Can perjury ever be justified? Can it ever be your moral duty to commit perjury?

Today in English criminal courts the jury is presented with one or several charges against the accused and is required to reach a verdict of guilty or not guilty on each charge. However up untill 1913 the jury could come to a wider variety of verdicts, which, in effect changed the charge against the accused. See: The Proceedings of the Old Baily. It was common for juries to use this power in order to lessen the penalty suffered by the accused. This was especially true of capital offences. Thus at a time when theft of goods to the value of more than £50 carried a mandatory death penalty, a jury might declare that that the total value of six ten pound notes was only £20.

This practice known as "pious perjury" was widely approved of by the general public, and, indeed, by much of the legal profession. Indeed the general acceptance of the practice was one of the driving forces for the gradual reduction in the number of offences carying the death penalty. In England today there is no capital punishment but, if there were and I were on a jury where the accused were on trial for a capital offence, I would want the jury to commit pious perjury even if I were convinced the accused were guilty. I would also feel it was my moral duty to lie as a witness in order to save someone from a sentence of death. So my answers are "Yes perjury can sometimes justified." and "Yes, in some circumstances it can be your moral duty to commit perjury."

I am about to start a series of posts on Logic which you can find here. I will structure it like a course but I will not be providing any individual feedback appart from responses I make to reader's posts.¹ It will start from the beginning; I am not sure how far I will get but I intend to discuss a range of subjects including Aristotelian, Modal and Mathematical Logic (including Intuitionistic Logic.) Eventually I hope to get as far as Gödel's Incompleteness Theorem and beyond.

To follow what I am doing you will need to use the Coq Proof Assistant, an excellent piece of software. One of the aims of the course is to teach you how to use it. So if you've never heard of it before, no worries.f

There is a "course book", which is a bit old fashioned, but is cheap and excellent for my purposes. I will cover a whole host of things outside the book - I will use it for the Mathematical Logic part only - but, be warned, you won't be able to follow the course without it.

I find the use of Coq clarifies the subject in a way that makes it easier to discuss various philosophical issues that arise. I will have a post on how I have set up the software using the emacs editor on my GNU/Linux machine, but it also runs on Windows and Macs. Coq has it's own front end, and will also run inside emacs, which is how I use it.

Stuff you will need:

Mathematical Logic by Stephen Cole Kleene.

A classic text and cheap!

Coq Proof Assistant

You can download this for free.  This is a screenshot of a recent Coq session in emacs.  I've customized the colours to how I like them, so if you're thinking "yeuk!!", don't worry. If nothing on the screen shot makes sense, then that's as it should be.  If it does make sense then you're too advanced for this course!

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1. Unless someone wants to send me vast quantities of cash!

One of the joys of being a Dawkins basher is that you can do so while remaining almost toltally ignorant of his opiions.  You don't need to read The God Delusion because, well you already know what an evil atheist would say; don't you?  As for The Selfish Gene, the title says it all; doesn't it?  When you are writing for an audience of willful ignoramuses¹, you are can afford to indulge yourself with large helping of ignorance.  Besides the time saved doing relevant research can be profitably employed digging around for finding out whether or not Dawkins' great great uncle once knew someone who had once spoken to a Chinese opium smoker.

The Washington Post is stunned by the fact that:

Richard Dawkins says he's not entirely sure God doesn't exist,

While a Daily Telegraph: headline reads:

Richard Dawkins: I can't be sure God does not exist.

First this is six year old news.  He said as much in The God Delusion.  So to use language even a journalist can understand these headlines amounts to:

Richard Dawkins believs the same fing wot he rote in a bud sicks years ago.

However the Torygraph must think its readers are idiots as well as ignoramuses, ot they wouldn't have embedded a video.  If you listen to it carefully, something Torygraph jounalists seem congenitally incapable of, you will discover ther real story:

Richard Dawkins even less sure that God exists than when he wrote The God Delusion.

=============================

1] Chuckle, chuckle!  Who is he calling an ignoramus?  Shouldn't that be "ignorami"?  Well if you think that then the boot's on the other foot.  "Ignoramus" is a Latin word, but it is not the Latin for "ignorant person;" that would be "ignoratus."  It's actually the Latin for "we do not know" and ther's no reason, except affectation of learnedness, for Latinising its plural.

