Category Archives: Philosophy

The Problem with Probabilistic Arguments

One of the perennial problems of philosophy is the question of the existence of God. This question has traditionally revolved around the so-called “theistic proofs” and has a philosophical tradition going back at least to Plato. Some philosophers think there are successful theistic proofs (Swinburne or Craig, for example), others – probably the majority – think there are no successful proofs at all. Still others think the issue of proof is an interesting philosophical sideshow at best but is either irrelevant with respect to the rational justification of belief in God or has little, if any, positive religious value.

My own view – very briefly stated is:

There is a God, and there are arguments which lend some not insubstantial weight to theism. However, very few people – myself included – believe in God because of such arguments. Theistic beliefs seem to rest upon very different grounds.

In this article I want to say why I think the project of theistic (or atheistic) proofs is not a promising one.

Types of Proof

Theistic proofs typically come in two forms: a priori and a posteriori. A posteriori proofs are those which rely on some premise or other derived from experience. For example, the fine tuning argument or the Kalam cosmological argument both rely on certain things which we can only learn from experience: that the laws or constants of the universe are fine-tuned for life, or that the universe began to exist. An a priori proof, on the other hand, is an argument which is logically prior to and independent of experience. I can only think of one such argument: the ontological argument.

Sadly, whilst ontological arguments are very interesting it’s far from clear that any such arguments are successful. A posteriori arguments are therefore much more common. These types of arguments also come in two general forms: deductive demonstrations or some form of probabilistic argument.

Take the strictly logical deductions first. What would it mean for arguments of this type to prove the existence of God? Well, first of all we must be clear what “prove” means in this context. We aren’t thinking of proof in terms of mere logical validity or even arguments which have true premises but which no-one knows are true. To prove something means fundamentally to prove it to some specific person. So, the conclusion must follow from the premises, the premises must be true, and the premises must be acknowledged to be true by those we hope to convince.

It seems to me that we hit something of a snag here. Whilst I disagree with John Hick who reckons all such strict a posterior proofs necessarily beg the question, he’s almost certainly correct that anyone who accepts the premises of such arguments almost certainly already accepts the conclusion that God exists. Purely from my own experience I would hazard a guess that the vast majority who think the Kalam cosmological argument is a persuasive argument for the existence of God already believed in God prior to entertaining the argument. That’s no coincidence.

But perhaps even though such arguments do not succeed as strict demonstrative proofs they could be taken as providing pointers, clues or indications; in short they could be presented as probability arguments for the existence of God which appeal to a more informal kind of rationality. Are these any more successful?

Arguments such as the various design arguments or arguments from religious experience are amongst those which seek to establish the existence of God to some degree of high probability rather than logical certainty. The general form of such arguments is that “in view of some characteristic or other of the world it is more probable that there is a God than not; or, such features are better explained (or “to be expected”) on theism rather than naturalism.”

Now, quite clearly the probability at work here is not the sort of strict mathematical notion we come across in the physical sciences. The concept of probability that operates in various theistic (and atheistic) arguments must be nonmathematical, something along the lines of more reasonable or less reasonable acts of assent on the basis of the relative antecedent/intrinsic probabilities of theism or naturalism. The claim that is typically made is that it is more reasonable to interpret the universe in theistic terms than naturalistic terms (or vice versa).

But can this nonmathematical concept of probability be usefully applied to the question of God’s existence? It is of course a matter of fact that human beings have experienced things within the world from which they conclude that God exists or, more likely, on the basis of which their already existing conviction concerning the existence of God is strengthened or reaffirmed. Such conclusions are often couched in probabilistic language: “it seems more probable than not that…” or “it is overwhelmingly more probable that…” However, is it not the case that when used in this way the notion of probability is simply an expression of subjective judgments, a hunch, a feeling or a “how it just seems to me?”

