This is also what Strawson Jr. is arguing. But my question is - so what? ... [H]ow is this "absolutely free will" ... relevant to any human concerns? — SophistiCat

You could say this with almost any "problem" of philosophy. That's why the average person couldn't care less about philosophy. — Noah Te Stroete

I disagree. Good philosophical analysis should be relevant to its subject. This is why I think Galen Strawson's analysis fails: ostensibly, it is about something that is very relevant to us: moral responsibility, free will. But in actuality, the artificial construct around which Strawson builds his argument has rather little to do with those subjects. This, by the way, characterizes many discussions related to free will.

But it doesn't have to be so. And indeed, if you look around for philosophical literature on these subjects, you will find better examples. (Earlier in the thread I cited what I consider to be a better example from Peter Strawson, Galen's father.)

Our cranky and inarticulate friend has a point in that there is a difference between a conceptual definition of a number, which describes the properties that anything fitting the definition of a 'number' ought to have, and its particular theoretical construction, such as von Neumann's (which was designed to meet the requirements of the conceptual definition).

But my comment about numbers being sets (everything is a set in the set theory construction of mathematics - obviously) was made in the context of the preceding discussion, which Ikolos does not or will not follow.

This is false. There are sets of numbers, but number themselves are not at all sets — Ikolos

Of course they are.

I don't think cardinality offer a quantitative view of Infinity, since it is either a relation between a set and its elements or between its elements and numbers(e.g. a set is D-
infinite iff for every natural number the set has a subset whose cardinality is that natural number) or between sets(e.g. the cardinal of R is bigger than the cardinal of I) — Ikolos

Numbers are sets, in the usual axiomatizations, so cardinality very naturally fits our idea of quantity.

It seems to me that a person can be said to have an absolutely free will only if that person is in some mysterious sense self-created; that is, only if that person, in some way, was able to choose who they are (their character).
For, ultimately, it is the person's character which determines the motives to which he/she responds, or does not respond, and it is their character for which he/she feels responsible.
This I learned from Arthur Schopenhauer! — charles ferraro

This is also what Strawson Jr. is arguing. But my question is - so what? If that's how you define "absolutely free will," then, obviously, that's how it is. But how is this "absolutely free will" - a made-up thing that cannot possibly exist - relevant to any human concerns?

What do you think? Is this evolutionary approach reasonable to the studies of social sciences? — F.C.F.V.

I am afraid it wasn't very clear what question you were raising, and so unfortunately the discussion has been derailed into the perennial argument about universal morality.

Anyway, as best as I can tell, you are proposing that Hume's dictum can be vindicated if a naturalistic account of the origins of morality is true. Is this more-or-less what you are saying?

First, note that Hume, not having the benefit (?) of later developments in evolutionary psychology and social science, brought his own arguments to bear. What do you think of those?

Second, let's look at the title dictum: "The Rules Of Morality Are Not The Conclusions Of Our Reason." I think it is evident that it is not exactly true. When we don't have an instant moral clarity on some question, we often apply reason. However, it may be argued that when we trace our moral reasoning to its termini, we will always find some other moral rules there, which are themselves not based on reason.

One way to argue in favor of that position is to say that in point of fact, foundational moral principles are not chosen by each person through rational deliberation. To that end, one might try to show that moral values invariably come about non-rationally: either they emerge from our natural inclinations (moral instincts), or they are inculcated through upbringing, religious indoctrination, authority, social pressure, etc.

How does a particular historical account of the emergence of morality bear on this? That is not very clear. It seems to me that you would first need to establish the proximate causes of our moral judgements along the lines that I suggested above. Once that is done, you could further develop an account of those causes: evolution of moral instincts, social dynamics resulting in the emergence of social norms, etc., but all that seems to be surplus to requirements. You could counterfactually suppose that our moral principles are instilled in us by God, for example - and that would serve the argument just as well, because that too would be an instance of a non-rational origination of morality.

