Monday, 26 May 2014

My new purchase

Jonathan Pearce at The Tippling Philosopher draws attention to the ubiquity of UKIP's message and that their views are couched in terms that make them appear acceptable.

The National Front were openly fascist, racist and failed to appeal to anybody outside a few cranks and the skinhead movement. (The strength of the link between the NF and skinheads is the reason I took so long after going bald to cut my hair short, and still longer to actually shave it, so frightened was I to look like a racist gobshite).   The BNP were less open, less Nazi salutes, less hate speech and more hate insinuation.  Their appeal was broader, you could (at a stretch) vote BNP and claim not to be racist.  With UKIP it's quite easy: you vote UKIP because you want out of Europe.  Wanting out of Europe is perfectly acceptable, and as UKIP, the press and half the Conservative party incessantly bang on about how dreadful the EU is, anti-EU sentiment is becoming mainstream.

Worse than mainstream, there is now a real prospect of pro-EU sentiment becoming marginalised and, if not forgotton, entirely discounted.  There is a danger that we may quietly walk into a calamitous exit from the EU just because it becomes accepted "fact" that no-one wants in.

So I have bought one of these:

(I hope the shop concerned won't mind me using their picture if I give you the link to buy your own:

It's a bit like a European version of those little Stars and Stripes badges an American politician must wear on his lapel at all times on pain of being thought unpatriotic.

I also wear my EU version on my lapel.  Or, when I'm not at work, on my jumper/coat/shirt.  It doesn't "do" much.  But every so often someone will catch sight of it on the tube, the bus or in the street.  It may not consciously register but will, at least, subconsciously make the point that there is someone who is pro-EU.

Wouldn't it be great if other pro-EU people bought and wore their flag with pride (he hints)?


Saturday, 15 March 2014

Anderson and Welty reply!

Transcendental arguers for the existence of God are notorious for not actually putting forward much of an argument. So I was delighted when a scholarly article by James Anderson and Greg Welty (The Lord of Non-Contradiction: An Argumentfor God from Logic) appeared in the Evangelical Philosophical Society’s journal Philosophia Christi. So excited, in fact, that I submitted a short note for inclusion in the very next issue.
It wasn't accepted.
Oh well.
But now I find that not only was my note featured on the Evangelical Philosophical Society’s website but James and Greg have written a response (to mine and others’), also featured on the EPS website!
The original paper is here, my note is here, and the reply is here.
Right. Time to get a little more formal; switch from "James and Greg" to "Anderson and Welty" and so on:
My note refers to a ‘key lemma’ and Anderson and Welty’s reply focuses on this key lemma together with my arguments surrounding it. As this key lemma seems to be the crux of our disagreement it is worthwhile setting out why I think it key.
“The Lord of Non-Contradiction: An Argument for God from Logic” begins with the, largely, uncontroversial claim that the laws of logic are necessarily true. By the end of the paper we are invited to accept that the laws of logic are also necessarily true thoughts. There is more content in the latter than the former, content that can be argued to be contingent on God. My contention is that is mainly the claim
“(s)ince [the laws of logic] are true in every possible world, they must exist in every possible world.” (Anderson & Welty, 2011)
that allows the introduction of the excess content. Thus, it is key. (But it is not the argument, it is a step on the way, a lemma; if you will a “staging post”.)
Existence can be taken to imply possession of properties, natures, essential natures and the like together with various assumptions about what else is needed for these properties to subsist in. Or "being true" can be taken as a property in itself, entirely sufficient to establish existence of the laws of logic whether or not any other properties are held; in particular whether or not they are thought.
This is the equivocation: before the lemma discussion is limited to being true whether or not thought, after the lemma discussion surrounds a concept of "exists" that requires thought. Thought then entails a thinker, necessary thought a necessary thinker and then to God.  On the “left” we have “thought”, on the right we have “truth and thought”.  My note explored possible ways of making the link (“if thought and truth then thought” is valid, “if truth then truth and thought” is not).  Unfortunately the valid destroy Anderson and Welty’s argument whilst those that support it are invalid. This is as we should expect:
“That the laws of logic are necessarily true entails that they are true whether or not God exists.” (Lloyd, 2012)
Anderson and Welty, in their reply, claim that I offered no argument for that claim. One seems, frankly, entirely redundant. “Necessary” is “not contingent” and “P is not contingent on Q” is equivalent to “there does not exist a Q such that P is contingent on Q”: there is no need to list all the infinite non-existent Qs that P is contingent on or the existent Qs that P is not contingent on.
A reference to “impossible worlds” is then made charging that “necessary” does not entail existence in impossible worlds. I fail to see the point of this objection. Do they mean to suggest that a world without God is an impossible world? If so then (if the laws of logic are necessary) there is no possible world where God does not exist and the laws of logic do not exist.  In a footnote, presumably intended to be explanatory, they invite comparison with “(i)f the proposition God exists is necessarily true then it is true whether or not God exists” (Anderson & Welty, 2013) as if there is something problematical with this statement. What does “P whether or not Q” mean? Its logical meaning is, simply, “P”.  If we wish to emphasise the non dependence on Q: “if Q then P and if not Q then P”. Anderson and Welty’s “problematic” comparator, then, can be written:
□G entails □ (G®G) and □ (¬G®G)
"G ®G” , together with "G", entails "G". “¬G ®G” is just a long-winded way of saying “G”, as the truth table shows:

