> For mathematics, isn't sitting down to do the math and see if it
> works the same as 'field work'. I can make observations when I'm
> doing maths.
> I understand that there seems to be a difference here, but I wonder
> if it can't be seen as the same principle in a different context.
> Mathematical principles and formulas can certainly be falsified.
> Besides, geometry can actually be done, with a ruler! Isn't that
> empirical?

This is part of a debate that has been going on for quite some time - is maths
an empirical science, or to put it another way, do mathematicians make
discoveries about a world that exists "out there" in some sense (generally
called "Platonism"), or is maths merely an invention of the human mind - in a
sense that physics isn't, I mean! (Generally called "Aristotelianism"). Max
Tegmark claimed in his Scientific American article about parallel universes that
we are all "indoctrinated" with the Aristotelian viewpoint long before we know
anything about maths (not of course through any conscious intention, more likely
through our culture and/or mode of being). So it's quite an effort to grasp the
Platonic approach, and even then it's easy to dismiss it. Of course,
Aristotelians *do* have the added explanatory burden of saying just why maths is
so "unreasonably effective in the physical sciences" if it's only something
we've invented - I haven't as yet seen a particularly good explanation for that.

Charles

Suppose you see a ball, it's placed under a cup, the cup is slide along a table,
then the cup is raised, and the ball isn't there. Surprise!

What on earth has gone wrong? Do you need glasses?

No, you need theory! Balls and cups are more complicated than you realized. They
don't always behave in the simple way you expected. For example, they behave
differently in the presence of certain humans called conjurers (or conmen, or
illusionists, etc, depending on context).

The fact that "simple" objects can take on different behaviors in the presence
of other objects means that in order to make basic observations of the simple
objects, and avoid errors, you have to also work out if the relevant complex
objects are present or not. To do that, you need a theory of conjurers plus some
observations that you interpret in light of the conjurer theory.

Suppose you see two bricks, one of brick and one of wood, and you want to
predict which is heavier. Can you do this without theory? Of course not. Maybe
one is hollow. Is it plausible that one is hollow? Is that terribly unlikely, or
something worth being concerned with? One can't answer those questions without a
theory.

In general, whenever one observes something he needs a theory of whether a
conjurer (or various other things) has deceived him or not. It's true that
people generally don't devote *conscious* thought to this issue, but it's not
true that most reasonable people completely ignore it and don't know anything
about it. When they attend a magic show, or see a 3-cups-and-a-ball game on the
street, they become wary. They have an understanding of what circumstances to
look out for tricks in, and that theory is always running in the background
ready to send an alert to the conscious mind when needed.

If one had no theory of illusionists at all, one couldn't know if they are a
negligible factor or not. One couldn't know if it was reasonable not to think
about them, or not. So if one made his "basic" observations with no such theory,
and they turned out to be true, that'd be pure luck, not a reasonable way of
life.

In conclusion, *all* observation is theory laden.

-- Elliot Temple
http://curi.us/

2009/12/20 Bill Taylor <W.Taylor@...>

>
>
> ->> Surely most people would at least relax the definition to
>
> ->> "beyond reasonable doubt", where "reasonable" is OC at best
> ->> inter-subjective and in any event dependent on context.
> ->
> -> you're saying we can obtain knowledge that is beyond doubt?
>
> No; beyond *reasonable* doubt! You didn't appear to read the sentence
> immediately above your question!
>
> -> once we have that, what should we do with the remaining doubters?
>
> Oh - commit them to the flames, at least! Whether their families should be
> burnt with them, is a matter for debate, obviously....
>
> ->> Most people would say to cavil at this would be pointless combative
> debate.
>
> ->
> -> advocating Popper's view on fallibilism, on a Popperian list,
> -> is "combative debate"?
>
> I have no idea what this is supposed to mean, or how it relates to what I
> said.
>
> ->> There is also evidence.
>
> ->
> -> which is used in explanations.
>
> GOOD! We agree on this vital point, than. Excellent.
>
> ->> But there MUST be evidence before there can be ANY explanation,
>
> ->> good, bad or ugly!
> ->
> ->Popper's view is that there must be explanation before there can be
> evidence
>
> This is a very viable point! Well worth raising.
>
> It is true, that experimental results of beyond a certain complexity,
> are so theory-laden to interpret, that what they verify/falsify is not
> a particular statement, but a statement *within & as part of* a whole
> theory.
>
> This point is often much overlooked, and it is good to raise it.
>
> HOWEVER - this only applies to experiments of a certain complexity,
> a certain lower bound, as it were. Probably this includes all of science
> from about 1600 onwards. But "everyday common sense", which is after all
> the basis of science and almost anything else, (though supercedable if
> necessary), has, as its "experiments", experiences common to all,
> learned in one's infancy for the most part. For example, we all know
> that a brick is a lot heavier than a block of wood of about the same size.
> We can test it further if we like, but no-one seriously expects to
> find it false any more. These "basic experiments" lead to observations
> which are NOT theory-rich. The amount of theory involved in my brick
> statement is utterly minimal, and constant across a huge number of more
> complex extensions, Newtonian, relativistic, whatever.
>
> This matter, the essential difference (FAPP) between "basic observations"
> and "theory-laden observations" came up on this list before; in the debate
> about whether we can know, or rather what it COULD MEAN, that the universe
> is finite or infinite in spatial extent. Do people recall that one?
>
> This matter, basic vs theory-laden observations, is a very vital one
> in the philosophy of science, IMHO, and widely ignored!
> It should be addressed properly by wiser minds than mine!
>
>
> > b/c all observation is theory laden.
>
> So, no, not quite.
>
>
> > Observations have no meaning in total isolation.
>
> Except for the basic ones.
>


Well I'm glad at last that it is acknowledged that what we live... is what
we live (? o_O) and that an experience is *actually* experienced is beyond
doubt and not part of any theory... doubting your own existence
(consciousness) is meaningless, as for doubt there must be *at least* *one*
subject that experience (doubt).

Which makes the sentence 'I am conscious' undoubtable for the 'I' in the
sentence.

Regards,
Quentin


>
>
> > Would you like to offer us some criticism of that view?
>
> There you have it. Thanks for isolating this point, and thus allowing me
> to have another rant. ;-)
>
> -> Are you saying the difference between Popperian epistemology,
>
> -> and non-Popperian epistemology, is just a grammar debate?
>
> No, I can't imagine how anyone could have thought that was what I was
> saying!
>
> -- Wounded William
>
>
>



--
All those moments will be lost in time, like tears in rain.


[Non-text portions of this message have been removed]

On Dec 20, 2009, at 12:27 AM, Bill Taylor wrote:

>> Popper's view is that there must be explanation before there can be evidence
>
> It is true, that experimental results of beyond a certain complexity,
> are so theory-laden to interpret, that what they verify/falsify is not
> a particular statement, but a statement *within & as part of* a whole theory.
>
> HOWEVER - this only applies to experiments of a certain complexity,
> a certain lower bound, as it were. Probably this includes all of science
> from about 1600 onwards.  But "everyday common sense", which is after all
> the basis of science and almost anything else, (though supercedable if
> necessary), has, as its "experiments", experiences common to all,
> learned in one's infancy for the most part.  For example, we all know
> that a brick is a lot heavier than a block of wood of about the same size.
> We can test it further if we like, but no-one seriously expects to
> find it false any more.  These "basic experiments" lead to observations
> which are NOT theory-rich.  The amount of theory involved in my brick
> statement is utterly minimal, and constant across a huge number of more
> complex extensions, Newtonian, relativistic, whatever.
>
> This matter, the essential difference (FAPP) between "basic observations"
> and "theory-laden observations" came up on this list before; in the debate
> about whether we can know, or rather what it COULD MEAN, that the universe
> is finite or infinite in spatial extent.  Do people recall that one?
>
> This matter, basic vs theory-laden observations, is a very vital one
> in the philosophy of science, IMHO, and widely ignored!
> It should be addressed properly by wiser minds than mine!

One Popperian argument that *all* observations are theory laden, not just
complicated ones, is this:

There is more stuff to observe than we have time to pay attention to it all. One
always has to make decisions. One has a bunch of sensory data coming in, and we
only have time to look at a portion of it, and that not at maximum precision.
Without a theory to guide us, we are lost.

Popper compared us to searchlights rather than buckets. The point being we don't
just intake all the basic data around us, we have to decide where to focus our
limited data gathering abilities.

So, one needs some kind of observational strategy that contains some theory
about what is important to observe and what is sufficiently unimportant to
ignore. Observation of simple things is therefore theory laden.

As an example, sometimes a person "can't see the obvious" -- he has some sort of
mistaken theory chronically making him fail to notice something that's right in
front of him and which everyone else present noticed immediately. Sometimes his
theories about how to observe are so strong that he continues to miss the simple
thing after it's been pointed out to him several times -- it can take quite a
bit of explaining for him to learn a new way of observing that can see the basic
fact. One way this happens is that he has a mistake about where he points his
searchlight which can affect his ability to make even very simple observations.