Another way to argue for the thesis is to follow Hume in saying that as a matter of principle, it could not be otherwise. Reason, says Hume, does not motivate action (reason can tell you how best to achieve your goal, but it does not supply goals). "Reason is the slave of the passions." You cannot get from an is - facts, observations - to an ought - moral judgements - though reason. Therefore, only normative beliefs and inclinations can be the source of our moral judgements.

My claim is that mental phenomena supervene on the physical brain. Some difference in the brain is necessary for a change in the mental processes. Also the brain supervenes on mental processes. Any change in mental processes necessitate changes in the brain. Hence, my assertion that there is supervenience BETWEEN mental processes and the brain. — Noah Te Stroete

Some difference in the brain is necessary for a change in the mental processes and Any change in mental processes necessitate changes in the brain mean exactly the same thing: that mental processes supervene on brain processes. Not the other way around.

Anyway, I just wanted to draw your attention to your basic misunderstanding of supervenience in general.

There are A differences if and only if there are B differences. It goes both ways. Just Google “supervenience”. “If and only if” doesn’t just mean “if”. — Noah Te Stroete

You are misreading the definition that, I assume, you got from Google:

X is said to supervene on Y if and only if some difference in Y is necessary for any difference in X to be possible. — Supervenience - Wikipedia

Note the placement of IFF in the wiki definition.

Supervenience does not do away with cause and effect. The lower level physical realization is subject to cause and effect as is the higher level mental exercise. It's just that the two levels line up 1:1. — Noah Te Stroete

Supervenience is a one-to-many relationship ("No A changes without B changes," but not the other way around).

Sounds like an outright attack on morality to me. — Jamesk

Well, the title of the paper is kind of a giveaway... But not really. Strawson talks about "ultimate" moral responsibility (he uses half a dozen more such adjectives throughout the discussion). What this has to do with plain-vanilla moral responsibility that we actually live with is questionable. In my opinion, not nearly as much as Strawson implies. And yet the issue of sourcehood is not entirely irrelevant either. But Strawson with his blunt approach does not do a good job of tackling this question.

Crack open any textbook on calculus. The concept of the limit is one of the first things that is covered in a typical calculus course, right after the basics of set theory. You need to understand mathematics before you can discuss philosophy of mathematics.

No idea. — Devans99

Yes, that's exactly the problem.

I know the textbook definition, the question the OP poses is: 'is the textbook definition correct?'. — Devans99

The question in the OP indicates that you don't know or don't understand the textbook definition.

We can still have moral responsibility in the absence of freewill in the Libertarian sense. Strawson's approach is interesting, I haven't read the paper yet but I am interested in what he means by 'truly responsible' and if there is an angle of compatibilism there or not. — Jamesk

Strawson takes the conventional approach of closely linking free will with moral responsibility, so when he attempts to undermine (his) idea of moral responsibility, he also takes it to be an attack on the idea of free will.

What Strawson means by being 'truly responsible' is being the ultimate causal source of your actions. The key move in his argument against moral responsibility is this:

But to be truly responsible for how one is, mentally speaking, in certain respects, one must have brought it about that one is the way one is, mentally speaking, in certain respects. And it is not merely that one must have caused oneself to be the way one is, mentally speaking. One must have consciously and explicitly chosen to be the way one is, mentally speaking, in certain respects, and one must have succeeded in bringing it about that one is that way. — The Impossibility of Moral Responsibility

Where Strawson's position is similar to that of compatibilists is in that for him the question of determinism is irrelevant to the question of moral responsibility/free will - only in his case, he argues that "true" moral responsibility is impossible in any event (but those arguments are quite similar to those that have been used by compatibilists).

So whenever a limit is evaluated, it’s correct to use the approximately equals sign (~) rather than equals. — Devans99

No. Look up the definition of the limit in any modern textbook or online reference. Do not assume that what a mathematical notation "looks like" is what it literally means.