So the statement simplifies to "□G".
A further claim is that I “presuppose(d) that the laws of logic are not ontologically dependent on God”. There was, of course, no “presupposition”:“that P entails Q” is a statement of logical and linguistic analysis that takes no position, presupposed or otherwise, on the truth either of P or of Q.
(A reader interested in a proof of "that P is necessary entails P whether or not Q" is invited to consult the box at the foot of this post.)
At the end of my note I sketched out the idea that all arguments to God from logic are liable to fail. Naturally, anyone arguing that logic depends on God needs to argue that logic is contingent on God. There are plenty of people who are quite happy to accept logic's contingency, but on something much more mundane than God. Perhaps Paula thinks that the laws of logic are thought.  She is quite happy that they exist because there are beings, at least in this world, where there are minds, like Paula’s, that think them. Paula’s position is reasonable and the God-from-logic proponent requires necessity (having admitted contingency) in order to discomfit Paula’s position.  The God-from-logic proponent needs, so to speak, to place the laws logic in a world where Paula is not there to think them.  The laws of logic must be there, because they are necessary, but can’t (according to Paula) because they are contingent on her. The assumption of necessity per se though is not enough to save the argument.  Necessity removes the contingency and without contingency the laws of logic cannot be contingent on God.  So the laws of logic must be held both necessary and contingent.
Now P can be both necessary and contingent if the necessity is qualified. A proper subset of possible worlds is those possible worlds where the physical laws of our universe hold. The laws of physics could have been different, so there are possible worlds were they are different.  But we may limit our considerations to those possible worlds where the laws of physics do hold.  Something, such as the speed of light in a vacuum, which holds in all of these physically possible worlds, is physically necessary.  As the speed of light could have been different there is at least one ‘metaphysical’ world where it is.  Thus the speed of light in a vacuum is physically necessary and metaphysically contingent.
I do not think this helps the God-from-logic proponent. It rescues him from contradiction, but also rescues Paula.  She, herself, may adopt the position that the necessity of the laws of logic she has been presented with is a qualified necessity.  She may admit that the laws of logic are X-ly necessary and still maintain that they are Paula’s- mind-ly contingent.
There is much to do, should anyone wish to pursue it, in analysing the interrelations of qualified necessity.  On first sight it would seem that metaphysical contingencies can be physically necessary but metaphysical necessities cannot be physical contingencies.  What of other ways of qualifying necessity; ontological, logical, epistemological and the like?
I suspect that no argument for God from logic will succeed mostly because I suspect that no combination of qualifications will place Paula in a bind and not give her the very tools to free herself. 
There is also the feeling that logical necessity is the nearest a qualified necessity gets to necessity simpliciter.  And logical necessity appears to take a special role in the argument.  Take Anderson and Welty’s own summary of the qualification of the contingencies in their argument:
"The laws of logic are “contingent on God” only in the sense that they are metaphysically dependent on God’s existence, in precisely the way that God’s thoughts are metaphysically dependent on God’s existence. This doesn’t entail that the laws of logic exist contingently or are true contingently (where contingently is a modal operator equivalent to not necessarily)." (Anderson & Welty, 2013)

