On the Pond

A duckling on the village duck-pond today:

Failing the Turing Test

If a computer develops self-awareness, could it be distinguished from an actual human?

Yes: if you ask it about itself, then it will know about itself (that is what "self-awareness" means), but if you ask a human about herself or himself (or themselves or itself), then she or he (or they or it) will not really have much of a clue (not really).

The Village Duck-Pond

Underneath one of the willow trees, one Winter...

Sunlight

spilling out

The Irony Age

Inside China, there are few critics of China's lukewarm approach to climate change. And that lukewarm approach has been used to criticize the recent climate strikers here in the UK. On the radio the other day someone was saying: "Why should we go out of our way to do even more here, when the UK produces only 1% of the world's CO2, while China produces 30%? What would be the point, when any good we achieved would be swallowed up by all that China is doing?" If we agreed with that reasoning, then China's apathy would have spread over here.

Whereas, we need to get those achievements. We need to encourage everyone to do more. And in fact, every little helps. There is a huge amount of CO2 already out there, and we are wondering about adding a little bit more. That little bit extra would make the most extreme weather a bit more extreme, a bit more common. Consequently it is likely to be the cause of a very bad event. Surely we should try to avoid that very bad event. So it really is worth not adding that little bit of CO2, even at some cost. It is not unlike the straw that breaks the camel's back.

It is also not unlike jogging. When you first try to jog it is new, but then it becomes a wearisome chore. Still, if you make that bit of effort each day (and I must admit that I never did), then it becomes a healthy habit (or so I imagine). We do need our defenses against climate change to become natural parts of our lives. Not unlike our defenses against plagues (which only developed after devastating plagues).

And after all, if we do not defend against climate change, then we will really want to scapegoat China. And competitive populism can lead to war.

Ironically, a nuclear Winter would reverse global warming.

Nice weather for ducks!

Rain finally, and 15 ducklings on the village duck-pond, even though it is Autumn!

Charity Schools

The Labour Party recently voted to redistribute the property of private schools to other schools, a proposal to reduce inequality that might make it into the manifesto for the next election in the form of, say, a pledge to end the charity-tax-status of private schools. However, the wealthiest parents already pay a lot of tax towards such things as general education (and the NHS) whilst paying for their own private education (and private health care). And what happens if private schools do lose their charitable tax status? As it is, the wealthiest people already have plenty of ways of avoiding paying tax. And the private schools might make up the difference by ending their scholarships to poorer pupils.

In a state of nature, parents educate their own children (the Baker children grow up in a bakery, naturally learning all about baking, and similarly for everyone else), with the children of the rich getting private tutors. Inevitably, each important extended family develops its own subculture. And eventually the important families feud. The Labour party is calling Eton and Harrow "feudal," but the idea of educating the children of the rich altogether (under the control of a national church, with a monastic ethos) is a way of reducing the kind of feuding that plagues many countries to this day (which is presumably why the posh private schools are called "public schools" in this country). After WWII, Labour reduced inequality with class mobility driven by better education for those from poorer backgrounds. But what if the consequence of that is a stupider working class (voting for Brexit and Boris) and a middle class full of people who are more interested in making money than morality?

The Labour party would say that that was not its fault: it wanted a different outcome. But would that not be like a gambler who lost all his money saying that it was not his fault because he wanted a different outcome.

And to prevent private schooling, you would have to stop people buying non-fiction books, so that you could only get them from public libraries. Otherwise, the children of the rich would grow up surrounded by their own private library. And you would have to stop people paying babysitters and tutors. You would also have to prevent people from sending their children abroad to get educated; indeed, since you cannot control what happens abroad, you would have to stop children from going abroad at all. And so on and so forth.

How to Turn Matter into Antimatter

1) Turn matter into electricity, using a nuclear power station.

2) Turn that electricity into light of a particular frequency.

3) Those photons decay into particle/antiparticle pairs.

Brexit, Boris and Statistics

In the 2016 Brexit referendum, only 38% of the electorate voted to leave the EU.

