The Nature of Paradox

So, I wrote about paradoxes in Hands Off Our Logic, God-Boy and someone complained that by calling it a paradox, I had validated WLC's 'Cosmological Proof' by means of saying that "it is right for being wrong".

At first my reaction involved thinking that this person was clearly confused, but then I wondered if, perhaps, I think about paradoxes in a slightly different way to most people.  If that is so, then I should clarify what I mean when I use the term "paradox".

I've actually written about paradoxes a few times (Patently Paradoxical Pabst's Perplexing Performance, WLC Takes Us for a Ride, There is no Twin Paradox, Immovability and a series on the Bertrand Paradox) but it was in my response to Melchior regarding the Bertrand Paradox that, possibly, I have most clearly articulated my position on what a paradox means.

Let me try again.

As far as I am concerned, thinking only about the strictest meaning of the term "paradox", if a statement is paradoxical then it is:

• wrong,
•  self-referential, or
•  self-referential and wrong

If you are thinking through the logic associated with a proposition and you come across a paradox, then there is something wrong with either the proposition or your thinking about it.  (Note that we can use paradoxes to identify where our thinking is incorrect, but we can't use them to bootstrap the non-existent into existence.)  For this reason, I tend to think in terms of resolving a paradox - which means identifying the problem in thinking that leads to the appearance of a paradox.  Once you've eliminated the problem, then you no longer have a paradox.

There are some paradoxes for which the problem cannot really be eliminated, because a statement is in some sense self-referential, but these tend to be either meaningless or vague.  An example is the classic "this statement is false".  Sure, it's paradoxical, but it's also meaningless, since it refers only to itself.  Another is the even more classic "all Cretans are liars" (as spoken by a Cretan).  It's only paradoxical if you define "liar" to mean a person who always lies, as opposed to the rather more accurate, if also somewhat vague definition - namely someone who lies (with some undefined frequency).

Where a paradox is meaningful (at least in some sense), it tends to arise because of limitations on logic.  Russell's paradox, for example, is self-referential, but it's not meaningless because of its application to set theory. That said, it did show that naïve set theory was flawed, so it is amenable to a trivial resolution.  Another paradox that can be trivially resolved is the paradox of the stone.  The paradox hangs on the notion of omnipotence.  Once you accept the fact that omnipotent beings can't exist, the "paradox" dissipates.

It's worth noting that logic works within a framework.  For example, we could look at a simple syllogism:

(Major Premise) if A then B → (Minor Premise) A → (Conclusion) therefore B

Using this form, we could conclude that, given that I have walked the dogs, the dogs will be tired.  What we can't conclude, using this syllogism, is that the form of the syllogism is true and valid.  Trying to avoid the assumption that the form of the syllogism is true and valid leads to a sort of paradox:

if a syllogism of the form

• if A then B → A → therefore B

is true and valid then the syllogism

• if I have walked the dogs then the dogs will be tired → I have walked the dogs → therefore the dogs will be tired

will be true and valid

→

a syllogism of the form

• if A then B → A → therefore B

is true and valid 

→

therefore the syllogism

• if I have walked the dogs then the dogs will be tired → I have walked the dogs → therefore the dogs will be tired

will be true and valid

While this seems to be saying that the conclusion is conditional on the truth of the minor premise, which is always the case for syllogisms of this form, the whole structure itself is in the form of the syllogism that is the subject of the minor premise (as shown by the colour coding, showing Major Premise, Minor Premise and Conclusion).

Now when I say this is a "sort of" paradox, I don't mean that it is necessarily an "actual" paradox.  Remember I said that we can use paradoxes to identify where our thinking is incorrect.  What this means is that we have falsifiability.  If this structure ever fails, then we say that we have falsified this form of syllogism.  It's about as scientifically rigorous as you can get, as well as being logically rigorous.

Similarly, we can test science scientifically and we do so all the time.  Our working hypothesis is that the scientific method always works - and this is a falsifiable hypothesis.  If we come across any situation in which rigorous application of the scientific method doesn't work, then (pseudo-paradoxically) we will have used the scientific method to show that the scientific method doesn't always work.  Good luck with that!

Scientism

I stand accused of scientism.  I’m only rarely accused of it directly, but by association I am pretty much accused on an on-going basis – via the accusations levelled at people with similar views on the world to mine.

Most of these accusations are meaningless, made by people who don’t understand science and who therefore cannot distinguish between legitimate and illegitimate applications of science.  I do, however, have a vicarious sense of indignation over the accusation of scientism levelled by Professor Ian Hutchinson, a nuclear physicist who also happens to be a theist.

