I have five objects (O1, O2, O3, O4 and O5) and three machines to measure them with (M1, M2 and M3).
I know that M1 weighs the objects and have been told that M2 and M3 are also scales. With M1 I can place the objects in order of weight which is, conveniently the same order as the numbering I've given them:
OM1: O1 then O2 then O3 then O4 then O5
When I measure the objects with M2 I get a different order. M2 gives the same reading for O2 and O3 and the same reading for O4 and O5. I have a partial order:
OM2: O1 then both O2 and O3 then both O4 and O5
Although it is possible that M2 measures something other than weight I'm quite happy to accept that it does measure weight but is less sensitive than M1.
With M3 I get a third order:
OM3: O1 then O3 then O2 then O4 then O5
This, again, is different from OM1. But the difference between OM1 and OM3 is different from the difference between OM1 and OM2. And this difference tells me that M3 isn't measuring weight. O3 can't be both heavier and lighter than O2: the machines must be measuring different things.
What is it that makes OM3 support the conclusion that M3 is measuring a different quality to M1? It isn't that the order is different, OM2 is different. It isn't any of the things usually used to characterise orders (OM1 and OM2 are both linear orders, OM2 isn't).
So what is the nice, neat, mathematical term for the type of difference between OM1 and OM3 that lets me reach my conclusion?
Monday, 29 July 2013
I have five objects (O1, O2, O3, O4 and O5) and three machines to measure them with (M1, M2 and M3).
Tuesday, 13 November 2012
Wednesday, 15 August 2012
Bristol University’s Alexander Bird has defended the good old cumulative epistemic approach to scientific knowledge:
Science (or some particular scientific field or theory) makes progress precisely when it shows accumulation of scientific knowledge; an episode in science is progressive when at the end of the episode there is more knowledge than at the beginning. ("What is Scientific Progress?" Noûs 41 (2007) 64–89. available here).
I, like other mad-dog Popperians, do not think that science can progress like this. Science, the Popper-nutter argues, does not produce “knowledge”, in the sense of “justified/warranted true belief”. Now, Bird has a different definition of “knowledge” from the “standard” view of knowledge as “justified/warranted true belief”, but on Bird’s view of knowledge, knowledge does entail justification. The Popperian view is that justification cannot be had: thus no knowledge. I’d go further and deny that any of our theories (especially the interesting ones) are true.
And I’m a bit iffy about the “belief” bit. What need to go around believing stuff: just provisionally adopt them and get on with it.
What any form of enquiry, not just science, produces is “conjectures” or, if we want to be brutally frank, “guesswork”. Yet the average Popperian is also convinced that our enquiries do progress and is also convinced that they progress quite a bit. In fact, a lot.
Now how would this be possible if enquiry is guesswork? I want to sketch out a way that we can secure a progression in our enquiries without conditions I think cannot be met, implied by the cumulative knowledge view. There are conditions, three, that I hope to show are sufficient to entail a progression. Two of these conditions can be readily met, the third needs, to say the least, a little work on. Whether this progression can be thought of as progress (a progression from social drinking to alcoholism is hardly progress) is largely a matter for elsewhere, but I will have a little bit to say on this later.
What it is a progression of
First, though, I want to say what it is a progression of. It is a progression of Popper’s “Objective Knowledge”. The ‘objectivity’ of the ‘knowledge’ Popper discussed lay in its abstraction from any knowing agent. This ‘knowledge’ lies not in the minds of individuals but in libraries, journals, in computer records and, in so far as they entail declarative statements, in the traditions and norms of a society. The genome of the gorilla, for example, is not “known” by anybody; though, as it is recorded in an accessible manner, it is “known”.
Whilst this is in contrast to other concepts of knowledge that concentrate on just those questions of whether and how S knows p the contrast is not problematical. It is generally accepted that there is ‘this type’ of knowledge and ‘that type’ of knowledge and all that is required is make sure everyone is clear on which type is the current subject of debate; which I hope I have done above.
More of an issue is whether it is “knowledge”, being neither true nor, consequently, justified. The calor theory of heat, spontaneous generation of life, that matter is made up of four elements and so on are just plain false. Yet they were treated as being true, were taught, accepted, used in calculations and held their place in the body of statements society at a particular time called ‘knowledge’.