Note, in particular the status of truth.  The metaphysical contingency of the laws of logic does not mean that they are not necessarily true.  That does not sit well with:

“(O)ne can logically argue against God only if God exists” (Anderson & Welty, 2011)

Just what are Anderson and Welty to say to someone who argues against God using logic? “Yes, yes, it may be true that God does not exist but part of the logic you use to conclude that is ontologically suspect”?

Proof that □P entails □(Q®P) & □ (¬Q®P)
◊¬ (Q®P) v ◊¬ (¬Q®P)
Negation of the conclusion: “possibly not (Q®P) or possibly not (¬Q®P)”
To test the first option we need to open up a new possible world. As (by hypothesis) “possibly not (Q ® P)” there must be a world that has ¬(Q ® P)
¬(Q ® P)
And here it is.
5 is true (and thus (Q ® P) false) just when Q is true and...
P is false
But from our premise, P is in this world
Lines 7 and 8 contradict
Open up another world. As “¬(¬Q ® P)” is (by hypothesis) possible there must be a world that has ¬(¬Q ® P).This need not be the same world as before, so a new one is needed.
¬(¬Q ® P)
10 is true (and thus (¬Q ® P) false) just when ¬Q is true and...
P is false
But from our premise, P is in this world
Which, again, is a contradiction


Anderson, J. N. & Welty, G., 2011. The Lord of Non-Contradiction: An Argument for God from Logic. Philosophia Christi, 13(2).
Anderson, J. N. & Welty, G., 2013. In Defense of the Argument for God from Logic. [Online]
Available at:
[Accessed 15 3 2014].
Lloyd, T., 2012. An Equivocation in Anderson and Welty’s “Argument for God from Logic”. [Online]
Available at:
[Accessed 15 3 2014].


Monday, 6 January 2014

Review of "Cold-Case Christianity" by J. Warner Wallace

It was raining.  It always rains in England.  I don’t know why I live in the goddam country.  Maybe I’m a sap. Maybe it’s because I’m English.

I wasn’t going out in this weather, though.  I poured myself a slug of whisky (no ice) and browsed for something to read.  And here was this book by some cop.  Homicide.  Hard-nosed  and cynical.  He specialised in “cold cases”.  He cracked the ones no one else was able to.  Then he turned his attention to Christianity.  Hard-nosed atheist cop became hard-nosed Christian cop. 

This was going to be interesting.  I was going to get someone who went through the evidence and sifted what’s reliable from what’s not.  He’d knock down the easy arguments, the curve balls of the usual apologist.  So I bought the book and started to read.  There was some good stuff: interesting anecdotes about past cases here, good principles of detection there.  He’s a bit weak on his understanding of abduction.  But what did I expect? C. S. Peirce with a badge?  

But as I went on I had a creepy feeling.  It all sounded too familiar.   Why is he giving me the spiel about pre-suppositions? Where does the Kalam Cosmological Argument fit into evidence?  Or the Teleological, Axiological, or Ontological arguments?  The TRANSCENDENTAL argument?  Gimme a break.  That’s not evidence. That argument is put forward by people who think giving evidence is sinful!   Then there is Habermas’ (Gary’s, not Jurgen’s) “facts” surrounding the resurrection.  Most scholars, apparently, agree on these facts.  So this hard-nosed detective, supposedly able to really get to grips with evidence, who tests his witnesses, who takes nothing for granted just accepts these “facts” because, hell, “they say”. 

