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+\chapter{Selfish Comparative Optimism: A Rejoinder to Nagasawa's \emph{Problem of Evil for Atheists}}
+\chaptermark{Selfish Comparative Optimism}
+\chapterauthor{Wilson Sugeng,
+\textit{University of St Andrews}}
+
+
+% Makes the section headings be formatted so it does `Section 1:', instead of just '1'
+\renewcommand*{\thesection}{Section~\arabic{section}:} 
+% \thesubsection might use \thesection, therefore it is also redefined
+\renewcommand*{\thesubsection}{\arabic{section}.\arabic{subsection}}
+
+
+\begin{quote}
+Yujin Nagasawa's problem of systemic evil (POSE) argues that systemic
+evils like natural selection pose a greater challenge to
+atheism/non-theism than to theism, as they conflict with ``modest
+optimism'': the view that the world is fundamentally ``not bad.''
+Nagasawa suggests theism resolves this by appealing to a heavenly bliss,
+offsetting natural evils, a strategy unavailable to
+atheists/non-theists. However, I argue that atheists/non-theists are
+better equipped to address POSE because they are not constrained by the
+theistic commitment to a categorically good world.
+
+In Section $1$, I critique two theistic approaches to POSE. Extreme
+optimism defends the actual world as the best possible one, requiring
+problematic justifications such as free-will and ``only-way'' theodicies
+to explain systemic evils as necessary. Neutral optimism, while allowing
+for multiple good worlds, still struggles to reconcile systemic evils
+with a benevolent God, merely shifting the problem to other possible
+worlds.
+
+In Section $2$, I explore how atheists/non-theists can bypass POSE. They
+can adopt personal, rather than cosmic, optimism, valuing their own
+existence without affirming the world's overall goodness. Alternatively,
+they can embrace comparative optimism, viewing existence as better than
+non-existence without attributing intrinsic value to natural processes
+like evolution. These flexible approaches free non-theists from the
+philosophical burdens tied to systemic evils.
+
+In Section $3$, I argue that even if POSE persists, atheists/non-theists
+can ``borrow'' theists' theodicies without committing to their
+metaphysical assumptions. By adopting naturalistic or subjective
+frameworks, non-theists can justify their modest optimism without the
+theological constraints imposed by theism. This demonstrates that POSE
+ultimately challenges theistic frameworks more than atheistic ones.
+\end{quote}
+
+\vspace{\credgap}
+
+\section*{Introduction}
+
+In \emph{The Problem of Evil for Atheists,} Yujin Nagasawa develops a
+problem of systemic evil (POSE) that he claims challenges both
+atheists/non-theists and theists alike.\footnote{When I say, ``God'' and
+  ``Theism'' in this paper, I assume an omniscient, omnipotent, and
+  omnibenevolent singular/simple creator.} He identifies a tension
+between two widely held theses: 
+
+\begin{enumerate}[leftmargin=42]
+\def\labelenumi{(\arabic{enumi})}
+\item
+  Systemic evil: The process of natural selection necessitates
+  significant suffering and pain for countless sentient animals.
+\item
+  Modest optimism: Overall and fundamentally, the environment in which
+  we exist is not bad.\footnote{Yujin Nagasawa, \emph{The Problem of
+    Evil for Atheists} (Oxford University Press, 2024), 133, 140.}
+\end{enumerate}
+
+\noindent While theists naturally affirm modest optimism due to their belief in a
+benevolent creator God, Nagasawa observes that atheists/non-theists are
+also generally grateful for their existence.\footnote{Nagasawa,
+  \emph{The Problem of Evil for Atheists}, 161.} For instance, popular
+atheist Richard Dawkins suggests that contemplation of the law-like
+evolutionary processes behind our existence puts us ``in a position to
+give thanks for our luck in being here''---not a gratitude directed
+towards any agent or being, but rather a ``gratitude in a
+vacuum.''\footnote{Richard Dawkins, ``The Greatest Show on Earth
+  Live'' (lecture, University of Auckland, Auckland, New Zealand, 13
+  March 2010).} Nagasawa sees this as inconsistent: expressing
+existential gratitude without acknowledging the systemic evils
+underpinning it implies a tacit endorsement of these evils.
+
+To illustrate this tension, Nagasawa adapts Janna Thompson's apology
+paradox, which holds that regretting an unjust historical event can be
+problematic if one's existence depends on that event. For example, a Jew
+whose grandparents met during the Holocaust faces a paradox: to regret
+the Holocaust may seem to imply regretting her own existence.\footnote{Janna
+  Thompson, ``The Apology Paradox,'' \emph{The Philosophical Quarterly}
+  50\emph{,} No. 201 (2000): 471.} Thompson resolves this by
+distinguishing between regretting \emph{how} one came to exist and
+\emph{that} one exists---the Jew can regret \emph{how} her grandparents
+met, without regretting \emph{that} they met at all.\footnote{Janna
+  Thompson, ``The Apology Paradox,'' \emph{The Philosophical Quarterly}
+  50\emph{,} No. 201 (2000): 475.} Applied to POSE, this seems to suggest that one can regret the
+mechanisms of natural selection without regretting the outcome of our
+existence.
+
+However, Nagasawa argues that this resolution fails in the context of
+POSE. Unlike historical events, natural selection is not a contingent
+circumstance but a fundamental feature of the natural world.\footnote{Nagasawa,
+  \emph{The Problem of Evil for Atheists}, 167.} To reject it is not to
+regret a particular pathway to existence, but to undermine the very
+conditions that make existence possible. That is, there is no possible
+world where natural selection does not govern nature and beings like us
+still exist.
+
+Theists, Nagasawa argues, are better positioned to defend modest
+optimism, drawing on ``heavenly bliss'' theodicies that justify or
+outweigh earthly suffering with the promise of an afterlife. These come
+in two forms: (1) as a deferred justification, where evolution is
+acceptable because it leads to eternal reward, and (2) as a utilitarian
+offset, where infinite heavenly bliss outweighs finite worldly
+suffering. Because atheists cannot appeal to such concepts, POSE, he
+claims, presents a more serious problem for atheists.
+
+Contrary to Nagasawa, I argue that atheists and non-theists are better
+positioned to address POSE because they are not constrained by the
+theistic requirement to see the world as overall categorically good. To
+support this claim, I first critique two theistic attempts at resolving
+systemic evil, namely extreme and neutral optimism, illustrating their
+shortcomings. Subsequently, I explore how atheists/non-theists might
+effectively sidestep POSE by adopting personal rather than cosmic
+optimism, or by embracing a comparative optimism which sees existence as
+preferable to non-existence without categorically endorsing the systems
+that facilitated it. Finally, I turn Nagasawa's borrowing argument
+around to propose that, even if POSE remains challenging,
+atheists/non-theists can strategically adopt theistic theodicies without
+their accompanying metaphysical assumptions, thereby reducing POSE's
+impact and revealing it to be ultimately a greater challenge for
+theistic frameworks than for atheistic or non-theistic ones.