This could explain some of the rather peculiar results in calculus? — Devans99

No.

Oops! That explains the striking change of attitude. Thanks for the correction :)

Were I to take up the task of writing a book on free will again, I would read opposing views extensively, as I did for my book on naturalism. Until I do take up that task, Strawson is not likely to be on my reading list. — Dfpolis

Suit yourself. Only why would I bother to read what you have to say, whether in a book or in a forum post, given that you don't know what you are talking about?

Reading the full argument prompts me to observe that responsibility as something that we practice every day has less to do with "making one the way one is, mentally speaking" and more to do with trying to influence other people, events, and the condition of things. — Valentinus

I don't think that is quite right either. I am actually more in agreement with what Strawson Strawson's dad wrote in his earlier essay Freedom and Resentment (your utilitarian attitude here could be identified with that of the "optimist" in Strawson's essay).

Edit: Andrewk corrected my blunder.

Yesterday on a different forum, I was referred to a video in which Galen Strawson purportedly proved that free will is impossible. — Dfpolis

Instead of relying on someone's summary of a Youtube video, you should read some of Strawson's papers, such as The impossibility of moral responsibility (1994)

(I am not on Strawson's side, BTW)

There was a table set out under a tree in front of the house, and the March Hare and the Hatter were having tea at it: a Dormouse was sitting between them, fast asleep, and the other two were using it as a cushion, resting their elbows on it, and the talking over its head. 'Very uncomfortable for the Dormouse,' thought Alice; 'only, as it's asleep, I suppose it doesn't mind.'

The table was a large one, but the three were all crowded together at one corner of it: 'No room! No room!' they cried out when they saw Alice coming. 'There's plenty of room!' said Alice indignantly, and she sat down in a large arm-chair at one end of the table.

'Have some wine,' the March Hare said in an encouraging tone.

Alice looked all round the table, but there was nothing on it but tea. 'I don't see any wine,' she remarked.

'There isn't any,' said the March Hare.

'Then it wasn't very civil of you to offer it,' said Alice angrily.

'It wasn't very civil of you to sit down without being invited,' said the March Hare.

'I didn't know it was your table,' said Alice; 'it's laid for a great many more than three.'

'Your hair wants cutting,' said the Hatter. He had been looking at Alice for some time with great curiosity, and this was his first speech.

'You should learn not to make personal remarks,' Alice said with some severity; 'it's very rude.'

The Hatter opened his eyes very wide on hearing this; but all he said was, 'Why is a raven like a writing-desk?'

'Come, we shall have some fun now!' thought Alice. 'I'm glad they've begun asking riddles. — I believe I can guess that,' she added aloud.

'Do you mean that you think you can find out the answer to it?' said the March Hare.

'Exactly so,' said Alice.

'Then you should say what you mean,' the March Hare went on.

'I do,' Alice hastily replied; 'at least — at least I mean what I say — that's the same thing, you know.'

'Not the same thing a bit!' said the Hatter. 'You might just as well say that "I see what I eat" is the same thing as "I eat what I see"!'

'You might just as well say,' added the March Hare, 'that "I like what I get" is the same thing as "I get what I like"!'

'You might just as well say,' added the Dormouse, who seemed to be talking in his sleep, 'that "I breathe when I sleep" is the same thing as "I sleep when I breathe"!'

'It is the same thing with you,' said the Hatter, and here the conversation dropped, and the party sat silent for a minute, while Alice thought over all she could remember about ravens and writing-desks, which wasn't much.

The Hatter was the first to break the silence. 'What day of the month is it?' he said, turning to Alice: he had taken his watch out of his pocket, and was looking at it uneasily, shaking it every now and then, and holding it to his ear.

Alice considered a little, and then said 'The fourth.'

'Two days wrong!' sighed the Hatter. 'I told you butter wouldn't suit the works!' he added looking angrily at the March Hare.