What’s going on?  Maybe I should take a tip from the author: pay as much attention to how it is said as what is said.  How is the guy arguing?  False dichotomies? Check.  Glossing over obvious difficulties? Check.  Conflation of “Christian” with “Fundamentalist Christian”? Check.  Oh and what’s this?  Misrepresentations of others statements.  Bingo!

This is a guy with the same fundie belief as the rest of the fundies.  He’s got the same set of weak arguments as the rest of them.   And he’s come to this book with those beliefs and arguments already in place.  

I don’t believe the subtitle.  I don’t believe this is a homicide detective investigating the claims of the Gospels.  I suspect this is a fundie apologist who thinks he has a gimmick.  “Hey” he thinks, “I’m a homicide cop, why don’t I use that to add some gloss to the usual spiel”.


Thursday, 2 January 2014

Review of "Is God a Moral Monster" by Paul Copan

Well, is God a moral monster?  In looking at Copan’s answer to the question I’ll draw a distinction between “factual” monstrosity and “moral” monstrosity.

A factual statement does not automatically coincide with a moral statement.  If person A clenches his fist and brings the fist, at speed, into contact with the face of person B then person A has punched person B.  This is just a plain fact. 

Whether person A, though, did wrong depends on other factors.  If person B was trying to rob person A then person A has a good case for arguing that he bears no guilt for the punch.  The fact is unavoidable, the guilt not.

Absent God and a certain view of ethics, though, there are some actions that are universally condemnable and, so, we can move straight from establishing the facts to (adversely) judging the morals of the situation.  Genocide, for example, has no excuses.  If person A attempted to wipe out a complete people, then there is no argument about whether they did so wrongly.  Establishing that person A did attempt to wipe out a complete people is enough to establish the fact of genocide and moral culpability.

Let’s call acts and characteristics where establishing the facts also establishes the moral judgement “monstrous”.    Dawkins’ characterisation of the Old Testament God gives some examples:
“(J)ealous and proud of it; a petty, unjust, unforgiving control-freak; a vindictive, bloodthirsty ethnic cleanser; a misogynistic, homophobic, racist, infanticidal, genocidal, filicidal, pestilential, megalomaniacal, sadomasochistic, capriciously malevolent bully.”

Whether someone is jealous is a fact, as is whether they are proud, or petty or (given a concept of “justice”) unjust, and so on.  If they exhibit these characteristics we can say that they are “factually monstrous” and, as all of these (especially together) need only the fact to be established to establish moral culpability, if they are factually monstrous then they are morally monstrous.

There is a problem with this reasoning where one subscribes, as Copan does, to the idea that morality derives from God (“divine command ethics” or “DCE”).  If morality derives from God then God can do no wrong.  Were God to exhibit these characteristics then He would not be morally monstrous, under DCE the idea is absurd.  God would, though, still be factually monstrous: if He were jealous then it would be a fact that He was jealous.  
-          Ignoring DCE anyone who is factually monstrous is also morally monstrous,
-          With DCE the factual and moral monstrosity are separate issues.

As a result, without DCE, a defence of the Old Testament God requires an argument that these apparent facts are nothing of the sort.  Either that the events described did not happen, or they have been mischaracterised as jealous, proud, petty and unjust ethnic cleansing, misogyny, homophobia and so on.
DCE, though, gives Copan an alternative defence.  Yes, God may be a jealous, proud, petty and unjust….but He is morally entitled to be.  A God may be a jealous, proud, petty and unjust…. and still be good.

And this argument Copan relies on. 

Perhaps, rightly, thinking that showing that God is not a factual monster is more persuasive, Copan begins by arguing that the straightforward reading is incorrect.  Things have been misinterpreted, the Mosiac law was an “interim” measure, the laws on slavery were a great improvement on other laws in the region at the time, and so on.  But there are places where this argument fails. 

