1. Critique
Issue 1, Michaelmas 2016
Published by the Durham University Undergraduate
Philosophy Society

2. Editor’s Preface
I would like to welcome you all to the newly launched (rebranded) undergraduate philosophy journal,
Critique, published by the Durham University Undergraduate Philosophy Society. It is a great honour
(not to mention a pleasure) to get to read and publish some of the finest work our undergraduates have to
offer. I have tried to keep this first edition short in order to highlight the main focus of the journal—the
publicationofstudent workwhich deservesto(and might not otherwise)reach awideraudienceofstudents
and academics. Below, you will find discussions of causality, depression and possible worlds. Aside from
the spectrum of topics covered, the style reflects another well-entrenched virtue in the Philosophy
department at Durham:methodological pluralism. Or, to avoid the jargon, an open minded approach to
philosophising. I was struck by this incisive passage by Stanley Cavell whilereceiving my first submissions
to the journal, it is a long quote but one well worth reading more than once:
“[I]t seems to me commonly assumed among the serious philosophers I know that whenthey look
into a new article they will find not merely a number of more or less annoying errors, but that
they will find thewholeeffort fundamentally wrong,insensibility ormethod orclaim.Evenwhen
it is good—that is, when it contains one interesting or useful idea—the interest or usefulness
cannot simply be taken over as it stands into one’s own thought, but will require independent
development or justification from withinone’sown procedures. It often happens that what makes
an article or passage famous is its enunciation of a thesis which theprofession is fully prepared to
annihilate. The refuting of Mill on “desirable,” or Moore on “indefinable,” or Wittgenstein on
“private language,” have become private industries,established more than one living. These can
be disheartening facts, especially among the young who are entering the profession and still
deciding whether it can support life—as though the profession as a whole has forgotten how to
praise, or forgotten its value.”1
I hope, in the short time I will be in charge of thispublication, that this journal canserve as praise for those
published and asa demonstration of thevalue of philosophising for those lucky enough to read it.Looking
to the future, (against Cavell’s disheartening facts and in line with the pluralismI spoke about above) I will
be interviewing local lecturers to document and disseminate theirexciting work to a wider audience,so it
is worth keeping an eye on our Twitter for updates on future issues:@DUPS_Critique.
Finally, I will end with some administrative duties. Any and all requests for reproduction of the work
contained in thisjournal should be addressed to nathan.davies@durham.ac.uk.Any submissions for future
issues should also be sent to the same e-mail. Criterion for submission of essaysis that they are under5000
words and must have received a first, as for other contributions(poems, short stories etc.) the word limit
is the only criteria.
Thank you for reading, I hope you enjoy it.
Nathan Davies
1
Cavell, Stanley. (1976) ‘Must we mean what we say?’, Cambridge University Press. pp.xx-xxi
1

3. Contents
“Why is there something rather than nothing?” Is this a meaningful question? Do you think this
question is answerable?
Daniel Foggin p.3
Depression and the Phenomenology of Intersubjectivity: A Gadamerian approach to depression
Constantin Mehmel p.10
Illustrating Pearl’s Approach to Causality by Examples, and Responding to Cartwright’s
Criticisms
Kim Tullar p.17
2

4. “Why is there something rather than nothing?” Is this a meaningful
question? Do you think this question is answerable?
Daniel Foggin
Introduction
In this essay I will begin by arguing that “why is there something rather than nothing?" (WSR) is a
meaningful question to ask as it is not able to be dismissed on the groundsof it being senseless,dispensable
or insoluble1
,which I offer as my definition of meaningfulness (and in the processI forgo the question of
answerability).I will thenpresent possible answers to the question, focussing on the egalitariantheories of
Robert Nozick and Peter van Inwagen. I will argue that the probability distributions they wish to use are
not valid for infinitely many possible worlds in their current formulation, and conclude that if an
egalitarian theory is to succeed in convincing us of why there is something rather thannothing, it is with
a large, bounded number of possible worlds.
Is the question meaningful?
There are many ways by which we can determine whether an utterance, such as an utterance of WSR, is
meaningful or not, though I do not wish to wade through the theories here. Instead,I will outline A. R.
Lacey's argument to show that WSR should not be dismissed at face value, and assume that thisis in and
of itself an appropriate ground to claim that the question can be asked meaningfully. In Robert Nozick,
Lacey claims that WSR is “rarely discussed by philosophers,partly becauseit is often assumed to be either
senseless, or dispensable, or insoluble. It might be thought senseless by someone who thought ... that we
cannot understand a question unless we know what would count as an answer to it”.2
While we do not know what would definitively count as an answer to such a question, there has been
sufficient investigationinto what might count for it to not seem senseless. Indeed, if it were senseless, we
would struggle to even comprehend what was being asked (as opposed to feigning confusion or calling for
‘therapeutic’ chargesof senselessness).He continues “the questionmight be thought dispensable if it were
a necessary fact that there is something,although thiswould need to be shown”.3
Since it is not apparent
that it is necessary that thereis something, the meaningfulness of the question cannot bedismissed on the
grounds of dispensability. Or, if it is a necessary fact that there issomething, it doesnot seemimmediately
apparent, and an explanation of such a fact would thenguarantee that thequestion was meaningful.
1
(Lacey, 2001)
2
(Ibid, p.177)
3
(Ibid)
3

5. Finally, “if a problem is known to be insoluble,like that of squaring the circle, or trisecting an angle using
only ruler and compasses, we would indeed waste our time trying to solve it, but might still be left
philosophically puzzled and unwilling to dismiss it as senseless”.4
In this last case, the question does not
seem initially insoluble as it is not paradoxical. Furthermore, it has not been proved that it is impossible
for an answertoexist in theway that Lacey'sexampleshave.Trying toprovethat ananswertothisquestion
is not possible would still require a level of philosophical investigation that we can understand to be
meaningful. The investigation that showed the problemof squaring the circle to be insoluble resulted in
thediscovery that 𝜋𝜋 isnot only irrational but transcendental —by nomeansatrivial or meaninglessresult.
I will therefore maintain that this question fulfils the definition of meaningfulness because it has been
shown that it isn’t senselessor dispensable,and if it is insoluble it’s not altogether clear that this means it
isn’t worth trying to answer it (which would presumably be the only interesting practical consequence of
labelling it ‘unanswerable’).GiventhislatterclaimIwill adoptaliberal attitudetowardattempted ‘answers’
to the question in order to see what we can learn from discussing them. So I will now move straight to
discussing proposed ‘answers’ to thequestion.
Possible answers
Robert Nozick's5
first discussionabout answerstotheWSR concernsinegalitariantheories:“theyhold that
one situation or a small number of states 𝑁𝑁 are natural or privileged and in need of no explanation”.6
This
concept of holding certain states of affairs as natural is common among theories such as Newtonian
mechanics, where rest is the natural state.7
Such theories are “especially well geared to answer questions of
the form “why is there X rather thanY"”.8
It is understandable that, in trying to answer the title question,
we would first explore an inegalitarian theory as the question is of a form that presupposes an inegalitarian
state of affairs: embedded in the structure of “why is there something rather than nothing?" is the
supposition that it is unusual that there is something, as if we would expect nothing in the absence of any
‘force’ (or reason). Nozick's exploration of how something could be produced from a privileged nothing
state9
has been widely dismissed, with Smith describing it as “quite absurd, standing as littlemore than an
imaginative play on words”.10
Inegalitarian theories will always rely on states that require no explanation,
which can easily be seen as problematic, given that we would need to be able to explain why certain states
require no explanation. It is for this reason that an egalitarian theory is considered.
Nozickcreateshisegalitariantheoryby applying “aversionoftheprincipleofindifferencefromprobability
theory”11
to ways that might obtain. The principle of indifference, according to Keynes, who coined the
term, “asserts that if there is no known reason for predicating of our subject one rather than another of
4
(Ibid)
5
(1981)
6
(Nozick, 1981, p.121)
7
(Ibid)
8
(Ibid)
9
(1981, p.122)
10
(1987, p.6)
11
(Nozick, 1981, p.127)
4