Over a third of the electorate voted to remain in the EU, while 28% did not bother to vote either way. The percentage voting to leave was higher than the percentage voting to remain, but this referendum was primarily a measure of the will of the people for a particular change, not a contest, despite the political rhetoric. And various factors made it a fairly poor measure, despite the high turnout. Some people, for example, treated it as an opportunity to deliver a protest vote, a vote for a more general change, by voting against both the Prime Minister and the status quo.

Did the 2016 results deliver a mandate for change? Should that Prime Minister have regarded Brexit as mandatory?

To see why not, you only have to consider the 28% who did not bother to vote, who were bothered neither by the status quo, nor by the thought of change. Did those people contribute to any such mandate? Hardly. To see why that matters, consider how big the vote had to be, for there to be a mandate. Had this been a matter that Parliament was indifferent about, then 38% (52% of the turnout) could have been good enough. Why not? But the people were asked, in that referendum, about a change that the majority of their democratically elected representatives did not want, and which the Prime Minister himself did not want. Had more than half of the electorate said that they did want that change, then perhaps their representatives should have taken that result to be mandatory, even if they did not think that Brexit was a good idea; why not? But, that was not what happened. What happened was that there was much talk of a mandate for Brexit, and a lot of other talk. What happened was politics.

All that politics was and is entirely appropriate, because it is up to our democratically elected representatives how to interpret such measures of the will of the people.

There were party manifesto commitments in the 2017 general election. But even those do not make Brexit mandatory, because people vote for a person, not a party, and the influence of a party manifesto on the average voter is arguably less than the influence of the showmanship of the leader of that party. Boris was not the leader of his party in 2017. He is now our Prime Minister, though; and he observes that there was nothing about a deal in the referendum question. As though that means that there was a mandate for Brexit whether deal or no-deal, or deal obtained by means of a threat of no-deal, or whatever. But there was never any such mandate, in the sense of something mandatory, for anything that Parliament did not want. Such a mandate does not trump the political rhetoric; talk of such a mandate is simply part of the political rhetoric. What should trump the rhetoric is logic and the facts, such as the fact that only 38% of the electorate expressed a desire for this rather democratically unpopular change.

Surely the people think that, when it comes to running the country, showmanship should be less important than the facts of the matter.

[Postscript: apparently not!]

What if there is a proof?

Even if a proof that there is a God is, as I believe it is, hidden beneath the foundations of modern mathematics, the experts will, I am sure, not want to waste their valuable time checking whether there is or not. But perhaps it would be different elsewhere.

And perhaps it could have been different here. If Cantor's paradox is essentially a proof that there is a God, then anyone who could have noticed Cantor's generalized diagonal argument could have discovered that proof. Cantor found his paradox by introducing infinite ordinal numbers, and the ancient Greek paradox of Achilles and the tortoise is a reason to introduce infinite ordinal numbers. Could a similar paradox have been discovered by the mathematicians of the ancient world? Might that have been part of the motive for Plato's Form of Forms? Or part of the justification for the doctrine of the Trinity? It is too late to know now (the experts might say that they do know that that is not the case, but if there is such a proof beneath the foundations of modern mathematics then there always was such a proof).

I also wonder whether the work of Russell in the period 1901 to 1906 had any connection with Einstein's 1905 paper. Russell's obscure mathematics flew in the face of logic, and not too dissimilarly, Einstein's obscure mathematics survived being contradicted by empirical observations. Furthermore, Einstein, like Cantor, was in the Leibnizian tradition (not the Newtonian tradition). And after all, the powers of the world would presumably have liked to keep the truth about high energy physics as secret as they could. Still, it is for that reason impossible to know either way now (although the experts would say that they do know that that is almost certainly not the case).

Still, if God did create this universe in such a way that there was this proof, then we might expect the universe to be full of people taking themselves to be living in God's family (and if Einstein was wrong about the light-speed-limit, then that might make a tangible difference to us).

Where have you been?

The One remains, the many change and pass;
Heaven’s light forever shines, Earth’s shadows fly;
Life, like a dome of many-coloured glass,
Stains the white radiance of Eternity,
Until Death tramples it to fragments.