Copan seems to realise that he is not persuasive in arguing that the genocides and ethnic cleansing were not genocides and ethnic cleansing and argues, in effect, that God judged and if He judged then it’s right.  No argument is offered to persuade us that the supernatural killing of Uzzah for touching the ark in order to protect it was not petty, unjust, and vindictive other than it not being petty, unjust, and vindictive if God decides that’s what should happen.  Copan defends the death penalty for breaking the Sabbath by referencing other draconian punishments.  “Often, when first-time violations were committed in the midst of this fledgling nation, a harsh punishment came with it.” (p 89) Copan admits the facts of the monstrosity and relies on this being God’s decision for a moral defence.

The starkest example of the application of DCE comes when Copan references a study on attitudes to the destruction of Jericho.  Two versions of the story of Jericho were put to schoolchildren, the biblical story and one re-set in China without the intervention of God.  The children disapproved of the actions when in a non-theological setting but assessed the self-same facts approvingly when God was involved.  Copan approves of this difference: God could morally require factually monstrous acts because He had judged the Canaanite culture “irredeemable” and had the right so to do (p161).

This is disturbing.  That there are adherents to DCE means there is a class of person for whom nothing is so vile, so monstrous, so disgusting that, were they to believe it was commanded by God, they would give the vile, monstrous, disgusting actions their wholehearted approval.  More, we must be wary that there might be no act so vile that these people would not, on that account, refuse to believe that it was commanded by God.

Disturbing, but is the book any good?  I do not hold to DCE, but there are arguments for the view that can be made.  Following from this there is a defence of the Old Testament God that could be made: it doesn’t matter how factually monstrous He is, He is not morally monstrous.

As noted above, though, Copan does not limit himself to this defence.  Copan also seeks to remove the impression that the Old Testament God is factually monstrous. It’s a difficult task and, ironically, the attempt just makes matters worse (at least to this reader).   There is always the retort to the Dawkins-like objector that they simply misrepresent the Old Testament.  Perhaps the objector has not even read the Old Testament.  Or, if they have, they haven’t studied it.  Or if they have then they have missed out historical context, or their understanding of Hebrew is poor, or...  But here we have someone who has studied the Old Testament, who has researched the historical context, who has looked into the Hebrew behind the translations.  Reading Copan we can be confident that, no, the death penalty for dissolute sons is not a misreading.  Neither are God’s fits of rage when the Israelites flirt with other gods, or His prohibitions against intermarriage.  As one, vicariously, studies the Old Testament it seems to be better established that God really is all those things Dawkins accused him of being, not less.  Together with that, many of Copan’s defences fall well short of the mark.

Take God’s “jealousy”.  Copan points out, rightly, that some jealousy is good.  He gives the example of a woman who, hyperbolically, threatens to shoot her husband if he were ever unfaithful.  (p 35).  This would be fine for a defence of a God who emphasised His devotion to a people by, jokingly, threatening to enslave them all if they ever crossed him.  It’s not a defence of a God who actually does that (Judges 3:8).  The jealousy of God described by Copan is not the jealousy of the not-actually-trigger-happy wife.  God’s jealousy is the jealousy of the husband who slaps his wife for smiling at the waiter.  It is the jealousy of the wife who hits her husband because he went to the office Christmas party, were there were other women in a social situation.  

Misogyny?  One of Copan’s counter-arguments is that mothers are mentioned alongside fathers in a number of places! His counter to the enforced marriage of a raped woman is that was for her benefit. I find this argument rather repulsive, it’s reminiscent of slave owners and colonialists pleas that their actions were there to help the (inferior) slaves and natives. 

The nadir is Copan’s argument that the Israelites’ interactions with the Canaanites, Amorites, Perizzites, Amalekites et. al.  weren’t “ethnic cleansing”. 

