Re: Underdetermination and Scientific Realism

[Andrew Bacon <andrew.bacon@lmh.ox.ac.uk>]

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OK, I've come into this debate a bit late so you'll have to bear with me. 


1. UT clarification
2. Realism - metaphysical or epistemological thesis?

===


1. In his original e-mail Tasker denies UT on the basis that under a certain
reading of 'equally well supported by the evidence' you can categorically
specify the universe.

This sounds like an equivocation to me, so I'll try and give a more precise
definition of 'equally well supported by evidence' in terms of 'empirical
equivalence' which I believe is how the thesis is usually described, and
hopefully show how UT is true.

Definition: Two possible worlds are empirically equivalent iff there is no
possible observation which a human could perform which would distinguish the two.

Roughly these two worlds generate the same observable events, but may differ in
unobservable ways. I mention humans since for example God if s/he exists
presumably has a 'birdseye view' of the world. Denote empirical equivalence of w
and w' as w ~ w'. UT then states |[w*]| > 1 (the equivalence class of the actual
world is non-trivial). The stronger claim is that |[w*]| is greater than or
equal to aleph-0.

To show that UT is in fact correct I shall give three examples (my own examples
- so no guarantees of quality).


a) Topologically circular time vs. repeating event series. This example I think
best highlights the idea behind UT. Imagine a world where time is loops back on
itself (so every event in it is before itself - this will look like a circle if
you draw a visual aid). Now take the the event series in this world and paste an
infinite amount of copies of this series into a world where time is linear
(looks like a line when drawn out). These two worlds are topologically (hence
metaphysically) different, yet the event series is the same, in particular the
observable events are the same. Note: we must reject the principle of identity
of indiscernables or relationism with respect to time (i.e. adopt substantival
time) if this is a genuine metaphysical possibility - this is not a problem
however, since these two options seem incompatible to me anyway.

b) Time (or space) is dense vs. time (or space) is continuous. That is, the
timeline is either isomorphic to Q (the rational numbers) or it is isomorphic to
R (the real numbers). These two hypothesis are empirically equivalent. Since our
measuring instruments may only ever record a rational number (finite decimal
place accuracy) there is no possible experiment that would tell us which is
true. (Note: our theory of differentiation and integration over variables such
as time or distance would have to be replaced with difference equations.) Note
also that the hypothesis that time is discreet is not empirically equivalent to
these two, while there is no experiment that could disprove time is discreet
this is only half of the equivalence. There are experiments that could prove
time is discreet, namely finding the smallest unit of time or length.

c) The Copenhagen interpretation of QM vs. the Bohmian interpretation. Again
similar argument - this one is, however, a real conflict between scientists. One
interpretation takes quantum particles to supervene on their probability
distribution over space and time, the other postulates particles (with hidden
variables) on top of this.


In defence of the stronger version of UT (|[w*]| >= aleph-0) Putnam has put
forward two very interesting arguments. These arguments probably go further than
UT, and would probably be best called IR (indeterminacy of reference). 

His first argument goes as follows. Given any theory (scientific or what have
you - the only stipulation is that, when formalised, the language contains more
than one name/predicate used) there are many isomorphic models, these can be
obtained by permuting the referents of each term. For finite domains with n
named elements there are n! isomorphic but distinct models for the theory, for
infinite domains, many more.

His second argument goes even further, it says for any theory (with certain
stipulations) there are infinitely many *non-isomorphic* models. This relies on
a result in mathematical logic called the Lowenheim-Skolem theorem, which says
any countable first order theory with an infinite model, has a countable model,
and a model of size K for each infinite cardinal K. Since these models have
different cardinalities there's no way they can be isomorphic. This means that
any scientific theory which is firstorderizable (yes it's a word, cf Boolos) is
not categorical (and  I think it is a fairly reasonable assumption to suppose
that a scientific theory should be firstorderizable). 