-- Elliot Temple
http://curi.us/

2009/12/20 Elliot Temple <curi@...>

>
>
> On Dec 19, 2009, at 7:26 AM, Rudi Voigt wrote:
>
> > On Dec 16, 2009, at 7:04 AM, Bruno Marchal wrote:
> >
> >>> ? ? ? ? ? ? ? ? ? (In many university, including the one where I am
> >>> teaching, mathematics belongs the faculty of science, and is
> >>> considered as science by all mathematician. You are the first I hear
> >>> saying that mathematics is not a science.
> >>
> >> In the US it's not considered science.
> >>
> >> But the important thing is: what makes a science? Popper gave a
> >> demarcation criterion which is that if you use experimental tests
> >> in a field then it's scientific. Math has no experimental tests, so
> >> it's not a science just like philosophy isn't a science for the
> >> same reason.
> >
> > Elliot, I've got my 'The Logic of Scientific Discovery' by Karl Popper
> right here, and I have read it a few times in the past, I cannot find the
> part you are referring to.
> >
> > His whole argument about demarcation of science (chapter 4) is
> > about the impracticality of positive proof and his suggestion of
> > using 'falsifiability' as a demarcation criteria (chapter 6).
>
> I think this refers to *sections* 4 and 6 of chapter 1.
>
> By falsifiability here Popper means empirical falsifiability.
>
>
> > He basically says that any hypothesis that is formulated in such a
> > way that it is possible to prove it wrong falls within the scope of
> > science.
> >
> > Can you give me an idea of where might find 'experimental tests in
> > a field' mentioned as a criteria in Popper?
>
> On page 18 i LScD Popper writes:
>
> > But I shall certainly admit a system as empirical or scientific
> > only if it is capable of being *tested* by experience. These
> > considerations suggest that not the *verifiability* but the
> > *falsifiability* of a system is to be taken as the criterion of
> > demarcation. In other words ... *it must be possible for an
> > empirical scientific system to be refuted by experience*.
>
> This paragraph offers a criterion demarcating science from non-science.
> Science is "possible ... to be refuted by experience". Science is "capable
> of being tested by experience".
>
> Being tested by "experience" (I'd rather say observation), with the
> possibility of a refutation, is the experimental tests I referred to.
>

Why is experience here relate to "reality based experimental test" ?




--
All those moments will be lost in time, like tears in rain.


[Non-text portions of this message have been removed]

>
> ->> Most people would say to cavil at this would be pointless combative
debate.
> ->
> -> advocating Popper's view on fallibilism, on a Popperian list,
> -> is "combative debate"?
>
> I have no idea what this is supposed to mean, or how it relates to what I
said.

it needs the full context which you've unquoted:


>> On this basis, it is reasonable to say some things are known reliably.
>> The simplest facts about everyday life.  The simple to medium results
>> of mathematics.  (Not the medium everyday facts, nor the difficult math.)
>>
>> Most people would say to cavil at this would be pointless combative debate.
>
> advocating Popper's view on fallibilism, on a Popperian list, is "combative
debate"?

so it goes like this:

There are 4 Popper-contradicting sentences, then a statement that objecting to
them is pointless combative debate.

Popper was clear that there are no basic or simple facts that get special
epistemic status. Popper said *all* observation is theory laden. That is open to
disagreement, but it's not open to announce that any further advocating of
Popper's view is pointless and combative.


-- Elliot Temple
http://curi.us/

On Dec 20, 2009, at 12:27 AM, Bill Taylor wrote:

> ->> Surely most people would at least relax the definition to
> ->> "beyond reasonable doubt", where "reasonable" is OC at best
> ->> inter-subjective and in any event dependent on context.
> ->
> -> you're saying we can obtain knowledge that is beyond doubt?
>
> No; beyond *reasonable* doubt!  You didn't appear to read the sentence
> immediately above your question!
>
> -> once we have that, what should we do with the remaining doubters?
>
> Oh - commit them to the flames, at least!   Whether their families should be
> burnt with them, is a matter for debate, obviously....

you're saying we obtain some knowledge (using some method, or meeting some
criteria, which you haven't specified) and then people aren't allowed to doubt
it anymore. further doubt is deemed irrational or something bad. right?


-- Elliot Temple
http://curi.us/

To observe simple things with no theories means no theory *of our sensory
organs*.

That means no theory about when they are reliable, and when they are in error.

No theory of when we are hallucinating, or not.

No theory of when we are dreaming, or not.

No theory of when our eyes have been cut out with a knife, or not.

No theory of blindfolds.

And so on.

How can we possibly do observing without such theories? When we cut an onion,
and our eyes water, and our vision gets a little blurry, we'll mistakenly regard
the onion itself as having become blurry. And so our basic observations will go
wrong.

And when we dream, we'll regard everything we see (which looks simple) as being
just as real as anything else we've seen, since we have no theory to guide us
not to do that.

In conclusion, *all* observation is theory laden.

-- Elliot Temple
http://curi.us/

Here is another argument that even simple observations are theory laden:

How do we know what will be simple? Surely we can't know without either a theory
to tell us, or having already observed it to find out.

To observe something to find out if it's simple, do we need a theory?

If we don't, this implies we can observe *anything* without a theory, at least
in some limited way.

So now the basic observations have expanded. First you get to observe anything
at all and, with no theory, know if it's simple or complicated. And then if it's
in the simple category you can observe it again and learn all about it, still
with no theory. At least that's what is claimed.

So now we're judging simple and complex with no theories. That means no theory
of complexity (which is a branch of physics). It means no theory of whether
there are internal parts that may be relevant (like a TV has). No theory of how
what we see in this instant relates to what we say last instant (no theory of
motion, no theory theory of time and how objects can persist over time). No
theory of fungibility or sameness (no understanding of the relationship between
two different paperclips and ways they are the same and different, no
understanding of the same paperclip through time, etc).

The world is nonsense with these restrictions. In a nonsense world, you can't
tell what is simple and what is complex, because everything is confusing.
Therefore you can't judge complexity levels without having a theory first.
Therefore you can't tell which are the simple things you're allowed to observe
with no theory, without a theory. Therefore you can't observe with no theory.

-- Elliot Temple
http://curi.us/

Raw sense data is, well, raw. Consider the iPhone accelerometer. Every so often
it gives you 3 numbers labeled x, y, and z.

How do you go from those numbers to even a basic understanding of which way
gravity (and any other force) is pulling, which is the thing it measures? [1]

With math. How do you program that math into your app? I don't know, first you
have to read a bunch of documentation and explanation. You need a lot of theory
to make the raw data at all useful.

What if you want to know if the iPhone is being shaken? Or track any kind of
changes over time?

Then you need quite a lot more theory and code than it took to figure out the
direction of gravity.

My eyes are not simpler than my accelerometer. The data coming in is far more
than 3 numbers at a time. Parsing it into some useful, meaningful form is
*hard*.

Consider that my eyes are not *one* photon detector. They are many (of two main
types, plus there's manufacturing error to consider so the ones "of the same
type" are not identical). To see what's in front of me, in the normal human
sense, requires taking the raw data from *many* detectors and figuring out how
to piece it together. The location of each detector has to be taken into
account. The two eyes have to be considered separately in order to places things
better in 3D space. And what does each detector really tell me? Just a tiny
piece of data about a photon that hit my eye. It does not directly tell me which
changes in colors indicate a change in object. It does not tell me that an
object is made of brick or of wood.

Just like with the accelerometer, except more so, the "raw" data from my eyes is
hard to interpret. It takes substantive knowledge to make sense out of it.

So, people have sense data coming in. It has to be interpreted. This
interpretation is done in the light of theories (knowledge). Whether those
theories are inborn into our sense organs (or a part of our brain separate from
our conscious mind), or whether the interpretation is done in our mind in
software (or a mix of both), in any case there is interpretation being done.
Whether we have control over the process, or not, whether we can change how it
works in the future, or not, it still exists, it still can contain errors, and
it still is a substantive layer between "simple" observations and raw sense
data.

In conclusion, *all* observation is theory laden.


[1] I'm not positive that's what it measures. I may have misunderstood. Which
only emphasizes my point that raw data itself is complicated. As we see in this
case, to parse raw data one requires a good theory of how the sense organ works
and what it measures. If it's actually measuring something else then I could go
badly wrong.

By the way, in what conditions does the accelerometer work? For example, will it
stop working under water? Will it stop working at certain temperatures high or
low? To properly interpret its data you need to know those limits, don't you?
That is more theory of how the sense organ works that is needed to avoid errors.

-- Elliot Temple
http://curi.us/

>> I think he was right, but I also think it is easy to go too far
>> the other way.
>>
>> Postmodernism in a nutshell.
>
> Really? I'm surprised to hear you say so. I thought postmod was
> something quite different. But no matter.

It's a long while since I read up heavily on Pomo, but I'm pretty certain some
proponents - I'm not sure who, now, but I think Jean Baudrillard may have been
one - have proposed - in heavy disguise, of course ("under erasure", perhaps) -
that Popper showed that no views can be proved, and that therefore all views are
equally valid. To put it in a nutshell.

> The point is that "degrees of" is a very silly goal to seek to
> achieve. (Unless you're a Bayesean, OC, which I'm not.) I merely
> reduce it all to two degrees -
>
> 1) true beyond reasonable doubt [TBRD]; and
> 2) still under investigation; and I suppose a third...
> 3) false beyond reasonable doubt (I think this is Popper/Deutsch's
> "falsified")
>
> To attempt some sort of numerical scale in between, is silly (or
> Bayesean).
>
> In practise, (3) usually reduces to "analytically shown to be
> rubbish", for everyday beliefs at least.

OK, that sounds very reasonable. In fact it sounds close to the view I went on
to espouse in the post you're replying to, although no doubt I did it in a less
precise, more hand-waving manner. My apologies if I misunderstood your comments,
as appear to be the case. Which makes the rest of this post maybe a bit
redundant, but I will plough one...

> I thought Descartes (and many before him) had already shown that!
> (Excepting the rather useless "cogito", OC.)

Hmm, yes, I guess so. But surely Popper made it into a criterion for rationally
evaluating theories, rather than a blanket statement of ignorance (to
nutshellise a few centuries of debate...) Or have I misread him, too? (Sigh!
Must get new specs...)

Except for the cogito, which may or may not be useless. On that point
hinges...

> All of the same type as above. Only Bruno seems to base a philosophy
> on taking such possibilites seriously.

I'm not sure about that. I think that Bruno is doubting the commonly
accepted form of what Max Tgemark calls the ERH (external reality
hypothesis), and he is trying to show that the appearance of a material universe
is consistent with a particular form of the MUH (mathematical universe
hypothesis) known as the computational hypothesis - the theory that human
consciousness is a complex computation, and hence (er, assuming I haven't
misread the CTT as well, of course) emulable, at least in theory, by any digital
computer with enough resources. Deducing the existance and appearance of an
external reality from the basis that people are computational histories, without
any a priori bias about how those histories are instantiated, sounds to me like
(a) a follow-up on the "cogito", and (b) a radical and fascinating approach to
science (assuming that is in fact what's being done, of course - I may have
misread Bruno, that's probably even more likely...!) It's one of those things
that is either crazy, or crazy enough to be true. (Time will tell, to quote that
eminent scientist Doctor Who.)