The problem, as I see it, is that there is a huge number and variety of relevant considerations. Some seem to clearly point towards theism; others clearly to naturalism. For example, even theists would agree that the problem of evil counts to some degree against theism, for why else would they seek to answer it? On the theist side at least some of the following provide some weight in favour of theism: fine-tuning, objective moral values, consciousness, contingency, certain other human traits such as free will and rationality, and even the phenomena of religious experiences. Atheists of course try to present interpretations of such things so as to fit them into their own worldview, whatever that is (typically materialism/naturalism). Likewise with the atheist, he presents arguments from evil or hiddenness and the theist tries to give these an understanding which helps them to sit within their overall theistic way of seeing the world. None of the many factors that we could consider seem to point so unequivocally in one direction such that only one explanation or interpretation is possible; despite the fact that in isolation they point one way or the other, each can be fitted into a theistic or naturalistic worldview. Put simply: there is no single piece of evidence for either view which cannot be incorporated into the contrary view by the mind of a person operating with different presuppositions.

So, can acceptance of one interpretation or the other be said to be more reasonable in the face of the total evidence? Someone may be convinced of Christian theism after reading a Lee Strobel book, but of course Strobel doesn’t entertain contrary arguments. All he achieves is the rather jejune conclusion that the existence of God is more probable on X, Y or Z, a conclusion an atheist could easily grant. Often when apologists (theist or atheistic) claim the evidence as a whole points clearly one way rather than the other it’s not unreasonable to conclude that his research has been infected with confirmation bias. We must treat theism and naturalism as comprehensive wholes, each with their own particular strengths and weaknesses. But which of the various hypotheses squares best with our whole experience of the universe?

How can we say one is more probable than the other? Can we count points in favour of each? So, consciousness and morality in favour of theism gives us a score of 2-0? Add in the problem of evil: 2-1? If 10 items go in favour of theism and only 8 in favour of atheism does theism win by 2 points? That method hardly seems promising. Some factors will be clearer evidence one way than other factors. Some considerations will carry weight – even substantially greater weight – than others. Moreover, there will be no agreed objective way of weighing the various items. It all starts getting rather vague and subjective. Judgments on these matters are personal and intuitive: each of us simply makes a judgment call, and if we seek to apply the notion of probability here we can only legitimately do so on the understanding that it no longer has any objective meaning.

On the methods typically adopted by theistic and atheistic apologists alike there seems no objective sense in which one worldview rather than the other can be described as “more probable.” It’s fairly uninteresting to point out that to theists theism seems more likely, whilst to naturalists naturalism seems more adequate. The reason for this lies, I think, in that they are judging from very different standpoints, with different criteria and presuppositions. We aren’t the wholly rational impartial observers we might like to paint ourselves as. Each of us, for better or worse, is a complex of many factors and influences: our upbringing, our background experiences, our cultural milieu, our peers, our education, our innate temperament and dispositions, and much else besides. These things provide the spectacles through which we view our world. It is largely for these reasons that I find, say, Swinburne’s attempt to convince us that the existence of God is 97% probable, or a naturalist’s attempt to tell me that the immensity of the universe is more probable or more expected on naturalism rather than theism, to be borderline laughable. Of course, great minds make such claims; the claims are no less risible for that.

In the final analysis I can see very little grounds to think the dispute can be settled by appeal to some agreed procedure or by referring to some alleged objectively ascertainable probabilities.

Can my opponents convince me otherwise? Probably not…

Stephen J Graham

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Is Stephen J Graham an Apologist?

Last week I was referred to, in a critical article, as an “apologist.” I confess that I winced every time I read that description. I’ve never regarded myself as an apologist, and find it quite irritating when the label is applied to me. What then am I? On this website I describe myself as a “philosophical theologian;” on Twitter I use: “philosopher,” “theologian,” “writer,” and “researcher.” My academic background – what I actually studied and graduated in at university – is philosophy and theology; my major research interest being philosophy of religion. For this reason I suppose “philosophical theologian” is the most accurate label, if a label is required.

To some minds, however, this doesn’t exclude my also being an “apologist.” It might be thought that since I occasionally criticize atheist arguments or (less often) advance arguments in favour of theism, then I must be an apologist. But surely that can’t be correct. Take atheist philosopher Stephen Law, for example. Law writes articles and essays in defense of atheism, he has taken part in debates with theists, and has advanced a number of arguments against theism or doctrines of some particular brand thereof. And yet we would not fairly and correctly call him an “atheist apologist,” despite the fact that he frequently engages in the sort of activity that might rightly be labelled an “apologetic” – a defense of one’s believings or disbelievings in some matter.

So, how do we distinguish between apologetics and philosophy of religion?