There were other peoples in Canaan when the Israelites turned up.  Sometimes the Israelites moved in and intermingled, sometimes the Israelites accepted others into their lands, sometimes the Israelites had good relations with their neighbours.  But sometimes the Israelites invaded other people’s lands with the express aim of moving them off the land and the Israelites on.  

To move into a people’s territory with the express intention of removing that people from that territory so the territory can be occupied solely by another people is ethnic cleansing.  And when Israelites invaded other people’s lands with the express aim of moving them off the land and the Israelites on they ethnically cleansed.  It is as clear as forming a fist and bringing it rapidly into contact with someone’s chin is punching them.  It’s a simple fact of the matter.

Copan argues that, elsewhere in the Bible, God issues demands for racial inclusivity.  That, elsewhere in the Bible, the Israelites followed this command.  That, elsewhere in the Bible, the Israelites were pretty hard on themselves. (p 163) This is all utterly irrelevant.  It matters not whether they had a consistent policy of ethnic cleansing, whether ethnic cleansing was an aberration or whether they were otherwise really nice guys.  It matters not whether the Canaanites deserved to be ethnically cleansed (p 164): if x is an instance of justified ethnic cleansing then x is an instance of ethnic cleansing.  

Copan though, just will not have it.  We can add to the faults of the DCE adherents the tendency not just to justify the monstrous, not just to accept the monstrous as the word of God but also the willingness to deny the clear evidence of monstrosity staring them in the face.

And a simple refusal to accept the facts in front of you cannot make for a worthwhile work.


Friday, 20 December 2013

Is the Logical Problem of Evil back on?

The logical problem of evil, the argument that the existence of evil is logically incompatible with the existence of God, seems like a dead duck.  Yes, there is evil, but evil is perfectly compatible with a good God.  God may have good reasons for producing or allowing evil.
As a result many people have given up on logical arguments from evil.  They turn to evidential arguments; granted some evil is compatible, is the huge quantity of it compatible with a good God? Even evidential arguments from evil seem to be in trouble from our lack of knowledge.  The evil, even the huge amounts we see, may be necessary for the good.  With our limitations we would never know that God is not carefully maximising the balance of good over evil.

The thing is, unless thoroughgoing utilitarianism is correct, morality does not work this way.

You cannot just give a reason for an act and carry on as if this forgives everything.  “I hurt the child because it was fun” or “I needed to do administer pain inducing chemicals to see if they worked” just won’t wash.  When one excuses (or even praises) an otherwise immoral act one does so because the reason for the apparently bad act is a greater good.  We may stick needles in a baby to vaccinate her against dangerous diseases.  We may administer pain inducing chemicals as part of an attempt to save the life of a child with cancer. In both cases the good, immunity from disease and life, greatly outweighs the bad. 

But a greater quantity of good is still not enough.  If I stick needles in a child I may really enjoy it, it may fantastically improve my life way more than the brief pain reduces the child’s enjoyment of life.  If there is any doubt in the matter of the benefit/disadvantage balance I may recruit a number of people who enjoy watching needles being stuck into children and share the pleasurable experience.  I may add more and more observers gaining more and more enjoyment but at no point does the benefit to myself and the observers morally outweigh the pain to the child. 

The child is an end in herself, not to be used and abused for other’s benefit.  There is a principle involved here: where appeal is made to good outweighing evil: the evil to each individual must be outweighed by good to that individual.

I might feel guilt after sticking needles into a child and try to “make it up” to the child.  Cakes, toys, ice cream or money to buy cakes, toys and ice cream may be proffered.  The benefits accrue to the child, I may even be generous enough that the benefits from the gifts outweigh the needles.  If so, do the gifts excuse my act?  No: I could, just as easily have given the cakes, toys and ice cream without sticking needles in the child.  The needles are unnecessary for the cakes, toys and ice cream.  There is another principle involved: to act as a moral reason the evil must be necessary to secure the good.