I’d like to look at this accusation in a rigorous scientific way in order to ascertain whether I am in fact a “scienterrist”.  To do this I have to propose a hypothesis and test it against the evidence.

Hypothesis – neopolitan is a scienterrist

Before go any further, I should clarify my terms:

The being “neopolitan” is me, I am not talking about various misspellings of “neapolitan” or any other person who might coincidentally have the moniker “neopolitan”.

A “scienterrist” is a person who practices, holds to or can otherwise be justifiably accused of “scientism”.  The term “scienterist” is also used, but it is not as amusingly close to George W Bush’s mispronunciation of “terrorist”.

The meaning of “scientism” varies depending on who you are talking to.  We will use Hutchinson’s definition, but first let’s look at some of the other definitions.

WLC describes scientism as “the view that we should believe only what can be proven scientifically. In other words, science is the sole source of knowledge and the sole arbiter of truth”.

Humble Don uses a definition that he ascribes to WLC and JP Moreland, “the view that science is the very paradigm of truth and rationality. If something does not square with currently well-established scientific beliefs, if it is not within the domain of entities appropriate for scientific investigation, or if it is not amenable to scientific methodology, then it is not true or rational. Everything outside of science is a matter of mere belief and subjective opinion, of which rational assessment is impossible. Science, exclusively and ideally, is our model of intellectual excellence.”  As such, “there are no truths apart from scientific truths, and even if there were, there would be no reason whatever to believe them.”

In Humble Don’s own paraphrasing, scientism is held by “skeptics who appeal to the scientific method as evidence against Christianity” and “suggests that all valid knowledge must be empirically verifiable; there should be physical evidence to back it up”.

These are strong versions of scientism, effectively saying “it’s either science or it’s not true and it isn’t worth knowing”.

Michael Shermer, on the other hand, espouses a weak version of scientism, writing that scientism “is a bridge spanning the abyss between what physicist C. P. Snow famously called the ‘two cultures’ of science and the arts/humanities” and the Wikipedia entry on scientism has Shermer describing it as “a worldview that encompasses natural explanations, eschews supernatural and paranormal speculations, and embraces empiricism and reason”.  This is quite a positive definition of the term and if this was what Hutchinson meant by it, I would have to agree that I am a scienterrist by nature.

Critical definitions are not limited to apologetically inspired versions such as those crafted by the likes of WLC, Moreland and Humble Don.  To quote Wikipedia again, there are two pejorative uses of the term scientism:

1. To indicate the improper usage of science or scientific claims.   This usage applies equally in contexts where science might not apply, such as when the topic is perceived to be beyond the scope of scientific inquiry, and in contexts where there is insufficient empirical evidence to justify a scientific conclusion. It includes an excessive deference to claims made by scientists or an uncritical eagerness to accept any result described as scientific. In this case, the term is a counterargument to appeals to scientific authority.
2. To refer to "the belief that the methods of natural science, or the categories and things recognized in natural science, form the only proper elements in any philosophical or other inquiry," or that "science, and only science, describes the world as it is in itself, independent of perspective" with a concomitant "elimination of the psychological dimensions of experience."

While I might be overstretching myself if I were to criticise the veracity of Wikipedia, I do think that the first use of scientism is wrong.  This might be because people use the term incorrectly, of course, but the improper use of science or scientific claims is perhaps better described using reference to either pseudoscience or the formal logical fallacy “appeal to (scientific) authority”.

The second use of scientism, according to Wikipedia, seems to accord closely with the ideas of WLC, Moreland and Humble Don – although there is no mention of scientism lining up with the specific complaint that science is sometimes used to discredit the claims of Christianity.

However, since the charge of scientism was levelled by Hutchinson, we should see what he meant by the term.

Hutchinson addressed the topic at length in “Monopolizing Knowledge” and more briefly on the Biologos Forum.  In the former (quoted in the header to the latter), he defines scientism as “the belief that science, modeled on the natural sciences, is the only source of real knowledge”.  In the forum article, he describes scientism as “a philosophy of knowledge. It is an opinion about the way that knowledge can be obtained and justified. However, scientism rapidly becomes much more. It becomes an all-encompassing world-view; a perspective from which all of the questions of life are examined: a grounding presupposition or set of presuppositions which provides the framework by which the world is to be understood. In other words, it is essentially a religious position.”

O-kay … in so much as having a presupposition is a religious position, if scientism becomes a gounding presupposition or a set of presuppositions then it becomes a religious position.  Gotcha.  But let’s talk about what scientism is, rather than what Hutchinson claims that it becomes.  (I’ve already addressed the notion of the null hypothesis [see On Evidence]: the only valid presupposition is the presupposition of nothing and nothing makes for a very insubstantial framework.)