It’s not not terribly easy to say. The lines are often blurred and we even find individuals who engage in both – the most obvious example being William Lane Craig, who is rightly considered as a “philosopher of religion” or an “apologist.” Moreover, there are those who are incorrectly called apologists despite the fact that their work has obvious apologetic import – Alvin Plantinga, for instance. In any event, even though presenting cut-and-dried criteria isn’t possible, and even though the two areas often overlap, to my mind there are a number of general features distinguishing philosophy of religion – or philosophical theology – from apologetics.

Firstly, and most importantly, we must ask ourselves what are the aims. In philosophy of religion – or philosophy generally – the aim is to discover truth and rationally compelling arguments wherever they should lead. By contrast, apologetics is often the defence of what one already believes, a search to find arguments for conclusions already arrived at, and to persuade others of one’s conclusions using arguments, even if those arguments are not the reason why one believes himself. We might put it thus: philosophy of religion asks: “is X coherent and true,” whilst the apologist asks: “Since X is coherent and true, how can we prove it and persuade people.” In speaking of the “paradox of apologetics,” Paul Draper describes the difference this way: apologists seek to justify their religious beliefs; philosophers of religion seek to have beliefs that are justified. He goes on to argue that the nature of apologetics – seeking to justify one’s religious beliefs – is inevitably biased and therefore cannot ground justification. Thus, “paradoxically one cannot obtain justification for one’s religious beliefs by seeking it directly.” We must, then, seek truth rather than justification. Of course this isn’t non-problematic, and frequently it isn’t clear whether someone is doing apologetics or philosophy of religion, but that there is a difference somewhere here seems relatively clear.

Secondly, and following from the above, philosophers of religion must accept risk in a way apologists rarely do. For the apologist – again, generally – philosophy is the handmaiden of theology. By contrast, for the philosopher of religion philosophy will – if necessary – criticize theology and contradict its deliverances. Philosophers must be – and often are, in my experience – much more prepared to abandon even the most cherished beliefs they hold. Apologists tend to have a much greater sense of allegiance to their beliefs, such that even the thought of abandoning some belief is anathema.

Thirdly, philosophers of religion test and critique their own position just as often as they construct arguments for it, and often assist others in doing so. For example, Alvin Plantinga (incorrectly called an apologist, in my view) has on occasion spent hours with critical colleagues to help them be even more effective in their critique. I’ve never witnessed the same charity from “apologists.”

Readers who regard themselves as apologists might well be spitting feathers by now. And perhaps this response is justified and I’ve been unduly harsh. Part of the problem is that the word apologetics can mean different things and be used in different ways. In its simplest form it means merely to give a defense of what one does or believes – like Socrates giving an “apology” to the Athenian court when faced with the charges of denying the gods of Athens and corrupting the youth. Or Paul Draper giving a defense of naturalism. Or Alvin Plantinga rebutting the problem of evil. If this is all we mean by “apologetics” then anyone who ever argues for a position they hold or who defends it against objections is engaging in “apologetics.” But, of course, “apologetics” means more than this. So much so that an entire industry has sprung up in apologetic writing, by authors correctly labelled “apologists.” I’m thinking here of people like Lee Strobel, Frank Turek or J Warner Wallace. What Strobel does, for instance, is not what I do. Strobel can barely bring himself to be critical of a single theistic argument or piece of Christian evidence. If he is critical at all he passes over such arguments in silence so as to focus only on those things he thinks helps sell his beliefs to others. His work is largely about giving answers, the sort that come well-packaged and shrink-wrapped. It’s far too neat to be identified as philosophy of religion, which is a much messier business. No-one could accuse Strobel of criticising Christianity and theistic beliefs just as much or more than atheism – a charge a Christian apologist levelled at me last week.

I suppose ultimately it’s this kind of popular “industry apologetics” I have a strong aversion to, and this that I have in mind when I reject the label of “apologist.”