'It was the best butter,' the March Hare meekly replied.

'Yes, but some crumbs must have got in as well,' the Hatter grumbled: 'you shouldn't have put it in with the bread-knife.'

The March Hare took the watch and looked at it gloomily: then he dipped it into his cup of tea, and looked at it again: but he could think of nothing better to say than his first remark, 'It was the best butter, you know.'

Alice had been looking over his shoulder with some curiosity. 'What a funny watch!' she remarked. 'It tells the day of the month, and doesn't tell what o'clock it is!'

'Why should it?' muttered the Hatter. 'Does your watch tell you what year it is?'

'Of course not,' Alice replied very readily: 'but that's because it stays the same year for such a long time together.'

'Which is just the case with mine,' said the Hatter.

Alice felt dreadfully puzzled. The Hatter's remark seemed to have no sort of meaning in it, and yet it was certainly English. 'I don't quite understand you,' she said, as politely as she could.

'The Dormouse is asleep again,' said the Hatter, and he poured a little hot tea upon its nose.

The Dormouse shook its head impatiently, and said, without opening its eyes, 'Of course, of course; just what I was going to remark myself.'

'Have you guessed the riddle yet?' the Hatter said, turning to Alice again.

'No, I give it up,' Alice replied: 'that's the answer?'

'I haven't the slightest idea,' said the Hatter.

'Nor I,' said the March Hare.

Alice sighed wearily. 'I think you might do something better with the time,' she said, 'than waste it in asking riddles that have no answers.'

'If you knew Time as well as I do,' said the Hatter, 'you wouldn't talk about wasting it. It's him.'

'I don't know what you mean,' said Alice.

'Of course you don't!' the Hatter said, tossing his head contemptuously. 'I dare say you never even spoke to Time!'

'Perhaps not,' Alice cautiously replied: 'but I know I have to beat time when I learn music.'

'Ah! that accounts for it,' said the Hatter. 'He won't stand beating. Now, if you only kept on good terms with him, he'd do almost anything you liked with the clock. For instance, suppose it were nine o'clock in the morning, just time to begin lessons: you'd only have to whisper a hint to Time, and round goes the clock in a twinkling! Half-past one, time for dinner!'

('I only wish it was,' the March Hare said to itself in a whisper.)

'That would be grand, certainly,' said Alice thoughtfully: 'but then — I shouldn't be hungry for it, you know.'

'Not at first, perhaps,' said the Hatter: 'but you could keep it to half-past one as long as you liked.'

'Is that the way you manage?' Alice asked.

The Hatter shook his head mournfully. 'Not I!' he replied. 'We quarrelled last March — just before he went mad, you know — ' (pointing with his tea spoon at the March Hare,) ' — it was at the great concert given by the Queen of Hearts, and I had to sing

"Twinkle, twinkle, little bat!
How I wonder what you're at!"

You know the song, perhaps?'

'I've heard something like it,' said Alice.

'It goes on, you know,' the Hatter continued, 'in
this way: —
"Up above the world you fly,
Like a tea-tray in the sky.
Twinkle, twinkle — "'

Here the Dormouse shook itself, and began singing in its sleep 'Twinkle, twinkle, twinkle, twinkle — ' and went on so long that they had to pinch it to make it stop.

'Well, I'd hardly finished the first verse,' said the Hatter, 'when the Queen jumped up and bawled out, "He's murdering the time! Off with his head!"'

'How dreadfully savage!' exclaimed Alice.

'And ever since that,' the Hatter went on in a mournful tone, 'he won't do a thing I ask! It's always six o'clock now.'

When the internet first truly impinged on my retarded consciousness (early in the 2000s), I had two instinctive and profound concerns, which have only increased, in breadth and depth, with the intervening years, to the point where I'm now driven to consider it, on the whole, a positively cancerous presence in our lives (quite beyond the latest backlash against its widespread, systemic, and increasingly devastating abuse). — Brian Jones

I am sure that people have said this about television, radio, moving pictures, newsprint, printed books, hand-written books, letters, even writing itself. (Indeed, Socrates allegedly bemoaned writing's detrimental effects on memory.) Not to mention such horrors as theater and social clubs.