6. several alternatives, then ... the assertionsof each of these alternatives have an equal probability”.12
Nozick
implicitly commitshimself to the claim that it is unknown to us how it is decided what obtains, as this is
a precondition for the application of the indifferenceprinciple.
Nozick claims that “there are many ways 𝑤𝑤1, 𝑤𝑤2 … for there to be something, but there is only one way
𝑤𝑤0 for there to be nothing”13
, and then asks us to “assign equal probability to each alternative possibility
𝑤𝑤𝑖𝑖 assuming it is a completely random matter which one obtains”.14
However, depending on how we are
to interpret “many ways 𝑤𝑤1, 𝑤𝑤2 …” Nozick's proposed probability distribution could be problematic. It is
possible that the ‘many ways’ Nozick is referring to is some arbitrarily large number 𝑁𝑁, which we may not
know, but we could at least bound. If this is the case,then 𝑃𝑃(𝑤𝑤𝑖𝑖), the probability of way 𝑤𝑤𝑖𝑖 being the way
the world obtains, is equal to 1/𝑁𝑁, as we are assigning equal probability to 𝑁𝑁 many ways, which is well
defined under the axioms of probability. (A simple illustration of uniform probability over 𝑁𝑁 many ways
can be given by considering a fair 6-sided dice, where the probability of a certain face landing face-up is
1/6, as there are 6 ways).
However, the common mathematical interpretation of ‘𝑤𝑤1, 𝑤𝑤2…’ would bethat there are infinitely many
ways. (Indeed, if Nozick was meaning to refer to some arbitrarily large number, 𝑁𝑁, of possible worlds,the
more conventional notation would be ‘𝑤𝑤1, 𝑤𝑤2 … 𝑤𝑤𝑛𝑛’).In this instance, assigning equal probability to each
alternative is not well defined. Intuitively, using 𝑃𝑃( 𝑤𝑤𝑖𝑖) = 1/𝑁𝑁, we find that the probability of the i-th
way-the-world-could-be, being the one which actually obtains, is equal to zero. This is because we would
have lim
𝑁𝑁→∞
𝑃𝑃( 𝑤𝑤𝑖𝑖) = lim
𝑁𝑁→∞
1
𝑁𝑁
= 0. (This limit notation is necessary to speak meaningfully about infinity.
The first equality is true by our definition of the probability of it being the i-th way that obtains,and the
second equality is a basic result from analysis).15
Before offering a more comprehensive proof of why it is not possible to distribute probability in this way,
there are some assumptions being made about the nature of ways (that might obtain) that are worth
justifying, though I believe that Nozick would have no reason to disagree with these assumptions. Firstly,
ways are being treated as discrete.‘Discrete’ is being used to say that there can only be a whole number of
ways, not that different ways have no similar properties (they are numerically distinct, not necessarily
distinct in content).This is becauseit is not sensible to speak of there being ‘eleven-and-a-half ways’ that
might obtain(afractional numberofways),or4√2 waysthat might obtain(anirrational numberofways).
Secondly, it is not sensible to speak of −17 ways that might obtain (a negative number of ways) despite
−17 being understandable as a ’whole’ number of ways.Because of this,the only meaningful value we can
assign to the number of ways that might obtain (𝑛𝑛) is a natural number, i.e.such that 𝑛𝑛 ∈ ℕ. (Here I will
understand the set of natural numbers as {0,1,2, …}, the reason I adopt the non-negative integer set is
because even though the ‘nothing-way’ counts as one way the world could be, which is different from
12 (1929, p.42)
13
(1981, p.127)
14
(Ibid)
15
See (Sutcliffe, 2014,p.31) for a discussion of the basic result.
5

7. saying there are no ways the world could be, Nozick uses ‘0’ in his subscript to denote the nothing-way.
Nothing hingeson how we assign the symbols to the ways16
).
It is worth making clear my motivation for understanding the number of ways that might obtain as the
naturals ℕ, rather than any other set. Uniformprobability over any set reaching from −∞ to ∞, including
therealsℝ,is not well defined.However,uniformprobability overacompact interval [𝑎𝑎, 𝑏𝑏] iswell defined,
and because of the completeness of ℝ, there are infinitely many elementsin such a compact interval. It
may be possible to map an infinite number of ways that might obtain, or possible worlds, onto such a
compact interval where the probabilities at hand are well defined. However, it is clear that Nozick has
made no such attempt and so I shall now formulate a more comprehensive proof of why the probability
distribution he has actually proposed is not well defined. Theaxioms of probability are given by Borovkov
as follows17
:
1. 𝑃𝑃(𝜔𝜔) ≥ 0
2. 𝑃𝑃(Ω) = 1
3. 𝑃𝑃(⋃ 𝑤𝑤𝑖𝑖
∞
𝑖𝑖=0 ) = ∑ 𝑃𝑃(𝜔𝜔𝑖𝑖)∞
𝑖𝑖=0
Where Ω is the entire samplespace.
In our case, Ω is the set of all possible ways { 𝑤𝑤0,𝑤𝑤1, 𝑤𝑤2 …} that might obtain. In asking us to assign equal
probabilitytoeach alternativepossibility,Nozickiscommittingustoaprobabilitydistributionthatviolates
the axioms of probability as follows:
• By the principle of indifference, let the probability that the i-th possible world obtains 𝑃𝑃(𝑤𝑤𝑖𝑖)be
such that 𝑃𝑃( 𝑤𝑤𝑖𝑖) = 𝑝𝑝, for some 𝑝𝑝 ≥ 0 (in accordance with thefirst axiom).
• We know that Ω = { 𝑤𝑤0,𝑤𝑤1, 𝑤𝑤2…} = ⋃ 𝑤𝑤𝑖𝑖
∞
𝑖𝑖=0 (this is true analytically, they are merely different
ways of writing the same set)
• By thethird axiom, 𝑃𝑃(⋃ 𝑤𝑤𝑖𝑖
∞
𝑖𝑖=0 ) = ∑ 𝑃𝑃(𝑤𝑤𝑖𝑖)∞
𝑖𝑖=0 = 𝑝𝑝 + 𝑝𝑝 + 𝑝𝑝 + ⋯(again,thisistrueanalytically,
the sigma notation being used here simply says that we should sum all of the individual
probabilities)
• We now have two cases to consider:
If 𝑝𝑝 > 0, 𝑝𝑝 + 𝑝𝑝 + 𝑝𝑝 + ⋯ = ∞
If 𝑝𝑝 = 0, 𝑝𝑝 + 𝑝𝑝 + 𝑝𝑝 + ⋯ = 0
16
This treatment was prompted by a discussion with the editor. The editor would also like to apologise for the pun.
17
(2013, p.13)
6

8. Neither situation is able to fulfil the second axiom (that is that there does not exist a 𝑝𝑝 ≥ 0 such that
𝑝𝑝 + 𝑝𝑝 + 𝑝𝑝 + ⋯ = 1) meaning the distribution is not valid. It is important to note here that I am not
claiming that conventional axioms of probability hold over all possible worlds. However, since Nozick’s
egalitarian argument18
relies on conventional probability axioms to arrive at his conclusion, this invalid
distribution is problematic.
Peter van Inwagen also explores possible answers to the question in ‘Why isthere anything at all?’, arriving
at an egalitarian theory similar to Nozick’s whose four premises are as follows19
:
(i) There are some beings;
(ii) If there is more than one possible world, there are infinitely many;
(iii)There is at most one possible world in which there are no beings;
(iv) For any two possible worlds, the probability of their being actual is equal.
van Inwagen explicitly states that infinitely many possible worlds are part of his argument, leaving his
egalitarian theory open to the same probabilistic criticism that Nozick’s has just been subjected to.
However, despite this, van Inwagen provides a good response20
to a further criticism from probability
theory. Allow it to beassumed that theaxioms of probability are not violated asthey were before. The sum
of the probabilitiesof all possible ways is such that ∑ 𝑃𝑃( 𝑤𝑤𝑖𝑖) = 1∞
𝑖𝑖=0 and the probability of a specific way
𝑤𝑤𝑖𝑖 being the way that obtains is still 𝑃𝑃( 𝑤𝑤𝑖𝑖) = 1/𝑁𝑁. Thenthe probability that a something-way obtains is
1 − 𝑃𝑃(𝑤𝑤0), where 𝑤𝑤0 is the single nothing-way. For an arbitrarily large 𝑁𝑁, the probability that a
something-way obtains is 1, as 𝑃𝑃( 𝑤𝑤0) = 0. But then do we not have the problem that the probability of
any particular way obtaining is also equal to zero? van Inwagen uses a dart board analogy to illustrate this
obscure result: “the probability of a dart’s hitting any particular point on a dart board is 0”21
, yet it is
obvious that it is not impossiblefor a dart to hit a dart board. This is because an event having probability
equal to zero is not equivalent to that event being impossible.Analogously,the probability of any specific
possible world being the one that obtains is 0, but this is not to say that it is impossible for anything to
obtain. If we were to formulate an egalitarian theory where possible worlds are mapped to ℝ as suggested
earlier, this could explain how it is that anything can obtain at all.22
However, van Inwagen’s egalitariantheory of why there is anything at all is still mathematically invalid
because his premises guarantee there being infinitely many worlds with equal probability of their being
actual. If there is to be an egalitariantheory that holds water,then, it is one where thenumber of waysthat
might obtain is bounded. This bound cannot simply be arbitrary if it is to exist. van Inwagen gives the
following defence of his second premise: “it may be pointed out that if there is more than one possible
world,thenthingscanvary;and it seemsbizarretosuppose,giventhekindsofpropertieshad by thethings
we observe, properties that seem to imply a myriad of dimensions along which these things could vary
18
(1981, p.127)
19
(1996, pp.95-96)
20
(1996, p.99)
21 (Ibid)
22 I will not pursue this line of thought in this criticism.
7

