ANU-Sydney-Kyoto Probability Workshop
Sydney, 29-30 June 2007
Timetable : Abstracts
: Venue : Registration
: Accommodation : Enquiries
Jointly organized by the Australian National University, the University
of Sydney and Kyoto University, this workshop coincides with a visit by
Yasuo Deguchi (Kyoto) and some of his research students.
Timetable
Abstracts
Sleeping Monty
John Cusbert
(Sydney)
I suggest an analogy between the Sleeping Beauty problem and
the Monty Hall problem by constructing a hybrid case. This analogy, if
it holds up, provides a reason for thinking that an apparently
plausible response to Sleeping Beauty might suffer from a similar
defect as a notoriously fallacious response to Monty Hall.
Belief and
Degree of Belief: A Problem with the Lockean Thesis
Weng Hong Tang
(ANU)
Abstract TBA
Evans'
Paradox and Proper Names in Thought: Critical Examinations on Evans'
Theory of Understanding Proper Names
Naoya Fujikawa
(Kyoto)
Evans' theory of
proper names has a paradoxical consequence; some of those who can
perfectly use a proper name to refer to its referent cannot properly
understand statements containing that name. In this paper, I try to
avoid this counter-intuitive consequence by taking into account what
Evans fails to appreciate, i.e., contibutions of social character of
proper names to entertaining thought about their referents we can use a
proper name as a tool for discriminating an object. I also illustrate a
type of thought component, 'proper name concept,' as I call it, that
Evans didn't consider. The proper name concept is object-file that
contains 'decriptions' or 'information' of referent and is connected to
the referent by social convention rather than by any relationships
between its contents and its referent.
Gruesome
Simplicity: A Guide to Truth
Aidan Lyon
(ANU)
Abstract TBA
On Fisher's
Statistical Inference
Kentaro
Yamaguchi
(Kyoto)
R. A. Fischer mathematically formalized the important
statistical methods, e.g. point estimation and scientific test etc. In
them, fiducial argument is especially original idea, which is no
counterpart in other schools of statistics. However, only few attempts
have so far at his conception of statistical inference, for
today's main schools of statistics are Frequentist began by J. Neyman
and E. S. Pearson, and Bayesian by L. J. Savage and D. V. Lindley etc.
while Fisherian school, called Likelihoodist, is minor. For
reasons mentioned above, the purpose of this presentation is to clarify
the significance of fiducial argument in comparison with the
conceptions of probability and statistics in other schools.
On Hume's
Probability
Kazuhiro
Watanabe
(Kyoto)
The aim of this presentation is to reconsider the gap between
the notion of Hume's probability and our modern notion of mathematical
probability. The gap between Hume and us, for example, is as follows.
If we toss a biased coin ten tines and it lands on heads eight times,
we conject (according to the modern notion of probability) the
probability that it lands on heads the next time is 8/10. This is
because we think about the ratio between the number of times the coin
lands on heads and the total number of times the coin has been tossed.
However, as B. Gower suggests, Hume's conclusion would differ from
this. For Hume, what matters when drawing probabilistic conclusions is
the difference between the number of observations favourable to the
intended outcome (landing on heads) and the number of observations
unfavourable to it (landing on tails). Consequently, in Hume's opinion,
the probability of the next coin landing on heads will be 6/10.
In my presentation, first I will outline earlier
investigations in to this topic, and then I aim to explore Hume's
apparently peculiar notion of probability in light of his theory of
belief.
How Are We to
Respond to McTaggart? Defence of Dynamic Conception of Time
Takeshi Sakon
(Kyoto)
McTaggart offered a dynamic conception of time, known as the
moving NOW, but he believed that it cannot be mantained so that time
itself never exists. What he meant to show is as follows: 1) time needs
such a change that what was future is now present and will become past:
and 2) for this to be possible, mutually incompatble tenses of futurity
(will), presentness (is) and pastness (was) are fundemental: but 3)
given the notion of the moving NOW, every event in time has all those
incompatible determinations: therefore 4) the change in question is
impossible, which in turn establishes that time is unreal. The purpose
of this presentation is to defend some dynamic theory of time, an
alternative to McTaggartean notion of the moving NOW. The conclusion
will be that, although not all tensed theories can explain the passage
of time, in some version of open-future theory a dynamic account of
time is feasible without any contradiction.