Now take Abigail.  Abigail was born in 3000 BCE and very shortly after birth contracted an agonising and fatal disease.  Nature and, thus, God tortured her to death. 

The sad fate of Abigail creates more than a difficulty for any theodicy.  There may be vast amounts of good in the world and all the evil that we see may be necessary for that good.  But none of the evil inflicted on Abigail is necessary for good that accrues to Abigail.  There is little good for Abigail in her earthly life, certainly not enough to outweigh the immense suffering.  Any good accruing to Abigail in the afterlife fails to defuse the evil inflicted whilst she is on earth.  An eternity of bliss in heaven may more than “make up” for the comparatively short period of pain on earth.  But no period of pain is necessary for any period of bliss in the afterlife.

The evil inflicted on Abigail is logically inconsistent with a good God.


Monday, 29 July 2013

Maths Terminology Query

I have five objects (O1, O2, O3, O4 and O5) and three machines to measure them with (M1, M2 and M3).
I know that M1 weighs the objects and have been told that M2 and M3 are also scales.  With M1 I can place the objects in order of weight which is, conveniently the same order as the numbering I've given them:

OM1: O1 then O2 then O3 then O4 then O5

When I measure the objects with M2 I get a different order.  M2 gives the same reading for O2 and O3 and the same reading for O4 and O5.  I have a partial order:

OM2: O1 then both O2 and O3 then both O4 and O5

Although it is possible that M2 measures something other than weight I'm quite happy to accept that it does measure weight but is less sensitive than M1.

With M3 I get a third order:

OM3: O1 then O3 then O2 then O4 then O5

This, again, is different from OM1.  But the difference between OM1 and OM3 is different from the difference between OM1  and OM2.  And this difference tells me that M3 isn't measuring weight.  O3 can't be both heavier and lighter than O2: the machines must be measuring different things.

What is it that makes OM3 support the conclusion that M3 is measuring a different quality to M1?  It isn't that the order is different, OM2 is different.  It isn't any of the things usually used to characterise orders (OM1 and OM2 are both linear orders, OM2 isn't).

So what is the nice, neat, mathematical term for the type of difference between OM1 and OM3 that lets me reach my conclusion?


Tuesday, 13 November 2012

Are Osborne and Little Dodging Tax?

Éoin Clarke is asking questions about the family firm, Osborne and Little Group Limited, that George Osborne has an interest in.  Reading his post (and especially a reply to a comment) suggests that Éoin is not just  asking question but “just asking questions”: his questions aren't questions but accusations.  These accusations boil down to Osborne and Little making a large Gross Profit, from which you would expect Corporation Tax to be paid, but “the accountants” have set to work artificially depressing the profits so that very little is paid.

My comments don't appear on Éoin's blog, so I'll have to comment here. 
Gross Profit
First off, in looking Gross Profit, Éoin is choosing the wrong measure.  Companies pay tax based on profit, not on Gross Profit and Gross Profit is no guide to Profit.
Profit is Turnover less expenditure. Gross Profit is Turnover less a part of that expenditure; the expenditure that directly varies with Turnover.  Gross Profit is Profit ignoring overheads.   You can’t tell how much Profit a company makes, or should make, by looking just at Gross Profit.  I you try then you’re trying to judge Profit by looking at Profit ignoring overheads:  you've just missed out half the equation.
Compare it with coming up with an estimate of Betelgeuse’s gravitational pull on the Earth just by considering Betelgeuse’s mass.  Without consideration of Betelgeuse’s distance from the Earth you haven’t got a “rough” estimate, or “some idea”, or a lower limit on what to expect, you've got a load of bollocks. 