9. continuously,that there might be just two or just 17 or just 510 worlds”.23
A priori, it doesseem asthough
infinitely many possible worlds is the more believable option.However, it may be possible to ascertain our
bound by other means. Cliff has spoken about24
the input of theoretical physics in the discussion of why
there is something rather than nothing: “It has been estimated that there are 10500 different versions of
string theory. Each one would describe a different universe with different laws of physics”.25
Even though
10500 is an incomprehensibly large number, it would still successfully act as a bound to the number of
possible worlds that could thenbe used in egalitarian probability calculations.
Conclusion
To conclude, WSR is certainly a meaningful question as far as the definition offered here is concerned. It
has been argued that given our lack of knowledge regarding how it is decided which way obtains, an
egalitarian theory is more convincing than an inegalitarian one. However, there are some serious
probabilistic issues with infinite numbersof possible worlds, an assumption made use of in both Nozick’s
and van Inwagen’s answers.Ultimately,if an egalitarian argument is to succeed in convincing us that it is
more probable that there is something than nothing, then it is to do so by taking there to be a large, but
bounded, number of possibilities.
23 (1996, p.101)
24 (2015)
25 (Found at 8:27 in 2015)
8

10. Bibliography
Borovkov, Alexander A. (2013) ‘Probability Theory’, London: Springer.
Cliff, Harry. (2015)‘Have we reached the end of physics?’, (Online)Availableat:
http://www.ted.com/talks/harry_cliff_have_we_reached_the_end_of_physics/transcript?language=en
(Accessed 2 March 2016)
van Inwagen, Peter, and Lowe, E. J. (1996) ‘Why is there anything at all?’, Proceedings of the
Aristotelian Society, Supplementary Volumes, Vol. 70, pp.95-120.
Keynes, J. M. (1929) ‘Chapter IV: The Principle of Indifference’, in A Treatiseon Probability. London:
Macmillan, pp.41-64.
Lacey, A. R. (2001) ‘Chapter VII: Metaphysics II: Explaining Existence’,in Robert Nozick. Chesham:
Acumen, pp.177-187.
Nozick, Robert. (1981)‘Why is there something rather than nothing?’, in Philosophical Explanations.
Oxford: Clarendon Press, pp.115-164.
Smith, Joesph Wayne. (1987)‘Essays on UltimateQuestions’, Aldershot: Avebury.
Sutcliffe, Paul. (2014)‘Calculus’, (Online) Available at:
http://www.maths.dur.ac.uk/~dma0pms/calc/notes.pdf
(Accessed 2 March 2016)
9

11. Depression and the Phenomenology of Intersubjectivity: A Gadamerian
approach to depression
Constantin Mehmel
Introduction
This paper attempts to sketch a phenomenological account of impaired intersubjectivity in depression.
Depression, I propose, can be framed as a ‘dialogical’ illness in that it fundamentally alters the way one
relates to other people and the presupposed shared background.I therefore argue that depression entails
what I call an altered ‘experience of the Other’. In order to understand how depression alters the
phenomenology ofintersubjectivity,IdrawonGadamer’sphenomenologyofunderstanding viathefusion
of horizons. I begin by sketching a Gadamerian perspective of an intact dialoguebetween two people. The
rest of thepaperisthendedicated tounderstanding thedifferingformsofdialoguethat occurindepression.
Gadamer on Dialogue
In order to portray an intact experience of the Other, and the phenomenology of intersubjectivity more
generally, we need to set out how understanding normally takes place between two people.For, I suggest,
that our experience of the Other (hereafter synonymousto ‘another person’)is inextricable from coming
to understand the Other and her claim regarding the mutual subject matter at hand. In other words, a
failure in understanding can explain our diminished experience of the Other,something key to depression
as I will show later on. To establish such an intact dialogue, we can turnto Hans-Georg Gadamer and his
phenomenology of understanding via the fusion of horizons.According to Gadamer, the starting point for
any dialogue between two people is that each interlocutor enters the dialogue from within a unique
horizon. Denoting “the rangeof vision that includes everything that can beseen from a particular vantage
point”1
, a horizon structures one’s experience of the Other. I bring along certain “tacit expectations of
meaning and truth”2
, through which I perceive the Other and her claim regarding the subject matter. In
light of this, it would be wrong to understand a horizon as a necessarily restrictive force. Although it does
limit our perception of possibilities, it provides at the same time the very conditions whereby we can
experience the Other in the first place.3
In fact, a horizon is not closed off, but rather open towards new
experiences. As Gadamer puts it,“[a] horizon is not a rigid boundary but something that moves with one
and invites one to advance further”.4
Whenever I experience something new, my horizon is expanding.
1
(GW1, p.307;TM, p.301), references to primary sources by Gadamer are given according to abbreviations listed
in the bibliography.
2
(Garrett, 1978,p.393)
3
see (GW2, p.224; PH, p.9)
4
(GW1, p.250;TM, p.238)
10

12. Underlying such openness, we can identify a more far-reaching claim that my horizon does not exist
independently from the Other’s horizon, but rather that both belong to a more fundamental, shared
horizon.5
Gadamer thus appears to advance the Heideggerian notion that we are always already in relation with
others, something that is crucial for our project of a phenomenology of intersubjectivity.Although both
interlocutorshaveauniquehorizonand thusexperiencethesubjectmatterdifferently,theyarenonetheless
attuned to each Other. This holds true regardless of whether or not the different perspectives lead to a
disagreement regarding the subject matter. Two people might experience things differently – and in that
sense ‘disagree’ – and yet, such divergence is only possible against the backdrop of a presupposed shared
background.6
Any dialogue therefore occurs withinwhat we might call a shared,intersubjective horizon in
the sense that both parties are already united by it: “I may say ‘Thou’, and I may refer to myself as over
against a Thou, but a common understanding always precedes these situations”.7
Hence, Gadamer
concludes, that the “formulation ‘I and Thou’ already betrays an enormous alienation”, since “there is
neither the I nor the Thou as isolated,substantial realities”.8
We can therefore extract from Gadamer’s work the view that any two people conversing with each Other
do not exist as two isolated realities. Rather, they share in a mutually constituted interpersonal reality,
which again is constitutive of their respective outlook onto the world. In fact, this wider interpersonal
horizon can be understood as a ‘transcendental condition’ in that, without it, the acquisition of
propositional knowledge about the Other would be impossible, and would thus leave the structure of
experiencing the Other compromised. In other words, such presupposed shared background makes it
possible for the two people entering a dialogue to come to an understanding. Both of their horizons can
fuse to a third more-encompassing one, the process of which Gadamer calls‘fusion of horizons’.
However, simply being attuned to each Other is not sufficient for what we might call a ‘successful’ fusion
of horizons, where appreciating the Other and her experience is appreciating it as unique and thus hers.
Gadamer emphasises a fundamental opennessthat needs to be present in a dialogue,without which “there
is no genuine humanbond”.9
Such mutual openness involves a willingness to be transformed by the Otherand thus what Gadamer calls
the ‘fore-conceptionof completeness’,that both interlocutors assume each Other’s claim to bemeaningful
and true.10
For, only if we deem the Other a possible dialoguepartner can we give her enough space to
articulate herself, hence acknowledging her as a person with a unique horizon. Otherwise, we risk
projecting ourselves onto the Other, whereby we would reduce her to an object-like status and
consequently dispense with her as a “moral phenomenon”.11
5
(GW1, p.309;TM, p.303)
6
(Ratcliffe, 2014a, pp.272, 273)
7
(GW2, p.223;PH, p.7)
8
(GW2, p.223;PH, p.7)
9
(GW1, p.367;TM, p.335)
10
(GW1, p.229;TM, p.294)
11
(GW1, p.364;TM, p.352)
11

13. From a Gadamerian perspective, we can therefore conclude that an intact dialogue aims at a fusion of
horizons with the Other, allowing us to experience and thus recognise the Other as a person.
Intersubjectivity and the experience of the Other is not something artificially constructed, contra views
“that the Other can first be given only as a perceived thing, and not as a living, as given ‘in the flesh’”.12
The experience of the Other cannot bean act of self-relatedness13
,emulating what it is like to be the Other
from the self’s viewpoint. For, this would assume a privileged access to the Other’s mind14
,whereby the
experience of the Otherwould bediminished and reduced to a projection of the self. Instead of being open
towards the Other and immediately recognising her experiences as something distinct and hers, such an
encounter of the Other would supersede both the distinction between ‘my’ and ‘your’ experience,and thus
between the self and the Other.15
Key to the phenomenology of intersubjectivity, however, is the mutual recognition of each Other as the
bearersof uniqueexperiencesthat cantransformus, without which thefusionofhorizonswill not succeed.
In other words, a phenomenology of intersubjectivity, as we have construed it here, involves both the
recognition of another person and the resultant fusion of horizons. This fusion changes the way both
interlocutors relate to each Other; not only has their knowledge of the subject matter enlarged but so has
their knowledge of the Other’s view on it. That is to say, the way one experiences the Other has been
altered as one’s horizon has been expanded,enabling an experienceof the Other that was impossibleprior
to the fusion.
However, this fusion should not just be understood in terms of two individual horizons expanding.For,
the prime focus is not on each of the interlocutors and their newly extended horizons, but on the event of
the fusion itself. Being mutually open towards each Other, they are united by their common aim of
understanding thesubject matter and thus experiencing the respective Other. This event structure can be
linked to what Gadamer captures elsewhere with his concept of ‘play’: “The primacy of the game over the
players engaged in it is experienced by the players themselves in a special way, where it is a question of
human subjectivity that adopts an attitude of play ... the game itself is a risk for the player. One can only
play with serious possibilities.... The attraction of the game, which it exercises on the player, lies in this
risk”.16
Applied to the fusion of horizons, both dialoguepartnersare guided by the dialogue itself, yielding to an
intersubjective dynamic.This is why the fused,third horizon constitutesa shared, intersubjective horizon
belonging to both rather than either of them exclusively. However, without the willingness to be
challenged, thus putting ourselves “into play ... through being at risk”17
, we cannot fuse horizons and
experience the Other. Sketching a Gadamerian perspective of an intact dialogue,we can thus infer that it
12
(GW1, p.95; SI, p.283)
13
(GW1, p.365;TM, p.353)
14
(GW1, p.365;TM, p.353)
15
The general difference between approaches open towards the Other and emulating the Other can also be cast in
non-Gadamerian terms as one between phenomenological and simulationist approaches to empathy. For an
overview and analysis of the extent to which those overlap, see (Ratcliffe, 2012 and 2014a).
16
(GW1, pp.111-112;TM, p.95) Italics are my own.
17
(GW1, p.304;TM, p.266) Italics are my own.
12