Many people go to fortune tellers to find out their future, paradoxically so that they can change it.  The mythological Oedipus tries and fails to do just this. But isn't this just because the predictions were not specific enough?  If he had been told he would marry his mother on a particular day then surely he could have avoided his fate merely by not getting married on that day.  Considerations of this sort lead to a thought experiment due to Martin Gardner that is supposed to show that determinism is false:

Suppose somone were to predict your future in the minutest detail and place this information in a database to which you had access, then surely you could find out what you were going to do next week and not do it.  Thus if determinism is true we have a situation where your future both can and can not be predicted.  Hence determinism is false.

Actually Gardner wanted to prove rather more than this, namely that we have libertarian free will.  Viewed from this point of view it is not a paradox at all,  but I like the name "Gardner's Paradox."  In any case, lets assume determinism is true and see if we can find a resolution to the paradox.

Curiously the resolution is related to the fact that you cannot bring about the past. Someone once joked that weather forecast would be more accurate if forecasters told you about yesterday's weather instead of tomorrow's. However the forecaster could also make it more accurate by going back into the past and changing the forecast, which we all know that is impossible.  But let's pretend for the moment that she could.  It will also be a good idea to simply Gardner's scenario and at the same time state it more precisely.

Let's suppose you have been trained so that you always obey orders of the type:

O. At time T₁, open the envelope in front of you and on your pad write down a different word to the word on the enclosed card.

At time T₀, the forecaster writes on the card the word she predicts you will write on your pad.  But, of course at time T₁,  you obey order O and write down a completely different word!  So the prediction is false, but if she could go back in time, she could make it true just by writing the new word on the card.  Or could she?  Well, no, because now at T₁,  you write down yet another word!  But then she goes back in time and.....

Doesn't this go on for ever?  Of course it does and an intelligent forcaster would take this into , and soon reaise that any forcasting algorithm contains an unending loop.  Doesn't this imply that she cannot, in principle, predict what you will write on the card and that therefore determinism is false?  Perhps Gardner is right after all!

Let's come at this from a slightly different angle.  Let L be the set of words in your language.  Determinism implies that there is a well-defined function f:L→L, it does not imply that this function has a fixed point, i.e. it does not imply that there is a word W such that W=f(W).  All we have shown is that although she can predict what word U you will write in respone to V, she cannot make the two words the same.  And why should she be able to; hadn't we set up O to make this impossible?  All we have shown is that f does not have a fixed point not tha determinism is false.

If it isn't clear what is happening here, consider an NOT gate.  This is an electrical device with one input and one output.  It can take two possible input values, call them T and F, and always outputs the other value.  Think of supplying an input as telling the NOT gate your predicion of the output.  Clearly you will always get it wrong, but this does not imply that the NOT gate's output is indeterminate.  On the contrary, it's the fact it's determinate that makes you wrong.

However this solution to Gardner's Paradox has this rather intriguing implication:

Assuming determinism is true and that you are capable of actions analagous to O,  it is impossible for you to have know or in any other way have access to all your actions before they happen.

Moral: Don't consult fortune tellers; it's a waste of time!

What do all these have in common: a banana, a member of the SWP, a Zoroastrian, a state registeres nurse, a Mexican, a Manchester City fan, a Jew, the King of France?

Answer:  I am none of these things.

If I seriously claimed to be one of these things, that would not make me one.  If subsequent investigation showed that I lacked one of the identifying features that would substantiate my claim, then my claim would be false.  What would a court of law make of my objection that no one had the right to dictate how I self-identify?

The inscription abouve the Romanesque arch at the entrance to Westminster Cathedral reads:

DOMINE JESU REX ET REDEMPTOR PER SANGUINEM TUUM SALVA NOS

Or

"Lord Jesus King and Saviour save us through your blood."  This refers to the fundamental tenet of Christianity, namely that Jesus Christ, the Son of God was crucified for our sins and rose on the third day.  A Christian may or may not believe in the Virgin Birth, the creation myth, the Trinity, or that the Bible is inerrant, but if you do not have this central belief then you are not, I repeat not, a Christian.  This is so, not by my criteria, but by the criteria of all the major Christian sects and by the overwhelming majority of the others.  The Christian churches, of course, know this to be the case and when they had political power, to claim to be a Christian yet not to have this belief was a burning offence.