Diachronic
Dutch books and desire change
Katie Steele (Sydney)
Abstract TBA
Undermining
and the Big Bad Bug
Rachael Briggs
(MIT)
David Lewis's 'Big Bad Bug' aims to show that Humean
Supervenience - 'a claim about the nature of laws' - is incompatible
with the Principal Principle-'a claim about the relationship between
chance and credence.' Lewis's argument relies on the phenomenon of
'undermining': if HS is true, then indeterministic laws of nature
accord themselves probability less than 1. Deterministic laws
also undermine themselves in a sense: if HS is true, then it's
nomologically possible that the deterministic laws be different. Does
deterministic undermining give rise to an analogue of the Big Bad Bug?
I argue that it does not. An explanation of why not illuminates interesting
differences between deterministic and indeterministic laws.
The Lore of
Large Numbers
Mark Colyvan
(Sydney)
In this paper I explore the uneasy relationship between the
law of large numbers and the gambler's fallacy. I argue that there is a
version of the gambler's fallacy that seems to be supported by the law
of large numbers. If I am right about this, then the style of inference
in question is not fallacious. This is good news for those inclined to
fall for this version of the gambler's fallacy (though it's of little
comfort for those of us who fall for gambler's fallacy in its most
general form).
Title TBA
Daniel Parker
(Virginia Tech)
Abstract TBA
The Modal
Interpretation of Algebraic Quantum Field Theory and Reality
Yuichiro
Kitajima (Kyoto)
In order to extend the Kochen-Dieks modal interpretation of to
algebraic quantum field theory, Clifton (2000) determined the maximal
beable algebra for each faithful normal state in a von Neumann algebra
under some conditions. But there are many faithful normal states where
that maximal beable algebra is trivial as pointed out by Clifton
(2000). In the presentation I will examine this problem.
The Lion,
the ‘Which?’ and the Wardrobe: Lewis as a Closet One-boxer
Huw Price
(Sydney)
Newcomb problems turn on a tension between two principles of
choice: roughly, a conflict between reasoning sensitive to the causal
features of the relevant situation, and reasoning sensitive only to
evidential factors. "Two-boxers" are guided by their causal beliefs,
and "one-boxers" by their evidential beliefs.
In this talk I note that a similar issue can arise when the modality in
question is chance, rather than causation. In this case, the conflict
is between a decision rule based on credences guided solely by beliefs
about chances, and a rule based on credences guided by other sorts of
probabilistic evidence. Far from excluding such cases, Lewis's famous
Principal Principle explicitly allows for them, in the form of the
caveat that credences should only follow beliefs about chances in the
absence of "inadmissible evidence".
All parties seem to agree that if we were to be given such inadmissible
evidence -- e.g., by an oracle -- then it would be rational to allow it
to trump our beliefs about chance. I want to suggest (i) that this is
analogous to accepting one-boxing, and hence (ii) that if one-boxing is
really uncontroversial in the case of chance, it should also be
uncontroversial in the case of causation: the orthodox position (viz,
two-boxing for causation, one-boxing for chance) is unstable.
Scepticism,
Knowledge and Context
Sho Yamaguchi
(Kyoto)
I think that there are many things in my surroundings, such as
a desk, a chair, or a person. However, this might be a mere fantasy,
because there remains the uneliminated possibility in which some
malevolent demons deceive me and make me believe that there are indeed
such things, even though this is not really so. This possibility is
truly a far-fetched, but it is a possibility nonetheless.
We should respect and include such an uncommon possibility in
lectures of philosophy, especially epistemology the systematic
exmination of knowledge. It would be inappropriate for students of
philosophy to neglect the possibility of such demons when asked about
the existence of an external world. In short, the possibility must be
considered seriously in the context of philosophy.
However, we should not consider such a possiblity in the court
of justice. Even if an unreliable lawyer claims that all the witnesses
of a crime were decieved by demons and were made to believe that the
accused committed the crime, it will nonetheless be wise to disregard
this possibility; jurors must ignore it in the context of a trial.