14. entails both mutual openness and trust towards the Other, without which we cannot appreciate the Other
and her experiences as hers.
Dialogue in Depression
Drawing on Gadamer’s phenomenology of understanding via the fusion of horizons has allowed us to
sketch a phenomenologyofintersubjectivity.Wehaveestablished howunderstandingnormallytakesplace
between two people and thus, more generally provided an account of an intact dialogue.In light of this, I
shall now apply these findings to the phenomenology of depression, elucidating the differing forms of
dialogue that occur in depression.18
Although ‘depression’ is used as an umbrella term for a number of diagnoses, I shall focus on a
phenomenological change in the experience of the Other that can be found in many autobiographical
accounts, all describing an impaired form of intersubjectivity. For instance, consider the following
statements19
:
“When I’m depressed I feel like my relationshipsare less stable and I trust others a lot less. I try to avoid
people, as they seem angry and irritated at me. ...I feel like a burden.”
“I find other people irritating when depressed,especially those that have never suffered with depression,
and find the ‘advice’ often given by theseis unempathetic and ridiculous.”
In these accounts, which I take to be representative of the aforementioned phenomenological change, we
can identify the two principal themes of isolation and lack of trust. Interpersonal relationsseem, at least
most of the time, bereft of any positive, warm dimension. Instead, the depressed person experiences the
Otherasa threat and alienating force,with whomshecannot enteragenuinebond.Oneway ofconstruing
this change in experiencing the Other is in terms of the fusion of horizons between two people, and thus
how understanding occurs.Whereas a mutual openness lies at the heart of an intact dialogue,a depressed
person is lacking such openness in virtue of not trusting the Other. As a result, she seems incapable of
putting herself ‘into play’ and ‘at risk’. Not yielding to the intersubjective dynamic of completely letting
go in the process of the dialogue, the depressed person prevents herself from fusing horizons with the
Other, thus from appreciating the Other as a person. Instead, the Other is reduced to a projection of the
depressed, constituting a threat.20
The lack of trust furthermoreexplains why otherpeople’sadvice is deemed ‘unempathetic and ridiculous’.
Key to the experience of the Other in an intact dialogue is the‘fore-conception of completeness’,as I have
outlined in the first section. The depressed personhowever does not seem to be in a position to presuppose
the Other’s claim to be meaningful and true, since she has reduced the Other to an object-like statusof
embodying (almost)nothing but a threat. That is to say, the possibility of interacting with the Other in a
way that could change the depressed person’shorizon is diminished. Hence, she does not feel understood
18
In this context, dialogue is understood broadly enough so as to encompass any communicative interaction
between two people.
19
(Ratcliffe, 2014a, p.274)
20
see also (Ratcliffe, 2014b,p.234)
13

15. by the Other, which in turn makes her feel even more isolated and like a ‘burden’.21
In fact, even if the
depressed person wanted to be understood, “[yearning]for connection”, a fusion of horizons could not
take place, as she “[is] rendered incapableof being with others in a comfortable way”.22
It is therefore plausible to infer that depression involves a diminished experience of the Other, more
generally animpaired formof intersubjectivity.Theaccount sketchedsofarreveals theinability toconnect
and thus experience the Other in a horizon-changing way. Without being in a dialogue with the Other
however, the depressed lacks the possibility “of immersion in a dynamic world that incorporates the
potential for meaningful change”.23
Instead, we find the depressed person completely shut off from the
world:
“I feel like I am watching the world around me and have no way of participating”.24
An intact dialogue always occurs within a shared, intersubjective horizon that unites both interlocutors.
This is why we concluded in the first section that the formulation of ‘I and Thou’ does not do justice to
our phenomenology of intersubjectivity, as both do not constitute two completely separate realities. The
above quote however seems to depart from such an account. Rather than being mutually attuned to each
Other, I suggest, the depressed person appears to fall out of such a mutual framework. What has been
viewed as a transcendental conditionin an intact dialogue, i.e. theinterpersonal horizon, is missing.This
leaves the structureof experiencing the Other compromised.Such a change that occursin depression“has
a profound effect upon one’s sense of agency”.25
What this involves can best be understood, I propose,
when broadly conceptualising the depressed person as what I call a ‘radical Other’.26
As sketched in the
first section, in a normal dialogue, two people experience things differently in virtue of each having a
uniquehorizon,and yet both belongtoashared,intersubjectivehorizon.Inadialoguebetweenadepressed
and non-depressed person however, the two perspectives at work differ more fundamentally. For, the
former does not seem to be part of the same framework as the latter,as established before. This is why the
depressed person does not feel understood but isolated, feeling completely detached from everyone else
without any possibility of taking part in the world. The lack of a mutually shared backdrop does equally
affect those interacting with thedepressed person in that she strugglesto relate:
“When I start to get depressed,I only filter through the negative messagesfrom friends and family ... As a
result, they soon learn to step on egg shells around me, they become less affectionate because I’m less
receptive. ... It’s a very hard thing to do to be able to step back and realize that someone who is depressed
is projecting their own thoughts onto others.”27
The seeming impossibility for the depressed person to fuse horizons thus affectsthe non-depressed person.
Being exposed to sheer negativity, the depressed person is likely reduced to an object-like status, being
21
Whether or not the feeling of isolation precedes the feeling of not being understood, in my view, does not have
any bearing on the presented Gadamerian reading.
22
(Karp, 1996,p.14)
23
(Ratcliffe, 2014a, p.277)
24
(Ratcliffe, 2014a, p.274)
25
(Ratcliffe, 2013, p.584)
26
This notion and its implications are inspired by Lévinas’s radical alterity (e.g. 1969,p.194).
27
(Ratcliffe, 2014a, p.279)
14

16. ‘unreachable’. Such reduction however appears problematic in that the depressed person becomes even
moreout of reach,if not actually beingavoided.Inotherwords,through suchareductionand theresultant
alienation, we run the risk of dispensing with the depressed person as a moral phenomenon, as another
personwith uniqueexperiences.Infact,thisriskisrevealing with respect tothephenomenological account
of impaired intersubjectivity in depression. Central to the experience of the Other is “an appreciation of
[her] potential to reshape one’s world”28
, the potentiality of which the depressed person seems to lack in
virtue of being ‘unreachable’. Even though the fusion of horizons thus cannot take place, we should
nonethelessattempt to‘realizethat someonewhoisdepressed isprojecting theirownthoughtsontoothers’
and avoid reducing the depressed person completely.For, “[much] of depression’s pain arises out of the
recognition that what makes me feel better – human connection – seems impossible in the midst of a
paralyzing episode of depression”.29
Hence, instead of dispensing with the depressed person as a moral phenomenon, our phenomenological
analysis points to the paradoxical situation of those who are depressed, feeling like a radical Otherherself
and yet ultimately not wanting to be reduced as such. This is why conclusive reports such as “the psyche
of the patient is too well understood”30
have to be treated carefully. On the one hand, they reveal the
depressed person’s diminished sense of agency, feeling isolated and lacking any interpersonal possibilities,
which again gives rise to an impaired form of intersubjectivity. On the other hand,it does not take much
from here to yield to a reductionist experience of the depressed, perceiving her as nothing more than an
object. This again could amount to the loss of the possibility of helping the depressed person, who is
however dependent on our willingness to engage with her in a transformative manner.
Conclusion
The aim in this paper has been to sketch a phenomenological account of impaired intersubjectivity in
depression. The claim has been that drawing on Gadamer’s phenomenology of understanding via the
fusion of horizons, helpselucidate how depression affects the phenomenology of intersubjectivity.Against
the backdrop of an intact dialogue betweentwo people, we have construed the differing forms of dialogue
that occur in depression in terms of the seeming impossibility of fusing horizons. No doubt the account
given here does not apply to all cases of depression, however, the reader will hopefully realise that such a
phenomenological sketch enables an understanding of depression that might otherwisenot be possible.
28
(Ratcliffe, 2014b,p.236)
29
(Karp, 1996,p.16)
30
(Minkowksi, 1970,p.178)
15

