I'm actually making an ontological argument, though I concede that I was not entirely clear.
Imagine I give you a box which I claim contains all the positive integers. You object because there are an infinite number of positive integers and no physical object can possibly contain an infinite number of things. So to prove my claim I invite you to query the box and ask it "Do you contain X" for any X you care to name.
So you ask: "Do you contain 1?" and the box answers "yes". "Do you contain 842198843?" Yes. "Do you contain Graham's number?" Yes. The busy-beaver number for a million-state Turing machine? Yes.
But then you ask it, "Do you contain negative one?" and the box answers "Yes." And now you protest: I claimed that the box contained only positive integers. No, I reply, I claimed that it contained all of the positive integers, not only the positive integers. In fact it contains all the negative integers too. But this in no way diminishes the power of my initial claim, because surely if it is noteworthy that I built a box that contains all of the positive integers then it must be twice as noteworthy that I built a box that contains all of the positive integers and all of the negative integers too!
So then you ask it, "Do you contain one half?" Yes. Again you protest because one half is neither a positive nor a negative integer, and again I respond with the same argument. "Do you contain pi?" Yes. Same argument. "Do you contain the Godel number of the proof that Peano arithmetic is consistent?" Yes. Ditto.
So you ask, "Do you contain a unicorn?" Yes. Aha! Now you've got me, because whatever else the box may contain, it obviously does not contain a unicorn. No, I reply, of course it does not contain an actual physical unicorn. It contains the phrase "a unicorn". In fact, it contains all possible phrases. It is not merely a box that answers "yes" to any question that is put to it. It is a box that in fact contains all numbers and phrases (is this starting to sound familiar?) and so "yes" is actually the correct answer to any question of the form, "Do you contain X" for any possible utterance X.
The LofB is just my box with a slightly different UI. It is a UI that does a better job than mine of obfuscating the fact that what it underneath the UI is completely uninteresting, and the question of whether or not my claim that the box "really contains" all the things that I claim it contains is just wordplay. The interesting question is not "to what questions will the box answer 'yes'" (or "What works does the LofB contain?") because the answer is "all of them." The interesting question is "What queries can be made of the box/LofB?" Because the queries have to exist in this universe and so they are subject to the constraints of the laws of physics. And in particular, their number is finite. Not only finite, but fairly small: less than 2^500 or so. It's a number that's so small you can actually write it out by hand in a matter of minutes!
It is that tiny subset of the vast space of possible queries that is the interesting thing. Of all the possible questions we could potentially choose to ask, we will only ever be able to ask a tiny, tiny subset of them. So we should choose wisely. And, I submit, quibbling further over the LofB would not be a wise choice.
Imagine I give you a box which I claim contains all the positive integers. You object because there are an infinite number of positive integers and no physical object can possibly contain an infinite number of things. So to prove my claim I invite you to query the box and ask it "Do you contain X" for any X you care to name.
So you ask: "Do you contain 1?" and the box answers "yes". "Do you contain 842198843?" Yes. "Do you contain Graham's number?" Yes. The busy-beaver number for a million-state Turing machine? Yes.
But then you ask it, "Do you contain negative one?" and the box answers "Yes." And now you protest: I claimed that the box contained only positive integers. No, I reply, I claimed that it contained all of the positive integers, not only the positive integers. In fact it contains all the negative integers too. But this in no way diminishes the power of my initial claim, because surely if it is noteworthy that I built a box that contains all of the positive integers then it must be twice as noteworthy that I built a box that contains all of the positive integers and all of the negative integers too!
So then you ask it, "Do you contain one half?" Yes. Again you protest because one half is neither a positive nor a negative integer, and again I respond with the same argument. "Do you contain pi?" Yes. Same argument. "Do you contain the Godel number of the proof that Peano arithmetic is consistent?" Yes. Ditto.
So you ask, "Do you contain a unicorn?" Yes. Aha! Now you've got me, because whatever else the box may contain, it obviously does not contain a unicorn. No, I reply, of course it does not contain an actual physical unicorn. It contains the phrase "a unicorn". In fact, it contains all possible phrases. It is not merely a box that answers "yes" to any question that is put to it. It is a box that in fact contains all numbers and phrases (is this starting to sound familiar?) and so "yes" is actually the correct answer to any question of the form, "Do you contain X" for any possible utterance X.
The LofB is just my box with a slightly different UI. It is a UI that does a better job than mine of obfuscating the fact that what it underneath the UI is completely uninteresting, and the question of whether or not my claim that the box "really contains" all the things that I claim it contains is just wordplay. The interesting question is not "to what questions will the box answer 'yes'" (or "What works does the LofB contain?") because the answer is "all of them." The interesting question is "What queries can be made of the box/LofB?" Because the queries have to exist in this universe and so they are subject to the constraints of the laws of physics. And in particular, their number is finite. Not only finite, but fairly small: less than 2^500 or so. It's a number that's so small you can actually write it out by hand in a matter of minutes!
It is that tiny subset of the vast space of possible queries that is the interesting thing. Of all the possible questions we could potentially choose to ask, we will only ever be able to ask a tiny, tiny subset of them. So we should choose wisely. And, I submit, quibbling further over the LofB would not be a wise choice.