Stephen J Graham


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Kids, Philosophy & Religious Objections

I always thought the idea of education was to learn to think for yourself.” – Robin Williams (as John Keating), Dead Poets Society


I’ve been thinking a lot recently about the importance of philosophical education for children in schools, and was delighted to find this recent article written by Stephen Law, a philosopher at Heythrop College:

In this article Law defends the teaching of critical thinking skills to children against some common objections. What is most amazing to me is that we should have to defend the teaching of critical thinking skills at all. And yet there really are people – Law cites a popular British columnist and a leading Rabbi – who are very influential, should be intelligent, and yet who oppose it. Law points out that many religious people would be absolutely fine with such a programme of education, and yet (as I too find in my own research) those who oppose it are typically religious.

But let’s look at a few positives first. It’s my own view that philosophy is of such fundamental importance that we should consider it alongside traditional staples of education such as mathematics or English. At its most basic philosophy is about reasoning well about all manner of subjects – from every day run-of-the-mill issues to the big questions of life, existence, meaning and morals. It can help us to cut through nonsense and waffle, spot reasoning mistakes in the work of news reporters, journalists, politicians, and even teachers, as well as analyze complex concepts and entire worlds of thought. In a mini interview Guy Longworth, a philosopher at Warwick University, captures neatly the importance of philosophy: “Many important questions – including truths about morality, aesthetics, the very general structure of reality, and our relation to that reality – can be known, if at all, only through philosophy.”

I recently took an IQ test (130 if you’re interested, and even if not I’m bragging) which included questions that the vast majority of the population gets wrong, and yet in order to get them right all you need are basic reasoning skills – the sort that understands nothing more complex than modus ponens or modus tollens. Apparently the failure to spot elementary reasoning mistakes is widespread. I’m reminded of an article I read a number of years ago which reasoned that because most rapes were committed by men that therefore most men were inclined to be rapists. Quantifier shift fallacy. Logic 101. Of course, philosophers also make mistakes and propound invalid and unsound arguments (I’ve propounded a few myself), but rarely so glaring and basic, and are typically more willing to abandon (or able to correct) a poor argument when the mistake comes to light.

Reasoning skills are vital. Does anyone seriously suggest that a lack of reasoning skills is a useful thing? Is it a bad thing that children learn skills that will assist them in analyzing complex problems, read carefully, critically assess all kinds of ideas, and explore the big and most interesting questions of human existence? Is there some supposed problem with teaching children to express themselves with clarity and precision, or how to construct a solid case for something? Learning to think for oneself is an important part of maturity and intellectual growth, the skills for which can be taught from quite an early age. I routinely use Lego to explore philosophical topics with my 7 year old son – ranging from free will, to right and wrong, good and evil, and the existence of God (see my blog post here: And none of it goes over his head. Kids tend to respond incredibly well to philosophical issues and problems, and often display a creative intelligence and curiosity that, sadly, many adults have long since lost. Whilst some people claim that we run the risk of raising a bunch of argumentative brats, I would argue that when properly taught philosophy should increase one’s levels of intellectual humility. After all, in philosophy we’ll see incredibly intelligent opponents stating their case, we’ll come to appreciate that even seemingly obviously wrong positions aren’t quite as silly as they look at first, and that when dealing with ultimate questions the answers are rarely straightforward.

The strength of philosophy as a discipline is well known. For instance, recent studies in the US have shown that university students who have studied philosophy at undergraduate level exceed other graduates on standardized professional and graduate school admissions tests (such as the LSAT, GMAT and the GRE). Incredibly enough philosophy graduates even perform better on verbal skills than English graduates, and unsurprisingly outstrip all other graduates on analytical skills. The following link and the graphs contained therein illustrate just how strongly philosophy graduates perform in contrast to other disciplines:

And thus it’s really no surprise to find philosophy graduates in all manner of careers from law to banking to journalism. So, it seems that philosophy is massively beneficial (though, of course, the philosophers reading this will point out that perhaps it is the case that smart people choose philosophy, not that philosophy makes one smart!). This evidence isn’t conclusive of course, but it’s highly suggestive that it’s a great discipline to study and master if one wishes to excel at a range of skills that are valuable both in life and to potential employers.