>> This leaves us with a dilemma: we can't reliably know anything,
>
> Except, BRD.

No, we don't *reliably* know those to be correct, we only "know them FAPP". My
point is more that we don't need something as abstract as being able to reliably
know something to get on with our lives. Perhaps I should have said "we can't
reliably know anything to be true," otherwise we have another linguistic debate
on what "reliably know" means. (But hopefully not, since I suspect that I agree
with you "FAPP" anyway... :-)

>> yet it's a point of trivial observation that we do,
>
> Which shows that most people are common-sensical about the BRD
> concept. Unfortunately, most people place their R in the BRD at
> *well* into the gullibility zone, which reduces their common-
> sensicality enormously.

This is a problem associated with how human brains and culture evolved to cope
with everyday life prior to inventions like agriculture and similar things which
set us on a path to gradually making the world a safer place for human beings.
Common sense is evolved/designed (in some ratio of genes to culture) to cope
with dangerous situations in which it isn't profitable to be too choosy about
false positives - it's better to see a bear in the heavens than to miss one in
the woods, to perhaps coin an aphorism.

>> [more] on some facts than others (we trust hydraulics whenever we
>> use the brakes in our car, for example,
>
> No we don't - most of us have no idea of what that is. What we trust
> is that the manufacturers have been doing their job properly and
> that government safety standards and checks are up to the mark.
> Whether either of these is BRD is highly debatable, mind you! A
> totally rational view might be to never take a vehicle ride
> anywhwere, but common sense also involves not making your life
> circumscribedly miserable on a point of principle! ;-)

Hmph. Sounds a teensy bit like hair splitting! We trust that the manuf have
studied the relevant science. My statement "cut out the middle man", but it
still stands, IMHO. We trust that brakes work, and that planes will stay up, and
so on, hence we at least implicitly trust the science behind them - amongst
other (occasionally wrong) assumptions - e.g. that no one has sabotaged the
brakes. But it's all a gamble, in varying degrees, as I said.

>> while most of us tend to be sceptical that an unusual
>> light in the sky is an alien spacecraft).
>
> Or that there's a benevolent being listening to your prayers and....
> ....oh no, hang on a minute...

Nice example. The benevolent being possibly comes from observations about how
people construct things - if you ask "where did all this come from?" an obvious
possible reply would be - "Big Juju made it, in a similar fashion to how we make
pots and spears and babies". (If so, this is clearly an example of early
inductive reasoning.) Once the notion has become entrenched in the culture, it
seems to have all sorts of advantages - it's a "meme" that carries on under its
own steam, and it gradually becomes more elaborate as time goes on.

>> We act as though some things are true "for all practical
>> purposes"
>
> Yes, often FAPP and BRD are co-incidental, though often (as with car
> brakes) FAPP is somewhat looser; but the PP part of FAPP is the
> anti-misery clause.

Maybe you could expand on that, I'm not sure I've grasped the subtlety of this
distinction.

>> "but how can we *know* that the scientific method works?"
>
> Who wants to know? Suck it and see. If you don't like it, ignore it;
> (and I hope you don't get to be a vehicle engineer!)

Well, that's what my friend said, more or less, and that was the point of my
anecdote! I only asked the question because I was going through a brief
postmodern phase (see above). Outside of which, I agree with you. I'm not sure
of the finer distinction between BRD and FAPP, but the story is intended to
illustrate that in practice our options are to either assume things FAPP - even
in relatively contentious fields like, say, string theory, this is what most
people are doing, most of the time - or go into the excessive (and useless) view
that I've called PoMo, but which could equally be called something like Radical
Popperianism, which says that since we can't prove anything 100%, we may as well
give up - or fly around on broomsticks rather than in aeroplanes, as someone
famously said (I think it was Francis Fukuyama).

>>> P.S. Has anyone else noticed how almost all these debates turn
>>> crucially on merely socio-linguistic matters of what is "common
>>> usage" of words?
>>
>> Well.....I'm sure you aren't the only one who pulls people up on
>> any number of points.
>
> Of course; but I'm speaking *specifically* of when a fierce debate
> is ONLY a debate about word usage. Am I the only one to whom such
> things stick out like a sore thumb? I can't credit THAT! Why does
> no-one else ever pull themselves (or others) up, for this
> egregiously useless type of conflict?

Hmm, this may stand out better to you than some people. You are the "canary in
the coal mine" of debate! But don't knock it...

>> because if you aren't diplomatic
>
> True, <sigh>, many people have much thinner skins than they ought.

Well, yes, I probably do. But I do think the emphasis should be the other way
around - that bullying is unacceptable, rather than that some people should
toughen up (if you slide the parameters a bit, this "toughen up" argument segues
into arguing that an abused wife or child "had it coming").

>> before you jump down their throat,
>
> Well, I hope I *never* do that on a first offense! Or even a second
> or third. But when people use up their social leeway and persist in
> silliness that has already been pointed out, they rather "have it
> coming", I would have thought.

Yes, well I've certainly had that experience! And I agree, I always give people
a very generous supply of rope.

>> And you do seem to be good at doing it with a light touch -
>
> Well thank you, that's very kind of you to say so; but I fear your
> friendly diplomatic charity is overwhelming your sense of justice
> in this case - I've been called well rude before now!

Well....I, at least, get the impression that you're prepared to think through
the other person's point of view, to give them plenty of chances to explain
themselves before you assume they must be barking up the wrong tree (IYHO), you
try to gently clarify things rather than just didactically laying out
"such-and-such must be true because I think so" - you don't tend to go into an
unprovoked rant (too often), or to wilfully misunderstand other people for the
sake of starting an argument, or . . . . Well, und so weiter. All the things
that make a polite and reasonable debater (probably more so than me, I'm
afraid...)

Charming (on this occasion :-) Charles

We need error correction.

People make mistakes. We aren't immune. We need to look out for them. We need to
form theories of what is (or might be) a mistake.

And then we need to create knowledge of non-mistaken replacements for our
mistakes. We need to learn from our mistakes, and avoid repeating them, and
avoid acting on them.

The idea of making simple or "basic" observations, with *no* theories, means
doing it with *no theory of error correction*. That's crazy! We need error
correction!

No error correction means no understanding of the frequency of mistakes, no
understanding that mistakes are possible, no understanding of which things are
mistaken or not, no correcting or improving on any mistakes. It means whether
one is right or wrong is all down to luck, not skill or knowledge or theories.

In conclusion, *all* reasonable observation is theory laden because we need to
use our theories of error correction, not just rely on pure luck.

-- Elliot Temple
http://curi.us/

>> Elliot, I've got my 'The Logic of Scientific Discovery' by Karl
>> Popper right here, and I have read it a few times in the past, I
>> cannot find the part you are referring to.
>>
>> His whole argument about demarcation of science (chapter 4) is
>> about the impracticality of positive proof and his suggestion of
>> using 'falsifiability' as a demarcation criteria (chapter 6).
>
> I think this refers to *sections* 4 and 6 of chapter 1.
>
> By falsifiability here Popper means empirical falsifiability.
>
>> He basically says that any hypothesis that is formulated in such a
>> way that it is possible to prove it wrong falls within the scope
>> of science.
>>
>> Can you give me an idea of where might find 'experimental tests in
>> a field' mentioned as a criteria in Popper?
>
> On page 18 i LScD Popper writes:
>
>> But I shall certainly admit a system as empirical or scientific
>> only if it is capable of being *tested* by experience. These
>> considerations suggest that not the *verifiability* but the
>> *falsifiability* of a system is to be taken as the criterion of
>> demarcation. In other words ... *it must be possible for an
>> empirical scientific system to be refuted by experience*.
>
> This paragraph offers a criterion demarcating science from
> non-science. Science is "possible ... to be refuted by experience".
> Science is "capable of being tested by experience".
>
> Being tested by "experience" (I'd rather say observation), with the
> possibility of a refutation, is the experimental tests I referred
> to.
>
> You can find more on Popper's view on this in Conjectures and
> Refutations. See chapter 11 titled "The Demarcation Between Science
> and Metaphysics". Read the whole thing, but here is one snippet
> from page 345 in my edition (in section 2):
>
>> a system is to be considered as scientific only if it makes
>> assertions which may clash with observations

OK Thanks (and quite refreshing to see someone actually reads Popper, besides
me), but I still don’t see how that excludes mathematics from science.

For mathematics, isn’t sitting down to do the math and see if it works the same
as ‘field work’. I can make observations when I’m doing maths.

I understand that there seems to be a difference here, but I wonder if it can’t
be seen as the same principle in a different context.

Mathematical principles and formulas can certainly be falsified. Besides,
geometry can actually be done, with a ruler! Isn’t that empirical?

I am starting to see where you get your point, I mean that there is a
difference between maths and for instance particle physics or biology where you
can actually go out and do stuff and take measurements to see if you hypothesis
is correct, but it bothers me because I know quite a few mathematicians working
at universities who consider themselves scientists and their work to be science.

Looking at the Wikipedia page for Mathematics I get the idea that this is more a
discussion about language, about the definition of the word science, than a
discussion about mathematics or the meaning of that word. Here’s what wiki says;

http://en.wikipedia.org/wiki/Mathematics#Mathematics_as_science

Rudi

p.s. by the way, I checked, but in my edition of Popper the larger sections are
called ‘Parts’ and the smaller sections ‘Chapters’, although the chapters are
numbered continuously throughout the book, as are the paragraphs. Must be a
different translation.

>>> Popper believed that looking for degrees of reliability of one's
>>> knowledge is a mistake for several reasons.
>
>> I think he was right, but I also think it is easy to go too far the other
> way.
>
>Postmodernism in a nutshell.

Really?   I'm surprised to hear you say so.  I thought postmod was something
quite different.  But no matter.

>>> We have no viable procedure for reliably attaining reliable knowledge.
>
>>This depends on how reliable you want your "reliable" to be!
>
>Surely you just contradicted yourself, Bill?

No.