+
+\section{Two Theist Modest Optimists}
+\subsection{Extreme optimism}
+
+The first theist modest optimists---extreme optimists---claim that
+because God actualised the best among all possible worlds, systemic evil
+must necessarily exist in all good worlds. Although Gottfried Wilhelm
+Leibniz does not himself discuss systemic evil and predates evolution,
+his \emph{Theodicy} (1710) presents a system where given God's
+omnibenevolence and omniscience---if a possible world is better than the
+actual, then God would either not be good enough to desire the best for
+the world, or ignorant in not knowing which world is the
+best.\footnote{G. W. Leibniz, \emph{Theodicy,} edited by Austin Farrer,
+  translated by E. M. Huggard (Open Court Publishing Company, 1985),
+  249.}
+
+As an implication, extreme optimists must affirm Nagasawa's claim that
+no possible world exists in which natural selection does not govern
+nature; for if God is necessary, then no other world is possible.
+Natural selection must therefore serve an instrumental role in the
+world's goodness. Building on this system, Austin Farrer argues that the
+removal of any such purported evil systems will undermine God's
+mechanism for bringing about the best world. The goodness of a physical
+system, for instance, inherently includes the potential for mutual
+interference, leading to evils like predation. Without this
+interference---if this world were a ``magically self-arranged garden''
+free of competition for space or resources---physicality itself ceases
+to exist.\footnote{Austin Farrer, \emph{Love Almighty and Ills
+  Unlimited} (Collins, 1962), 53-54.} Removing such systems would
+be akin to relieving an animal's pain ``by the removal of its nervous
+system; that is to say, of its animality.''\footnote{Austin Farrer, \emph{Love Almighty and Ills Unlimited} (Collins, 1962), 51.}
+Regretting natural selection thus implicitly challenges God's
+rationality and goodness in creating us as physical beings rather than
+spiritual entities.\footnote{Austin Farrer, \emph{Love Almighty and Ills
+  Unlimited} (Collins, 1962), 67.}
+
+An immediate difficulty with extreme optimism is that claiming this
+world to be the best possible one is hard to reconcile with the presence
+of seemingly avoidable evils observed throughout nature. This tension is
+captured ironically in the eponymous character of Voltaire's
+\emph{Candide} (1759) who insists that this is the best possible world
+as he faces a world plagued with wars, earthquakes, and
+slavery.\footnote{Nagasawa, \emph{The Problem of Evil for Atheists,}
+  129.} Or when Darwin questions why God permitted the creation of the
+Ichneumonidae who brutally feeds inside the living bodies of
+caterpillars.\footnote{Charles Darwin, ``22 May 1860 Letter to Asa
+  Gray,'' Darwin Correspondence Project, accessed on 5 December 2024,
+  https://www.darwinproject.ac.uk/letter/DCP-LETT-2814.xml.} This
+presents a major challenge: extreme optimism struggles to align with
+observable, avoidable evils unless it denies these empirical
+observations---as some Creationists do---or reinterprets such systemic
+evils as necessary.\footnote{Paul Prescott, ``The Secular Problem of
+  Evil: An Essay in Analytic Existentialism,'' \emph{Religious Studies}
+  57 (2021): 102.}
+
+Granting natural selection's empirical truth, theists generally present
+two kinds of theodicies for \emph{why} God actualised natural selection.
+Firstly, theists have adapted the free-will theodicy to address some
+non-agential non-human suffering. In traditional free-will theodicies,
+God permits agents the capacity to choose evil over good as the goodness
+of human agency outweighs the risks of their choosing evil. In one
+adaptation, Richard Swinburne argues that animal pain and suffering
+exists as examples of evil actions humans can inflict on each other.
+Predation therefore exists as an educational tool for humans to observe
+and understand how to commit evil, thereby enabling their capacity for
+moral choice.\footnote{Richard Swinburne, ``Natural Evil,''
+  \emph{American Philosophical Quarterly} 15\emph{,} No. 4 (1978): 299.}
+
+Secondly, theists have adapted a variation of the soul-making theodicy
+known as the ``only-way'' theodicy, arguing that certain natural goods
+can only develop through natural selection. Holmes Rolston observes that
+the predator-prey cycle is instrumental to the beautiful diversity of
+animals, where ``The cougar's fang has carved the limbs of the
+fleet-footed deer, and vice versa.''\footnote{Holmes Rolston III,
+  \emph{Science and Religion: A Critical Survey} (London: Templeton
+  Foundation press, 2006), 134.} While Young-Earth Creationism may have
+created this diversity instantaneously, Christopher Southgate argues
+that natural selection is the only way creatures can develop into
+biological ``selves'' with their own interests and
+behaviours.\footnote{Southgate, \emph{The Groaning of Creation}, 58.}
+This offsets any evolutionary evils for it culminates into complex
+``selves'' that conform to God's image.\footnote{Southgate, \emph{The Groaning of Creation}, 72.} This
+``selving'' must come independently, for Peter van Inwagen argues that
+an irregular world is a defect: God who constantly intervenes and
+violates his own laws is either a irrational or evil.\footnote{Peter van
+  Inwagen, ``The Problem of Evil, the Problem of Air, and the Problem of
+  Silence,'' \emph{Philosophical Perspectives} 5 (1991): 143-45.} So,
+common to both free-will and ``only-way'' theodicies is a notion that
+some ultimate good offsets the evils of natural selection as an
+instrument.
+
+However, these two theodicies only defer the problem of evil to another
+system underlying the challenged system. For instance, free-will
+theodicies must still address Pierre Bayle's objection: If God's
+omniscience foresees that giving humanity free will inevitably results
+in unrighteousness, then God is either reckless or cruel to ``gift''
+humanity agency, knowing it would lead to their harm and judgment under
+his wrath.\footnote{Pierre Bayle, \emph{Historical and Critical
+  Dictionary: Selections,} translated by Richard H. Popkin and Craig
+  Brush (Hackett, 1991), 177.} Echoing Bayle, Robert John Russell
+questions, ``Why did God choose to create \emph{this} universe with
+\emph{these} laws of physics knowing that they would not only make
+Darwinian evolution unavoidable, and with it the sweep of natural evil
+in the biological realm?''.\footnote{Robert John Russell, ``Natural
+  Theodicy in an Evolutionary Context,'' in \emph{Cosmology: From Alpha
+  to Omega} (Fortress Press, 2008), 259.} It appears, then, that extreme
+optimism is burdened with regressive manifestations of the problem of
+evil.
+
+In sum, while extreme optimists attempt to reconcile systemic evil with
+the claim that this is the best possible world through the use of
+free-will and ``only-way'' theodicies, such strategies ultimately defer
+rather than resolve the problem. Faced with empirical evidence of
+seemingly gratuitous suffering, they must either deny these realities or
+accept increasingly speculative theological explanations. While extreme
+optimism may appeal to the heavenly bliss defence, it still does not
+explain \emph{why} natural selection is the best possible means towards
+that end without returning to this regress or begging the question. As
+such, extreme optimism appears ill-equipped to resolve the tension
+Nagasawa identifies between systemic evil and modest optimism. So,
+theists must either concede that natural selection is not the best
+necessary instrument in the best possible world, or following Bayle and
+Russell accept the former's pessimism or latter's ``agnostic cosmic
+theodicy'' in accepting that POSE cannot be answered.\footnote{Robert John Russell, ``Natural Theodicy in an Evolutionary Context,'' in \emph{Cosmology: From Alpha
+  to Omega} (Fortress Press, 2008), 255.}
+
+
+\subsection{Neutral optimism}
+
+
+The second theist modest optimists, the neutral optimists, reject that
+the actual world is necessarily the best, but rather affirms that God
+actualised one of many possible overall good worlds. For instance,
+Robert Merrihew Adams argues that extreme optimism inappropriately
+imposes a utilitarian standard of moral goodness to God's
+omnibenevolence. Instead, he argues that traditional Judeo-Christian
+ethics account for God's goodness in terms of his grace---an inclination
+to love that is not based on the merit of the one being
+loved.\footnote{Robert Merrihew Adams, ``Must God Create the Best?'',
+  \emph{Philosophical Review} 81 (1972): 324.} Indeed, core to Abrahamic
+monotheism is an affirmation of God's aseity, his self-sufficiency and
+independence from any external cause or necessity. \footnote{Ian A.