17. Bibliography
Ratcliffe, M. (2012)‘Phenomenology as a Form of Empathy’,in Inquiry:An Interdisciplinary Journal of
Philosophy, Vol. 55, No. 5, pp.473-495.
– (2013) ‘Depression and the Phenomenology of Free Will’, in The Oxford Handbook of Philosophy
and Psychiatry (ed.K.W.M.Fulford et al.), pp.574-591.
– (2014a) ‘The Phenomenology of Depression and the Nature of Empathy’ in Medicine,Health Care
and Philosophy, Vol. 17, No. 2, pp.269-280.
– (2014b) ‘The structure of interpersonal experience’ in Moran, D.and Jensen,R. (ed.) Phenomenology
of Embodied Subejctivity,Springer, Dordrecht, pp.221-238.
Gadamer, H.-G. (1993ff) Gesammelte Werke, 7th edition, Mohr Siebeck, Tübingen.(GW)
– (2008) Bd.1: Hermeneutik I: Wahrheit und Methode.Grundzüge einer philosophischen
Hermeneutik.
– (1993) Bd.2: Hermeneutik II: Wahrheit und Methode.Ergänzungen, Register.
– (1976) Philosophical Hermeneutics (trans. Linge, D.E.), University of California Press, Berkeley.(PH)
– (2004) Truth and Method, 2nd revised edition, (trans.Weinsheimer,J. and Marshall,D. G.),
Continuum, London. (TM)
Garrett, J. E. (1978) ‘Hans-Georg Gadamer on “Fusion of Horizons”’, in Man and World, Vol. 11, No.
3/4, pp. 392-400.
Karp, D. (1996) ‘Speaking of Sadness: Depression, Disconnection, and the Meaningsof Illness’,Oxford:
Oxford University Press.
Lévinas, E. (1969)‘Totality and Infinity’, (trans. Lingis,A.), Pittsburgh: Duquesne University Press.
Minkowski, E. (1970)‘Lived Time: Phenomenological and Psychopathaological Studies’, (trans.Metzel,
N.), Evanston: Northwestern University Press.
16

18. Illustrating Pearl’s Approach to Causality by Examples, and Responding
to Cartwright’s Criticisms
Kim Tullar
Abstract
In the year 2000, Judea Pearl’s ‘Causality’ was published, providing an expansive account of the Bayesian
networks (henceforth ‘bayes nets’)approach to causality,emphasising its practical, mathematical nature.
Whilst not all aspects of Pearl's approach are persuasive, I believe its core should be accepted by
philosophers,scientists and statisticians alike. Yet Pearl's approach isnot widely taught; most students will
graduate without even hearing about it. This paper aims to rectify this issue somewhat, and persuade
readers of the core of Pearl's approach by giving a few examples implementing it in section 1.In section 2,
I address some of Nancy Cartwright's criticisms of the approach, arguing that whilst important,they can
be answered.
1. Example Applications of Pearl’s Approach
Pearl's approach to causality is really just one version of the bayes nets approach to causality1
and I will
make use of some of the other bayes nets approaches2
despite focussing on the account proposed by Pearl.
1.1 The Lawn Example
We begin with a simple example demonstrating the basics of utilising bayes nets to understand causality,
adapted from Pearl3
. Say we want to build a causal model for how a lawn can get wet. A simple model is
that rain can cause wetness, a sprinkler can cause wetness, and those are the only causal relations. This
model is represented by the graph of Figure 1, where 𝑅𝑅 represents rain, 𝑆𝑆 thesprinkler,and 𝑊𝑊 thewetness
of the lawn.
1
(Woodward, 2013, Stanford Encyclopedia of Philosophy)
2
(Glymour, 2010)
3
(2000, p.15)
Figure 1
17

19. The arrows of Figure 1 represent direct causality with respect to thevariables included in the graph. Let us
take a moment to negatively define what ‘direct causality’ means in general. 𝑋𝑋 is defined as not directly
causing 𝑌𝑌 iff, if 𝑋𝑋 causes 𝑌𝑌 at all, it is only via other variables included in the graph. What precisely is
meant by ‘via’ another variabledepends on one’s account of causation. Bayesnets are commonly taken to
suggest a non-reductive, manipulationist account of causation4
, on which 𝑋𝑋 does not directly cause 𝑌𝑌 iff
holding all other causesof 𝑌𝑌 in the graph constant, or just every other variablein the graph, would render
𝑌𝑌 constant no matter the value of 𝑋𝑋.5
In any case, we omit an arrow from 𝑋𝑋 to 𝑌𝑌 whenever we know 𝑋𝑋 is
not a direct cause of 𝑌𝑌.
Returning tothelawnexample,thebayesnetsapproach asksustofind out whichvariablesareconditionally
‘d-separated’,so that we can drawconclusions about their probability distribution. d-separation is defined
by Pearl as in definition 1.6
Definition 1. A path from 𝑎𝑎 to 𝑏𝑏 is a sequence of edges in any direction beginning with 𝑎𝑎 and ending
with 𝑏𝑏, for instance 𝑎𝑎 ← 𝑐𝑐 → 𝑏𝑏. We say a path from 𝑎𝑎 to 𝑏𝑏 is d-separated by a set of nodes 𝐶𝐶 iff
1. It contains a chain 𝑖𝑖 → 𝑐𝑐 → 𝑗𝑗, 𝑖𝑖 ← 𝑐𝑐 ← 𝑗𝑗 or 𝑖𝑖 ← 𝑐𝑐 → 𝑗𝑗, where 𝑐𝑐 ∈ 𝐶𝐶, or
2. It contains a chain 𝑖𝑖 → 𝑐𝑐̅ ← 𝑗𝑗, where 𝑐𝑐̅ ∉ 𝐶𝐶, and no descendant of 𝑐𝑐̅ is in 𝐶𝐶.
If all paths from 𝑎𝑎 to 𝑏𝑏 are d-separated by 𝐶𝐶, we say 𝑎𝑎 and 𝑏𝑏 are d-separated given 𝐶𝐶, which we write
𝑎𝑎 ⫫𝑑𝑑 𝑏𝑏 | 𝐶𝐶. If 𝐴𝐴 and 𝐵𝐵 are sets of nodes, and for all 𝑎𝑎 ∈ 𝐴𝐴, 𝑏𝑏 ∈ 𝐵𝐵, we have 𝑎𝑎 ⫫𝑑𝑑 𝑏𝑏 | 𝐶𝐶, thenwe say 𝐴𝐴 and
𝐵𝐵 are d-separated given 𝐶𝐶, which is written 𝐴𝐴 ⫫𝑑𝑑 𝐵𝐵 | 𝐶𝐶.
The bayes net approach to causality holds that if the causal graph is ‘correct’ (we will come to what this
means in section 2.1), and if 𝐴𝐴 ⫫𝑑𝑑 𝐵𝐵 | 𝐶𝐶, then 𝐴𝐴 is independent of 𝐵𝐵 given 𝐶𝐶 in the probability
distribution, which we write 𝐴𝐴 ⫫ 𝐵𝐵 | 𝐶𝐶. By observing Figure1, we see that the only d-separation implied
by the graph is 𝑅𝑅 ⫫𝑑𝑑 𝑆𝑆. Therefore, assuming our model is correct, we have 𝑅𝑅 ⫫ 𝑆𝑆. This is equivalent to
the fact that the joint distribution7
can be factorised as:
Pr(𝑅𝑅, 𝑆𝑆, 𝑊𝑊) = Pr(𝑅𝑅) Pr(𝑆𝑆) Pr( 𝑊𝑊| 𝑅𝑅, 𝑆𝑆), (1)
Where each variable is conditioned on its parents and,for simplicity (inthis example and thenext), I will
assume all the variables are binary,with 1 representing truth, and 0 falsity. For instance, if we assume the
probability of rain is 0.4 (Pr(𝑅𝑅 = 1) = 0.4), the sprinkler being off is 0.8 (Pr(𝑆𝑆 = 0) = 0.8), and that
4
(Woodward, 2013, sect. 1)
5
(Glymour, 2010,pp.171,172)presents a similar definition.
6
(2000, pp.16-17)
7
For simplicity, we talk of a `joint distribution' by itself without defining it relative to a sample (the Frequentist
approach) or a belief-state (the Bayesian approach). When it is relevant, we will adopt the Frequentist approach for
the purposes of this paper. Cartwright (2001,p.244)and Glymour (2010,pp.165,168)seem to favour it, given their
talk of populations, though, confusingly, Glymour seems happy to appeal to prior probabilities (2010, p.194).
18