> If you agree that "looking for
> degrees of reliability of one's knowledge is a mistake"

The point is that "degrees of" is a very silly goal to seek to achieve. (Unless
you're a Bayesean, OC, which I'm not.)  I merely reduce it all to two degrees -

1) true beyond reasonable doubt [TBRD]; and
2) still under investigation;           and I suppose a third...
3) false beyond reasonable doubt (I think this is Popper/Deutsch's "falsified")

To attempt some sort of numerical scale in between, is silly (or Bayesean).

In practise,  (3) usually reduces to "analytically shown to be rubbish", for
everyday beliefs at least.

> then how can you decide "how reliable you want your "reliable" to
> be" ?

I addressed that point - TBRD - check back for details if you want.

> What Popper shows (AFAIK) is that you can't be certain about
> anything,

I thought Descartes (and many before him) had already shown that!
(Excepting the rather useless "cogito", OC.)

>It's always *possible* that the Earth isn't round,

Well it isn't, OC, but it's a lot more round than flat.  This is one of
those everyday things that is TBRD.   Of course one can doubt ANYthing,
if one wants to be radically sceptical, but it's a totally pointless PoV.

> - we may be living in "The Truman Show" or all be plugged in
> to the Matrix, and *everything* we know may be false

All of the same type as above.  Only Bruno seems to base a philosophy on taking
such possibilites seriously.

>This leaves us with a dilemma: we can't reliably know anything,

Except, BRD.

> yet it's a point of trivial observation that we do,

Which shows that most people are common-sensical about the BRD concept.
Unfortunately, most people place their R in the BRD at *well* into the
gullibility zone, which reduces their common-sensicality enormously.

> [more] on some facts than others (we trust hydraulics whenever we use
> the brakes in our car, for example,

No we don't - most of us have no idea of what that is.  What we trust is that
the manufacturers have been doing their job properly and that government safety
standards and checks are up to the mark.  Whether either of these is BRD is
highly debatable, mind you!  A totally rational view might be to never take a
vehicle ride anywhwere, but common sense also involves not making your life
circumscribedly miserable on a point of principle!  ;-)

> while most of us tend to be sceptical that an unusual
> light in the sky is an alien spacecraft).

Or that there's a benevolent being listening to your prayers and....
....oh no, hang on a minute...

> We act as though some things are true "for all practical purposes"

Yes, often FAPP and BRD are co-incidental, though often (as with car brakes)
FAPP is somewhat looser; but the PP part of FAPP is the anti-misery clause.

> "but how can we *know* that the scientific method works?"

Who wants to know?   Suck it and see.  If you don't like it, ignore it;
(and I hope you don't get to be a vehicle engineer!)

>> P.S. Has anyone else noticed how almost all these debates turn crucially
>> on merely socio-linguistic matters of what is "common usage" of words?

> Well.....I'm sure you aren't the only one who pulls people up on any number
> of points.

Of course; but I'm speaking *specifically* of when a fierce debate
is ONLY a debate about word usage.  Am I the only one to whom such
things stick out like a sore thumb?  I can't credit THAT!  Why does
no-one else ever pull themselves (or others) up, for this egregiously
useless type of conflict?

> because if you aren't diplomatic

True, <sigh>, many people have much thinner skins than they ought.

> before you jump down their throat,

Well, I hope I *never* do that on a first offense!  Or even a second or third.
But when people use up their social leeway and persist in silliness that has
already been pointed out, they rather "have it coming", I would have thought.

> And you do seem to be good at doing it with a light touch -

Well thank you, that's very kind of you to say so; but I fear your friendly
diplomatic charity is overwhelming your sense of justice in this case -  I've
been called well rude before now!

-- Beleaguered Bill

->>> Popper believed that looking for degrees of reliability of one's
->>> knowledge is a mistake for several reasons.
->
->> I think he was right, but I also think it is easy to go too far the other
-> way.
->
->Postmodernism in a nutshell.

Really?   I'm surprised to hear you say so.  I thought postmod was something
quite different.  But no matter.

->>> We have no viable procedure for reliably attaining reliable knowledge.
->
->>This depends on how reliable you want your "reliable" to be!
->
->Surely you just contradicted yourself, Bill?

No.

-> If you agree that "looking for
-> degrees of reliability of one's knowledge is a mistake"

The point is that "degrees of" is a very silly goal to seek to achieve.
(Unless you're a Bayesean, OC, which I'm not.)  I merely reduce it all to
two degrees -

1) true beyond reasonable doubt [TBRD]; and
2) still under investigation;           and I suppose a third...
3) false beyond reasonable doubt (I think this is Popper/Deutsch's "falsified")

To attempt some sort of numerical scale in between, is silly (or Bayesean).

In practise,  (3) usually reduces to "analytically shown to be rubbish",
for everyday beliefs at least.

-> then how can you decide "how reliable you want your "reliable" to be" ?

I addressed that point - TBRD - check back for details if you want.

-> What Popper shows (AFAIK) is that you can't be certain about anything,

I thought Descartes (and many before him) had already shown that!
(Excepting the rather useless "cogito", OC.)

->It's always *possible* that the Earth isn't round,

Well it isn't, OC, but it's a lot more round than flat.  This is one of
those everyday things that is TBRD.   Of course one can doubt ANYthing,
if one wants to be radically sceptical, but it's a totally pointless PoV.

-> - we may be living in "The Truman Show" or all be plugged in
-> to the Matrix, and *everything* we know may be false

All of the same type as above.  Only Bruno seems to base a philosophy on
taking such possibilites seriously.

->This leaves us with a dilemma: we can't reliably know anything,

Except, BRD.

-> yet it's a point of trivial observation that we do,

Which shows that most people are common-sensical about the BRD concept.
Unfortunately, most people place their R in the BRD at *well* into
the gullibility zone, which reduces their common-sensicality enormously.

-> [more] on some facts than others (we trust hydraulics whenever we use
-> the brakes in our car, for example,

No we don't - most of us have no idea of what that is.  What we trust is that
the manufacturers have been doing their job properly and that government
safety standards and checks are up to the mark.  Whether either of these
is BRD is highly debatable, mind you!  A totally rational view might be to
never take a vehicle ride anywhwere, but common sense also involves not
making your life circumscribedly miserable on a point of principle!  ;-)

-> while most of us tend to be sceptical that an unusual
-> light in the sky is an alien spacecraft).

Or that there's a benevolent being listening to your prayers and....
....oh no, hang on a minute...

-> We act as though some things are true "for all practical purposes"

Yes, often FAPP and BRD are co-incidental, though often (as with car brakes)
FAPP is somewhat looser; but the PP part of FAPP is the anti-misery clause.

-> "but how can we *know* that the scientific method works?"

Who wants to know?   Suck it and see.  If you don't like it, ignore it;
(and I hope you don't get to be a vehicle engineer!)

->> P.S. Has anyone else noticed how almost all these debates turn crucially
->> on merely socio-linguistic matters of what is "common usage" of words?

->Well.....I'm sure you aren't the only one who pulls people up on any number
->of points.

Of course; but I'm speaking *specifically* of when a fierce debate
is ONLY a debate about word usage.  Am I the only one to whom such
things stick out like a sore thumb?  I can't credit THAT!  Why does
no-one else ever pull themselves (or others) up, for this egregiously
useless type of conflict?

-> because if you aren't diplomatic

True, <sigh>, many people have much thinner skins than they ought.

-> before you jump down their throat,

Well, I hope I *never* do that on a first offense!  Or even a second or third.
But when people use up their social leeway and persist in silliness that has
already been pointed out, they rather "have it coming", I would have thought.

-> And you do seem to be good at doing it with a light touch -

Well thank you, that's very kind of you to say so; but I fear your friendly
diplomatic charity is overwhelming your sense of justice in this case -
I've been called well rude before now!

-- Beleaguered Bill

->> Surely most people would at least relax the definition to
->> "beyond reasonable doubt", where "reasonable" is OC at best
->> inter-subjective and in any event dependent on context.
->
-> you're saying we can obtain knowledge that is beyond doubt?

No; beyond *reasonable* doubt!  You didn't appear to read the sentence
immediately above your question!

-> once we have that, what should we do with the remaining doubters?

Oh - commit them to the flames, at least!   Whether their families should be
burnt with them, is a matter for debate, obviously....

->> Most people would say to cavil at this would be pointless combative debate.
->
-> advocating Popper's view on fallibilism, on a Popperian list,
-> is "combative debate"?

I have no idea what this is supposed to mean, or how it relates to what I said.

->> There is also evidence.
->
-> which is used in explanations.

GOOD!   We agree on this vital point, than.   Excellent.

->> But there MUST be evidence before there can be ANY explanation,
->> good, bad or ugly!
->
->Popper's view is that there must be explanation before there can be evidence

This is a very viable point!  Well worth raising.

It is true, that experimental results of beyond a certain complexity,
are so theory-laden to interpret, that what they verify/falsify is not
a particular statement, but a statement *within & as part of* a whole theory.

This point is often much overlooked, and it is good to raise it.

HOWEVER - this only applies to experiments of a certain complexity,
a certain lower bound, as it were.  Probably this includes all of science
from about 1600 onwards.  But "everyday common sense", which is after all
the basis of science and almost anything else, (though supercedable if
necessary), has, as its "experiments", experiences common to all,
learned in one's infancy for the most part.  For example, we all know
that a brick is a lot heavier than a block of wood of about the same size.
We can test it further if we like, but no-one seriously expects to
find it false any more.  These "basic experiments" lead to observations
which are NOT theory-rich.  The amount of theory involved in my brick
statement is utterly minimal, and constant across a huge number of more
complex extensions, Newtonian, relativistic, whatever.

This matter, the essential difference (FAPP) between "basic observations"
and "theory-laden observations" came up on this list before; in the debate
about whether we can know, or rather what it COULD MEAN, that the universe
is finite or infinite in spatial extent.  Do people recall that one?

This matter, basic vs theory-laden observations, is a very vital one
in the philosophy of science, IMHO, and widely ignored!
It should be addressed properly by wiser minds than mine!

> b/c all observation is theory laden.

So, no, not quite.

> Observations have no meaning in total isolation.

Except for the basic ones.