+  McFarland, \emph{From Nothing: A Theology of Creation} (Westminster
+  John Knox Press, 2014), 61.} If God were obligated to create the best
+possible world in order to express his power or love, then his
+omnipotence and omnibenevolence would become contingent on something
+external---namely, the existence of that world---thereby undermining his
+aseity. It follows, therefore, that a being who never exists is not
+wronged by not being created, since existence itself is not owed to any
+potential being.\footnote{Adams, ``Must God Create the Best? 319-20.}
+Furthermore, beings in the actual but not best world have no right to
+complain, lest they express an unmerited claim for special treatment or
+violate modest optimism.\footnote{Adams, ``Must God Create the Best? 319-20.} God's omnibenevolence,
+therefore, does not demand that he create the best world possible.
+
+As an implication, neutral optimists can entertain that there is a
+possible world without natural selection where we exist. However, two
+considerations may constrain this possibility. Firstly, this possible
+world must be logically coherent. Thomas Morris argues that if God's
+omnipotence is committed to what is logically and semantically possible,
+God becomes a ``delimiter of possibilities.''\footnote{Thomas V. Morris,
+  ``The Necessity of God's Goodness,'' \emph{New Scholasticism} 59
+  (1985): 425.} That is, as God's existence is necessary in all possible
+worlds, those worlds must reflect his omnipotence by being logically
+coherent and his omnibenevolence by being overall good. This means that
+if a world without natural selection either fails to be logically
+coherent or cannot sustain overall goodness without introducing other
+systemic evils, it may not be a genuine possibility after all. Secondly,
+this limitation implies that a possible world without natural selection
+where we exist is not necessarily better or worse than the actual world.
+It could very well be that following the ``only-way'' theodicies, the
+goodness of true biological selves must necessarily come through natural
+selection and that this outweighs the evil of natural selection.
+Regardless, the neutral optimist is distinct in that they can be
+grateful for their existence without necessarily implying that natural
+selection is instrumentally good.
+
+One obvious challenge against neutral optimism is its shifting
+definition of God's omnibenevolence may not be intuitively satisfying.
+For instance, Adams's definition of God's ``grace'', which does not
+require universal benevolence to all creatures, may only be satisfactory
+to some Calvinists or those within certain theological traditions. While
+this conception asserts that natural selection does not need to be
+justified as instrumentally good, the reality and impact of systemic
+evil make it difficult for suffering beings to reconcile that God's
+omnibenevolence does not require him to show grace to them, in tension
+with their own intuitions about what it means to be loving. However, as
+this critique may hold less weight for those aligned with certain
+Calvinist doctrines, where such a conception of grace is more readily
+accepted, it will be set aside as a doctrinal matter.
+
+A more universal challenge is that even if a neutral optimist can
+maintain modest optimism about their existence while affirming systemic
+evil through yearning for another possible world, logical constraints on
+such worlds mean that regretting the evils of the actual world may
+require relinquishing goods unique to its constitution. For example,
+recalling Swinburne's free-will theodicy, a possible world without
+natural selection might lead to it not having human agency. Similarly,
+recalling Southgate's ``only-way'' theodicy, a world without natural
+selection could lack independent selves. If the existence of goods like
+human agency or autonomous selves carry significant moral weight, then
+removing the conditions that produce them (i.e., natural selection) may
+render the alternative world no longer overall good---and thus not
+genuinely possible. At best, such possible worlds without natural
+selection might not involve a loss of goods significant enough to
+undermine modest optimism. At worst, the trade-offs could introduce
+greater problems of evil. A creationist world, for instance, implies
+that God played a direct role in designing cruel beings like the
+Ichneumonidae than if they developed independently through evolution.
+
+Comparing extreme and neutral theistic optimism, both conceptions of
+modest optimism requires that the world is overall good. This is because
+evidence of systemic evils must be outweighed by some other goodness or
+burdened with a theodicy. This, however, is not a requirement for
+atheist/non-theist optimism.
+
+\section{Two atheist/non-theist modest optimists}
+\subsection{Personal optimism}
+
+The first atheist/non-theist modest optimist approach argues that the
+scope of existential gratitude can be limited to the personal level
+without axiologically considering the world as an aggregate. While
+Dawkins expresses his gratitude for existing despite unfavourable odds,
+he regrets that, ``Nature is red in tooth and claw. But I don't want to
+live in that kind of a world. I want to change the world in which I live
+in such a way that natural selection no longer applies.''\footnote{Frank
+  Miele, ``Darwin's Dangerous Disciple: An Interview with Richard
+  Dawkins,'' \emph{The Skeptic}, 27 October 2010,
+  \url{https://www.skeptic.com/eskeptic/10-10-27/}.} However, we can
+resolve Dawkins' apparent disjunct by affirming \emph{personal}
+existential optimism directed at one's own existence while rejecting
+\emph{cosmic} existential optimism that the world is overall good. This
+is not methodologically novel; Asha Lancaster-Thomas observes that even
+within individuals' lifetimes, we are grateful for some parts of our
+lives, but not parts characterised by pain and suffering such as a
+painful chronic illness.\footnote{Asha Lancaster-Thomas, ``Can Heaven
+  Justify Horrendous Moral Evils? A Postmortem Autopsy,''
+  \emph{Religions} 14, No. 296 (2023): 6.}
+
+An implication of personal, but not cosmic, optimism is that their
+existential gratitude does not need to consider the axiology of natural
+selection. One could remain axiologically agnostic towards the
+instruments of their existence, while valuing the goodness of their
+personal existence. Guy Kahane emphasises this distinction by arguing
+that even if natural selection is a causally fundamental instrument to
+our existence, it is axiologically irrelevant as instrumental value
+alone does not add any overall value to the world.\footnote{Guy Kahane,
+  ``Optimism without theism? Nagasawa on Atheism, Evolution, and Evil,''
+  \emph{Religious Studies} 58 (2022): 706.} Under this conception, one
+could even be cosmically pessimistic but still be optimistic about their
+personal life as they experience it. Modest optimism is thus
+reinterpreted to affirm attitudinal optimism, that we are grateful to
+exist in this world; but not axiological optimism, that the world is
+overall good.\footnote{Guy Kahane, ``Optimism without theism? Nagasawa on Atheism, Evolution, and Evil,'' \emph{Religious Studies} 58 (2022): 702.}
+
+However, after disregarding pessimism, personal optimism appears
+empirically challenged as most personal optimists are often implicitly
+also cosmic optimists. Responding to Kahane, Nagasawa grants that
+personal optimism does not necessarily entail cosmic optimism. However,
+he argues that this reformulation of modest optimism changes the target
+of POSE, which defines modest optimism as affirming both attitudinal and
+axiological optimism.\footnote{Nagasawa, \emph{The Problem of Evil for
+  Atheists,} 184.} For he argues that rational personal optimists who
+procreate implicitly believe that the world they are bringing their
+child into is overall a good place.\footnote{Nagasawa, \emph{The Problem of Evil for
+  Atheists,} 184.} The personal, but
+not cosmic, reformulation of modest optimism, therefore, seemingly
+misses the original target of POSE and is only applicable to a minority
+of anti-natalist pessimists like David Benatar.