As beneficial as studying philosophy seems to be, there are opponents; and as already stated these opponents tend to be religious. This baffles me – a “non-Calvinist Presbyterian!” I first attended university to study chemistry but found I wasn’t interested in it enough to study it. I decided to switch to what I was interested in: theology and philosophy. I remember the look on the face of a church elder when I told him I was going to study theology – sheer delight. I remember how his faced changed when I added “and philosophy” – sheer horror. “You’ve got to watch that philosophy!” was his advice. To be honest, in my experience, the study of philosophy is much more conducive to religious belief than studying theology. Theology was often dry and tedious, not to mention full of shockingly poor reasoning. I ended up approaching the subject primarily as a philosopher than a theologian, choosing theology modules that were more philosophical in nature – such as Christian thought and world religions, though admittedly the Old Testament always fascinated me. Philosophy, by contrast, was much more of an “adventure of the mind.” It was in my philosophy classes that I met authors who forever changed how I think – William James and Alvin Plantinga being particularly influential on me. Moreover, they changed how I think as a theist in ways that theologians rarely did (though I happily give a nod in the direction of NT Wright, one particular exception).

So what lies behind this suspicion of philosophy on the part of many religious believers? I suspect the biggest problem is simply ignorance – ignorance of what philosophy does. Or perhaps ignorance that considers it synonymous with rabid atheism. Ignorance too of the fact that there are many philosophers who are both religious and of the highest academic standing: Plantinga, Swinburne, Craig, Evans, Davis, Pruss, Helm, Hick (deceased), Wolterstorff, Alston (deceased), McGrew, Stump, Leftow. So many, in fact, that atheist philosopher Quentin Smith complained that God is alive and well in His one academic stronghold – philosophy departments.

But I think more than ignorance is at work. I detect a strong level of fear: the fear of risk. What if we study philosophy and it turns out that the case for God crumbles and atheism appears to be the truth? Some Christians prefer the discipline of apologetics to philosophy of religion for this reason. Apologetics is about defending what one believes. Philosophy of religion is about seeking the truth wherever that may lead, even if it leads away from the beliefs that one currently holds. There’s no real way to assuage such fears – such a risk will always be present in any truth seeking discipline. But as a theist I honestly cannot imagine being in the position of having to give up theism. It’s a risk, sure, but a small one, I’ve discovered. In any event if one is sure of one’s faith what is there to fear of any discipline that seeks to discover truths about reality?

The teaching of philosophy would be greatly beneficial to children. So important, I think, that the fears of a largely religious minority should not have veto power over it. Thus it’s difficult to disagree with Stephen Law when he concludes: “all children should, without exception, be encouraged to think critically – and thus philosophically – even about the moral and religious beliefs they bring with them into the classroom. Religious parents should not be able to opt out.”

Stephen J. Graham

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Responding to Philosophical Arguments – The High Road & The Low Road

I want to look at two different ways of responding to philosophical arguments: one I call the “High Road” and the other the “Low Road.” “What do these terms mean, Stephen?” I’m very glad you asked dear Reader. I’ll briefly discuss each with appropriate examples.

William Lane Craig’s Challenge

In his debates it’s common for Craig to present an argument such as the Kalam Cosmological Argument:

1. Everything that begins to exist has a cause.
2. The universe began to exist.
3. Therefore the universe has a cause.
4. [And Craig goes on to argue that this cause must be timeless, incorporeal, and personal]

Craig then throws down the gauntlet to his opponent: you need to defeat this argument by saying which of the premises you are rejecting and why. Now, I suspect this might be a debate tactic on Craig’s part, but it seems as if he thinks that in order to rationally reject an argument you must dispute or falsify at least one of the premises, or at least show that it’s not as plausible as its negation. But, this is incorrect. We don’t necessarily have to dispute the premises of an argument to be justified in rejecting the conclusion.

Take the Kalam argument above (which I’m incredibly fond of). The atheist might not know which premise is wrong. In fact, both might strike him as prima facie true. But, does that mean he must accept the conclusion on pain of irrationality? I don’t think so. He might not be able to claim: “Not (1),” or be able to demonstrate “Not (2),” however, he might still be within his rational rights in asserting: “Not (1) and (2).”

At first glance this might strike someone as suspect, but it’s perfectly legitimate and incredibly common. In the case above the atheist who doesn’t know how to challenge premise 1 or 2 might still have other overriding evidence or reasons against the conclusion. For example, perhaps he holds there is good reason to think the concept of a timeless incorporeal person is incoherent. Therefore, since this argument leads to the existence of a timeless incorporeal person it must be defective somewhere, even though he might be stumped as to precisely which premise is wrong.