> Would you like to offer us some criticism of that view?

There you have it.  Thanks for isolating this point, and thus allowing me
to have another rant.   ;-)

-> Are you saying the difference between Popperian epistemology,
-> and non-Popperian epistemology, is just a grammar debate?

No, I can't imagine how anyone could have thought that was what I was saying!

-- Wounded William

On Dec 19, 2009, at 12:54 PM, Charles Goodwin wrote:

> What Popper shows (AFAIK) is that you can't be certain about anything, which
> of course includes the amount of reliability you can place on knowledge.
> It's always *possible* that the Earth isn't round, or that it doesn't orbit
> around the Sun - we may be living in "The Truman Show" or all be plugged in
> to the Matrix, and *everything* we know may be false (as Descartes more or
> less put it).


This is not what Popper shows.

Well, he does show that. But it's a small subset and it's misleading to think of
that as his accomplishment.

Popper does more than show mistakes are *possible* and that fallibilism is
*technically* true.

He argues, extensively, that mistakes are *common*, which means fallibilism is a
*useful attitude in general*, not just an irrelevant limiting case.


You can pick up on this attitude in Popper's book title "All Life Is Problem
Solving". For life to revolve around problem solving, there have to be plenty of
problems. Plenty of things that go wrong. Plenty of errors to correct. Not just
a remote possibility we're living in the Matrix.

I wrote about this recently, here:

http://curi.us/1468-fallibilism

You may also like to remember DD's TED talk where he says "problems are
inevitable" and consider his attitude to problems in that talk. It wasn't that
one problem per millennia is inevitable, as a technicality. It was that problems
are common, and always will be common (but that's OK b/c we can solve them).

-- Elliot Temple
http://curi.us/

On Dec 19, 2009, at 7:26 AM, Rudi Voigt wrote:

> On Dec 16, 2009, at 7:04 AM, Bruno Marchal wrote:
>
>>> ? ? ? ? ? ? ? ? ? (In many university, including the one where I am
>>> teaching, mathematics belongs the faculty of science, and is
>>> considered as science by all mathematician. You are the first I hear
>>> saying that mathematics is not a science.
>>
>> In the US it's not considered science.
>>
>> But the important thing is: what makes a science? Popper gave a
>> demarcation criterion which is that if you use experimental tests
>> in a field then it's scientific. Math has no experimental tests, so
>> it's not a science just like philosophy isn't a science for the
>> same reason.
>
> Elliot, I've got my 'The Logic of Scientific Discovery' by Karl Popper right
here, and I have read it a few times in the past, I cannot find the part you are
referring to.
>
> His whole argument about demarcation of science (chapter 4) is
> about the impracticality of positive proof and his suggestion of
> using 'falsifiability' as a demarcation criteria (chapter 6).

I think this refers to *sections* 4 and 6 of chapter 1.

By falsifiability here Popper means empirical falsifiability.

> He basically says that any hypothesis that is formulated in such a
> way that it is possible to prove it wrong falls within the scope of
> science.
>
> Can you give me an idea of where  might find 'experimental tests in
> a field' mentioned as a criteria in Popper?

On page 18 i LScD Popper writes:

> But I shall certainly admit a system as empirical or scientific
> only if it is capable of being *tested* by experience. These
> considerations suggest that not the *verifiability* but the
> *falsifiability* of a system is to be taken as the criterion of
> demarcation. In other words ... *it must be possible for an
> empirical scientific system to be refuted by experience*.

This paragraph offers a criterion demarcating science from non-science. Science
is "possible ... to be refuted by experience". Science is "capable of being
tested by experience".

Being tested by "experience" (I'd rather say observation), with the possibility
of a refutation, is the experimental tests I referred to.


And here is my dictionary on science:

> the intellectual and practical activity encompassing the systematic
> study of the structure and behavior of the physical and natural
> world through observation and experiment


The dictionary, too, insists on an empirical component to science.

You can find more on Popper's view on this in Conjectures and Refutations. See
chapter 11 titled "The Demarcation Between Science and Metaphysics". Read the
whole thing, but here is one snippet from page 345 in my edition (in section 2):

> a system is to be considered as scientific only if it makes
> assertions which may clash with observations



-- Elliot Temple
http://curi.us/

On 18 Dec 2009, at 04:30, Bill Taylor wrote:

>
> I have ignored most of this last article, due to its repetitive and
> plangent tone; but there is one substantial point here worth noting:-
>
> -> Does Church thesis entail, or not, the existence of a
> (mathematical)
> -> machine which is universal with respect to computability?
>
> Not exactly, no. The existence of a universal "machine" is *proved*,
> by construction, in a standard mathematical way, without need for any
> new axioms or fancy "theses".


I doubt so. The existence of a Turing universal machine is proved by
the usual mathematical way, and this is what you can do for any
precise universal system. With Church thesis, all those equivalent
definitions of computability, becomes acceptable as a definition of
computability. You need Church thesis to obliterate "Turing" to have a
universal machine".

If not you confuse a theory with the subject of that theory. This
would be like defining reality by the wave function. It is like
forgetting philosophical premises in a philosophical (or in
engineering) reasoning.

> The only relevance to this, of Church's "thesis", is in the legitimacy
> of the use of the word "universal", in the sentence excerpted above.

So we do agree! You were quite unclear above. This is what I insist
on; CT makes the term "universal" legitimate.


> We need look at the context and epoch when Church's thesis (CT) was
> formed.
> At that time, there was still a lot of ferment about what math was
> actually "about", what its "material cause" was.

?

> Set theory had been
> introduced for some time, and proven very effective as a unifying
> concept,
> but was still widely held in suspicion as a genuine basis for all
> math.

(It is out of topic, but I don't follow you. Set theory was thought
quite genuine for the whole of math, the problem was that the "naive"
Cantor theory was contradictory).

> There was still a lot of "logicist" thinking around, (which subsequent
> history has obviated, to a great extent). People were still wondering
> just *what* reasoning could be firmly relied on.

Like today, except that today we know that there is no way to
formalize completely the ways of reasoning, as opposed to computing.
Provability power, once formal, can always been extended in always
debatable way.  Of course, for all practical purpose everyone agree on
a large part of the provability means. But working on fundamental
issues force us to note that fundamental fact: formal provability
depends on the choice of the formal theory. formal computability is a
notion independent of the choice of formal systems. Exactly the same
function are computed or not by lambda calculus, or quantum computer.
Not exactly the same arithmetical truth are proved by Peano Aritmetic
or Zermelo-Fraenkel Set theory.
With Church thesis, computability is an absolute notion.
And there is no equivalent notion notion for provability, nor for
learnability (except for an exotic universal leaner, but I don't want
be technical).


> Then, studying these matters, several workers independently found
> various
> ways of "founding" the computational/logical ideas about naturals,
> that
> could be seen to be relatively free from problems. This had been
> prefigured
> a little by Post; when suddenly Herbrand, Kleene, Godel and Church
> himself
> found others, which were quickly seen to be equivalent.

Gödel missed the "Church thesis", as he explains himself to Davis. His
general recursive function was universal, but he did not believe in
this, until he read Turing's paper.

>
> At the time, and in the ferment, this was truly a bolt from the blue!
>
> Here, independently, several workers had found the same thing from
> different points of view. This remarkable confluence of research,
> this expression of a "spirit of the times", was so profound, that
> people,
> Church in particular, felt it necessary to give it voice and form.
> So "Church's thesis" was born.


Church did not understand the "thesis" aspect of Church thesis. He
opposed to that label. For him it was a definition. It is Kleene who
invented the label "Church's Thesis", shown later to be equivalent
with Turing's thesis, by Turing.
A rumor (or a joke) is that Church would have accepted the idea that
his definition was really a thesis on his death bed.
I have read all Church, and have found only critics of the idea that
it was a thesis. For Church the computable function was defined by his
lambda calculus.
Post is the first to discover "Church thesis", which he describes as
natural law. He discovered, its incompletness consequence, and the
Lucas Penrose argument that we are not machine, and the (very
important) machine's refutation of that argument. Post anticipated
also my own contribution (mechanism => immaterial monism), but changes
his mind, apparently, after a conversation with Turing.
Like Churchill and Lewis Carroll, Emil Post saw it all!


> But really, it was/is largely a big nothing. It was, one the one hand,
> a pious hope that any future attempt to do the same thing in yet a
> different
> way would turn out to be equivalent. But as "the same thing" was not
> identifiable, (nor ever has been), except *as expressed by* CT, it is
> merely a self-fulfilling prophecy, an empty comment or "thesis".
> It is thus, on the other hand, and in view of the above, now to be
> seen
> merely as a DEFINITION of what we mean by "computable", (regarding
> naturals).

So you follow Church ???
But that definition makes sense only thank to Church thesis. We can
logically doubt Church thesis.
Also the incompleteness theorem is a direct (one diagonalization)
consequence of Church thesis. It would be like to claim that Gödel's
theorem is a direct consequence of a definition.
It makes no sense, although I am aware that, since Church, there is a
tradition (by a minority) to believe that we can defined computability
by this or that universal system. I think it is just a trick by
mathematicians who dislike that their field rest on a philosophical or
naturalistic, or theological, assumption.


> Of course, there remained the distant possibility, (between 1933 and
> 1937),
> that someone might come up with a procedure that most reasonable
> people would
> describe as "computable", but that was in fact more extensive than
> this.
> Remote, but slightly plausible.



Of course. That is the point, so honesty forces us, in the fundamental
science to put the cart on the table. Church thesis is a theory, an
hypothesis.


> Then, at last, in 1937 came the ground-breaking paper of Turing,
> (so much beloved by but misinterpreted (IMHO) by Deutsch), in which he
> attempted to identify what a reasonable "computer", human or
> mechanical,
> might or might not be able to do. The result was the Turing machine,
> which was easily seen to be yet another equivalent, and brought in
> its train
> a host of new results and ideas, including much simpler and snappier
> proofs
> of older results. CT has thus often gone under the new name of
> Church-Turing
> thesis, CTT, IMHO quite properly.