+
+Responding to this, Nagasawa's formulation of modest optimism is already
+limited to the scope of``the environment in which we exist.'' The
+specific environment of individual experiences does not necessarily
+include the predation experienced by other preyed beings. Indeed, this
+does not preclude the modest optimist from being selfish for bringing a
+child into the world. Or disregarding the pains of the world, a
+personally optimistic individual can choose to be ignorant of the
+world's plights by never contributing to charitable causes to use the
+money to instead maximise personal pleasures. It is not evident,
+therefore, that most personal optimists must also be cosmic optimists.
+
+\subsection{Comparative optimism}
+
+The second atheist/non-theist modest optimist approach argues that
+modest optimism only views the world as \emph{comparatively} good, but
+not necessarily \emph{categorically} good. That is, the world must only
+be \emph{comparatively} better than non-existence, rather than
+positively good. This distinction is significant, as Nagasawa's
+comparative argument for theism seems to present the axiology of the
+world in binary categorical terms. Theism's appeal to a heavenly bliss
+allows for a world with more goodness rather than evil.\footnote{Nagasawa, \emph{The Problem of Evil for Atheists,} 171.} But because atheists/non-theists are not committed to affirming
+an omnibenevolent God, Kahane argues that they are not obliged to claim
+that their existence is categorically good, or that the world contains
+more goodness than evil. Indeed, even under Leibniz's extreme optimism,
+the world is not necessarily categorically good, just that it is
+comparatively the best of all possible worlds.\footnote{Kahane,
+  ``Optimism Without Theism,'' 713.}
+
+An implication of a comparatively better, but not categorically good,
+optimism is that natural selection does not have to be categorically
+good. Assuming that existence in itself is a good greater than all kinds
+of non-existence, an actual world with systemic evil is better than any
+unactualised world. So, modest optimism's ``not bad'' is equated to
+being comparatively better than non-existence. Opposing theism's appeal
+to the supernatural, this essentially lowers the requirement for modest
+optimism.
+
+One major challenge is that this comparative-goodness version of modest
+optimism closely borders on pessimism, and therefore demands an account
+of why existence, despite systemic evils, is fundamentally and overall
+better than non-existence. The pessimist Benatar, for instance, argues
+that the absence of pain is always good, even if no one benefits,
+whereas the absence of pleasure is only bad if someone is deprived by
+it. This asymmetry supports his claim that existence, with its
+inevitable suffering, may be worse than non-existence, which guarantees
+goodness with no badness.\footnote{David Benatar, \emph{Better Never to
+  Have Been: The Harm of Coming into Existence} (Oxford University
+  Press, 2006), 30.}
+
+Responding to Benatar, the optimist can follow Thaddeus Metz's argument
+against Benatar's claim that the absence of pain is good, describing the
+absence of pain as \emph{not bad} rather than \emph{good.}\footnote{Thaddeus
+  Metz, ``Are Lives Worth Creating?'', \emph{Philosophical Papers} 40,
+  No. 2 (2011): 241-45} Otherwise, the atheist/non-theist modest
+optimist can simply appeal to the previously-discussed personal, rather
+than cosmic, optimism. All modest optimism demands is that according to
+myself, it is better for me to exist than for me not to exist. Indeed,
+Benetar seems to grant this notion, as he distinguishes a present-tense
+``life worth continuing'' and future-tense ``life worth
+starting.''\footnote{Benatar, \emph{Better Never to Have Been,} 22-23.}
+Personal optimists often experience instances where the goods of
+actualised pleasure outweigh the evils of pain, resulting in a net
+utility that makes existence preferable to non-existence. So, unless one
+is personally pessimistic, there is nothing paradoxical about claiming
+one's personal life is better to exist than not exist.
+
+Combining these two approaches, the atheist/non-theist, can commit to a
+personal and comparative form of modest optimism that still accounts for
+the categorically systemic evil of the cosmos. Unlike theistic extreme
+optimism's commitment to the instrumental value of natural selection as
+a part of God's providence, personal optimists can simply remain
+agnostic about natural systems' axiological value. But while theistic
+neutral optimists can adopt a similar approach to the
+atheism/non-theism's comparative (not categorical) goodness, they remain
+committed to both that possible worlds must overall be good, and that
+God's creative ability is bound to logical laws, so that the possible
+worlds they yearn for must necessarily contain some other kind of
+systemic evil that requires a theodicy . The personal optimist on the
+other hand need not make this consideration of the overall goodness of
+other possible worlds. So, whilst theism can appeal to the heavenly
+bliss, the non-theist can simply bypass POSE without needing to address
+it.
+
+\section{Borrowing Theism's Optimism Without its Metaphysics}
+
+But even if atheists/non-theists remain burdened by POSE due to perhaps
+their cosmic or even categorical optimism, I propose that they can
+``borrow'' the theodicies used by theists to justify their modest
+optimism. This reverses Nagasawa's theistic strategy, which claims that
+theism's supernaturalist ontology (encompassing both natural and
+supernatural realms) subsumes the atheist/non-theist's naturalist
+ontology (limited to the natural world), thus allowing theists to
+``borrow'' atheist/non-theist responses to POSE.\footnote{Nagasawa,
+  \emph{The Problem of Evil for Atheists,} 173.} However, Nagasawa does
+not address the fact that supernaturalist ontologies bring additional
+axiological presuppositions---namely, that an omnibenevolent God exists
+and that his creation must necessarily be overall and categorically
+good. Non-theists, by contrast, can adopt the theist's belief that the
+world is overall good using the theist's rationalisations, without
+committing to these broader metaphysical claims about God. In essence,
+atheists/non-theists can justify their optimism in the face of POSE
+without having to commit to the theist's wider ontological framework.
+
+Borrowing from extreme theistic optimism, the atheist/non-theist can
+still view natural selection as categorically good by appealing to the
+same free-will and ``only-way'' theodicies---without relying on
+theological assumptions. For instance, they may regard natural selection
+as instrumentally necessary for the emergence of goods like human
+free-will or biological selves and affirm these outcomes as
+categorically valuable in themselves. There is nothing inherently
+theological in valuing such features of natural history. While theists
+might argue that moral value requires an objective grounding in God, the
+atheist can respond in two ways: either by offering a naturalistic
+foundation for moral value, or by treating such value judgements---and
+the modest optimism they support---as subjective, grounded in personal
+or shared human perspectives. On this view, modest optimism need not
+depend on the objective truth of its content but rather functions as an
+attitudinal stance. Accordingly, theist theodicies can be borrowed by
+non-theists as explanatory tools, enabling them to affirm the world's
+overall goodness without committing to metaphysical claims that theists
+traditionally used to justify them.