Reframing the hypotheses in light of Hutchinson’s definition of scientism:

Hypothesis – neopolitan holds that science, modelled on the natural sciences, is the only source of real knowledge

Now we need to know what “modelled on the natural sciences” means.  If you read the first instalment of Hutchinson’s contribution to the BioLogos Forum, you will note that he wishes to distinguish between two meanings of “science” – the classical understanding derived from scientia being the Latin for “knowledge” and the modern usage meaning “the study of the natural world”.  Therefore “modelled on the natural sciences” is merely a clarification that science is being used in the modern sense, not the classical sense.  Taking this under advisement, we may strike the containing clause from the hypotheses.

Hypothesis – neopolitan holds that science is the only source of real knowledge

If we skip over the word “real”, the claim that science is only source of knowledge seems implausible.  If that were the case, then the vast majority of people would know nothing and even those who use the scientific method would only know that which has been the subject of personally conducted experiments.  This would be a ridiculous claim, most likely linked to an overly zealous restriction on the use of the term “knowledge”.

However, Hutchinson is guilty of placing a restriction on the use of the term “knowledge”.  He’s talking about “real” knowledge.  We might be tempted to think of “real knowledge” as referring to knowledge about the natural world, or empirical knowledge, but then this is precisely the sort of knowledge that science, as Hutchinson defines it, deals with.  This turns his claim into “scientism is the belief that the methods by which you obtain knowledge about the natural world are the only methods by which you obtain knowledge about the natural world” – which is a sloppy form of tautology.  I’m willing to give Hutchinson more credit than that.

However, it remains unclear what Hutchinson means by “real knowledge”.  So far as I can see, he does not provide a definition – if anyone out there has seen one, please let me know.

There are, however, hints as to what Hutchinson might mean.  First, he’s a nuclear physicist so I doubt that he is restricting himself to material facts.  Second, there’s this extract from his Biologos Forum article:

Science requires reproducibility. But in many fields of human knowledge the degree of reproducibility we require in science is absent. This absence does not in my view undermine their ability to provide real knowledge. On the contrary, the whole point of my analysis is to assert that non-scientific knowledge is real and essential, just not scientific.

Sociologists today acknowledge that sociology does not offer the kind of reproducibility that is characteristic of the natural sciences. Even so, they feel they must insist on the title of science, because of the scientism of the age.

History is a field in which there is thankfully less science envy. Obviously history, more often than not, is concerned with events in the past that cannot be repeated. History is crucial knowledge but cannot be made into a science.

The study of the law (jurisprudence) is a field whose research and practice that cannot be scientific because it is not concerned with the reproducible. The circumstances of particular events cannot be subjected to repeated tests or to multiple observations.

Economics is a field of high intellectual rigor, but the absence of an opportunity for truly reproducible tests or observations and the impossibility of isolating the different components of economic systems means that economics as a discipline is qualitatively different from science.

Politics is a field, if there ever was one, that is the complete contradiction of what scientists seek in nature. It seems a great pity, and perhaps a sign of the scientism we are discussing in this series, that the academic field of study is referred to these days almost universally as Political Science.

These disciplines do not lend themselves to the epistemological techniques that underlie natural science's reliable models and convincing proofs. They are about more indefinite, intractable, unique, and often more human problems. In short, they are not about nature.

The problem with this (apart from the fact that he says that knowledge about humans is not knowledge about nature, as if humans were somehow set apart from nature – something that might be true in his theology, but is not actually true) is that Hutchinson has just set up another tautology.  Science, according to Hutchinson, is about reproducibility and “Clarity” (Hutchinson’s capitalisation) and “real knowledge” includes fields that he claims involve unreproducible facts.  Therefore, of course science – using his definition – is not going to be valid in other fields which – via his definition – aren’t scientific.  What he’s claiming, without clarifying it (proving that his argument is not scientific in his own terminology), is that science is purely “hard science” (“natural science”) and nothing else – and that real knowledge encompasses everything, up to and including soft science (sociology, economics, politics), scholarship (history, law) and maybe even art.

So, rephrasing the hypotheses again:

Hypothesis – neopolitan holds that hard science is the only source of real knowledge, including knowledge that arises only from soft science, scholarship and art

I suspect that I have, at this stage, some evidence against the hypothesis.  I fully comprehend and accept that it is not possible to source all “real knowledge”, where “real knowledge” is knowledge that arises from hard science, soft science, scholarship and art, if I use only hard science.  I can even use a Venn diagram to see that the hypothesis is invalid:

Therefore, the hypothesis must be rejected and, ladies and gentlemen of the jury, I am thus not guilty of the charges of scientism as laid by Professor Ian Hutchinson.