Better then would be:   Babbage-Post-Turing-Markov Thesis. But "Church-
Turing" is OK.
I have personal source making me think that Babbage could have the
smell of Church thesis, not by inventing his universal machine, but by
discovering the universality of the system he used to describe the
functioning of its machine.
You exaggerate the importance of Turing's paper. Church lambda
calculus, like the Shoefinkel Curry combinators have more to say on
the computations structures than Turing's analysis, which is more
pedagogical, but relies somehow on comp implicitly. he has to use the
hypothesis of finiteness of the mind state in his argument.
Post 1946 papers founded recursion theory, and the study of the degree
of uncomputability.
So show that a function is computable, you don't need Church thesis.
But today that something is NOT computable, you need Church thesis.


> As Godel famously noted, after 1937 there was no longer any doubt that
> Turing had nailed it, and that Turing computability WAS computability.
> Later equivalents, such as Markov's, and computer languages, were no
> longer
> expected to hold any real surprises. Attempts by Kalmar, referenced in
> Rosa Peter's seminal book, have effectively been laughed out of
> court by
> ignoring them. (As has also a more recent attempt by Christian Calude,
> who really ought to know better.)

[No comment]

> So, informal "computability" has been DEFINED (by CT) as Turing
> computability.

This is like defining truth by"what I prove", or "reality" by "my
theory". It works for doing recursion theory, but it is dishonest when
applying recursion theory to fundamental question.

> But note it is ONLY A DEFINITION!! Nothing more.


<sigh>



> It is a definition
> giving an informal (but felt to be definite) concept, a formal and
> precise
> expression. No more nor less than, say, Weirstrass's final and
> successful
> attempt to define "continuity", a formerly informal but thought-to-
> be-definite
> concept, by means of epsilon-delta continuity, (as applied to real-
> to-real
> functions). [Side note: this was actually fairly precisely prefigured
> in words, as far back as Newton, in his replies to Berkley.]


Change the topology, you get different notion of continuity. The
concept of continuity is very variable according to the spaces
involved, but also from the logic involved (with intuitionist analysis
it is consistent to add Brouwer's idea that *all* function are
continuous). Set of continuous functions from some spaces can de
different according to the existence of not of some large cardinal, etc.
With Church thesis, an epistemological concept (computability) becomes
as absolute as the natural numbers. It is the same object for
classical and constructivist. This is unique in the story of math.
Despite many precise formal notion of provability, their extension
(set of theorems) are different and depends of the axioms, rules, etc.

> Yet this is never referred to as "Weirstrass's Thesis", or even
> the "Cauchy-Weirstrass thesis", as it otherwise ought.

Because there is no epistemology involved.

> But merely
> because the history and spirit of the time of elucidation. There was
> no "bolt from the blue", in the case of continuity; or of convexity,
> or smoothness, or dozens of other previously-informal concepts in
> math.
> So those do not get poncy "Thesis" names! All that CTT notes is that
> it (computability) is one of the many informal concepts that is
> suitably
> defined by one clear agreed definition; as opposed to one of the
> many that
> do not, such as connectedness, real-number computability,
> measurability,
> or even set/class-hood. It is ultimately just a linguistic matter.
>
> And that is the SOLE meaning of CT. Just a definition. Better called
> the Church-Turing Definition.


No, you need to believe in Church thesis to understand the generality
of your definition. You seem to agree with this above.

> And it is worth noting what it does NOT say,
> or even talk about, (along with its close cousin, Godel completeness).
>
> In spite of the pontifications of experts talking outside their area
> of expertise, such as Lucas and Penrose, they do NOT talk about,
> imply,
> or have anything to do with what humans can or cannot do, or think;
> or what real-life computers (present or future) can or cannot do,
> or think; or with what human consciousness is about. All such matters
> are egregiously unwarranted extensions; and people who casually
> fling about
> references to CT in these contexts achieve nothing but a display
> of their lack of understanding of the essential issues.

You are talking like a Copenhagen Philosopher who asserts that quantum
mechanics does not apply to the macroscopic world, but only to proton
and electron in the laboratory, under special condition.

If we assume we are relatively digitalizable entities (comp), then
computer science applies to us, for the same reason that if we believe
QM correct, quantum mechanics applies to us.

I am aware that there are many abuse of Gödel's theorem, but this is
why I have both specialized myself in  mathematical logic and computer
science, and have made verified the work by many experts. You are
still invited to ask question if there is anything you find unclear.
If for you CT is true by definition, then my derivation should even be
more easy.

Have you a problem with the first person indeterminacy? The universal
dovetailer? The movie graph argument (a bit subtler than the rest).

I have no clue at all what it is that you don't understand. I can
imagine you dislike the result, but that should be a reason to
motivate you to find an error in the reasoning.

Don't say "incomprehensible". Just say, I don't understand this line,
or that line, or, how you get this from that, etc.

The subject is not easy. Some people take some time to understand the
notion of qualia, and the difficulty of the mind-body problem. The
thought experiments are there to pave a way into the difficulties.

It needs some works and training like in any fields.

If you dislike thougth experiences, you can also consider only what
can be extracted from the logic of self-reference, which is a way to
substitute ideally self-referentially correct machine at the place of
the "thought experimenter". But then you need a serious acquaintance
with the content of Boolos and Smorynski books.

You will hardly defeat my enthusiasm. I think that the discovery of
the Löbian universal machine is the discovery of the mathematician by
the mathematicians. With CT, I can explain why it belongs to a more
general form of self-recognizance, which may serve as model for the
apparition of life, apparition of thought, apparition of language,
apparition of computer, etc. Each time a universal layer accelerate
the development of another universal layer.

Sorry for the plangent tone, but it is unnerving when people don't
play the fair game and use pure form of authoritative pseudo-arguments
like " what you say is a sequence of incomprehensible craps".
You should think like that: the proof of the incompatibility of
materialism and mechanism has been given.
It is up to you to show where it is wrong, if you think otherwise.

If it is completely invalid, it should be easy to invalidate quickly,
given that it is precise in the way it proceeds, and use only well
accepted definitions, just recasted in an interdisciplnary deductive
reasoning.
I use only elementary basic notion in three field: "philosophy of
mind", quantum mechanics, theoretical computer science (logic).

Don't let people believe that nobody understand it, because that is
dishonest advertising. Many understand many part of it, and it is
enough to get the point that there may be something there. And some
took the time to search for an error, and admit not having find it,
and rationalists proceed like that.


Bruno Marchal

http://iridia.ulb.ac.be/~marchal/





[Non-text portions of this message have been removed]

>> Popper believed that looking for degrees of reliability of one's
>> knowledge is a mistake for several reasons.

>I think he was right, but I also think it is easy to go too far the other
way.

Postmodernism in a nutshell.

>> We have no viable procedure for reliably attaining reliable knowledge.

>This depends on how reliable you want your "reliable" to be!

Surely you just contradicted yourself, Bill? If you agree that "looking for
degrees of reliability of one's knowledge is a mistake" then how can you
decide "how reliable you want your "reliable" to be" ? I think perhaps a
better way to put it would be that looking for degrees of reliability is a
*gamble*, rather than a mistake, but one we're forced to take, both in
everyday life and in science. And that this is where David Deutch and his
arguments for what should be "taken as more likely" come in.

What Popper shows (AFAIK) is that you can't be certain about anything, which
of course includes the amount of reliability you can place on knowledge.
It's always *possible* that the Earth isn't round, or that it doesn't orbit
around the Sun - we may be living in "The Truman Show" or all be plugged in
to the Matrix, and *everything* we know may be false (as Descartes more or
less put it).

This leaves us with a dilemma: we can't reliably know anything, yet it's a
point of trivial observation that we do, in fact, place greater reliability
on some facts than others (we trust hydraulics whenever we use the brakes in
our car, for example, while most of us tend to be sceptical that an unusual
light in the sky is an alien spacecraft). We act as though some things are
true "for all practical purposes" and just get on with the job of trying to
find out more about the world.

When I went through a brief "hyper-Popperian phase" at university, I got
into a discussion with one of my friends, and asked questions like "but how
can we *know* that the scientific method works?" - to which he replied
"It'll just have to do until something better comes along!" Which I think is
fair enough, upon reflection: the fact that we can't be certain about
knowledge is about as useful, in practice, as knowing that there ain't no
sanity clause. It's all very well to say that "maybe tomorrow this will all
be overturned," but in practice it's pointless - it's like saying life's a
piece of shit, when you look at it - so we may as well give up trying to do
anything.

> P.S. Has anyone else noticed how almost all these debates turn
crucially
> on merely socio-linguistic matters of what is "common usage" of
words?
> Wouldn't it be nice to see some real science debate?
>
> Why do I have to be the only one who keeps pulling people up on
these points,
> like a crusty old grammar teacher!?

Well.....I'm sure you aren't the only one who pulls people up on any number
of points. Possibly other people do it for different things from you. But
one has to be careful when "pulling people up", because if you aren't
diplomatic and make a genuine effort to understand what the other person is
saying before you jump down their throat, you'll just get a flame war, and
no one ends up any the wiser. And you do seem to be good at doing it with a
light touch - so perhaps that's why you've been "elected" to the post of
crusty old grammar teacher...!

Charles

On Dec 19, 2009, at 3:40 AM, W.Taylor@... wrote:

>>> The one thing I "believe" in with the least amount of doubt is that
>>> life evolved.
>
> This naivety was barely worth replying to, but reply was made...
>
>> How do you measure doubt accurately? What are the units? What is the
>> methodology?
>
> All good questions, even if it is a bit like taking candy from a baby.
>
>> Popper believed that looking for degrees of reliability of one's
>> knowledge is a mistake for several reasons.
>
> I think he was right, but I also think it is easy to go too far the other way.
>
>> We have no viable procedure for reliably attaining reliable knowledge.
>
> This depends on how reliable you want your "reliable" to be!
>
> If you insist on *absolute certainty*, then we can be utterly certain
> of nothing beyond the Cartesian "cogito", (and even then only when we are
> cogitating it!)   OTOH, most reasonable people would agree that this
> would be laying far too heavy a burden on the word "reliable".
> Surely most people would at least relax the definition to
> "beyond reasonable doubt", where "reasonable" is OC at best
> inter-subjective and in any event dependent on context.

you're saying we can obtain knowledge that is beyond doubt?

once we have that, what should we do with the remaining doubters?