The Low Road

What this example illustrates is the “low road” approach to responding to philosophical arguments: rejecting the conclusion without attacking a specific premise.

Take another example, this time from Justin Schieber, co-host at Reasonable Doubts. In his debate last year with Max Andrews, Schieber offered this argument against the existence of the Christian God:

(1) If the Christian God exists, then “GodWorld” [a world containing no non-God objects] is the unique Best Possible World.
(2) If GodWorld is the unique Best Possible World, then the Christian God would maintain GodWorld.
(3) GodWorld is false because the universe exists
(4) Therefore the Christian God does not exist.

Now, here again the “low road” approach can be utilized. We can illustrate this by the following Leibnizian counter-argument:

(5) If GodWorld is the unique best possible world, then the Christian God would maintain GodWorld.
(6) The Christian God has not maintained GodWorld
(7) Therefore GodWorld is not the unique best possible world.

Leibniz is approaching the question from a different position altogether. Leibniz’s notion that we live in the BPW follows from his belief in an omnipotent and perfectly good creator. Leibniz is also famous for a contingency argument in favour of God, and many other Christians have offered a variety of other arguments in favour of their worldview. Some claim particular religious experiences; others that their belief is in some way “basic.” Before such types Schieber’s argument is likely to fall flat. Why? Because even if they can’t say where his argument goes wrong, they may have reason to reject the conclusion. They can, in effect, say “there’s something wrong here because 4 is in fact false.” Such Christians might well be stumped as to precisely where the argument goes wrong, but that it goes wrong they may well be fairly confident.

The Leibnizian counter-argument, then, effectively flips Schieber’s argument: agreeing that God will create the best possible world, but arguing that because this universe exists then GodWorld is not in fact the unique best possible world.

The High Road

But, of course, Leibniz wouldn’t leave the matter there. He would also adopt what I call the “high road.” The reader can probably already guess what this is: rejecting an argument by undercutting at least one of the premises. Leibniz, I think, would agree with premise (2) of Schieber’s argument – and in fact his own theodicy turns on the fact that God has made the best possible world – so would turn his fire on premise (1). Leibniz might point out that God is inherently creative, desiring to create in order share his goodness beyond the bounds of his own being. So, if the Christian God exists then non-God objects are precisely the kinds of things to be expected, and premise 1 would be patently false. So, if God exists and desires to create finite beings to express his creativity and love then GodWorld would not be the unique Best Possible World.

Other philosophers – Aquinas, for example – would attack premises (1) and (2) for using what Aquinas regarded as an incoherent notion: the “best possible world.” I disagree with Aquinas on this point, but his comments are instructive if only to illumine just how slippery the concept of the “best possible world” actually is. How are worlds to be compared in order to judge World 1 better than World 2? Anyone seeking to make use of the concept needs to give a precise definition and account of what they mean by the term. Some people mean a world that contains no creaturely imperfection. Others mean a world in which the greatest number of compossible beings exist. In fact, how are we to understand the word “best”? Best for whom? For God? For the beings that exist in some given world? Or do we mean best in some kind of impersonal ontological sense like “most perfect kinds of being?” We quickly see that the concept of the best possible world is typically laden with all kinds of assumptions and value judgements (not to mention confusions!). In fact, I think John Hick is ultimately quite right when he says: “The question whether this is the best possible world will…depend upon a prior question concerning God’s purpose in creating man and setting him within the kind of world in which he finds himself. The best possible world will be that which best serves the purpose that God is seeking to fulfill by means of it.” This view of “best” is instrumental in nature and inextricably linked to God’s purposes. If Hick is correct – and there’s much to unpack here – then asking the question about the best possible world aside from any consideration of God’s purpose in creating will always misfire.

But I digress. The point here isn’t to refute Schieber’s argument, but rather to illustrate the different strategies that could be employed in such a refutation. Ideally I think we should always strive for a “high road” response. The “low road,” whilst perfectly intellectually feasible still leaves us with the puzzle of where some argument goes wrong. That might satisfy some people, but it shouldn’t be enough for those of us with some degree of intellectual curiosity.

Stephen J Graham

The Andrews v Schieber debate can be listened to here:

Blogger SKepticism First has written a companion piece to this article, which can be read here:


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