2. In response to Andy Stephenson he also says:

"I think you conflate the ontological and epistemological claims of scientific
realism. It?s true that UT does not challenge the existence of the unobservable
world, but this does not contribute anything to our epistemological
predicament. "

I am under the impression that 'realism' is a *metaphysical* thesis - namely the
thesis that there is a real world, the world that our scientific theories
aproximate. Realists are not committed to the further claim that all these facts
are accessible to us. If the realist epistemology was that all the metaphysical
facts are discoverable empirically then they are in deep shit (I am ignorant of
the literature so I thankfully know of no-one who holds this view).


 "The problem that i think remains, and which this version of UT brings out
nicely,  is the justification for issues such as beauty, ellegance etc as
reason to choose between supposedly valueless theories. If issues such as these
are all that can be relied upon to choose a theory then the theories are
extremely value laden, and this brings problems for the scientific reaslist
stance."

This is a problem for scientists not philosophers. As a philosopher I believe
that there is a metaphysical reality out there, but I must remain agnostic as to
which one it is. 

As for superstring theorists, twistor theorists, quantum loop gravity etc...
they may think they are doing physics but they are not! They are doing metaphysics.


-- 
Andrew Bacon
Lady Margaret Hall
07830048336
http://users.ox.ac.uk/~lady1900



> To reply to this message or start a new topic please email: BUPS-DIS@bups.org
> 
> 
> 
> 
> Much attention has been given to defending scientific realism from the
> underdetermination thesis (UT), while the truth of the thesis itself seems to
> have been accepted as obviously true. I believe that UT is often expressed
> ambiguously, and that shoring up the thesis in such a way that it poses a
> genuine challenge to realism renders it beyond rational defence.
> 
>      Scientific realism: the doctrine that there exists a world beyond our
> observation which it is the aim of science to correctly describe, and that it
> is generally successful in doing so. Moreover, we are capable of discerning
> when a theory is correct in describing the unobservable world.
> 
>      The underdetermination thesis: for any given scientific theory, t, there
> will be an indefinite number of theories which are incompatible with t, and yet
> which are equally well supported by the evidence as t. UT is supposed to
> threaten realism since we can never be in a position to know that we have
> thought of the correct theory.
> 
> The problem with UT is that the phrase ?equally well supported by the evidence?
> is ambiguous. One popular suggestion is that a theory is supported by observed
> instances of its empirical consequences. So, for example, the theory that water
> boils at 100 degrees implies that this pot of water should boil when it reaches
> 100 degrees. When this event is observed, then we have a confirmatory instance
> of the theory. The assumption here is that ?positive instance? = ?confirmatory
> instance?. Given this assumption, I think UT does pose a challenge to realism.
> Unfortunately for UT, this just isn?t how science works.
> 
> I assert (a) that not all positive instances of a theory are confirmatory, and
> (b) that not all confirmations of a theory come from observations of its
> positive instances.
> 
> Argument for (a): imagine you and I are sitting by a duck pond. I notice that
> all the ducks in the pond are male, and I hypothesise that all ducks in the
> world are male. Naturally you ask me to support my hypothesis. I reply that all
> positive instances of a theory are confirmatory, and therefore, the very same
> ducks which initially prompted my hypothesis count as good evidence for it.
> 
> Argument for (b): scientists take into account other virtues when assessing
> theories, e.g. coherence with other theories, consilience, predictive power, no
> ad hockery.
> 
> So just because two theories have the same empirical consequences, that doesn?t
> mean that they are equally well supported. If the argument against realism is
> to have any force it must assert that there will be an indefinite number of
> equally well supported theories, when ?support? is defined in the way I have
> gestured towards. But the arguments one tends to encounter for UT entitle it to
> a much cruder definition of ?support?, a definition which assumes that all and
> only positive instances of a theory are confirmatory. 
> 
> Take for example the Kripkensteinian argument about rule following. For any
> sequence of numbers there will be many different functions which describe
> different ways of continuing the sequence, and which are equally well supported
> by the original sequence. However persuasive this reasoning may be in
> mathematical examples, this way of justifying UT seems to assume the fallacious
> principle of confirmation which I diagnosed above.
> 
> Does anyone know a better way of arguing for UT ? one which better approaches
> the true nature of confirmation in science?  
> 
> 
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