We should also not blame philosophers for
mentioning the possibility of deceiving demons. On the other
hand, we should not blame the jurors for ignoring this. However, the
question that arises is whether we can do this consistently. The
problem can be solved with the help of David Lewis' theory of knowledge
and context. In reading my paper, I examine this theory and apply it to
several problems of the same type.
Title TBA
Andy Egan
(ANU/Michigan)
Abstract TBA
The
transcendental character of scientific evidence: a study on probability
theory and
statistical test
Yasuo Deguchi
(Kyoto)
Statistical tests are widely used in many fields of science.
They form the framework within which scientific evidence is first made
possible. But on what evidence, if any, the framework itself is based?
Both Bayesian and classical statistics are based on some claims about
facts or factual claims. Those factual claims are neither supported by
empirical evidence nor established as a priori argument as rational.
They are transcendental rather than empirical, and super-rational
rather than rational or irrational.
Fugitives
from the Law of Averages
Roy Sorensen
(Dartmouth)
In the short story “The Law” Robert M. Coates describes a
breakdown of the law of averages. There are traffic jams at midnight,
runs on food items, and theatres alternate erratically between being
empty and full. Congress steps in to force people to behave as if the
law of averages works. The story seems to show that we can faultlessly
conceive a break down of the law of large numbers. So if conceivability
implies possibility, then this mathematical law is contingent. The
story also suggests that empirical evidence can refute a mathematical
law. I relate these ideas to the more familiar issues raised by
probabilistic laws.
Hybrid
Formalism for Topological Space
Katsuhiko Sano
(Kyoto)
We consider hybrid logic from the viewpoint of topological
space in a broad sense, which inlcudes David Lewis's system of spheres
for counterfactual conditionals [Lewis 1973]. Hybrid logics, whose
roots trace back to A. N. Prior, are extended modal logics with a new
sort of propositional variable: "nominals" (semantically, names for
possible worlds). First, we introduce hybrid formalism and its
topological semantics, and explain its advantages over modal formalism.
Second, we reveal the connection between hybrid formalism and David
Lewis's countefactual logic. Finally, we provide Hilbet-style
axiomatizations for logics of our formalism and establish their
completeness and decidability.
The World
According to De Finetti: Ope-rationality
Joseph Berkowitz
(Sydney)
Bruno de Finetti is one of the founding fathers of the
subjectivist school of probability, where probabilities are interpreted
as rational degrees of belief. His work on the relation between the
axioms and theorems of the probability calculus and rationality is
among the corner stones of modern subjective probability theory. De
Finetti maintained that rationality requires that an agent’s degrees of
belief be coherent. A common view has it that degrees of belief are
coherent only if they are represented by a probability function. I
propose that de Finetti had a different view: an agent’s degrees of
belief are coherent if they could be represented by a set of
probability functions, each of which corresponds to a subset of the
agent’s degrees of belief in events that can (in principle) be jointly
verified. On this view, coherence imposes weaker constraints on degrees
of belief.
This qualification of the common notion of coherent degrees of
belief may seem insignificant. Yet, as I argue, it has implications for
subjective interpretations of quantum probabilities, which have become
very prevalent. Discussions of non-locality in the EPR experiments
focus on the probabilities of ‘incompatible’ properties, which cannot
be jointly verified. The assumption that in this experiment, there is a
single probability distribution over the dispositions of particles to
display these properties on the corresponding measurements entails
certain probabilistic inequalities, the so-called ‘Bell inequalities’.
These inequalities are violated by quantum mechanics. Thus, if
representing degrees of belief by a single probability function is a
necessary condition for coherent degrees of belief in these
dispositions, agents will necessarily have degrees of belief that
contradict the quantum-mechanical predictions. On the other hand, since
incompatible properties cannot be jointly verified, on my
interpretation followers of de Finetti’s theory are not committed to
such inequalities. Accordingly, unlike followers of the standard
interpretation of de Finetti theory, one may believe that the
dispositions to display incompatible properties in EPR experiments
exist before the measurements and are reliably reflected in the
statistics of the measurement outcomes.