+
+Borrowing from neutral theistic optimism, the atheist/non-theist can
+still affirm that the actual world is not necessarily the best possible
+world, but still trust that it is better to exist than not to exist. The
+lack of a requirement for atheists/non-theists to commit to the idea
+that the world is categorically good allows for a more flexible
+position. Even if systemic evils suggest that the world is not
+fundamentally good, the personal optimist can still maintain a stance of
+cosmic neutrality. They can accept the world as it is---flawed, but not
+necessarily bad in a way that undermines their gratitude for existing.
+Indeed, without a commitment to an omnibenevolent God who governs over
+all creation's actions, the non-theist can simply adopt a position of
+gratitude for the outcomes of those processes without ascribing moral or
+intrinsic value to these violent/harsh (but not immoral) systemic
+processes themselves.
+
+This strategic borrowing highlights a key asymmetry: while theists must
+reconcile systemic evil with a metaphysical commitment to a
+categorically good creation, non-theists can adopt similar explanatory
+frameworks without such constraints. In doing so, they preserve the
+practical benefits of modest optimism without incurring the theological
+debts that weigh down the theistic response to POSE.
+
+\section*{Conclusion}
+
+POSE, therefore, remains a problem only for theists as their conception
+of modest theism must commit to the belief that a good God would create
+a categorically good world. This commitment imposes significant burdens
+ontheist extreme optimists, whose belief that the actual world is the
+best possible world obliges them either to embrace pessimism, appeal to
+mystery, or present a theodicy for systemic evils. And while responses
+like the free-will and ``only-way'' theodicies may present \emph{prima
+facie} defences to POSE, they only regress into deeper manifestations of
+the problem of evil unless the theist begs the question or makes an
+appeal to mystery. Likewise, theist neutral optimists, who holds that
+the actual world is only one of many possible worlds that are not
+necessarily the best ones, remain committed to asserting that world is
+overall good---which is still difficult to reconcile with or even
+amplifies the existence of systemic evils.
+
+In contrast, the atheist/non-theist can either borrow the
+theist's theodicies, or maintain a personal comparative optimistic
+stance that disregards POSE overall. By selfishly narrowing modest
+optimism to the personal level, the atheist/non-theist can disregard
+systemic evils while remaining grateful for their own lives as they
+experience it. Furthermore, their non-commitment to categorical goodness
+allows them to value comparatively their personal lives as better than
+non-existence, even if by borrowing neutral optimism, they accept the
+world as it is and appreciate the outcomes of systemic processes like
+natural selection without assigning moral or intrinsic value to them.
+
+
+\newpage  
+\section*{Bibliography}
+
+\refsection
+
+\begin{hangparas}{\hangingindent}{1}
+Adams, Robert Merrihew. ``Must God Create the Best?''
+\emph{Philosophical Review} 81 (1972): 317-332.
+
+Bayle, Pierre. \emph{Historical and Critical Dictionary: Selections.}
+Translated by Richard H. Popkin and Craig Brush. Indianapolis, IN:
+Hackett, 1991.
+
+Benatar, David. \emph{Better Never to Have Been: The Harm of Coming into
+Existence}. Oxford University Press, 2006.
+
+Darwin, Charles. ``22 May 1860 Letter to Asa Gray.'' Darwin
+Correspondence Project. Accessed on 5 December 2024.
+\newline
+\url{https://www.darwinproject.ac.uk/letter/DCP-LETT-2814.xml}.
+
+Dawkins, Richard. ``The Greatest Show on Earth.'' Lecture, University of
+Auckland, Auckland, New Zealand, 13 March 2010. Accessed on 3 May 2025.
+\newline
+\url{https://www.auckland.ac.nz/en/alumni/whats-happening/alumni-video-and-audio/alumni-videos-richard-dawkins.html}.
+
+Rolston III, Holmes. \emph{Science and Religion: A Critical Survey.}
+London: Templeton Foundation Press, 2006.
+
+Farrer, Austin. \emph{Love Almighty and Ills Unlimited.} Collins, 1962.
+
+Guy, Kahane. ``Optimism without theism? Nagasawa on atheism, evolution,
+and evil.'' \emph{Religious Studies} 58 (2022): 701-714.
+
+Lancaster-Thomas, Asha. ``Can Heaven Justify Horrendous Moral Evils? A
+Postmortem Autopsy.'' \emph{Religions} 14, No. 296 (2023).
+
+Leibniz, G. W. \emph{Theodicy.} Edited by Austin Farrer. Translated by
+E. M. Huggard. Open Court Publishing Company, 1985.
+
+McFarland, Ian A. \emph{From Nothing: A Theology of Creation.}
+Westminster John Knox Press, 2014.
+
+Metz, Thaddeus. ``Are Lives Worth Creating?'' Philosophical Papers 40,
+No. 2 (2011): 233-255.
+
+Miele, Frank. ``Darwin's Dangerous Disciple: An Interview with Richard
+Dawkins,'' The Skeptic. 27 October 2010.
+\newline
+\url{https://www.skeptic.com/eskeptic/10-10-27/}.
+
+Morris, Thomas V. ``The Necessity of God's Goodness.'' \emph{New
+Scholasticism} 59 (1985): 418-448.
+
+Nagasawa, Yujin. \emph{The Problem of Evil for Atheists.} Oxford
+University Press, 2024.
+
+Prescott, Paul. ``The Secular Problem of Evil: An Essay in Analytic
+Existentialism.'' \emph{Religious Studies} 57 (2021): 101-119.
+
+Russell, Robert John. ``Natural Theodicy in an Evolutionary Context.''
+In \emph{Cosmology: From Alpha to Omega}. Fortress Press, 2008.
+
+Southgate, Christopher. \emph{The Groaning of Creation: God, Evolution,
+and the Problem of Evil.} Westminster John Knox Press, 2008.
+
+Swinburne, Richard. ``Natural Evil.'' \emph{American Philosophical
+Quarterly} 15\emph{,} No. 4 (1978): 295-301.
+
+Thompson, Janna. ``The Apology Paradox.'' \emph{The Philosophical
+Quarterly} 50, No. 201 (2000): 470-475.
+
+Van Inwagen, Peter. ``The Problem of Evil, The Problem of Air, and the
+Problem of Silence,'' \emph{Philosophical Perspectives} 5 (1991):
+135-165.
+
+\end{hangparas}
\ No newline at end of file
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+
+\chapter{A Defence of the Interpretational Account of Validity}
+\chaptermark{A Defence of the Interpretational Account of Validity}
+\chapterauthor{Audrey Hammer,
+\textit{University of Cambridge}}
+
+\begin{quote}
+Both the interpretational account and the representational account
+provide contrasting accounts of validity for natural-language arguments.
+While the interpretational account captures formal validity, unlike the
+representational account, it does not capture materially valid
+arguments. Therefore, materially valid arguments are viewed as
+counterexamples to the interpretational account. I motivate why we may
+want to defend the interpretational account over the representational
+account and then proceed to defend the interpretational account using
+the suppressed premise strategy. The first objection to the suppressed
+premise strategy is by Stephen Read, who argues that the supressed
+premise is redundant. My contribution is to demonstrate how his
+objection fails. I also discuss and defend the suppressed premise
+strategy against other objections, which concern the nature of the
+supressed premise and the problem of modus ponens.