Internet is a fact, the way we live now - just like all those other novelties that I just mentioned were in their day (and many still are today). This is not to say that acquisition of these artifacts constitutes progress - inexorable betterment of humanity. They are just facts of life, and railing against them is as sensible as railing against the weather.

Ok, the question is about premiss (b) any orderly system can be simulated on a Computer. — ssu

Yes, after I posted that, I realized that I overreached a bit. There are indeed "regular" systems that nevertheless cannot be simulated to arbitrary precision (indeed, if we sample from all mathematically possible systems, then almost all of them are uncomputable in this sense). However, most of our physical models are "nice" like that; the question then is whether that is due to modelers' preference or whether it is a metaphysical fact. Proponents of the simulation hypothesis bet on the latter, that is that the hypothetical "theory of everything" (or a good enough approximation) will be computable.

So how do we ask a Computer something to what there exists a correct model, but it cannot compute it? Well, simply by a situation where the correct answer is depended on what the computer doesn't do, in other words, negative self-reference. You get this with Turing's Halting Problem. Now you might argue that this is quite far fetched, but actually it isn't when the computer has to interact with the outside World, when it has to take into account the effects of it's own actions. Now, in the vast majority of cases this isn't a problem (taking it's own effects into account on the system to be modelled). Yes, you can deal with it with "Computer learning" or basically a cybernetic system, a feedback loop. — ssu

It is difficult to understand what you are trying to say here, but my best guess is that you imagine a simulation of our entire universe - the actual universe that includes the simulation engine itself. That would, of course, pose a problem of self-reference and infinite regress, but I don't think anyone is proposing that. A simulation would simulate a (part of) the universe like ours - with the same laws and typical conditions.

Good point. Would you also say that most of the time we aren't self-aware, as that is, in essence, self-reflection? Would you also say that self-awareness and concsiousness are two separate things (one can have one without the other). — Harry Hindu

"Self-awareness" is a rather broad rubric, which includes awareness of one's location, for instance. We are talking more specifically about "thinking about thinking," which, it seems to me, we rarely actually do, and even then we would be registering something that happened in the past. It is hard to think of two things at once, let alone telescoping an infinite recursion of thought about thought about thought, etc. into one moment.

If I were to internally ask myself, for example, if the punch would hurt, would I be thinking it would or thinking that I think it would? — Kranky

If Mike Tyson is about to punch you in the face, the only thing you should be thinking is: "Run away!"

And no, you wouldn't have time to think "I am thinking about running away." That requires self-reflection, which you are capable of, but it doesn't happen automatically. Most of the time you are not thinking about thinking.

Trump has got nothing to do with it. He simply made the correct call — hks

Trump's point was that climate change was not to blame (he is still in denial), and making that point was probably the only reason why he spoke out on the issue at all. He was not wrong (except when he foolishly compared California to Finland), but he was not right either.

Some people from Paradise, CA are hell-bent on rebuilding. Well, maybe it just isn't a good idea to rebuild in harms way. — Bitter Crank

They say that lightning doesn't strike the same spot twice, which is the opposite of true. An old wartime superstition says that a shell doesn't strike the same spot twice, which is not true either, but at least if you hide in a shell crater, you are better protected from nearby hits. But in this case maybe the thinking is good: all that built-up fuel has burned out and it will be a while before it has time to grow back and dry out. And they could be better prepared next time.

Are you serious? Well, to give an easy example: if you would model reality with just Newtonian physics, your GPS-system wouldn't be so accurate as the present GPS system we now have, that takes into account relativity. — ssu

And if you do it with Lego blocks it will be less accurate still (funnier though). But I am not sure what your point is. Do you suppose that computers are limited to simulating Newtonian physics? (That's no mean feat, by the way: some of the most computationally challenging problems that are solved by today's supercomputers are nothing more than classical non-relativistic fluid dynamics.)