According to a recent Ipsos MORI Poll, out of those who self-identified as Christians in the last UK Census:

Just a third (32%) believe Jesus was physically resurrected, with one in five (18%) not believing in the resurrection even in a spiritual sense; half (49%) do not think of Jesus as the Son of God, with one in twenty-five (4%) doubting he existed at all.

If these people are Christians, I'm Napoleon.

1. I can conceive of a being whom no worse can be conceived.
2. But it is worse for such being to exist in reality than in the imagination.
3. Therefore, the being of which I conceive must necessarily exist in reality.
4. Evil deliberately committed by a  person is worse than evil caused in any other way.
5. Therefore He is a person.
6. An evil being that is omnipotent and omniscient is clearly more evil than one who is not.
7. Therefore He is omnipotent and omniscient.
8. Logically there can only be one omipotent omniscient being.
9. Therefore any such being is Him.
10. This omnipotent being must be metaphysically responsible for everything.
11. Therefore He created the Universe.
12. Therefore one God exists and is supremely evil.

The following seems to be a meta-ethical truth:

(A) If A ought to be the case and A implies B then surely B ought to be the case.

To many (A) just seems intuitively obvious and any number of instances of it can be exhibited:

(A1) If I ought not lie on oath and not lying on oath implies my saying I saw Joe last Thursday then surely I ought to say I saw Joe last Thursday.

(A2) If George ought to repay his debts and repaying his debts implies implies his giving Fred £100 then surely George ought to give Fred £100.

The intuitive "obviousness" of (A) seems to rest on examples like (A1) and (A2). Nevertheless there is something weird about (A).  For instance B could be "2+2=4".  Do we really want to say "2+2=4" ought (in the moral sense) to be true?

The Good Samaritan Paradox is supposed to show that this general principle is wrong.  Actually I do think it is wrong, not just wrong but seriously confused, which, of course, means that the Good Samaritan Paradox is no longer a paradox.  But before discussing the paradox, I will say what I think is wrong with (A), namely that it's "ought" is, to coin a term, free-floating but:

There is no such thing as a free-floating "ought."

One often hears complaints such as "The streets ought to be swept."  Deontic Logic fans would want to express this something like:

O(S)

where O means something like "it ought to be the case that" and S means "the streets be swept."  However the latter is ambiguous it could mean "someone or other sweep the streets" or could mean "the streets be in a state of having been swept."  It is easy to see that it is the former that was intended, whereas the formalism of Deontic Logic only works well with the latter interpretation.  Given the original statement it is always pertinent to ask "And who do you think should do the sweeping?"

In other words "ought", in its ethical sense alway implies agency.  Sometimes the agent is specified: "I ought to get up earlier;" sometimes not: "The streets ought to be swept."  We may leave it comletely open who this agent is: God, the local council, Fred the Ted; but it is always there.  There is no free-floating "ought" or, to coin a new term,  a statement including "ought" can always be agentified.

A quick look at (A1) and (A2) reveals that they are both agentified.  So lets agentify (A):

(A*) If some agent ought to do A and doing A implies doing B then that agent ought to do B.

Hmm.. Looks OK to me!  Moreover (A1) and (A2) are instances of (A*).  I submit that (A*) expresses the intuition behind (A).

The Paradox Itself.

I could leave things here, but some readers may never have heard of the Good Samaritan Parodox. Here it is:

1. It ought to be the case that the Good Samaritan help the stranger who has been attacked.
2. The Good Samaritan helps the stranger who has been attacked.

   But 2 implies:

3. The stanger has been attacted.

   So from (A) we conclude:

4. The stranger ought to have been attacked.

I think we can safely ignore the diverse attempts to show that this is not a paradox and the ways people have re-written the paradox to defeat these efforts.  Why bother?  (A) is totally confused.

Introduction.

As is well known, Alvin Plantinga has proved God exists by using modal logic to show He is a necessary being.  But as I shall show in my post it is possible to use a slightly more complicated argument to prove the much more earth shattering result that my teapot is also a necessary being.  This leads to the Teapot Existence Theorem which can be stated as "my teapot exists" Now it is worth considering what the implications of this are. You may well say to me "Didn't you know that already?"  Of course I knew it exists, just as Alvin Plantinga knew all along that God exists.  The point is that now you know that my teapot exists.  Now you can know that for certain that it exists without having to go the the bother of coming round to have tea with me. Of course there will be those who won't be convinced but that just shows they don't understand sophisticated metaphysics.