20. the probability of the lawn being wet given rain and the sprinklerbeing off is 0.6 (Pr( 𝑊𝑊 = 1 | 𝑅𝑅 = 1, 𝑆𝑆 =
0) = 0.6), then the probability that it rained, and the sprinkler was off, and the grass was wet, is:
Pr(𝑅𝑅 = 1, 𝑆𝑆 = 0, 𝑊𝑊 = 1) = 0.4 × 0.8 × 0.6 = 0.192. (2)
This is an example of how bayes nets methodshelp us get probabilities from causes.
A sceptical reader may wonder whether equation 1 would still hold if we had used a more sophisticated
model for lawn wetness.According to bayes nets methods,a sufficient condition for equation 1 is that rain
does not cause the sprinkler, thesprinkler does not cause rain, they have no common cause, and there are
no sampling biases.We shall explore why thisis sufficient in section 2.1.
1.2 The Smoking Example8
Say we are studying whether smoking causes lung cancer or not. We have observed a correlation between
smoking and lung cancer, but it could be due to a common cause, such as a gene which causes people to
be both more likely to smoke and more likely to have lung cancer. Say we know that smoking, if it causes
cancer at all, only causes it by causing build-up of tar in the lungs, and the gene, if it exists, only affects tar
by increasing propensity to smoke. Letting 𝑆𝑆 stand for smoking, 𝑇𝑇 stand for tar in the lungs, 𝐿𝐿 stand for
lung cancer, and 𝑈𝑈 stand for the possible unobserved gene affecting 𝑆𝑆 and 𝐿𝐿. Figure 2 shows the causal
model.
By conducting a randomised survey of 1,000 subjects,let us supposewe collect the data given in table 1.
8
This example is adapted from (Pearl, 2000,pp.83-88).
Figure 2
19

21. From this data and the causal model, bayes netsmethods tell us how to calculate thecasual effect of 𝑆𝑆 on
𝑇𝑇, of 𝑇𝑇 on 𝐿𝐿 and of 𝑆𝑆 on 𝐿𝐿. For any variables 𝑋𝑋 and 𝑌𝑌, the total causal effect of 𝑋𝑋 on 𝑌𝑌 is defined to be
Pr(𝑌𝑌 | do(𝑋𝑋)), where ‘do’ is a special operator, which represents intervening to set the value of 𝑋𝑋; see
definition 2.9
Definition 2. Consider a directed, acyclic graph of the variables 𝑋𝑋1, …, 𝑋𝑋𝑛𝑛. Assume the graph is a bayes
net. Then the joint probability distribution of the variablescan be written:
Pr(𝑋𝑋1,… , 𝑋𝑋𝑛𝑛) = Pr(𝑋𝑋1 | pa(𝑋𝑋1))… Pr(𝑋𝑋𝑛𝑛 | pa(𝑋𝑋𝑛𝑛)), (3)
Where pa(𝑋𝑋𝑖𝑖) is the set of parents of 𝑋𝑋𝑖𝑖 in the graph. The distribution
Pr(𝑋𝑋1,… , 𝑋𝑋𝑖𝑖−1, 𝑋𝑋𝑖𝑖+1 …, 𝑋𝑋𝑛𝑛|do(𝑋𝑋𝑖𝑖)) is given by regular Bayesian conditionalisation on the pseudo-joint
distribution:
Pr′(𝑋𝑋1,…, 𝑋𝑋𝑖𝑖−1, 𝑋𝑋𝑖𝑖+1 …, 𝑋𝑋𝑛𝑛) = ∏ Pr � 𝑋𝑋𝑗𝑗 �𝑗𝑗≠𝑖𝑖 pa(𝑋𝑋𝑗𝑗)). (4)
This is equivalent to saying:
Pr(𝑋𝑋1,… , 𝑋𝑋𝑖𝑖−1, 𝑋𝑋𝑖𝑖+1 … , 𝑋𝑋𝑛𝑛 | do(𝑋𝑋𝑖𝑖))
= � Pr� 𝑋𝑋𝑗𝑗 � pa(𝑋𝑋𝑗𝑗))
𝑗𝑗≠𝑖𝑖, 𝑋𝑋𝑖𝑖∉pa� 𝑋𝑋𝑗𝑗�
� Pr� 𝑋𝑋𝑗𝑗 �pa� 𝑋𝑋𝑗𝑗�, 𝑋𝑋𝑖𝑖).
𝑗𝑗≠𝑖𝑖, 𝑋𝑋𝑖𝑖∈pa(𝑋𝑋𝑗𝑗)
(5)
The causal effect of 𝑆𝑆 on 𝑇𝑇 is Pr(𝑇𝑇| do(𝑆𝑆)). If 𝑆𝑆 has no direct causal effect on 𝑇𝑇, then it has no causal
effect on 𝑇𝑇 at all, and so Pr(𝑇𝑇| do(𝑆𝑆)) should be uniform with respect to 𝑆𝑆; forcing someoneto smoke or
not should have no effect on their chance of having tar deposits in their lungs. It can be shown that
Pr(𝑇𝑇| do(𝑆𝑆)) = Pr(T | 𝑆𝑆); to put this another way, we should not control for anything when calculating
9
The semantic interpretation of the do-operator is, in my opinion, one of the fundamental philosophical
assumptions of bayes nets methods, along with the causal markov condition. However, Cartwright does not
criticise its use in her essay, so we will allow this assumption for the purposes of this paper.
Table 1: Breakdownof Smoking,Tar andLung Cancer in Subjects
20

22. the effect of 𝑆𝑆 on 𝑇𝑇. Thus we can calculate (from the data in thetable):
Pr(𝑇𝑇 = 1 | do(𝑆𝑆 = 1)) = Pr(𝑇𝑇 = 1 | 𝑆𝑆 = 1) ≈ 19/21, (6)
And
Pr(𝑇𝑇 = 1 | do(𝑆𝑆 = 0)) = Pr(𝑇𝑇 = 1 | 𝑆𝑆 = 0) ≈ 1/19. (7)
So our data strongly suggests that smoking has a direct causal effect on tar, increasing the chance of tar
dramatically.
Similarly, the causal effect of 𝑇𝑇 on 𝐿𝐿 is Pr(𝐿𝐿 | do(𝑇𝑇)), which should beuniform with respect to 𝑇𝑇 if 𝑇𝑇 has
no direct causal effect on 𝐿𝐿.It can beshownthat Pr(𝐿𝐿 | do(𝑇𝑇)) = ∑ Pr(𝐿𝐿 | 𝑇𝑇, 𝑆𝑆)Pr(𝑆𝑆)𝑠𝑠 ;whencalculating
the causal effect of tar on lung cancer, we should control for smoking.Using our data, we obtain:
Pr(𝐿𝐿 = 1 | do(𝑇𝑇 = 1)) ≈ 1457/3800 ≈ 0.38 (8)
And
Pr(𝐿𝐿 = 1 | do(𝑇𝑇 = 0)) ≈ 547/6800 ≈ 0.08. (9)
So our data strongly suggests that tar has a direct effect on lung cancer, increasing the chances of cancer
considerably.
As we have established that smokinghasapositiveeffect on tar,and tarhasa positiveeffect on lung cancer,
we know that smoking has a positive effect on cancer. But how much would someone’s risk of lung cancer
go up if they started smoking?The answeris given by:
Pr(𝐿𝐿 = 1 | do(𝑆𝑆 = 1)) − Pr(𝐿𝐿 = 1 � do(𝑆𝑆 = 0)� (10)
= � Pr( 𝑇𝑇 | 𝑆𝑆 = 1)
𝑇𝑇
� Pr(𝐿𝐿 = 1 | 𝑆𝑆, 𝑇𝑇) Pr(𝑆𝑆) − � Pr( 𝑇𝑇| 𝑆𝑆 = 0) � Pr(𝐿𝐿 = 1 | 𝑆𝑆, 𝑇𝑇)Pr(𝑆𝑆)
𝑆𝑆𝑇𝑇𝑆𝑆
≈
6329
17850
−
16221
144400
≈ 0.24 (11)
So smoking increases one’s risk of lung cancer by about 24%. In this example, we have seen how bayes
nets methods allow us to: infer causality from probabilities,identify which variables to control to estimate
effects; and calculate the result of interventions.
1.3 The abstract example
21

23. So far, we have utilised prior causal knowledge in combination with data to reach further causal
conclusions. In this example10
we consider how to obtain a causal model without using any prior causal
knowledge whatsoever. The idea is that by using the data observed, we can conclude what the conditional
independenciesinthevariablesare,and hencenarrowdownthepossiblecausal modelstoonly thosewhich
could generate such conditional independencies via the d-separation criterion. Rather than narrowing
down models laboriously by checking through each possible model individually, algorithms have been
created to perform the function quickly.The problemwith this sort of exampleis that actually finding the
conditional independenciesfrom a dataset can be a complicated statistical matter.So we will instead state
the real causal structure at play, assume we are able to derive the conditional independencies from a
sufficiently large sample,and apply Glymour's PC algorithm (which was thefirst attempt to make Pearl’s
IC algorithm practically implementable) to those indeterminacies.
The real model is given in Figure 3. The model could represent,for instance, a game of chance, where 𝑊𝑊
and 𝑋𝑋 aretherollsof independent dice, 𝑌𝑌 yourscore,randomised around 𝑊𝑊 and 𝑋𝑋,and 𝑍𝑍isyourwinnings,
randomised around 𝑌𝑌. In any case, the conditional independencies shown in the graph, using the d-
separation criterion are: 𝑊𝑊 ⫫ 𝑋𝑋, 𝑊𝑊 ⫫ 𝑍𝑍 | 𝑌𝑌, 𝑊𝑊 ⫫ 𝑍𝑍 | 𝑋𝑋, 𝑌𝑌 , 𝑋𝑋 ⫫ 𝑍𝑍 | 𝑌𝑌, and 𝑋𝑋 ⫫ 𝑍𝑍 | 𝑊𝑊, 𝑌𝑌. We also
assume the causal model is stable, which means that these are the only conditional independencies: so
¬(𝑌𝑌 ⫫ 𝑍𝑍) for instance.11
As stated before, we assume we observe a large dataset of 𝑊𝑊, 𝑋𝑋, 𝑌𝑌, 𝑍𝑍 jointly, and we are able to correctly
determine what the conditional independencies are. We will not define the PC algorithm for simplicity,
10
Taken from (Glymour, 2010, pp.181-182)
11
(Pearl, 2000,p.48)
Figure 3: Real Model
22