>
> On this basis, it is reasonable to say some things are known reliably.
> The simplest facts about everyday life.  The simple to medium results
> of mathematics.  (Not the medium everyday facts, nor the difficult math.)
>
> Most people would say to cavil at this would be pointless combative debate.

advocating Popper's view on fallibilism, on a Popperian list, is "combative
debate"?


>
>> What we can do instead is focus on good explanations, and rule out
>> bad explanations and criticized explanations.
>
> We can certainly do the latter, but the former is too sweeping in its
> apparent certification of "good explanations" as the sole criterion.
> There is also evidence.

which is used in explanations.

>  Firstly the evidence of everyday experience
> and senses, "common sense" always duly criticized and sifted, OC.
> Which is not always done, hence the uncommonness of common sense!
> Secondly, the more rigorous evidence of scientific experiemnt,
> (which I tend to think of as merely "refined common sense").
> But there MUST be evidence before there can be ANY explanation,
> good, bad or ugly!

Popper's view is that there must be explanation before there can be evidence,
b/c all observation is theory laden. Observations have no meaning in total
isolation. Would you like to offer us some criticism of that view?

>
> I feel the poster has ignored this point in his enthusiasm.
>
> -- Balancing Bill
>
> P.S.  Has anyone else noticed how almost all these debates turn crucially
>       on merely socio-linguistic matters of what is "common usage" of words?
>       Wouldn't it be nice to see some real science debate?
>
> Why do I have to be the only one who keeps pulling people up on these points,
> like a crusty old grammar teacher!?

Are you saying the difference between Popperian epistemology, and non-Popperian
epistemology, is just a grammar debate?



-- Elliot Temple
http://curi.us/

On Dec 16, 2009, at 7:04 AM, Bruno Marchal wrote:

>> ? ? ? ? ? ? ? ? ? (In many university, including the one where I am
>> teaching, mathematics belongs the faculty of science, and is
>> considered as science by all mathematician. You are the first I hear
>> saying that mathematics is not a science.
>
> In the US it's not considered science.
>
> But the important thing is: what makes a science? Popper gave a
> demarcation criterion which is that if you use experimental tests
> in a field then it's scientific. Math has no experimental tests, so
> it's not a science just like philosophy isn't a science for the
> same reason.

Elliot, I've got my 'The Logic of Scientific Discovery' by Karl Popper right
here, and I have read it a few times in the past, I cannot find the part you are
referring to.

His whole argument about demarcation of science (chapter 4) is about the
impracticality of positive proof and his suggestion of using 'falsifiability' as
a demarcation criteria (chapter 6).

He basically says that any hypothesis that is formulated in such a way that it
is possible to prove it wrong falls within the scope of science.

Can you give me an idea of where  might find 'experimental tests in a field'
mentioned as a criteria in Popper?

I have never heard anyone suggest that mathematics isn't a science. In fact,
most mathematicians I've known tend to think it is the only real science.

Rudi

>> The one thing I "believe" in with the least amount of doubt is that
>>  life evolved.

This naivety was barely worth replying to, but reply was made...

> How do you measure doubt accurately? What are the units? What is the
> methodology?

All good questions, even if it is a bit like taking candy from a baby.

> Popper believed that looking for degrees of reliability of one's
> knowledge is a mistake for several reasons.

I think he was right, but I also think it is easy to go too far the other way.

> We have no viable procedure for reliably attaining reliable knowledge.

This depends on how reliable you want your "reliable" to be!

If you insist on *absolute certainty*, then we can be utterly certain
of nothing beyond the Cartesian "cogito", (and even then only when we are
cogitating it!)   OTOH, most reasonable people would agree that this
would be laying far too heavy a burden on the word "reliable".
Surely most people would at least relax the definition to
"beyond reasonable doubt", where "reasonable" is OC at best
inter-subjective and in any event dependent on context.

On this basis, it is reasonable to say some things are known reliably.
The simplest facts about everyday life.  The simple to medium results
of mathematics.  (Not the medium everyday facts, nor the difficult math.)

Most people would say to cavil at this would be pointless combative debate.

> And we have no procedure for judging amount of doubt or
> reliability, no way to measure it.

True, but we can make reasonable attempts to assess evidence, and to determine
when things are beyoind reasonable doubt.  Though it is notable that people
with agendas frequently stretch "reasonableness" to breaking point and beyond!

> What we can do instead is focus on good explanations, and rule out
> bad explanations and criticized explanations.

We can certainly do the latter, but the former is too sweeping in its
apparent certification of "good explanations" as the sole criterion.
There is also evidence.  Firstly the evidence of everyday experience
and senses, "common sense" always duly criticized and sifted, OC.
Which is not always done, hence the uncommonness of common sense!
Secondly, the more rigorous evidence of scientific experiemnt,
(which I tend to think of as merely "refined common sense").
But there MUST be evidence before there can be ANY explanation,
good, bad or ugly!

I feel the poster has ignored this point in his enthusiasm.

-- Balancing Bill

P.S.  Has anyone else noticed how almost all these debates turn crucially
        on merely socio-linguistic matters of what is "common usage" of words?
        Wouldn't it be nice to see some real science debate?

Why do I have to be the only one who keeps pulling people up on these points,
like a crusty old grammar teacher!?



----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.

>> > Of course I know the importance of experimental tests, and this is
>> > why I insist so much that computer science makes theology not only
>> > a theoretical science, but an experimental science too. This comes
>> > from the fact that machine's physics is a part of machine's theology.
>>
>> I suspect that to many people (such as Bill) that sounds like so
>> much gobbledegook.

It is complete and utter nonsense.   "Not even wrong".

> I think you're right -- Bruno's "theology" just means what a machine
> "believes" -- specifically about itself and its universality, within
> its system, as compared to what it can prove.

This too is nonsense.

The person/s who made these comments is either very bad at technical English
or just trying to provocatively stir up a hornets' nest.

-- Wiping-out William


----------------------------------------------------------------
This message was sent using IMP, the Internet Messaging Program.

> Here, independently, several workers had found the same thing from
> different points of view. This remarkable confluence of research,
> this expression of a "spirit of the times", was so profound, that
people,
> Church in particular, felt it necessary to give it voice and form.
> So "Church's thesis" was born.

Sounds similar to the more recent "M theory" in physics....!

Incidentally, for lay people like me who aren't particularly familiar with
the CTT, the wikipedia entry
http://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis gives an overview,
including this statement (which I imagine Bill endorses) :

"the fundamental premise behind the theses-the notion of what it means for a
function to be "effectively calculable" (computable)-is "a somewhat vague
intuitive one". Thus, as they stand, the "theses" remain hypotheses and
cannot be proven."

Probably also of interest on this forum is the "Church-Turing-Deutsch
principle": http://en.wikipedia.org/wiki/Church-Turing-Deutsch_principle

Charles

I have ignored most of this last article, due to its repetitive and
plangent tone; but there is one substantial point here worth noting:-

-> Does Church thesis entail, or not, the existence of a (mathematical)
-> machine which is universal with respect to computability?

Not exactly, no.  The existence of a universal "machine" is *proved*,
by construction, in a standard mathematical way, without need for any
new axioms or fancy "theses".

The only relevance to this, of Church's "thesis", is in the legitimacy
of the use of the word "universal", in the sentence excerpted above.

.......

Maybe this is time for my CT essay, which will thus be shorter than intended.

We need look at the context and epoch when Church's thesis (CT) was formed.
At that time, there was still a lot of ferment about what math was
actually "about", what its "material cause" was.  Set theory had been
introduced for some time, and proven very effective as a unifying concept,
but was still widely held in suspicion as a genuine basis for all math.
There was still a lot of "logicist" thinking around, (which subsequent
history has obviated, to a great extent).  People were still wondering
just *what* reasoning could be firmly relied on.

In this ferment, faith in the reality of the "reals" was wavering, and
people were wondering how far the "naturals" could be trusted as a basis.
It was realised that they were a grand "rock-bottom", crystal-clear basis
on which to found all math, that had much firmer reality than the ethereal
sets or the vague reals.  But mathematical philosophers/logicians were
still unsure how much could be trusted, about *operations* on and with them,
particularly "computing" style operations, which OC at that time was not
even a precisely formulated concept in itself.

Then, studying these matters, several workers independently found various
ways of "founding" the computational/logical ideas about naturals, that
could be seen to be relatively free from problems.  This had been prefigured
a little by Post; when suddenly Herbrand, Kleene, Godel and Church himself
found others, which were quickly seen to be equivalent.

At the time, and in the ferment, this was truly a bolt from the blue!

Here, independently, several workers had found the same thing from
different points of view.  This remarkable confluence of research,
this expression of a "spirit of the times", was so profound, that people,
Church in particular, felt it necessary to give it voice and form.
So "Church's thesis" was born.

But really, it was/is largely a big nothing.  It was, one the one hand,
a pious hope that any future attempt to do the same thing in yet a different
way would turn out to be equivalent.  But as "the same thing" was not
identifiable, (nor ever has been), except *as expressed by* CT, it is
merely a self-fulfilling prophecy, an empty comment or "thesis".
It is thus, on the other hand, and in view of the above, now to be seen
merely as a DEFINITION of what we mean by "computable", (regarding naturals).

Of course, there remained the distant possibility, (between 1933 and 1937),
that someone might come up with a procedure that most reasonable people would
describe as "computable", but that was in fact more extensive than this.
Remote, but slightly plausible.

Then, at last, in 1937 came the ground-breaking paper of Turing,
(so much beloved by but misinterpreted (IMHO) by Deutsch), in which he
attempted to identify what a reasonable "computer", human or mechanical,
might or might not be able to do.  The result was the Turing machine,
which was easily seen to be yet another equivalent, and brought in its train
a host of new results and ideas, including much simpler and snappier proofs
of older results.  CT has thus often gone under the new name of Church-Turing
thesis, CTT, IMHO quite properly.