That's from Shelley’s Adonais, 1821.

BLOOM!

Logical Reference

Vienna, 1893, a countess glances at a robin and decides to paint it. A few days later, her terrible painting of a robin is put up in one of the many corridors in her palace, where it remains for half a century. The countess had not signed her painting, with anything other than the year, and so when her painting was found by the Nazis, they thought that it must be valuable because of where it was. These Nazis were from the Ruhr, so they took the painting to be a bad painting of a fat goldfinch. And because they could see that it would make Hitler's paintings look relatively good, they sent it to Berlin. In Berlin, it was catalogued as Der Fette Stieglitz and put with all the other paintings that the Nazis thought were terrible. After the war, it was taken to Moscow, where it remained for half a century until it was sold to an American, who thought it a fine example of early modern art. He hung it in his dining room.

New York, dinnertime, the owner of the painting points to it and says “that bird was very well fed,” starting a conversation that slowly moves on to who the unknown artist might have been a student of. The owner of the painting and the other diners all assumed that “that bird” referred to an imaginary goldfinch dreamt up by some sadly forgotten genius. But we know that it referred to a European robin, do we not? After all, imagine that we are looking through a warped and dirty window at a robin in bad light: if I thought that it was a fat goldfinch, and I pointed to it and said “that bird is fat,” would I be wrong? Maybe not, but I would certainly be talking about a robin, and it might not be a fat robin. And if we had been looking at a very bad photograph of a robin, or at a mediocre painting of a robin, or even at a terrible painting that we did not understand, what difference would that make?

Doubting the existence of Gardeners

What Do Philosophers Do?

For myself, I just notice such facts as:

(A) The overwhelming majority of professional mathematicians are not going to be wrong about what numbers are.

(B) The overwhelming majority of mathematicians assume, in their professional work, that numbers are axiomatic sets.

(C) Numbers are not axiomatic sets.

The conjunction of (A), (B) and (C) would be a contradiction, were the mathematicians of (B) not just assuming that numbers are axiomatic sets for the purposes of proving theorems from axioms, as I suspect they do. But many analytic philosophers deny (C), because of that apparent contradiction. Such philosophers also ask questions like: “Do numbers (or sets) exist? If they do, where are they? If they don’t, then what does ‘2’ refer to?”

The implication is that since numbers (or sets) are abstract objects, hence if they do exist then they exist in some Platonic realm of abstract objects, raising the question: “How is it that we can access that realm, in order to know such properties of numbers as arithmetic?” To see how stupid such questions are, one only has to ask such questions as: “Does value exist; and if so, where is it?” Clearly some things have value, but it makes no sense to ask where it is (or what colour it is); such questions hardly further the analytical task of describing accurately what value is.

A question similar to the one about numbers might be: “Do shapes exist?” Shapes are instantiated in, and abstracted from, shaped things, clearly; and similarly, whole numbers are instantiated in, and abstracted from, numbers of things. That is basically what John Stuart Mill said (in passing); it is only common sense, although his observation was jumped on by a founder of analytic philosopher, Gottlob Frege (incorrectly).

Fissix

F is six

in ancient Greek,
and "fissix" sounds like physics,
and the external physical world is perceived in six basic ways:

Looking at it with our eyes,
hearing it with our ears,
smelling it with our noses,
tasting it with our tongues,
feeling it with our skins, and
knowing which way is up, via our inner ears.

People tend to forget about that sixth way of perceiving the external physical world because people tend to think of the sixth sense as being an ability to see spirits, or some vague sense of impending doom, or a sense of being stared at. Is there a sense of being stared at? Would that be a seventh way of perceiving the external physical world? Or a way of perceiving the external mental world? Are ghosts ectoplasmic, or psychic? I suppose that if psychologists demonstrated that there is a sense of being stared at, and if they got a good materialistic theory of how it worked (involving, say, the nature of quantum-mechanical collapses), then philosophers would say that that was indeed a seventh way of perceiving the external physical world. That is all very iffy though.