24. but in applying it to our conditional independencies, we are actually able to completely reconstruct the
graph of Figure 3. So in this case, bayes nets methods allow us to go from probabilisticknowledge alone,
to a complete correct causal model (in general, it will not be possible to determine the entire causal model
from the conditional independencies, but at least part of the model can bespecified).
The PC algorithm assumes we observe all causally relevant variables.But this assumption is not necessary.
Algorithms exist for reconstructing the causal structure, as best as possible, even when one makes no
assumptions about what one has failed to observe. I omit such examples for simplicity.
2. Responding to Cartwright’s Criticisms
In this section, we focus on the criticisms Cartwright gives in her 2001 essay ‘What is wrong with Bayes
Nets?’12
, my responses to Cartwright are built upon the responses Glymour has given.13
In Cartwright’s
essay sheattackstwoassumptionsofbayesnetsmethods:thecausalmarkovcondition(CMC);and stability
in causal models.
2.1 The Causal Markov Condition
Firstly, we address the issue of defining the CMC. The CMC is supposed to provide a link between
causality and probability by claiming that causality works like a bayes net,and henceis fundamental to all
bayes nets methods. Glymour understands the CMC to hold for a set of variables iff the true causal
structure for that set of variables operateslike a bayes net.14
A causal model can bedefined as operating like
a bayes net iff, if 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌 | 𝑍𝑍, then 𝑋𝑋 ⫫ 𝑌𝑌 | 𝑍𝑍 on the probability distribution.15
Pearl implicitly accepts an
equivalent definition, and proves that the CMC must hold for deterministic,acyclic causal models with
mutually independent errors.16
Furthermore, Pearl argues that if we commit ourselves to including all
common causes of variables, and to Reichenbach’s Principle (RP) that dependence between 𝑋𝑋 and 𝑌𝑌
implies 𝑋𝑋 causes 𝑌𝑌, 𝑌𝑌 causes 𝑋𝑋 or 𝑋𝑋 and 𝑌𝑌 have a commoncause,thentheerror variablesina deterministic
graph must be independent,and so if our graph is acyclic, the CMC holds. However, neither Pearl nor
Glymour believe the CMC will always hold.17
The problem with the preceding accounts of the CMC is that they are, like theRP, vulnerable to sampling
bias.Aswe will seein moredetail below,thisiswhy Cartwright isabletoconstructcounter-examplesbased
on sampling bias.18
Toavoid theproblemofsamplingbias,oneshould definetheCMCinaway equivalent
to: ‘if 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌 | 𝑍𝑍, 𝑆𝑆 on the true causal structure, where 𝑆𝑆 indicates inclusionin one’s sample, then 𝑋𝑋 ⫫
12
`What is Wrong with Bayes Nets?' was republished in Cartwright's collection `Hunting Causes and Using
Them', however I will focus on the 2001 version.
13
(2010)
14
(2010, p.175)
15
There are many equivalent definitions, but this is most useful for the purposes of this paper.
16
(Pearl, 2000,p.30)
17
(Pearl, 2000,pp.44-45), (Glymour, 2010, pp.200-201)
18
(Cartwright, 2001,p.259)
23

25. 𝑌𝑌 | 𝑍𝑍 in one’s sample’. Note that there is still a connection to the RP, as 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌 | 𝑆𝑆 iff 𝑋𝑋 does not cause
𝑌𝑌 (there is no directed sequence 𝑋𝑋 → ⋯ → 𝑌𝑌), 𝑌𝑌 does not cause 𝑋𝑋, there is no common causeof 𝑋𝑋 and 𝑌𝑌,
and if 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌 then 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌 | 𝑆𝑆 (which can be interpreted as the independence of 𝑋𝑋 and 𝑌𝑌 not being
influenced by sampling bias).
However, our definition is still problematic,because it assumesa ‘truecausal structure’,which is assuredly
very fine-grained. Ideally,we want a definition of the CMC which allows us to work at a coarser level as
well. So I suggest a more refined definition,based on the definition of d-seperation.
Definition 3. Let the jointly observed variables in the sample be 𝑋𝑋 = (𝑋𝑋1, …, 𝑋𝑋𝑛𝑛). Let inclusion in the
sample be denoted by 𝑆𝑆. Let 𝐶𝐶 ⊂ 𝑋𝑋. If 𝑎𝑎 causes 𝑏𝑏, not only via some 𝑐𝑐 ∈ 𝐶𝐶 ∪ 𝑆𝑆, we say there is a causal
path 𝑎𝑎 → 𝑏𝑏. If 𝑎𝑎 only causes 𝑏𝑏 via some 𝑐𝑐 ∈ 𝐶𝐶 ∪ 𝑆𝑆, we say there is a causal path 𝑎𝑎 → 𝑐𝑐 → 𝑏𝑏. Causal paths
can be joined: for instance, if there is a path 𝑎𝑎1 → ⋯ → 𝑎𝑎 𝑛𝑛 and a path 𝑎𝑎 𝑛𝑛 ← ⋯ ← 𝑎𝑎 𝑛𝑛+𝑚𝑚, then there is a
path 𝑎𝑎1 → ⋯ → 𝑎𝑎 𝑛𝑛 ← ⋯ ← 𝑎𝑎 𝑛𝑛+𝑚𝑚. If a causal path from 𝑎𝑎 to 𝑏𝑏 contains a chain
1. 𝑖𝑖 → 𝑐𝑐 → 𝑗𝑗, or 𝑖𝑖 ← 𝑐𝑐 ← 𝑗𝑗, or 𝑖𝑖 ← 𝑐𝑐 → 𝑗𝑗 for some 𝑐𝑐 ∈ 𝐶𝐶 ∪ 𝑆𝑆, or
2. 𝑖𝑖 → 𝑐𝑐̅ ← 𝑗𝑗 for some 𝑐𝑐̅ ∉ 𝐶𝐶 ∪ 𝑆𝑆, where 𝑐𝑐̅ does not cause anything in 𝐶𝐶 ∪ 𝑆𝑆,
Then we say that the causal path from 𝑎𝑎 to 𝑏𝑏 is causally d-separated by 𝐶𝐶 ∪ 𝑆𝑆, we say 𝑎𝑎 ⫫𝑐𝑐𝑐𝑐 𝑏𝑏 | 𝐶𝐶, 𝑆𝑆. If
for all 𝑎𝑎 ∈ 𝐴𝐴, 𝑏𝑏 ∈ 𝐵𝐵, we have 𝑎𝑎 ⫫𝑐𝑐𝑐𝑐 𝑏𝑏 | 𝐶𝐶, 𝑆𝑆, then we say 𝐴𝐴 ⫫𝑐𝑐𝑐𝑐 𝐵𝐵 | 𝐶𝐶, 𝑆𝑆. The causal markov condition
states that if 𝐴𝐴 ⫫𝑐𝑐𝑐𝑐 𝐵𝐵 | 𝐶𝐶, 𝑆𝑆, then 𝐴𝐴 ⫫ 𝐵𝐵 | 𝐶𝐶 in our sample.
I believe this adequately defines the CMC in a way which doesn’t require reference to a ‘true’ underlying
graph,though Iamnot certain.Futureworkshould attempttoprovethat 𝐴𝐴 ⫫𝑐𝑐𝑐𝑐 𝐵𝐵 | 𝐶𝐶, 𝑆𝑆 iff 𝐴𝐴 ⫫𝑑𝑑 𝐵𝐵 | 𝐶𝐶, 𝑆𝑆
for any underlying model.TheproblemsCartwright posescanalwaysbephrasedintermsofan underlying
model anyway, so we will work with ⫫𝑑𝑑.
Now I will address Cartwright’salleged counter-examplesto the CMC, showing that they are not true
counter-examples to my definition of the CMC. The first counter-example Cartwright gives is of two
causescooperating toproduceoneeffect ina populationhomogenouswith respect tothat effect.19
Ibelieve
that Cartwright intends the sort of causal model given in Figure 4, where 𝑋𝑋 and 𝑌𝑌 cooperate to cause 𝑍𝑍,
but 𝑍𝑍 influences inclusion in the sample 𝑆𝑆 (which can also be thought of as the sampling population).In
this case, Cartwright rightly pointsout that, whilst 𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌, often ¬(𝑋𝑋 ⫫ 𝑌𝑌)| 𝑆𝑆. Our CMC gets around
this conundrum,because it is perfectly possible that ¬(𝑋𝑋 ⫫𝑑𝑑 𝑌𝑌)| 𝑆𝑆, henceallowing ¬(𝑋𝑋 ⫫ 𝑌𝑌)| 𝑆𝑆.
19
(2001, p.259)
24