As Godel famously noted, after 1937 there was no longer any doubt that
Turing had nailed it, and that Turing computability WAS computability.
Later equivalents, such as Markov's, and computer languages, were no longer
expected to hold any real surprises.  Attempts by Kalmar, referenced in
Rosa Peter's seminal book, have effectively been laughed out of court by
ignoring them.  (As has also a more recent attempt by Christian Calude,
who really ought to know better.)

So, informal "computability" has been DEFINED (by CT) as Turing computability.

But note it is ONLY A DEFINITION!!   Nothing more.  It is a definition
giving an informal (but felt to be definite) concept, a formal and precise
expression.  No more nor less than, say, Weirstrass's final and successful
attempt to define "continuity", a formerly informal but thought-to-be-definite
concept, by means of epsilon-delta continuity, (as applied to real-to-real
functions).  [Side note:  this was actually fairly precisely prefigured
in words, as far back as Newton, in his replies to Berkley.]

Yet this is never referred to as "Weirstrass's Thesis", or even
the "Cauchy-Weirstrass thesis", as it otherwise ought.  But merely
because the history and spirit of the time of elucidation.  There was
no "bolt from the blue", in the case of continuity; or of convexity,
or smoothness, or dozens of other previously-informal concepts in math.
So those do not get poncy "Thesis" names!  All that CTT notes is that
it (computability) is one of the many informal concepts that is suitably
defined by one clear agreed definition; as opposed to one of the many that
do not, such as connectedness, real-number computability, measurability,
or even set/class-hood.  It is ultimately just a linguistic matter.

And that is the SOLE meaning of CT.   Just a definition.   Better called
the Church-Turing Definition.  And it is worth noting what it does NOT say,
or even talk about, (along with its close cousin, Godel completeness).

In spite of the pontifications of experts talking outside their area
of expertise, such as Lucas and Penrose, they do NOT talk about, imply,
or have anything to do with what humans can or cannot do, or think;
or what real-life computers (present or future) can or cannot do,
or think; or with what human consciousness is about.  All such matters
are egregiously unwarranted extensions; and people who casually fling about
references to CT in these contexts achieve nothing but a display
of their lack of understanding of the essential issues.

-- Bill Taylor.

----- "Charles Goodwin" <charlesrobertgoodwin@...> wrote:

> > Of course I know the importance of experimental tests, and this is
> > why I insist so much that computer science makes theology not only
> > a theoretical science, but an experimental science too. This comes
> > from the fact that machine's physics is a part of machine's
> > theology.
>
> I suspect that to many people (such as Bill) that sounds like so
> much gobbledegook. (Apologies in advance to all concerned if not.)
>
> The idea that computer science make theology into an experimental
> science sounds ridiculous, on the face of it (I suspect many "Very
> Reverend" people would find the idea astonishing!) I *think* I know
> what you mean, though as mentioned the language gap sometimes
> doesn't help with this sort of thing...

I think you're right -- Bruno's "theology" just means what a machine
"believes" -- specifically about itself and its universality, within
its system, as compared to what it can prove.

On Dec 17, 2009, at 5:01 AM, john stifter wrote:

> The one thing I "believe" in with the least amount of doubt is that life
evolved.

How do you measure doubt accurately? What are the units? What is the
methodology?

Popper believed that looking for degrees of reliability of one's knowledge is a
mistake for several reasons. We have no way to get our bearings on any absolute
scale of truth. We are often mistaken, not just about ideas but about our
judgment of the quality of those ideas; making such a judgment adds a second
thing to be wrong about. We have no viable procedure for reliably attaining
reliable knowledge. And we have no procedure for judging amount of doubt or
reliability, no way to measure it.

What we can do instead is focuss on good explanations, and rule out bad
explanations and criticized explanations.

-- Elliot Temple
http://curi.us/

On 17 Dec 2009, at 04:25, Bill Taylor wrote:

>


> This is largely a terminological difference between the Anglo-Saxon
> world
> and the Continental world. As I like to say, in philosophy, the
> English
> channel is much wider than the Atlantic! In Anglo, "science" means
> specifically, experimental, physical science. Contintentally, I
> gather,
> it means merely any "serious study", more or less, so includes math
> and many humanities topics as well.

Looking for "mathematical sciences" I found about 500000 citations in
the anglo talking world.


> There IS a serious distinction, and that is the method of VALIDATION,
> of results and statements. In math, it is by proof; in science proper,
> it is by experiment


Science proper = natural science, then. I am afraid that by doing this
confusion you are including implicitly in science a part of
Aristotelian theology. This may explains why you have some problem
with cognitive and theoretical computer sciences.


> The two are already confused beyond redemption. Sneaky religious
> apologists have debased the word so that the latter meaning is all
> that
> can be safely attributed. It is best not to use it in secular
> contexts.

It is the standard word used in belief theory, cognitive science,
applied logic, artificial intelligence, etc. Just google on the net.
The late creator of my AI department is the author of a theory called
Transfer Belief Model, and has been considered as a leader in belief
theory. Sullyan shows what happen to machine *believing* in classical
logic when they reason on themselves.

> It is not. I know, for example, that Athena was born fully armed
> from the head of Zeus, which most men in the street do not know.
> (And of course, I do not *believe* it - though some men once did.)

Athena is a fiction. It is true, about some fiction, that she was born
fully armed. And it happens you know that.
Here I think that you were committing a confusion of context, and are
using the term "know" in a way which contradict directly what most
analytical philosophers agree on. They talk of course about one of the
simplest meaning of "know", not on all its rich everyday use in
natural language.

How would you say the following sentence: "John believed that (a +
b)^2 was equal to a^2 + b^2, but now he know that a term was lacking".
You will certainly not say: "John knew that  (a + b)^2 was equal to
a^2 + b^2, but now he believes better".


> Knowledge, belief, fact and information are all separate and to some
> extent
> orthogonal things, and too easily confused, as you are doing.

You are the first who criticized my use of it. Read the reports of my
thesis by Paul Gochet, an analytical philosopher, expert on Quine, who
has studied the thesis in deep, as you can see by its reports (see my
url), and has a reputation of being quite crisp on the use of the
vocabulary.
Knowledge is traditionally axiomatized by the modal logic S4 (which
contains Kp -> p).

Could you give me reference of papers in analytical philosophy and
logic which use the term knowledge in your sense?

Usually, those who believes that knowledge of P cannot be defined,
even in a first approximation, by the conjunction of believing in P
with the truth of P, are made by those who believes that we can know
for sure that we are awake, and thus reject the dream argument in
metaphysics. But "video-game" makes it possible to show that the dream
argument is valid in the computationalist theory.

> -> Surely you believe in prime numbers, don't you?
>
> That is a really silly expression, on several counts, including
> grammatical.

Could you be more specific?

> Yes, patience, patience, it's a busy time of year. I know I've
> promised
> a post on Church's thesis, and it's coming. Mind you, I haven't
> promised
> to show "where you're wrong", as I don't follow your arguments. You
> will
> have to deduce it for yourself, from my post.

Does Church thesis entails, or not, the existence of a (mathematical)
machine which is universal with respect to computability?
I said also that CT makes computability universal, where
incompleteness makes provability relative to a theory.
This is what you pretend to be false. Have you an equivalent thesis
for provability? This is what you told me.

Also, to say that you will not show where I am wrong because you don't
follow the argument, is quite weird. It is roughly equivalent with
saying: I will not show where you are wrong because you are wrong.

> -> you still have not answered what is wrong in my papers,
>
> Likewise. They are incomprehensible. They start out seemingly
> sensibly,
> then somehow, before one knows it, they are meaningless.



Where? Could you give an example of a meaningless statement you would
have found in any of my papers?

Since a long time, you make a lot of very strong affirmations, but
without ever providing any justification for them. Everybody can see
that now. I don't have to insist, and I will not.

Although I am tempted to continue so, if only due to my interest in
the question: "why do some humans judge before understanding?".

Your very use of "incomprehensible" is already a bit alarming. It is
like saying "I don't understand and nobody will ever understand it".
And this without being an expert of the field.
And without asking any question? And despite the works has been
academically defended, which could at least make you more polite, more
cautious, more humble. Gosh, my work is a remind that the mind body
problem is not yet solved, notably by comp.

Why do you do that? Bill. Why?

   I provide the reasoning in 8 steps, and I like to ask people, if
interested in the mind body problem (of course), to tell me at which
step they have a problem of understanding. It works well up to my PhD
defense (but unluckily a price in Paris spread some Brussels' lies
about this work).

Then I provide the "interview of the Löbian universal machine" (to be
short). This is more involved technically, but is "easy" with respect
to a good passive understanding of two or three books in computability
and mathematical logic.

Incomprehensible? I don't think so. Unbelievable? Yes. Provably so.
(with "believe = Gödel's beweisbar of the Löbian machine, like in the
lovely books by Raymond Smullyan).

This list is the FOR list, open to the many worlds view.  Is it so
difficult to conceive that there could already be a many world view of
arithmetic? And I provide the tool to compare the two.

Are you aware that many people dismissed both what I said, and the
many worlds of Everett and Deutsch, as being incomprehensible?

I don't think it is incomprehensible.  The line has been made enough
elementary so that, if you are willing to play the game, you have to
say where the reasoning became invalid, or where you feel you miss
something, or , well something.  Look at the Brussel's reports, even
them acknowledge there is nothing wrong.

Incomprehensible? Or just in contradiction with your own
(undoubtable?) beliefs?

Bruno Marchal

http://iridia.ulb.ac.be/~marchal/





[Non-text portions of this message have been removed]

> Of course I know the importance of experimental tests, and this is
why
> I insist so much that computer science makes theology not only a
> theoretical science, but an experimental science too. This comes
from
> the fact that machine's physics is a part of machine's theology.

I suspect that to many people (such as Bill) that sounds like so much
gobbledegook. (Apologies in advance to all concerned if not.)

The idea that computer science make theology into an experimental science
sounds ridiculous, on the face of it (I suspect many "Very Reverend" people
would find the idea astonishing!) I *think* I know what you mean, though as
mentioned the language gap sometimes doesn't help with this sort of thing...

Charles