That has to be the strawman argument of the month. Where did I say "conscious beings are outside any general order of things"?

Definitions do matter. If we talk about Computers, then the definition of how they work, that they follow algorithms, matters too. — ssu

Well, the idea behind the simulation hypothesis is that (a) there is a general, all-encompassing order of things, (b) any orderly system can be simulated on a computer, and possibly (c) the way to do it is to simulate it at its most fundamental level, the "theory of everything" - then everything else, from atoms to trade wars, will automatically fall into place. All of these premises can be challenged, but not simply by pointing out the obvious: that computers only follow instructions.

Apokrisis explains this very well on the previous page — ssu

I am not sure what that business with instability is about, but I haven't really looked into this matter. I know that the simulation hypothesis is contentious - I have acknowledged this much.

And also the Simulation Hypothesis generally asks us to believe the simplest compatible story. So once we start going down the solipsistic route, then a Boltzmann brain is the logical outcome. Why would you have to simulate an actual ongoing reality for this poor critter when you could just as easily fake every memory and just have it exist frozen in one split instant of "awareness"?

Remember Musk's particular scenario. We are in a simulation that spontaneously arises from some kind of "boring" computational multiverse substrate. So simulating one frozen moment is infinitely more probable than simulating a whole lifetime of consciousness. — apokrisis

You need enormous probabilistic resources in order to realize a Boltzmann brain. AFAIK, according to mainstream science, our cosmic neighborhood is not dominated by BBs. BBs are still a threat in a wider cosmological modeling context, but if the hypothetic simulators just simulate a random chunk of space of the kind that we find ourselves in, then BBs should not be an issue.

Christianity initially developed as a marginalized and persecuted cult, and that is reflected in the tone of the scriptures, which is alternately grandiose, ingratiating, impatient, angry and despairing.

But by proving it by truth table wouldn't you already be relying on the inference as a valid method, since the truth table is the conjunction of the premises implying in the conclusion? — Nicholas Ferreira

In classical logic implication p->q is a given, so yes, it is a valid method by definition. It is defined as a truth function f(p, q) with a known truth table. Other logics may treat implication differently though.

I see the problem as being not just a difference in scale but one of kind. If you only had to simulate a single mind, then you don't even need a world for it. Essentially you are talking solipsistic idealism. A Boltzmann brain becomes your most plausible physicalist scenario. — apokrisis

Well, yes, you do need a world even for a single mind - assuming you are simulating the mind of a human being, rather than a Boltzmann brain, which starts in an arbitrary state and exists for only a fraction of a second. Solipsism is notoriously unfalsifiable, which means that there isn't a functional difference between the world that only exists in one mind and the "real" world. But if you are only concerned about one mind, then you can maybe bracket off/coarse-grain some of the world that you would otherwise have to simulate. Of course, that is assuming that your simulation allows for coarse-graining.

If you mean traditional logic, aka "laws of thought," there are different ways to axiomatize it. But modus ponens, for example, can simply be proven from the truth table.

Heh, that's a good point. I suppose that if you were only simulating one mind, you could make your simulation domain smaller than if you were, say, simulating the entire population of the earth.

Politically speaking, it is how we prepare our young for thinking that concerns me most. I am convinced the 1958 National Defense Education Act, and replacing education for independent thinking with groupthink and leaving moral training to the church, is what lead to the election of Trump and that same education many years ago, in a different country, resulted in the election of someone Trump seems to be role modeling. — Athena

Ugh... I wouldn't want to make moral training the business of the state - any state. I have been on the receiving end of such "moral training" (enforced state ideology) and I wouldn't wish it on anyone. It's as "groupthink" as it can get. Of course, you will object that good training is not groupthink. But if things always worked out as well as we wish they did, we wouldn't even be having this conversation now. And history shows us that when the state takes moral training into its hands, it's rare that anything good comes out of it, whatever the intentions.