1. Preliminary Definitions and Results.

Note:  I have used words like "theorem" and "lemma" just to show how sophisicated I am.

Definitiion 1 A necessary being is one which exists in all possible worlds.

There are some spoil-sports around who say that this definition doesn't really make sense untill you have tied down what you mean by a possible world.  There are yet other unsophisticates who say that since possible worlds don't actually exists, the nothing can exist inside them except in some metaphorical sense.  But for our purposes we can safely ignore them

The central result of the field is:

Lemma 1 (Plantinga's Lemma) God is a necessary being.

I shall not go over Plantinga's proof.  It is true that some people have said nasty things about it like that Plantinga does not really understand S5, or that he confuses "possibly" with "conceivably."  But as the phiosophically sophisicated know this is just being silly.

This has the important corollary:

Theorem 1 (Existence Theorem for God) God exists.

Proof

From Lemma 1, and the definition of necessary being, we see that God exists in all possible worlds.  Since the actual world is also a possible world, He must exist.

Now there is an important result of modal logic, actually a system called S5 (that impressed you, didn't it?), which states the following:

• If possibly necessarily X then necessarily X

Now you don't need to undestand what that means, the important thing is that you have to believe it because, after all, it is logic!

Now we are in a position to prove the following important result.  It is so important that I give three separate proofs of it:

Lemma 2 (Non-triviality Lemma) No possible world is empty.

Proof 1

From Lemma 1 every possible world contains God and hence is non-empty. QED

Proof 2

This proof is for those spoil-sports who pick holes in Pantinga's proof.

The number 2 exists in all possible worlds therefore no possible world is empty. QED

Proof 3

This one is for those who think that numbers don't really exist or that they live in some Platonic number heaven.  The proof has several steps:

1. Let X be the proposition that no possible world is empty.
2. If X is true then it is clear that it X is necessarily true.
3. In view of proofs 1 and 2 we must at least conceede that it is at least possible that X is true.
4. But 2 and 3 imply X is possibly necessarily true.
5. Modal logic now tells us that X is necessarily true. QED

2. The Existence Theorem for My Teapot

First I shall say something about the fundamental construction used in my proof of the Existence Theorem. I call it morphing over possible worlds.  My teapot is yellow but it is possible that it could be green.  This means that there is a possible world in which my teapot is green, and it should be noted that it is still my teapot.Now it could also be two inches taller which implies that there is a possible world in which it is green and two inches taller.  Now we can represent this as a two step process where the same object morphs over two possible worlds, and it is important to note that it remains the same object.  But we don't have to make such radical changes as that, we can morph our teapot one elementary pariticle across possible worlds and with such miniscule changes who can doubt that it remains my teapot?  Now it is clear that we can morph it into any material object, so let's suppose we morph it into a bunny rabbit

Now I know what you're thinking "Bunny rabbits have minds; where did that come from?"  Well if materialism is correct this is no problem.  So let's suppose dualism is correct.  Dualism depends on the thought that if an object has a mind then it is metaphysicaly possible that it might not.  That is to say there is a possible world in which it does have a mind and another one in which it doesn't.  So you see even if we have only morphed to a bunny rabbit without a mind, we can in one step morph to one with a mind.  Now we could even morph all the way to God as it is well known that a person can actually be God, and, more controversially, some people think a piece of bread can.  So why not a bunny rabbit?

So now we come to the important result.  Again I shall give more than one proof

Lemma 3 My teapot is a necessary being.

Proof 1

Let T, be my teapot and W be the real world.  Let P be any possible world. From Lemma 2, using the Axiom of Choice, I must be able to choose an object O in P.

1. Construct a sequence W=P₀, P₁,... Pₙ=P of possible worlds over which my teapot gradually morphs into O. Call these objects T=T₀, T₁,... Tₙ=O.
2. For any m such that 0≤m≤n-1 I can make Tₘ sufficiently like Tₘ₊₁ for my modal intuitions to tell me they are the same object.
3. Therefore my teapot exists in P.
4. But P could be any possible world whatsoever. Therefore my teapot exists in all possible worlds. I.e. my teapot necessarily exists and is a necessary being. QED

It is worth noting that the proof does not depend on Plantinga's.  It follows that my teapot is a necessary being whether or not God exists.