What about the sixth way of perceiving the external physical world with our inner ears? Well, "going up in the world," people say, and "feeling a bit down." People naturally associate up with good and down with bad. But physics came of age when the heavens fell under its laws, in the seventeenth century, thanks to Newton.

By pursuing empirical truth, instead of the next epicycle, Britain began the industrial revolution and built the biggest empire the world had ever seen. And the other sciences followed in the footsteps of physics. In the eighteenth century chemistry emerged from alchemy, in the nineteenth century biology became Darwinian, and in the twentieth century physics became Einsteinian. But the twentieth century was a century of cultural wars, as well as actual wars that got bigger than wars had ever been. Soviet biologists doubted the Darwinian foundation of biology. A few mathematicians even doubted the set-theoretical foundation of twentieth-century mathematics. Still, no one doubted the quantum-mechanical foundation of chemistry. And no one doubted the Einsteinian foundation of high-energy physics, which was a little odd because quantum mechanics all but refuted the four-dimensionalism of Einsteinian spacetime.

Almost all of the physical evidence supported the equations of quantum mechanics and Newton's equations, and the rest of it was evidence that could only be perceived by physicists who were assuming Einstein's equations and making very expensive observations, funded by those with the funds to fund the military, observations that could hardly be independently verified.

Physicists are still pursuing the next dark object at the cutting-edge of high-energy physics, and inventing ever more elaborate Einsteinian theories; and philosophers are still giving "empirical truth" new definitions. But if you could choose between appearing professional and being able to learn, which would you choose?

Curry's Paradox

Last year’s new SEP entry on Curry’s paradox followed in Haskell Curry’s footsteps by saying nothing about where our reasoning goes wrong in such informal versions of the paradox as the examples in the introductory section of that entry, the first of which was as follows:

Suppose that your friend tells you: “If what I’m saying using this very sentence is true, then time is infinite”. It turns out that there is a short and seemingly compelling argument for the following conclusion:

(P) The mere existence of your friend’s assertion entails (or has as a consequence) that time is infinite.

Many hold that (P) is beyond belief (and, in that sense, paradoxical), even if time is indeed infinite.

[...]

Here is the argument for (P). Let k be the self-referential sentence your friend uttered, simplified somewhat so that it reads “If k is true then time is infinite”. In view of what k says, we know this much:

(1) Under the supposition that k is true, it is the case that if k is true then time is infinite.

But, of course, we also have

(2) Under the supposition that k is true, it is the case that k is true.

Under the supposition that k is true, we have thus derived a conditional together with its antecedent. Using modus ponens within the scope of the supposition, we now derive the conditional’s consequent under that same supposition:

(3) Under the supposition that k is true, it is the case that time is infinite.

The rule of conditional proof now entitles us to affirm a conditional with our supposition as antecedent:

(4) If k is true then time is infinite.

But, since (4) just is k itself, we thus have

(5) k is true.

Finally, putting (4) and (5) together by modus ponens, we get

(6) Time is infinite.

We seem to have established that time is infinite using no assumptions beyond the existence of the self-referential sentence k, along with the seemingly obvious principles about truth that took us to (1) and also from (4) to (5).

That may look rather formal to you, but formal logic is not even logic (it is mathematics); the above is just very well laid out. Note the two uses of modus ponens, the two sets of three steps, with the first three steps, (1), (2) and (3), all beginning “Under the supposition that”. You should note that because we cannot always use modus ponens within the scope of a supposition, e.g.:

(a) Under the supposition that modus ponens is invalid under a self-referential supposition, (A) implies (C).

(b) Under the supposition that modus ponens is invalid under a self-referential supposition, (A).

With (a) and (b) we have, under the supposition that modus ponens is invalid under a self-referential supposition, a conditional and its antecedent, but it would of course be absurd to use modus ponens within the scope of that supposition, to obtain

(c) Under the supposition that modus ponens is invalid under a self-referential supposition, (C).

There was, then, at least one step in the above argument for (P) that stood in need of some justification, i.e. the step to (3). Were no other step deficient in justification we could conclude, from the absurdity of (P), that the step to (3) was invalid.