That said, I might be guilty of the more gentle scientism as defined by Michael Shermer, but that’s another thing altogether.

D'Souza and the Village of Bill

Dinesh D’Souza introduced the village of Bill while participating in The Great Debate together with Ian Hutchinson arguing against the proposal that science has refuted religion, which was defended by Sean Carroll and Michael Shermer.

During the “cross-examination phase”, D’Souza raises the mystery of Bill.  He describes visiting a village (which seems based on figures from a Pew Forum Report) in which there are a hundred people, of whom 95 say they know someone called Bill, three of them say they don’t know the guy and two say that Bill does not exist.  D’Souza then rhetorically asks who you are going to believe.

This is a brilliant argument, but not for D’Souza.

If you had two disbelieving people in a village of 100 who are indistinguishable from any other villager (apart from their position on the existence of Bill) then you could easily check their rationality by asking any of the 95 who say that Bill exists to introduce you to Bill.

Say that you approach each of the 95 and ask them about Bill and their responses are something like:

·         Oh Bill’s not physically here, he built the village, created the villagers from dust and left

·         Bill is sort of here, was sort of here in the form of Young Billy and has always been here, and in fact everywhere

·         You can’t see Bill, he’s an immaterial, transcendent, timeless, personal sort of bloke

·         If you just open your eyes and your heart, you can welcome Bill into your life, but until you truly believe in him, you won’t see him or feel his presence

·         When Bill calls you, you will know him

·         You can’t see Bill with earthly senses, you just have to have faith

·         We will meet up with Bill once we die, he’s creating this place where we can be with him and praise him forever

·         To be honest I sometimes doubt that Bill exists too, but then I talk to an officially sanctioned proponent of the existence of Bill and she reassures me

·         I don’t know much about Bill, but everyone else seems to know him and that’s good enough for me

·         Young Billy did some miracles and stuff and was way cool and the people who first believed that Young Billy was the Son of Bill and stuff all agreed that Young Billy was the Son of Bill and some other stuff, not that I’ve actually read what they wrote because it’s all in this like old language and stuff, so of course there is a Bill, ooh, look, a butterfly

·         We’ll forgive you this once, being an outsider, but if you question the existence of Bill one more time, we will smite you

·         Bill must exist, because if he didn’t, there would be no basis for our morality

·         Young Billy died for our sins

·         Bill loves us so much that he sent Young Billy or himself or both or a third or perhaps two thirds of himself to Earth to have a really bad weekend for us so that he can forgive us for the fact that he, Bill, made us fitted for (but not with) the ability to sin

·         You don’t believe in Bill?  Don’t you realise that sinners will bask in Hell for an eternity?  Stop denying Bill for the sake of your immortal soul!

·         Lots of smart people through the ages have believed in Bill, even some of your scienteristic types, are you trying to tell me that you are smarter than them?  Even Einstein said “Bill does not play Scrabble” and “The Bill I believe in is a type of Bill who isn’t really Bill as most Billeists think of Bill, but a Bill who interacts with the universe in a similar fashion to luminiferous ether, ie not at all”

·         Don’t you come around here asking about Bill, the onus is on you to prove that Bill doesn’t exist and you can’t

·         Look, it’s obvious that Bill exists, he made the village, and us, and you, just last week.  From nothing!  The evidence is all available to you, so long as you don’t let yourself be misled by standard scientific methodology

·         If you really want to know Bill, you should read this book or come to one of our weekly “Let’s Talk about Bill” sessions.  Oh and by the way, don’t read the book literally, you have interpret it.  Actually, now I think about it, don’t read the book, just let me tell you the central message of the book.  Bill exists!  Isn’t that great!

Also say that you notice that the 95 are grouped into quite distinct groups based on the specifics of Bill: what they think that Bill looks like, what and who Bill likes, what Bill’s intentions are, the approved way of holding “Let’s Talk about Bill” sessions, the correct day for holding “Let’s Talk about Bill” sessions and the response to questions (polite disdain, amazement, declaration of crusade/jihad and so on).

Finally, say that not a single one of the 95 is able to lead you to the house where Bill lives.  They can’t show you a photo of Bill.  A team of forensic scientists are called in and no trace of Bill can be found.  The claims made about Bill are investigated and every single phenomenon that is attributed to Bill can be explained by other means.

Who are you going to believe now?

Are you going to believe the 95, many of whom need weekly meetings to remind themselves of their commitment to believing that Bill exists and many of whom, when questioned, reveal that they don’t really know the officially sanctioned details of Bill but do like the general idea of Bill?  Or are you going to believe the two, whose position is entirely consistent with the facts available – or perhaps the three who remain steadfastly agnostic and supposedly will believe in the existence of Bill if and when he turns up?