+\end{quote}
+
+\vspace{\credgap}
+
+\section*{Introduction}
+
+Validity, a key concept in logic, concerns whether an argument is
+truth-preserving. The interpretational account of validity defends the
+view that for an argument to be valid it must be formally valid. I turn
+first to the importance of logical form, its role in logic, generally,
+and validity, specifically. My discussion then moves to the
+interpretational account alongside its rival, the representational
+account. Both accounts face distinct issues. While I do not hold that
+the representational account is incoherent, I do hold that its
+formulation has weaknesses that are absent in the interpretational
+account, giving a motivation for preferring the latter rather than the
+former. Materially valid arguments, which are not formally valid,
+present counterexamples to the interpretational account. The remainder
+of the essay is devoted to showing how the suppressed premise strategy
+can defend the interpretational account against this main objection. The
+suppressed premise strategy will in turn be defended against pressing
+objections, primarily Stephen Read's objection that the suppressed
+premise is redundant. This objection to the supressed premise strategy
+aims to prove that there is a contradiction in adding a suppressed
+premise to an already materially valid argument, and my contribution is
+to show how this objection fails. I then go on to defend the suppressed
+premise strategy against a few other objections, including objections
+concerning the nature of the suppressed premise and the argument, and
+the problem of modus ponens. The result is a defence of the
+interpretational account of validity, using the suppressed premise
+strategy.
+
+\section*{Understanding the Relation Between Logical Form and Validity}
+
+Logic is considered the science of deduction: it deals with arguments
+and their validity. In formal logical languages, like truth functional
+logic and first order logic, we can capture validity using the standard
+notion of logical consequence. A formal argument is valid if the
+conclusion is a logical consequence of the premises. As Owen Griffiths
+and Alexander Paseau put it, ``A formal sentence $\phi$ is a logical
+consequence of a set of formal sentences $\gamma$ just if every model of $\gamma$ is a
+model of $\phi$''.\footnote{Owen Griffiths and Alexander Paseau, \emph{One
+  True Logic} (Oxford: Oxford University Press, 2022), 8.} Thus, we can
+describe the formal notion of validity for a logical language, using a
+model-theoretic notion of logical consequence.
+
+Once we have captured the notion of validity for logical languages, we
+can move on to understanding the concept of validity as applied to
+natural language, as the accounts of validity that will be discussed are
+accounts of validity for natural language. To understand validity as
+applied to natural language, we must introduce the concept of logical
+form. Logical form is generally considered to be a property of a
+sentence of natural language. The logical form of a sentence is when,
+keeping the logical constants fixed, the non-logical expressions get
+replaced with variables of the appropriate sort. Thus, the logical form
+of a sentence can be expressed using a schema. Given this schematic
+representation of form, we can follow Alfred Tarski in the view that
+logic is topic neutral, because a schema abstracts from the content of
+the sentence, only retaining the form of the sentence. For example, take
+the following sentence:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\item
+  Pigeons wear vests and cats wear hats.
+\end{enumerate}
+
+\noindent This sentence can be expressed using the following schema:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{1}
+\item
+  A $\land$ B.
+\end{enumerate}
+
+\noindent This is because the logical expression in sentence (1) is ``and'' which
+can be formalised using the symbol ``$\land$'', and the non-logical
+expressions in the sentence are ``pigeons wear vests'' and ``cats wear
+hats'', and thus these expressions are replaced with variables.
+
+One stipulation with this account of logical form, is that it requires
+us to have an understanding of what a logical constant is. Thus far
+formality has been captured by its topic neutrality, and since a
+demarcation of logical notions is crucial to form, it makes sense to
+construct this demarcation using this quality of topic neutrality. Here
+we can invoke Tarski's account of isomorphism invariance. Tarski defines
+logical notions using an analogy from geometry. Just as we may demarcate
+particular geometrical objects by their invariance under
+transformations, so too can we demarcate logical notions. Thus, ``we
+call a notion 'logical' if it is invariant under all possible one-one
+transformations of the world onto itself''.\footnote{Alfred Tarski,
+  ``What are Logical Notions?,'' \emph{History and Philosophy of Logic}
+  7\emph{,} (1986), 149.} To explain this further, we can consider an
+isomorphism to be a bijective function, so between two structures there
+is a one-one mapping, which preserves all the relevant relations. This
+isomorphism is the transformation that Tarski is speaking of. For a
+relation to be isomorphic invariant it must remain unchanged over this
+sort of transformation. A relation that is isomorphic invariant is thus
+indifferent to individual objects. The only notions that do this are
+logical notions, and this confirms neutrality. Thus, we can define a
+logical notion as being isomorphically invariant and non-logical notions
+as not being isomorphically invariant. This allows for the demarcation,
+which is necessary to define logical form.
+
+This understanding of logical form can now aid us in capturing the
+notion of formal validity for natural language. It is common in the
+literature to equate an argument being formally valid with it being
+valid in virtue of its form.\footnote{Mark Sainsbury, \emph{Logical
+  Forms: An Introduction to Philosophical Logic}, (Oxford: Blackwell,
+  2001): 37.} However, using this as a definition for formal validity is
+unsatisfactory, for we still need to define being valid in virtue of
+form, which I find to be no more informative than formal validity.
+Therefore, I define formal validity to be the following: an argument is
+formally valid iff it has a form which has only valid instances. An
+example of a formally valid argument is:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{2}
+\item
+  All men are mortal, Socrates is a man $\therefore$ \ Socrates is mortal.
+\end{enumerate} 
+
+\noindent The logical form of the argument can be captured using a schema, as
+described above. Given the use of quantifiers in (3), the schema of the
+argument is simply its first order formalisation (on the obvious
+formalisation key):
+
+\begin{enumerate}[leftmargin=42] 
+
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{3}
+\item
+  $ \forall x(Fx \rightarrow Gx), \ Fa \ \therefore \ Ga.$
+\end{enumerate} 
+
+\noindent There are no invalid arguments with this form, therefore all the
+instances of this form are valid, consequently the argument is formally
+valid. It is clear from this explanation that this definition of
+validity for natural languages coincides with the definition for formal
+languages, meaning that a natural-language argument is formally valid
+iff its formalisation is valid.