Of course, it would be more satisfying to see where precisely that step lacked justification, so presumably we need an analysis of what would in general count as justification for such a step. For now, note that in order to get to (3) we used modus ponens under the supposition that k is true, which was no less self-referential than the supposition that modus ponens is invalid under a self-referential supposition. In the step to (3) we had k being true instead of (A) implying (C), and “k is true” instead of (A).

To progress, we need to step back, I think, because I suspect that the reason why we find (P) to be beyond belief is that the above argument for (P) has exactly the same logical structure as a clearly invalid argument for the obviously false (Q):

Let your friend say instead: “If what I’m saying using this very sentence is true, then all numbers are prime”. Now, mutatis mutandis, the same short and seemingly compelling argument yields (Q):

(Q) The mere existence of your friend’s assertion entails (or has as a consequence) that all numbers are prime.

My suspicion is based on the fact that one could conceivably have a valid argument for

(S) The mere existence of “happy summer days” entails (or has as a consequence) that time is infinite.

For a start, the mere existence of some words can entail the actual existence of something important, as when Descartes proved that he existed: I think, therefore I am. But furthermore, there is a surprisingly valid argument from the existence of “happy summer days” to the probable existence of a transcendent Creator of all things ex nihilo (this links to that), and it might only take some tidying up to get to (S), because such a Creator is an omnipotent being endlessly generating a temporal dimension. (Such a Creator could possibly have a logical existence proof, because of its unique ontological status.) And of course, were there a valid argument for (S), then there would be an identical, equally valid argument for (P).

Anyway, a six-step argument for (Q) that is identical to the Curry-paradoxical argument for (P) would have, in place of k, some such l as “If l is true, then all numbers are prime”. And l is likely to be about as true as not, because (i) it is about as true as not that a contradiction follows from a statement that is about as true as not, since such a statement is about as false as not, and also because (ii) one informal meaning of l is the obvious meaning of the liar sentence “l is not true”, which is, if meaningful, about as true as not, according to my The Liar Proof. And of course, our logic is naturally suited to that part of our language where propositions are either true or else not true, exclusively and exhaustively. For a proposition that is otherwise, we have natural clarification procedures that enable us to construct new propositions that are more suited to logical reasoning. So, it seems likely that propositions that might be about as true as not should be ruled out from the use of modus ponens within the scope of a too-self-referential supposition (to say the least).

Curry’s paradox entered into the analytic philosophy of the Forties, where the logical paradoxes were in general thought to be reasons for replacing our informal logical reasoning with formal logical reasoning (via the mathematical philosophy of formal languages), on such grounds as that (i) one would not expect primates, even highly evolved primates, to be able to reason perfectly, and (ii) the physical sciences use mathematics to get to the underlying physical laws. However, why would such primates not take themselves to be reasoning perfectly adequately; and why should I be doing mathematics when I am really doing philosophy?

Sequence and Consequence

I add grains of sand to the same place, one by one, and eventually I have a heap of sand.

Originally I did not have a heap of sand, of course, and in between having such numbers of grains – just a few originally, and later on lots of them – there are numbers of grains with which I do not obviously have a heap, and do not obviously not have a heap.

Let n be some such number. Perhaps it is the case that when I have n grains of sand I have a heap of sand; but certainly, if that is not the case, then n grains is not a heap. So for all n, either n grains is a heap, or else n grains is not a heap. It follows logically that there must be some n, say N, such that N is large enough for N grains of sand to be a heap of sand, but (N – 1) is not large enough for (N – 1) grains of sand to be a heap of sand.

The problem is that the rather vague meaning of “heap” does not allow there to be such a number. Given any heap of sand, if I take just one grain away from it, then I would still have a heap of sand. Quite generally, if you take one unit away from any very large number of units, then you still have a very large number of units. So it must, after all, be false that for all n either n grains is a heap or else not. That is surprising, but at least we have a picture of how that can be false, with this picture of my adding grains of sand one by one. So while it is surprising, it is not beyond belief; it is not paradoxical (despite what many analytic philosophers seem to think).