To avoid confusion and, perhaps, dodge a difficult and tangential debate I will divert from Popper’s terminology (gasp as he avoids the Duhem thesis! Thrill as he sidesteps the Quine thesis!). The totality of the declarative statements of a society, generally accepted by that society, taught, used in calculations and held to be ‘knowledge’ will be called a ‘world model’ and denoted by W.
How the Progression arises
Let us take a feature, F, of World Models and create a structure by showing all possible World Models as points on an imaginary graph. Where one World Model has more F than another it is shown as “higher” than that other World Model. Where World Models are equal in F they are represented as at equal height.
We won’t stipulate exactly what F is, but assume that the more F a World Model has the better it is. As there are a lot more terrible World Models than “vaguely satisfactory” ones; more that are “vaguely satisfactory” than “quite good”; more “quite good” than “good” and just the one best World Model, our structure will resemble a (perhaps not very regular) triangle.
Now let us begin by formulating a World Model, W0, by any irrational or unreliable method you wish to adopt. We may use astrology, legend, or (my own favourite) drinking lots of Real Ale and blurting out the first thing that comes into our head. For the purpose of the argument it matters not which “method” is used, just that it is equivalent to pure guesswork; resulting in W0 occupying an essentially random position in the structure and being, decidedly, not formed of knowledge. W0’s position in the structure will have a vertical component and a horizontal component. We can call the value of the vertical component, more likely than not towards the lower part of the structure, “α”. A total guess of a World Model will, on average, give us a World Model with an F-rank of α. (We can ignore the horizontal component.)
We can either stick with W0, or we can adopt a new world model, W1. If we stick with W0, we remain with a World Model with an F-ranking of α. If we produce a rival World Model, W1, de nuovo, by repeating in its entirety the process used to formulate W0, we are likely, also, to end up with a World Model with an F-ranking of around α. Of course, we may guess repeatedly, choosing the highest ranking of our guesses and end up with a W1 with an F-ranking of α + x. If we continue guessing we may find a World Model ranked still higher. As, though, the de nuovo guesses will average around α most will be lower ranked than W1 and the higher the ranking of W1 the more improbable any “pure” guess will be an advance.
An alternative is not to formulate new World Model’s de nuovo but by adding new elements to and removing existing elements from W0 . Whilst the same irrational guess may be the sole “basis” of both the formulation of new elements and the decision to reject old elements, the distribution of new World Models will be not quite so random as a de nuovo guess: the guess is not “pure”. The new World Models will form a “cloud” around W0 : some higher, some lower, but all in proximity to α. Most will be lower than α. Similar comments to those made with regard to the shape of the overall structure will apply to the cloud. It is a lot easier to come up with theories that are worse than our current theories to create a new world model than it is to improve on current theories. The cloud, then, will be vaguely triangular weighted to “not as high as α”. Some of the World Models, though, will be higher that α and there will likely be a highest World Model that is not W0 . Each time we repeat the process of generating a number of World Model’s the highest generated World Model may form a different differential in ranking to the original World Model, but let us introduce the concept of a typical differential, “ß”. Choose the highest ranked model and we end up with a W1 with an F-ranking of, typically, α + ß.
Creating new World Models by guessing elements to add to W1 and guessing elements of W1 to remove will produce a cloud of World Models in proximity to α + ß with one, typically, at a location ß higher than α + ß. Choose this World Model and we end up with a W2 with a rank of, typically, α + 2ß. Repeating the process produces a cloud around α + 2ß, a World Model ß higher than that and a W3 of rank α + 3ß.
So we have a clear progression, (α, α + ß, α + 2ß α + 3ß… α + xß) dependent on:
- a decision to formulate new World Models by partial removal and addition of elements of the currently adopted World Model;
- our ability to reliably rank World Models on the basis of their F;
- a decision to change the World Model adopted only on the basis that the new World Model has a higher F-ranking than the currently adopted model.
Now I would say that “F” is “being like the truth” (“verisimilitude”) and, if I could ever get my act on it together, explain the nice neat clear exposition of it sitting in the back of my mind that shows just how easy it is to compare rival World Models for their verisimilitude. Others would also identify F with verisimilitude, but be a lot less sanguine about saying what it is and how to recognise it (some trivial things about lots of great minds trying to figure it out and, so far, failing).
It is desirable that World Models increase in verisimilitude over time and that desirability of verisimilitude would mean any progression of increasing verisimilitude would be progress. But the current fuzzy nature of our understanding of the concept must call into question whether we can reliably rank World Models on this basis.
