As I said last week, the purpose of any physical object lies outside that object. Therefore the purpose of the universe, if it exists, must also lie outside the universe. No amount of searching only within the universe will discover it.
Furthermore, the purpose of the universe may be focused on a very small portion of the universe: this, too, is in keeping with what we already know of the purpose of physical objects.
So, the universe may have a purpose. Neither its large size, its great age, or the failure of science to find that purpose within the universe is any evidence against it, for the use of these criteria immediately leads to false conclusions for objects which are known to have a purpose. But, if these are the wrong evidence to consider in searching for that purpose, what is the right evidence? What will allow us to go from "the universe may have a purpose", to "the universe does have a purpose", to "this is the purpose of the universe"?
As always, we apply Bayesian inference: a feature of the universe is evidence for the hypothesis that best explains, anticipates, or predicts that feature, and against the hypothesis that is comparatively worse at that task.
To begin, let's apply this technique on something smaller, and therefore easier to understand, than the universe - like a book. If a rational but ignorant alien came to the Earth and saw a book, what could he do to decide whether it has a purpose? Simple: according to Bayesian inference, he would take those two rival hypothesis - "this book has a purpose" and "it does not have a purpose" - then compute the probability that the book would have the features that it does starting from these hypothesis. Each feature would then be evidence for the hypothesis that calculated a higher probability for that feature. So, upon looking at a book, the alien would look at its peculiar shape - flat, rectangular sheets of paper of equal size stacked on top of each other and bound on one end - then compute that this is a highly unlikely shape for an object with no purpose. On the other hand, even if the alien does not know the exact purpose of a book, he knows that an object with a purpose would not be randomly made. Thus eliminating the randomly made objects from the possibility space, our alien could then compute a higher probability for an object with a purpose to take the shape of a book. Therefore, the "purpose" hypothesis better predicts the shape of the book than the "no purpose" hypothesis, and the shape of the book counts as evidence for the book having a purpose.
Notice that this neatly comes down to a simple question: what are the chances that the book would have its peculiar shape? Is that shape something that could come about randomly without a purpose, or is it unlikely and specific enough so that a purpose is the better explanation? This is a universal criteria: it applies to all kinds of objects. You can walk into some workshop or studio or kitchen that you know nothing about, apply this criteria to the objects in it, and correctly infer whether these objects have a purpose. Is that chunk of clay just leftover waste, or does it have a purpose? Are those chopped up vegetable parts going into a dish, or will they be thrown away? Does that sheet of paper have any writing, diagrams, or special folds on it, or is it in a state that could have come about randomly? Our approach handles all these situations, and correctly decides whether the object in question has a purpose.
So, our alien then concludes that the book has a purpose: its shape is peculiar enough that it is unlikely to have come about by purposeless chance. Note that the strength of this conclusion depends precisely upon how unlikely that is: if our "book" is only two sheets of paper stacked on top of each other, that might have come about through chance, and therefore the alien's conclusion is weak. But if our book is an intricate popup book of many pages and detailed construction, that is highly unlikely to have come about through chance, and our alien's conclusion is strong.
Note also that, as I said last week, nothing here depends on the physical size of the book. There are huge books with huge prints, whose largeness sends its own message and thereby serves its purpose. There are also tiny books: electronic books take up a minuscule amount of physical space. Also, the purpose of a book will never be found within the book itself. Even if it were to contain the words, "this book was written so that...", they would be meaningless unless it were actually read by someone, and that someone obviously cannot be the book itself. Meaning and purpose are always found outside the object itself, yet their existence can be inferred from the state of the object.
As I said, all this is generally applicable, as you may see for yourself with any of the objects around you. We can now apply this to the universe: does the universe have a purpose? Well, what are the chances that the universe would have the features that it has? This is not some arcane non-question that cannot be answered. Through science, we know a great deal about the features of the universe, and we know that these are NOT the features that a random universe would have. This is the fine-tuning argument: a random, purposeless universe is highly unlikely to result in a universe like ours - so unlikely, in fact, that in any normal, everyday usage, we would simply call it "impossible". This leads to the very firm, very strong conclusion that the universe does, in fact, have a purpose.
Next week, we will examine how to determine what that purpose is.
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"Is that shape something that could come about randomly without a purpose?" - a perfect test, if and only if you can judge the "could" perfectly. This test is therefore as accurate as one's ability to detect purposeful shape; and while that is something we can often sense, it's not always reliable.
Have you ever cooked Impossible Pie? You mix all the ingredients together, pour it all into a cake pan, and bake it. When you pull it out, it has a base, a filling, and a crust. Normally, random processes tend toward uniformity (put sugar and water together, and you'll have trouble separating them), but this is a contrary example: without purposeful energy, layers are produced, implying purpose. (Though in a paradoxical inversion, 'Poss Pie is very much purposeful, despite its signature ability being actually created by purposeless natural processes.)
Similarly, some objects will have shape that looks purposeful, but the purpose was actually somewhere else - such as off-cuts and leavings. The shape might be "whatever's left after I take out the shape I want", which is not very purposeful. (It still implies a creator, though.) And it's sometimes hard to recognize one from another; "the stone the builders rejected" was so ignored because it was thought to be a mere off-cut, but those builders didn't know that this piece was the perfect shape for a cornerstone/capstone (depending on your translation).
And of course, sometimes the purpose can be obscured, perhaps deliberately. If you look at a compressed file, apart from some headers and footers, it'll be a jumble of apparently-meaningless bytes; same with many forms of executable, audio, video, image, or other files. But there's definitely purpose in them, even though it's less obvious in 2GB of "Frozen plus OST.mkv" than in 20KB of source files used to create it. It's just harder to recognize.
But in many MANY cases, yes, you can detect purpose by shape/form. And even in some of the exceptions above, it's clear that there is still a creator, even if the object's purpose no longer exists.
I'll write a post about Bayesian probability soon. But for now, you're right that this isn't a perfect test, if only because nothing is. My argument is a statistical argument, and the degree to which you can employ it does depend on your ability to recognize certain things.