Are “the accountants” artificially depressing the profits?
Éoin implies that they are:
if you examine each of the three years you will see that after gross profit is calculated the accountants proceed to deduct all of that sum in various liabilities including "miscellaneous" liabilities of £1.7 million+ for 2011 and a total of £5 million for the 3 year period.”
This is nonsense.  “Liabilities”, miscellaneous or otherwise, are debts: you owe people.  Borrow money, don’t spend it all and you owe more than you spent.  Repay some of a loan used to fund expenditure and you owe far less than you spent.  Make profits, and losses, transfers and repayments and your liabilities bear no relation to your expenditure.  Debts are not expenditure and expenditure not debts
Whilst the statement that £1.7m was deducted from profit in 2011 is nonsense the claim that a total of £5m was deducted over three years is nonsense on stilts. 
A “liability” is something you owe at a certain point in time, rather like you are a certain height at a certain point in time.  Take your mortgage and how much you owe on it right now.  Take how much you owed a year ago, and the year before that, and so on.  Add up all these numbers.  Now, did you buy your house for that amount?  If you’re tempted to say “yes”, consider your height at six years of age, seven years of age, eight years of age and so on.  Add those numbers together, look me in the eye and tell me that you’re as tall as a house.

How Companies Avoid Tax
Ok, we know that Osborne and Little aren't making up liabilities to deduct from income because that makes about as much sense as accusing them of storing incandescence in jealousy.  But are Osborne and Little otherwise avoiding tax?
We can assume that companies want to make money.  It’s easy making a loss, but then you've, well, made a loss.  If you want to avoid tax by posting losses you want to actually make profits but make it look as if you’re losing money.  This, outside of fraud, is extraordinarily difficult.  And so companies do not tend to even attempt it.
A far, far easier way to for a multi-national company to reduce tax is to report all the profit they make fairly but to vary where they say they made their profits.  Say you make £100m, all over the globe, of which around £50m is made in the UK and £1m or so in a tax haven.  You’re going to be paying 24% on the £50m and the square root of nothing on £1m.  But you realise that, as you’re a multi-national, all your subsidiary companies are dealing with each other all the time.  And they charge each other for it.  So why not look at those intercompany invoices?  Maybe the subsidiary in the tax haven supplies all the coffee, or the web-site services, or owns the patents to your medicines.  So you bump up the price of the coffee, or the web-site services of or patent royalties by, ooh, £49m and suddenly you’re making £1m in the UK to be taxed at 24% and a nice big £50m to be taxed at the square root of nothing. 

Are Osborne and Little doing this?
 The short answer is “no”.  The slightly longer answer is “no, not even close”. We can tell this by looking at page 18 of the group accounts where there is a reconciliation of the expected taxation on profit (in this case, loss) at the UK rate and the actual tax.  It’s difficult for companies to pretend that expenses that didn't happen did, it’s very easy for tax authorities to do the reverse and, as mentioned, different jurisdictions have different rates of tax.  This statement shows the effects of all these varying little rules and rates.  In there is this entry:
“Foreign tax charged at higher rates”. 
The effect is small, £3,000, but notice the direction. That’s right, far from shipping profits away from the high to low tax jurisdictions, Osborne and Little leave profits in higher tax jurisdictions; decidedly not playing with intercompany charges to shelter profits.
Whislt I was writing this post Éoin commented on the proportion of Pricewaterhousecoopers LLP proifts paid as corporation tax. 
Why have Pricewaterhousecoopers LLP made £665m with a tax charge £23m (3.5%)?
Do you notice the letters "LLP"? It stands for "Limited Liability Partnership".  For taxation purposes a Limited Liability Partnership is a partnership not a corporation.  Partnerships do not pay corporation tax: the profits are divided between the partners and the partners pay income tax on their share of the profits. 
Support my research
Éoin has a "donate" button on his website asking us to "support" his research.  It would be good if he actually did some.  To an accountant, or anyone who knows about taxation, the basic errors, misunderstandings and not-even-being-wrongness are of a standard that rivals even this tweet:
Fair enough, Éoin isn't an accountant.  So ask one Éoin! Next time you have what looks like a great story of tax shenanigans find an accountant, buy her a beer and just check that you're not talking drivel.