+
+\section*{Two Accounts of Validity}
+
+We can now examine two model-theoretic accounts of validity for
+natural-language arguments. Generally, model-theoretic accounts of
+logical consequence are now viewed as more successful compared to other
+accounts of logical consequence, and the two accounts that are the focus
+of this essay are model-theoretic. As such the central thesis of both
+accounts understands logical consequence as concerning truth
+preservation across models.\footnote{This contrasts with proof-theoretic
+  accounts which hold that the nature of logical consequence involves
+  there being a proof from the premises to the conclusion.} The first
+account is the interpretational account of validity, which originates
+from Bolzano but was promulgated by Tarski.\footnote{Jc Beall, Greg
+  Restall, and Gil Sagi, ``Logical Consequence'', \emph{The Stanford
+  Encyclopaedia of Philosophy} (Summer 2024 Edition); Stephen Read,
+  ``Formal and Material Consequences'', \emph{Journal of Philosophical
+  Logic} 23, no. 3, (1994): 249.} This account holds that an argument is
+valid if there are no possible interpretations of the argument (except
+for a reserved class of logical interpretations) where the premises are
+true and the conclusion false. An interpretation of an argument is any
+argument that has the same logical form as the initial argument. The
+second account is the representational account of validity, which holds
+that an argument is valid if it is impossible for the premises to be
+true and the conclusion false.\footnote{Read, "Formal and Material
+  Consequences'', 250.}
+
+The interpretational account only accepts arguments that are formally
+valid. The account achieves this by examining different logical
+interpretations of the argument; if there is no interpretation that has
+true premises and a false conclusion then the argument is considered
+valid. On the other hand, the representational account allows for
+arguments that are materially valid, alongside those that are formally
+valid. Materially valid arguments are arguments in which the validity of
+the argument is in part due to the meaning of the non-logical terms
+involved. An example of a materially valid argument is:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{4}
+\item
+  Jill is a paediatrician $\therefore$ \ Jill is a doctor.
+\end{enumerate}
+
+\noindent The representational account intends to capture a more ``intuitive''
+notion of validity. Defenders of this account hold that materially valid
+arguments are contained within this intuitive notion of validity, and so
+an account of validity must capture material as well as formal validity.
+This belief is rooted in the idea that there is an analytic connection
+between certain words or phrases, and these connections make the
+argument valid, even though the argument is not formally valid.
+
+The main objection to the interpretational account is that it is subject
+to counterexamples, which take the form of materially but not formally
+valid arguments. To establish the success of the interpretational
+account we must meet this objection. One example of a materially but not
+formally valid argument is (5) above, and another is:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{5}
+\item
+  Adam is taller than Bill and Bill is taller than Cathy $\therefore$ \ Adam is
+taller than Cathy. 
+\end{enumerate}
+
+\noindent Neither of these arguments is formally valid, since there are invalid
+arguments with the same form as (5) and (6). The interpretational
+account would not accept that they are valid arguments given there are
+interpretations of (5) and (6) for which the premises are true and the
+conclusion false. A formalisation of these arguments in first order
+logic reveals their logical form:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{6}
+\item
+  $Fa \ \therefore \ Ga$ 
+\item 
+  $ (Tab \land Tbc) \ \therefore \ Tac $
+\end{enumerate}
+
+\noindent Another interpretation of each of these arguments demonstrates the point further:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{8}
+\item
+  Pat is a postman \ $\therefore$ \ Pat is a father.
+\item 
+  Alice is friends with Bonnie and Bonnie is friends with Carl \ $\therefore$ \ Alice is friends with Carl.
+\end{enumerate}
+
+\noindent These arguments are clearly invalid, yet they have the same logical form
+as (5) and (6), respectively. It is due to these alternative
+interpretations that (5) and (6) are not valid.
+
+However, the arguments (5) and (6) would be accepted under the
+representational account due to this account's use of modality. The
+representational account identifies logical consequence with
+metaphysical consequence. The reference to ``impossible'' in the
+representational account is a modal notion, whereas the interpretational
+account does not include such modal notions. The reference to ``no
+possible interpretations'' in the interpretational account may be made
+actual using substitutional classes, and thus does not need to rely on
+an analysis of modality.\footnote{Read, "Formal and Material
+  Consequences'', 252.} Yet, it is because of its use of modality that
+the representational account can attribute validity to (5) and (6), for
+there is no possible world where the premises of (5) and (6) are true
+and the conclusion false.
+
+On the other hand, modality is an issue for the representational
+account, for it requires that we have an analysis of
+modality.\footnote{It should be noted that this conversation concerns
+  analyses of the metaphysical notion of modality, which is distinct
+  from a discussion of modal logic, which is considered to be well
+  understood. Metaphysical modality deals with the fundamental nature of
+  modal notions, whereas modal logic is a formal system which reasons
+  about sentences containing modal operators.} Commonly, modality is
+cashed out in turns of possible worlds. This prompts the question of
+what a possible world is. The answers to this question are
+controversial. We have modal realists, like David Lewis, who endorse a
+view that possible worlds exist, as real concrete entities.\footnote{David
+  Lewis, \emph{On the Plurality of Worlds}, (Basil Blackwell, 1986) 2-3,
+  86.} Adopting this analysis for our account of validity would also
+mean adopting the ontological commitments of this account. Other
+analyses of modality include modal sceptics, who deny that modal
+statements can be known. In adopting this approach, we could not know
+whether our arguments are valid, which is entirely counterintuitive.
+While there are some more modest approaches to modality, like those
+taken by Stalnaker\footnote{Robert C. Stalnaker, ``Possible Worlds,''
+  \emph{Noûs} 10, no. 1, (1976): 65-75.} and Adams\footnote{Robert
+  Merrihew Adams, ``Theories of Actuality,'' \emph{Noûs} 8, no. 3,
+  (1974): 211-231.}, there are still issues surrounding whether these
+accounts can provide a reductive analysis. This is all to say that while
+modality is often invoked in philosophical topics, the debate
+surrounding modal notions is not uncontroversial, and thus any time it
+is invoked in a theory, that theory faces the same controversies. This
+is not to say that modal notions should never be used in philosophical
+theories, but just that we should be aware of the commitment and, all
+things being equal, adopt theories without modal notions. This gives us
+a motivation to prefer the interpretational account over the
+representational account. Indeed, Read, who accepts the representational
+account over the interpretational account, admits that the lack of modal
+notions in interpretational account is a possible motivation to prefer
+this account rather than the representational account.\footnote{Read,
+  "Formal and Material Consequences'', 252.}
+
+While this general criticism concerning the use of modal notions is
+important to note, there is a more specific problem with the
+representational account; namely, the identification of logical
+consequence with metaphysical consequence then provides no account of
+the importance of formality in logical consequence.\footnote{Beall,
+  Restall, and Sagi, ``Logical Consequence.''} Similarly, the account
+does not provide a basis for distinguishing between logical and
+non-logical vocabulary. This is because the representational account
+determines that all expressions used in the argument contribute to the
+validity of the argument. Consequently, the representational account
+undermines the topic neutrality of logic.
+
+Given that the representational account faces the above challenges, I
+suggest that this should motivate us to adopt the interpretational
+account instead. While I do not view these issues as being
+insurmountable, I simply hold that if there is an alternative we should
+favour it. If the problem of counterexamples to the interpretational
+account can be overcome, then this account becomes a preferrable
+alternative to the representational account of validity. I devote the
+remainder of this essay to considering and defending a possible solution
+the interpretational account can adopt to resolve the problem of
+counterexamples. This solution is the suppressed premise strategy.
+
+\section*{The Suppressed Premise Strategy}
+
+The suppressed premise strategy (hereafter SPS) can be employed by the
+interpretational account to overcome the problem of materially valid
+arguments. SPS holds that materially valid arguments have suppressed
+premises which when revealed make the argument formally valid, and thus
+valid under the interpretational account. These suppressed premises are
+true given they usually explicitly reveal true analytic connections
+between words.\footnote{Read views these suppressed premises not just as
+  true but as logically true because he associates logical truth with
+  analytic truth (Read, ``Formal and Material Consequences'', 258).