That is unless we tweak our definition of F. We do take World Models to be more or less like the truth than other World Models. A World Model that holds the earth to be a sphere appears more like the truth than a World Model that differs only in thinking the earth to be flat. A World Model that holds “homeopathy is junk” appears more like the truth than one that holds “there’s something in it. It helped my aunt with her hayfever so maybe it’ll cure cancer”. Ranking in terms of apparent verisimilitude may not reliably rank World Models in terms of actual verisimilitude. But it sure does rank them in terms of apparent verisimilitude.
We can, therefore, secure a progression in terms of apparent verisimilitude without accumulating justification, without accumulating truth, whithout “believing” our theories (just adopting them for use); in short without accumulating knowledge. And, as apparent verisimilitude is desirable in its own right, that progression is progress.
Monday, 23 July 2012
Wednesday, 4 July 2012
Certain forms of "Presuppositional Apologetics", including most of the forms floating around the internet, hold
1. The Bible is the inerrant word of God
2. To take anything extra-Biblical as evidence for God (“evidentialism”) is sinful
The same presuppositionalists are also rather fond of quoting 1 Romans 20 in support of a claim that atheists do, despite their protestations, believe in God every bit as much as the devout:
For the invisible things of him from the creation of the world are clearly seen, being understood by the things that are made, even his eternal power and Godhead; so that they are without excuseNow, from 1, this is the inerrant word of God. And this inerrant word of God cites extra-Biblical evidence for the existence of God. “(T)he things that are made” are not exhausted by the Bible: we would have a poor creator whose only work was a book. Yet “the things that are made” are presented as reason the non-Christian should or, indeed, does believe in God.
It seems that God is an evidentialist. And that presuppositionalists think He's wrong.
Sunday, 17 June 2012
There is a story that Picasso, on seeing the cave paintings at Lascaux/Altimara said "we have learnt nothing in 12,000 years". On the one hand, like many of these little stories, it may be apocryphal. On the other; if he had said it, he would have been right:
There has been a civil war in Thebes (Greek Thebes, not the Egyptian one) following the death of Oedipus. Oedipus' two sons have been on opposite sides of the the war and, before the play opens, have managed to kill each other. A chap called Creon (also related to Oedipus) becomes King and decides to restore some order. He orders the burial of one brother, Eteocles, who was a good chap. The other, Polyneices, though:
came back from exile, and sought to consume utterly with fire the city of his fathers and the shrines of his fathers' gods, sought to taste of kindred blood, and to lead the remnant into slaveryNot a nice guy. Something must be done. Or rather, nothing: Creon decrees that no one should bury him.
Antigone, daughter of Oedipus (we're talking Oedipus here: everyone's going to be related) disagrees. You should bury the dead. I hear your arguments about punishment and the security of the state and, well, you can stick them up your arse. You should bury the dead and, you know what, I'm going to bury him.
Creon has a point. For crying out loud, Polyneices was trying to destroy everything. Burial, like a fair trial or not being tortured is all well and good; but aren't Antigone's objections like those "airy-fairy civil liberties" idealist liberals go on about? Let us repeal the right to a burial act safeguard the lives and liberties of the citizens of Thebes.
Antigone also has a point. You've just got to bury the dead. Not to, like detention without trial, torture, suppressing civil liberties or allowing Bill Cash to decide what "rights" you have, is just immoral.
Morality versus practicality: off we go. Throwing in a few gods and the ancient Greek obsession with prophesy Sophocles just lets the story unfold from there.
And Sophocles not only lets a story run based on around major concerns of a society 2,500 years after his death but does it way better than most would do it today. This is a Greek tragedy: it all ends horribly. Nobody today seems to be able to "do" anything but a happy ending. Hollywood, in particular, doesn't seem able to cope with anything but "uplifting". This "it all works out well in the end" nonsense absolves the characters and, by proxy, us of responsibility for their and our actions. In a Greek tragedy the consequences of actions come home to roost. Big time.
It's a great play and a great production. A better, more relevant and more honest story than any likely to be served up today. We have learnt nothing: and forgotten much.
Wednesday, 23 May 2012
- People of faith: People who pretend to know things they don't know
- Interfaith initiative: Initiative of people pretending to know things they don't know combined with other people pretending to know different things which they don't know either
- The Faith Community: Community of Pretending to Know things you don't Know
- The Tony Blair Pretending to Know Things you don’t Know Foundation