause ‘and its continued existence as we know it’ plays in this premise. It is, at the very least ungrammatical. Perhaps you might expand on the thought? I might make a guess, and guess that you are trying to capture the thought that the continued existence of the world (‘as we know it’) requires time. With that, I have no problem.

3) This step contains a whole plethora of debatable assumptions, and unsupported assertions.

(a) You have not provided any support for the assertion that ‘time possesses qualities unlike any other phenomena’. Nor have you provided any support for the assertion that time is in fact a phenomena (possessing qualities). A ‘phenomenon’ is any observable occurrence [Macmillan Dictionary Online]. You have ignored the possibility that time is but a manifestation of the geometry of the 4 (or is it 11) dimensional space-time manifold. And you have ignored the possibility that time might be an ‘artificial construct’ like a center of gravity. In neither of these cases would time be a ‘phenomenon’ in the sense you need here.

(b) You have not provided any support for the assertion that time ‘shares qualities with the Christian conception of a deity’. Given that the qualities customarily associated with the ‘Christian conception of a deity’ are both highly debatable and mutually contradictory, many of which are unproblematically not qualities normally associated with time, it behooves you to provide some support for this assertion.

(c) What ‘positive evidence’? No evidence (positive or negative) has been provided. You have provided no evidence, assumptions, or even claims for what time is, or of what properties it might have. You have provided no evidence, assumptions, or even claims for what ‘such a God’ is, or of what properties she might have.

(d) You have not provided any criteria for what would count as being a ‘reasonable proposition’ to believe, or what factors would motivate a belief in such a ‘reasonable proposition’.

Now, admittedly, some of the missing elements of this argument may be treated as ‘standardly acknowledged background’ depending on the rest of the argument. But given the fact that the argument is being advanced to prove such a contentious conclusion, it demands more than simply unsubstantiated assertions to back it up. Which is more likely – that the author has discovered an argument that has eluded the brightest philosophers for many millennia, or that the author has made a factual or logical error? The overwhelming likelihood of the latter possibility demands a more detailed specification of the argument than you have provided here. If the author is in fact right, and the fully detailed argument is both valid and sound, he will have to prove it.

The author you mention may be an expert in science (although you provide no evidence of that), but he is certainly not an expert in logic or philosophy. If he had any familiarity with either, he would recognize that the argument as stated here is neither valid nor sound, nor an example of any of the 24 valid syllogism types. The argument is invalid because the conclusion is a non sequitur – the conclusion could be either true or false, but the argument is fallacious because there is a disconnection between the premises and the conclusion. The argument is unsound because at least one of the premises is not true. (In fact, I think all of them are false. But all that is required to render the argument unsound is that only one of them is not true.)


Reply by Helier Robinson

First of all there are two kinds of time: time as a dimension, and passage of time. The first is static, like a line, and the second our sensation of time passing, as if we are travelling along that temporal dimension. Many believe that passage of time is an illusion because of the difficulties that arise with it, but no one has been able to explain why we have such an illusion. It is fairly safe to say that problems with time give scientists and philosophers more trouble than any other problem. Which kind of time is your opponent talking about?

The nearest we can get to saying what time is, is to say that it is relational. Before and after are terms of temporal relations, and duration is a relation having earlier and later as its terms. So there’s no dispute that time is not a solid, liquid, or gas, a form of radiation or energy.

Are you sure that it is absolutely necessary for the world to have come into existence and its continued existence as we know it? The evidence for the big bang is very good, but ‘absolutely necessary’?

Concerning point three, what are the qualities that time possesses unlike any other phenomena, and what are the qualities that time shares with the Christian conception of a deity? Without more detail, this third paragraph does not make much sense.

Concerning the validity and soundness of the argument, it certainly is not a syllogism, which is an argument consisting of two categorical propositions and a categorical conclusion, with just three terms in the three propositions: the major term (the predicate of the conclusion), the minor term (the subject of the conclusion), and the middle term(which occurs in each premise). The argument you give has two propositions and a conclusion, but otherwise it is not a syllogism. In fact it has so little logical structure that it is hardly an argument at all. Perhaps you have done an injustice to your opponent by presenting it badly; if he feels so, ask him to rephrase it and send it back to us.


Answer by Shaun Williamson

James don’t worry about us being blatantly honest. Your friend doesn’t know what a syllogism is.

1. Is certainly true but who would ever think that time was a gas or a solid. Time is an abstract concept, it is not a physical thing.

2. Is nonsense but if it were true then we would not need the concept of a god who created the world. It the existence of the world is necessary then we don’t need a god to create it.

3. Time doesn’t share any qualities with the Christian concept of god. Time is an abstract concept, god refers to an individual being who may or may not exist.