Dutch -Book
Arguments Against Using Conditional Probabilities for Conditional Bets
Keith Hutchison
(Melbourne)
Suppose a gambler is betting against a bookie on the outcomes
of some chance process, and offers the betting ratio p(A) for each
outcome A. It is often argued that if the gambler uses the
standard conditional probability p(A&B)/p(B) for bets on A that
proceed if and only if B is found to be true, then his conditional bets
cannot be used by the bookie to generate a synchronic dutch book.
This result, however, is often interpreted epistemically, as
applying equally to bets that proceed if and only if B is ascertained
to be true. I show here that this generalisation of the result is
definitely false. I do this by displaying some dutch books that such a
strategy makes available to the bookie. All the bookie has to do
to guarantee himself a win is a tiny bit of elementary arithmetic, to
find the right stakes for 3 bets: the conditional bet; one against
A&B; and one on B. This is true even if the gambler’s original
credences are totally coherent, and also when they agree with what
would be widely recognised as the objective chances.
[back to
timetable]
Arrows and
Haloes: Probabilities of Conditionals and Desire-as-Belief
Alan Hájek
(ANU)
I will argue that two seemingly disparate debates turn out to
be closely related.
The first debate concerns probabilities
of conditionals. A number of authors, including Stalnaker and
Adams, have defended versions of the hypothesis that probabilities of
conditionals are conditional probabilities:
P(A --> B)
= P(B|A), if P(A) > 0.
The left-hand side is the probability of ‘if A, then B’; the right-hand
side is the usual conditional probability of B, given A. The
hypothesis, if true, would greatly illuminate the truth-conditions of
conditionals, long recognized to be recalcitrant beasts. A large
literature, initiated by David Lewis’ ‘triviality results’, has argued
that no interesting version of the hypothesis is true. I will survey
this literature and add some results of my own.
The second debate concerns desire as
belief. Lewis formulated and rejected an anti-Humean
thesis that desires are reducible to beliefs along the following lines:
des(A°) = P(A).
The left-hand side is the expected value of A, familiar from decision
theory; the right-hand side is the probability of a proposition that
might be understood as ‘A is good’.
The hypothesis, if true, would shed light on the nature of mental
states, their role in motivating rational action, and it would have
important implications for metaethics. Again, Lewis initiated a
considerable literature of negative results, and I will survey this
literature and contribute to it.
I will show that the two debates are strikingly parallel, and thus that
moves and counter-moves in one can be mimicked in the other. This is
illuminating in itself, and it allows one to see in advance how the
next epicycles of these debates will likely play out.
The
Statistics of Medical Randomized Control Trials are seriously
misleading and may be badly damaging medical research and practice
Neil Thomason (Melbourne)
In medical research, Randomized Control Trials (RCTs) are
regarded as the Gold Standard. They are not (or else, Gold isn't
all that its made out to be).
A crucial goal of any medical RCT should be to
answer the question: "If the patient were to undergo this
intervention, what would the effects probably be?" (Of course,
there are other important questions as well, e.g., "What percent of the
patients would actually comply with the regimen and to what degree?")
With animal RCTs, the experimenter can ensure that the
"subjects" follow the protocols. Thus, in animal RCTs, the
statistical analyses are relatively straightforward, essentially
comparing the results of the
ntervention arm directly to that of the placebo arm.
However, in most human RCTs, the statistical
challenge is much greater because many people don't follow the
protocol. To get around this, medical researchers do not
standardly compare patients who have followed their assigned protocols.
Instead, the standard technique is Intention-to-Treat (ITT)
analysis, which includes people who did not comply with the protocol to
which they were assigned. As a result, ITT analyses generally
underestimate a drug's therapeutic effects and overestimate its safety.
The
Relativity of Subjective Conditional Probability
Kenny Easwaran (ANU)
Abstract TBA
Venue
The conference will be held in the Main Quad Refectory (A14)
of the University of Sydney. A
map with directions to the Refectory is available here.
Registration
The workshop is free but advanced
registration is required for
catering purposes.
To register, simply send an email to john.cusbert@gmail.com with
the subject line "Please register me for the Probability Workshop"
(two-click
registration here).
Accommodation
There is plenty of accommodation within walking distance of
the University of Sydney. See below for a special conference deal.
|
The Haven Inn Sydney |
Special conference rate
of $109 per night!
|
Enquiries
Please direct all enquiries to John Cusbert at the following
email address:
john.cusbert@gmail.com