Proof 2

1. Some spoil sports have objected to Proof 1 on the grounds that there might be some number m at which Tₘ ceases to be my teapot.  
2. Unless they can give a reason in principle why this is not the case, the choice of m is entirely arbitrary and there is therefore no way of distinguishing between the different modal intuitions that would lead to different choices of m.
3. From 2 it follows that it must be possible that my intuitions are the correct ones. i.e. that possibly my teapot necessarily exists.
4. Apply in the rule that possibly necessarily X implies necessarily X,  we see that my teapot necessarily exists.  QED

Now we come to the all important:

Theorem 2 (Existence Theorem for My Teapot) My Teapot Exists.

Proof

This is immediate from Lemma 3 and the definition of a necessary being. QED

It is worth pausing for a while and contemplating the significance of this proof.  I have proved to you, gentle reader, who may never have come withing 1000 miles of my teapot that my teapot exists.  Using a sophisicalted metaphysical argument I have done so withour appeal to anything as messy as empirical evidence.

Advanced Results and an Open Problem

As I remarked the proofs of Lemma 3 and Theorem 2 do not depend on Plantinga's results.  However, on the assumption that God exists we can prove the remarkable theorem:

Theorem 3 (Divinity Theorem for My Teapot) My Teapot is God.

Proof

Let T, be my teapot and W be the real world.  Let P be any possible world. From Plantinga's Lemma P contains God.  As in the proof of Lemma 2, Construct a sequence W=P₀, P₁,... Pₙ=P of possible worlds over which my teapot gradually morphs into  God. Call these objects T=T₀, T₁,... Tₙ=God.  Just as my teapot retains its identity as we move forward over this sequence of possible worlds, so does God as we move backwards over them.  This is clearly only possible if my teapot actually is God. QED

There is only one flaw with this theory.  I call it the Peacock Paradox  I have proved to you withour a shadow of a doubt that my teapot exists.  If you search for "teapot" throughout the proof and replace it with "peacock", you will have a proof that my peacock exists.  However, I don't own a peacock.

Just as Russell's paradox wreaked Frege's logicism, so this paradox appears to put the kibosh on my sophisticated metaphysics.  However there might be a solution along the lines of Russell and Whitehead's ramified theory of types.  I do hope so because then I will be able to use very compicated notation and nobody will have a clue what I am jabbering on about. However for the moment the solution to the paradox is an open problem.

Tesco,  which makes £15,000 profit per employee per year has agreed to pay one of its unpaid slave's bus fare.  Would all the human rights and anti-slavery groups around the world that wish to congratulate the company for this unprecedented act of generosity please form an orderly queue.

Staff were affronted when David Cameron turned up unannounced at Newcastle Royal Victoria Infirmary last Wednesday.  For some reason nobody wanted to talk to him.  Indeed most tried to ignore him and his police protection completely.  But why did he need police protection?  Was he afraid of being mugged by a gang of intensive care patients?  Or maybe he was afraid of being run over by a wheelchair？  Or maybe he was in terror of the nurse who was heard to say "I am vehemently opposed to reforms they're bad for patients and bad for care"？ He certainly wasn't in the mood for actually talking to anyone as he didn't have the courtesy to reply.  He especially didn't want to talk to journalists as he had them locked up in the RVI waiting room.

He did, however, give an interview to the BBC.  In this and in the article on the BBCs web site, the hospital was not named, in fact the very fact that he was visiting a hospital at all was played down.  The video of his visit of course shows him wandering around chatting happily with staff and patients.  What am I talking about?  He is not filmed anywhere near anyone else; all you see of him is a talking head with no one else in shot.  There is no mention in the article of what actually went on, although it is hardly possible that the team from the BBC didn't notice.  Am I surprised by by the appalling standard of journalism at the Corporation?  Am I surprised at this obsequious toadying?  I am not but on the oher hand I can't believe it was done out of fondness for our brave Prime Minister.

There is a song I used to sing as a child.  I recommend David Cameron learns it as it may contain some useful advice:

Nobody loves me, nobody cares,

I think I'll eat some worms.

Big fat juicy ones, long thin skinny ones,

Worms that squiggles and squirms.

Bite their heads off, suck all the juice out,

Throw their skins away.

Ev'ry one's got it in for me,

So I eat worms three times a day.