I have read that among the culprits of these megafires are... firefighters. They have been pretty good at putting out small fires over the last half-century or so, which has resulted in the accumulation of combustible material. But really, it's an unfortunate combination of several factors, all working toward the same end.

Yet we know that the reality cannot be at all times accurately modelled with the idea of a clock-work mechanical universe. — ssu

Do we? How?

Anyway, I am not going to argue for or against the laws of nature. If you believe that conscious beings are outside any general order of things, then obviously you will reject the simulation conjecture for that reason alone. So there is nothing to talk about.

Look, if I were to say that not everything is purely mechanical and can be modelled to work as clock-work, would that mean that I'm implying that there are miracles? — ssu

Depends on how one defines miracles. If we assume the popular Humean view of miracles as violations of the laws of nature - which already implies that nature mostly behaves in law-like ("mechanical") fashion - then yes, that is what you are implying.

With the way the algorithm instructs them to do.

Notice the part "which wasn't at all described in the first program to be done". That part you see means that it's not following the instructions, it's not modifying it's code how it was instructed to do. — ssu

I am still trying to understand where (if anywhere) you are leading with these requirements for programs that spring into existence fully formed out of the blue. Are you trying to say that consciousness is a miracle? Many do think so, but why beat around the bush? Just come out and say it and we will be done.

Ok. Assume a computer that you give a program to run. The computer follows first the program, yet later you find it running a totally different program, which wasn't at all described in the first program to be done. — ssu

Yes, that's what evolutionary algorithms do: they modify part of their own code (the other part you may think of as the environment, which is subject to unchanging rules).

Or let's put this another way. Give me an example of a computer that doesn't follow an algorithm, instructions provided by a software or hardware program as said above. — ssu

Why? What would that prove?

As I said, the Computer has to have an algorithm. It cannot do anything without an algorithm and it cannot do something that algorithm doesn't say to do. It's Limited by it's algorithm. — ssu

First of all, most computer programs are algorithms that process data, so it is not just an algorithm that you put in - it is algorithm plus data, and data can bring in potentially unlimited information. Deep learning programs are already pretty impressive, to the point that they can fool some of the people some of the time. Second, what is to stop a computer from creating new algorithms, or indeed from evolving its own algorithms in response to inputs? That sounds suspiciously like what the brain is doing, and indeed that is the direction that some of the more advanced machine learning is taking.

Your argument is: computers just follow predefined rules. But if you are a physicalist, i.e. you believe that the world we live in is regular through and through, with no place for magic and the supernatural, then everything in this world - including you - just follow predefined rules (whether or not those rules were predefined by some sentient being is irrelevant to this discussion, as far as I can see).

Now, whether everything in the world can be computed is still a hotly disputed thesis, but this conundrum cannot be resolved by pointing out that computers just follow rules - the question is much more complex than that.

I know that Pruss is pretty clever, but that argument was singularly bad. He should have just left it where Leibniz did.

In which case, as you can see, given infinite time we'll progress towards a limit -- wherever that happens to be -- but that limit will not be infinite. — Moliere

Although log(x) grows sublinearly, it doesn't have an upper limit ;) But I take your point.

It irks me that people adopted "fake news" just because Trump used that term. — Terrapin Station

Trump hijacked the expression "fake news" without even understanding (or giving a shit about) its meaning - he just calls anything in the media that he doesn't like "fake news." But the term existed long before he got a hold of it, and was often used in connection with just the sort of right-wing conspiracy rags that Trump favors, as well as Russian troll farms that favor Trump. Of course, Trump being Trump, he insists that he coined "fake news." He probably thinks that "enemy of the people" is another of his brilliant rhetorical inventions (despite everyone telling him that it is a Stalinist phrase with a bloody history).