It is not, then, always the case that, given some description, either that description is true or else, if that is not the case, the description is not true. It could be that there is no fact of the matter of whether the description is true or not, as when meanings are a little vague and we have a borderline case. Now, in such cases the description cannot simply be neither true nor not true, as that is just to say that it is not true while ruling out its being not true. The only thing left for us to say is that it is about as true as not. In the picture above, the sand changes from not being a heap, to being about as much a heap as not, and then more a heap than not. That is just a fact, of such matters.

One consequence of the possibility of assertions being about as true as not is that there is a relatively simple resolution of the Liar paradox.

Note that it can indeed make sense to say that a proposition is about as true as not. Consider, for another example, how if I say of some artwork that I think good “That is not good” then I am lying. I am saying something false. What would be true would be for me to say that it was good. And if some artwork seems to me to be about as good as not – and you must allow me such a possibility, because such matters are matters of opinion – then it would be true for me to say that it was about as good as not. In such a case, it might make sense (as follows) for it to be about as true as not for me to say that it was good. And if so, and if we all agreed that a particular artwork, say Z, was about as good as not, then it would make sense for “Z is good” to be about as true as not. Does that make sense? Well, were it simply true to say that Z was good, then were “Z is not good” true too, it would follow that Z was good and not good, whereas the symmetry of Z being about as good as not means that we could hardly have one true and the other not true. And if it was instead not true to say that Z was good, so that it would not be the case that Z was good, then there would be a problem with it being not true to say that Z was not good, because that would mean that Z was good.

The Modal Paradox

Here in the actual world A we have a ship, let us name it the good ship Theseus, made of 1000 planks. Our first intuition X is that the same ship could have been made of 999 of these planks plus a replacement for plank #473. In possible-worlds terms that means there is another world B where the same good ship Theseus exists with all but one plank the same as in our world A, and only plank #473 different. But then in world B one has a good ship Theseus made of 1000 planks, and by the same sort of intuition, there must another world C where the same good ship Theseus exists with all but one plank the same as in the world B, but with plank #692 different. That means for us back in world A there is another world C where the good ship Theseus exists with all but two planks the same as in our world A, but with planks #473 and #692 different, so one could have two planks different and still have the same ship. The same sort of considerations can then be used to argue that one could have three planks different, or four, or five, or all 1000. But that is contrary to our other intuition Y [a ship made of a thousand different planks would have been a different ship].
     The modal paradox resembles well-known paradoxes of vagueness, such as the heap and the bald one, for which proposed solutions are a dime a dozen — except that here what seems to be vague is the relation of identity. And the idea that ‘is the very same thing as’ could be vague is for many a far more troubling idea than the idea that ‘heap’ or “bald’ is vague. Indeed, according to many, it is an outright incoherent idea.

From John P. Burgess, "Modal Logic, In the Modal Sense of Modality" pp. 40-1.
     In the fourth line Burgess says "by the same sort of intuition," which is a relatively weak sort of thing to say, and so it might be where the paradoxical reasoning started to go wrong. Our original intuition X was that in the actual world A, Theseus could have had one plank different and still have been the same ship. We know, equally intuitively, that X coheres perfectly well (somehow) with the intuition, Y, that in the actual world A, Theseus could not have a thousand planks different and remain the same ship. Whereas the ship in B is not exactly the same as the ship in A. And the meanings of all our words are rooted in A. The further we get from A, the more vague we might expect our meanings to become.
     In the first line of the second paragraph Burgess observes that proposed solutions to the paradoxes of vagueness are "a dime a dozen" and that means, I think, that anything I might say is bound to pointlessness; but, onward and upwards. And it is certainly the case that "the very same thing" often equivocates, as in the case of the famous clay statue: if that thing is squashed then, while it is the same lump of clay, it is no longer a statue at all. So let us look at a very different formulation of the ship paradox, one that does not involve modality at all. The following is by Ryan Wasserman, "Material Constitution", §1:

[...] the story of the famous ship of Theseus, which was displayed in Athens for many centuries. Over time, the ship’s planks wore down and were gradually replaced. [...] Suppose that a custodian collects the original planks as they are removed from the ship and later puts them back together in the original arrangement. In this version of the story, we are left with two seafaring vessels, one on display in Athens and one in the possession of the custodian. But where is the famous Ship of Theseus? Some will say that the ship is with the museum, since ships can survive the complete replacement of parts, provided that the change is sufficiently gradual. Others will say that the ship is with the custodian, since ships can survive being disassembled and reassembled. Both answers seems right, but this leads to the surprising conclusion that, at the end of the story, the ship of Theseus is in two places at once. More generally, the argument suggests that it is possible for one material object to exist in two places at the same time. We get an equally implausible result by working backwards: There are clearly two ships at the end of the story. Each of those ships was also around at the beginning of the story, for the reasons just given. So, at the beginning of the story, there were actually two ships of Theseus occupying the same place at the same time, one of which would go on to the museum and one of which would enter into the care of the custodian.

For myself, I do not think that the ship in the museum was the famous Ship of Theseus, I think that what was left of that ship is now the custodian's ship. But I concede that it could be that the museum ship is legally the ship of Theseus. It would then follow that the custodian's ship was not, for legal purposes, the ship of Theseus. So I think that there are at least two senses of "ship of Theseus" in play. What we can say about those senses is another matter. Our language is inextricably rooted in the usual events of the actual world. But it could be scientific to know that there are those two senses even before our theories of such senses have become a dime a dozen. And we might find clues as to what we should be saying from related puzzles.
     There are many intuitive puzzles about identity. For one example, suppose that the world that you are in splits into two worlds, so that you are in one while an identical person is in the other. You are the same person as the original you, of course, but so is the person in the other world. So, that other person is the very same person as the original you, who is the very same person as you, and yet that other person is not the very same person as you. So, either personal identity is not always a transitive relation, or else this scenario is impossible. And while the latter is certainly plausible, it seems to me to be the wrong sort of conclusion to draw from this scenario. Knowing whether it is the wrong sort of conclusion to draw or not may well be a prerequisite for getting anywhere with such puzzles as the modal paradox, because intuitions for "is the very same thing as" not ever being at all vague seem to be very similar to intuitions that it must always be transitive.
      For another example, it is conceivable that you change all of the molecules in your body as you eat and shit and eat and shit and so on and so forth; and you would also be aging. You would be the same person, of course; but if another person arrived now, with completely different molecules and a slightly different, older look to you, that would of course be a different person. Being the same person or not is not, it seems, a matter of what one is made of (a thought that is entirely consistent with our being incarnated souls that might possibly reincarnate). And in the real world, where we live our lives, being the same person or not is a matter of identifying someone from descriptions and pictures.

Force and Foreseeability

Some thinkers think that if there is a God, then God will know all about the future, because otherwise bad things might happen. About ten years ago I spent a few years trying to refute one such view as neatly as possible (see my result here), during which attempt I found a new theodicy (which I called "The Odyssey Theodicy") and discovered the mathematical proof that there is a God (who is not immutable) that I have recently been tidying up. Today I thought of this title to go with my original refutation; basically, my original thought was that God's power over God's creation gives God plenty of ability to know that good will definitely happen, without God needing to know all about the future. However, despite now having the sort of title that I like, for my thought, I find that I now have little interest in expressing as neatly as possible such academic thoughts. That is because my thought is so obvious that the view that I was refuting must have existed for some other reason than simply not knowing that thought. Could that view not have been clearer about its reasons, I wonder. But, that is just the academic way, it seems. I also now think that finding new theodicies is pretty pointless, though; consider this analogy: it is the first day of school, and things do not go well. And of course, you learn very little; but of course, that is no reason to have no first day of school. And the evidence that, if there is a Creator of all things, then it is an evil Creator, is a bit like that: if all of this was created by such a power, then there is very likely to be life after death (like further school days after the first, and then life after school, a life enhanced by prior schooling) because that would be better, and no less possible than this life; and so the worse this life is, the more likely there is to be life after death, if there is a God. The logic of such arguments is simple, and undeniable, and so the way the problem of evil is hyped up by mainstream analytic philosophers of religion is, clearly, pure rhetoric.