Catching a fly

 

Ducklings in October :

Cuddly ducks

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?