26. The next example Cartwright gives is of different causal effects in different populations being mixed
together.20
I found it hard to decipher how her example worked, but I suspect she meant something like
the following. In population 1, let 𝐴𝐴 → 𝐶𝐶 ← 𝐵𝐵, with joint probability:
Pr1(𝐴𝐴, 𝐵𝐵, 𝐶𝐶) = Pr1(𝐴𝐴)Pr1(𝐵𝐵)Pr1(𝐶𝐶|𝐴𝐴,𝐵𝐵) (12)
In population 2, let thecausal graph bethe same,but the distribution be:
Pr2(𝐴𝐴, 𝐵𝐵, 𝐶𝐶) = Pr2(𝐴𝐴)Pr2(𝐵𝐵)Pr2(𝐶𝐶| 𝐴𝐴, 𝐵𝐵) (13)
In both populations1 and 2, 𝐴𝐴 ⫫ 𝐵𝐵. Now consider the mixture population:
Pr(𝐴𝐴, 𝐵𝐵, 𝐶𝐶) = 𝑤𝑤1Pr1(𝐴𝐴, 𝐵𝐵, 𝐶𝐶) + 𝑤𝑤2Pr2(𝐴𝐴, 𝐵𝐵, 𝐶𝐶) (14)
20
(2001, p.259)
Figure 4: Cooperating Causeswith Sampling Bias
25

27. Where 𝑤𝑤1 + 𝑤𝑤2 = 1.
In this distribution, we may have that ¬(𝐴𝐴 ⫫ 𝐵𝐵). But this is fine, as there is in fact an unobserved variable
𝑇𝑇, representing which population is chosen, and so the causal graph is in fact as in figure 5.
The arrows in the graph are justified, as the difference in population makes a difference in marginal
distribution of 𝐴𝐴 (unless Pr1(𝐴𝐴) = Pr2(𝐴𝐴)), a difference in marginal distribution of 𝐵𝐵 (unlessPr1(𝐵𝐵) =
Pr2(𝐵𝐵)) and a difference in the dependence of 𝐶𝐶 on 𝐴𝐴,𝐵𝐵 (unless Pr1(𝐶𝐶| 𝐴𝐴,𝐵𝐵) = Pr2(𝐶𝐶| 𝐴𝐴,𝐵𝐵)).
Cartwright expresses dismay at having to draw so many arrows, but I don’t see the problem. Glymour also
holds that bayes nets methodswork on mixture populations.21
Cartwright points out that time-series of variables can be correlated, even if variables have no causal
relation. I will not deal with this example, as it requires time-series analysis; readers who are interested
should consult the bibliography. In short, Glymour argues that this “correlation” is not indicative of
probabilistic dependence, and that bayes nets methods can be applied by transforming the time-seriesin
standard ways.22
Finally, Cartwright asserts that products and by-products, when produced probabilistically are mutually
dependent,even conditional, on their cause. That is, she asserts that if 𝐵𝐵 ← 𝐴𝐴 → 𝐶𝐶, where 𝐵𝐵 and 𝐶𝐶 are
caused non-deterministicallyby 𝐴𝐴,then¬(𝐵𝐵 ⫫ 𝐶𝐶)| 𝐴𝐴.Thisisinstarkcontrast towhat bayesnetsmethods
say: 𝐵𝐵 ⫫ 𝐶𝐶 | 𝐴𝐴. Indeed, it is easy to create an example in which Cartwright’s claimis violated: if 𝐴𝐴 is the
roll of two dice, 𝐵𝐵 is randomised around the dice’s sum,and 𝐶𝐶 is randomised around their difference, then
𝐵𝐵 ⫫ 𝐶𝐶 | 𝐴𝐴. The question is whether Cartwright’s claimis ever true. I am sure it is in cases with sampling
bias, and it must be such cases which Cartwright has in mind;in which case, thesolution to these cases is
the same as earlier: the CMC should conditionon inclusionin the sample.
21
(2010, pp.164,206)
22
(2010, pp.164,202)
Figure 5: Mixture Model
26

28. 2.2 Stability
As we explained in section 1.3, stability is the assumption that the conditional independencies given by
applying the d-separation criterion to the causal model are the only conditional independencies. This
assumption is used as one of several jointly sufficient conditionsfor proving that algorithmssuch a PC will
always specify the correct causal model asspecifically as possible.23
If stability failsto hold of the true causal
structure, then applying PC may (but not necessarily) result in an incorrect model.
Cartwright’s argument boils down to asserting that stability is often violated for scientific data, and hence
we are not justified in applying algorithms such as PC to such data.24
However, Cartwright also confuses
thesufficiency of stabilityforalgorithmicmethodswiththenecessity ofstability forall bayesnetsmethods,
leading Cartwright to remark how odd it is that bayes nets methods prohibit the existence of causal
structures that violate stability.25
Ignoring Cartwright's conflation (which seemsto be due to Pearl's flawed justification of stability, which
we come to shortly),Cartwright gives anexample in which a drug (birth control pill) hasboth positive and
negative effects on an illness (thrombosis).26
She considers that we may want to develop a new version of
the drug, for which these effects cancel out, thus violating stability. This example is confused: bayes nets
methods do not assume stability when calculating the effects of interventions,such as changing the drug,
nor do they stop us from testing whether the effects cancel out. Cartwright's example would only be a
problem if the existing drug'seffects already cancelled out, i.e. we had littleto no knowledge of the prior
causal structure, and we wished to infer the structure by observation, using an algorithm such as PC.
Nevertheless, the fact that Cartwright'sexample is confused does not imply that stability always holds.
Pearl gives several justificationsof stability, but at least one of them is flawed. Pearl considers an example
in which two independent fair coins are flipped and a bell is tolled when the coins land the same.27
Pearl
notes that, in such an example, each variable is mutually independent of each other, but mutually
dependent conditionalonthethird.Aconditioncalledminimality (which wewill not define)isnot specific
enough for inferring the causal model from the observational data. Pearl asserts that the model 𝐶𝐶1 → 𝐵𝐵 ←
𝐶𝐶2, where 𝐶𝐶1, 𝐶𝐶2 are the coins and 𝐵𝐵 the bell, which is of course the correct causal model, is the only
minimal, stablemodel. Hence Pearl motivates stability as a more precise condition, allowing one to hone
in on the correct model. But, as Cartwright points out (and appears to become confused by, as above),this
model is not stable: in fact, there is no stable minimal model.So this is a legitimate instance of stability
violation on the true model.
Glymour addresses Cartwright’s concern by pointing out that some algorithms can be proved to work
without assuming stability.28
I offer that we should normally be able to detect instability by using our
23
(Glymour, 2010,pp.182-184)
24
(2001, pp.251-254)
25
(2001, p.252)
26
(2001, pp.246-253)
27
(2000, p.48)
28
(Glymour, 2010,pp.163-164)
27

29. knowledge about the variables. For instance, it seems clear in Cartwright’s biological example that it is
highly improbablefortwoindependent biologicaleffectstoperfectly cancel each otherout.If,ontheother
hand, we are dealing with fair coins and bells in which someone has deliberately set up a causal system, it
may well be that the causal system was set up to be unstable.
3. Conclusion
In section 1, I gave a few example applications of bayes nets methods. I showed how bayes nets methods
allow us to: consisely express causal knowledge, to infer probabilistic knowledge from causal knowledge,
to infer causal knowledge from probabilistic knowledge (with or without prior causal knowledge);and to
identify which variables to control for in order to calculate theeffect of interventions. In section 2, I built
on Glymour’s responses to Cartwright’s criticisms of bayes nets methods. In doing so, I argued that
Cartwright’s concerns could be rectified if we accept a new definition of the casual markov condition.
28

30. Bibliography
Cartwright, N. (2001)‘What is Wrong with BayesNets?’, The Monist, vol. 84, no. 2, pp.242-264.
Cartwright, N. (2007)‘Hunting Causes and Using Them: Approachesin Philosophy and Economics’,
Cambridge University Press.
Glymour, C. (2010) ‘What is Right with 'Bayes Net Methods' and What is Wrong with 'Hunting
Causes and Using Them'?’, British Journal for the Philosophy of Science, vol. 61, no. 1, pp.161-211.
Pearl, J. (2000) ‘Causality:Models, Reasoning, and Inference’,CambridgeUniversity Press.
Woodward, J. (2013)‘Causation and Manipulability’, in The Stanford Encyclopedia of Philosophy,
(Online), winter 2013 ed., E. N.Zalta, Ed., 2013. Available at:
http://plato.stanford.edu/archives/win2013/entries/causation-mani/
29