+  Since I have not made this association, I will avoid understanding
+  suppressed premises as logically true.} Since they are true, the
+addition of the suppressed premise is largely unproblematic, although
+this claim will be defended further.
+
+SPS applied to the argument (5) gives:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{10}
+\item
+  Jill is a paediatrician, all paediatricians are doctors $\therefore$ \ Jill is a doctor.
+\end{enumerate}
+
+\noindent This argument can be formalised as follows:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{11}
+\item
+  $Fa, \ \forall x(Fx \rightarrow Gx) \ \therefore \ Ga$
+\end{enumerate}
+
+
+\noindent There are no possible interpretations of the argument (11) that will
+have true premises and a false conclusion, thus under the
+interpretational account (11) is valid, although (5) remains invalid. Of
+course, this strategy applies to (6), where the suppressed premise is
+that ``taller than'' is transitive. No suppressed premise can be added
+to (9) or (10), since it is not true that all postmen are fathers, there
+is no analytic connection between being a postman and being a father,
+and the relation ``being friends with'' is not transitive.
+
+\subsection*{The Redundancy Objection}
+
+The first objection to SPS is put forward by Read and states that the
+suppressed premise is either false or redundant, and since it cannot be
+false it must be redundant. \footnote{Read, ``Formal and Material
+  Consequences," 257-9.} Read gives his argument as follows:
+
+\begin{quote}
+The extra premise is strictly redundant. For if the original argument
+were invalid, the added premise would not be logically true. Given that
+it is logically true, it follows that the unexpanded argument was
+already valid. Hence it was (logically) unnecessary to add the extra
+premise.\footnote{Read, "Formal and Material Consequences", 259.}
+\end{quote}
+
+\noindent This objection is best demonstrated using an example. Take argument (5),
+which is considered invalid under the interpretational account. Read
+says that because of its invalidity, it is possible for the premises of
+(5) to be true and the conclusion of (5) to be false. This entails that
+it is possible for Jill to be a paediatrician but not be a doctor. Yet
+the suppressed premise for this argument is that ``all paediatricians
+are doctors'', clearly contradicts the possibility Jill is a
+paediatrician and not a doctor. It follows if we accept that (5) is
+invalid, then we also accept that the suppressed premise is false. Yet
+this suppressed premise is true, so the initial assumption that (5) is
+invalid must be false, and therefore the addition of the suppressed
+premise is made redundant for it is not necessary for the argument to be
+considered valid. According to Read, the suppressed premise's redundancy
+means we should reject the interpretational account in favour of the
+representational account.
+
+Read's objection, while presented convincingly, lacks any actual force.
+This is due to a key error it makes: it presupposes the representational
+account, when it should presuppose the interpretational account. It is
+not the case that (5) is invalid because the premise ``Jill is a
+paediatrician'' is compatible with it being false that ``Jill is a
+doctor'', which (if true) is what the representational account would
+suppose, rather (5) is invalid because there is an interpretation of (5)
+for which the truth of the premises is compatible with the falsity of
+the conclusion. (9) is an interpretation of (5) for which it is
+compatible that it is true that ``Pat is a postman'' and false that
+``Pat is a father'', and therefore (5) is considered invalid under the
+interpretational account. Under the interpretational account, nothing
+specifically is said about the premises of (5), and so Read is wrong to
+infer that attributing invalidity to (5) will make the suppressed
+premise false. Since Read is wrong to assert that the invalidity of the
+argument shows the suppressed premise's falsity, he cannot then infer
+that since the suppressed premise is true, it must therefore be
+redundant. Under the representational account, invalidity is saying
+something about the specific premises of the argument under
+consideration. Yet under the representational account a materially valid
+argument, like (5), would not be considered invalid.
+
+Some may reply here that I am begging the question: why is it that we
+should assume the interpretational account and not the representational
+account? However, this line of thought is also mistaken. Read clearly
+starts by assuming that materially valid arguments are invalid, which is
+only the case under the interpretational account, not the
+representational account. From this assumption of invalidity, he
+attempts to prove a contradiction, but then uses the representational
+account's understanding of validity in this contradiction, even though
+the representational account would not attribute invalidity to something
+that is materially valid. However, if the interpretational account is
+used, then there is no contradiction in using SPS. In addition, this
+strategy is only used by the interpretational account. Thus, Read must
+assume the interpretational account if he is going to show a
+contradiction; given he does not use the interpretational account in his
+objection and that even if he did use the interpretational account there
+would be no contradiction, this implies that his objection holds no
+weight.
+
+\subsection*{Objections about the Nature of the Suppressed Premise and the
+Argument}
+
+A second problem for SPS is that we have not been committed to the view
+that the suppressed premise is logically true. This may lead to the
+question: why is it acceptable to add to an argument an extra premise
+that is not logically true? Surely only logically true propositions may
+be added to the premises of an argument to retain the same argument. To
+answer this question, an important point must be reiterated: I do not
+agree that the argument prior to the addition of the suppressed premise
+is the same argument as the argument after the addition of the
+suppressed premise. To me this point is obvious, for the two arguments
+have different properties: one argument is valid, the other invalid, and
+they have a different number of premises. Since we are speaking of two
+different arguments, I do not need to prove that the first argument is
+``retained'' in the second. However, this does not mean SPS can be used
+on any argument. If the premise ``all postmen are fathers'' is added to
+(9) then we have a new argument:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{12}
+\item
+  Pat is a postman, all postmen are fathers $\therefore$ \ Pat is a father.
+\end{enumerate}
+
+\noindent (13) is a valid argument, but we should not consider (13) to be using SPS. Therefore, we must identify what differentiates (11) from (13), and
+why (11) is determined as using SPS and thereby linking it closely with
+(5) in a way that (13) is not linked with (9). The difference is that
+the suppressed premise revealed in (11) that ``all paediatricians are
+doctors'' is true, but the premise ``all postmen are fathers'' is not
+true. Indeed ``all paediatricians are doctors'' is an analytic truth.
+However, it is not necessary that this be considered a logical truth. To
+begin with, there seems to be no necessity to consider analytic truths
+to be logical truths, particularly if we retain the commonly held view
+that logic has no special content. And secondly, the goodness of an
+argument can be characterised by whether it is sound, i.e., it is valid
+and has true premises, which does not require the premises to be
+logically true. So long as the suppressed premise is true, its addition
+to the argument does not hinder the chances of the argument being sound
+and should in fact improve this since the argument will now be formally
+valid. Since one of the characteristics of a suppressed premise is that
+it is true, there is no issue that it is not logically true. Considering
+(13), the premise ``all postmen are fathers'' cannot be a suppressed
+premise of the argument (9) for it is not true. Therefore, the
+suppressed premise does not need to be logically true, but this does not
+mean that SPS can be applied to any argument to make it valid.
+
+Moreover, we may consider that SPS might even allow us to consider
+contingent truths as suppressed premises. Let us suppose that it were a
+contingent fact that ``all postmen are fathers'', then it might make
+sense to consider this to be a suppressed premise of argument (9). Say
+Mr. Black presented argument (9) to Mr. White and both Mr. Black and Mr.
+White were aware that ``all postmen were fathers'', then the argument
+might be accepted as sound in the rhetoric (even though it is not
+formally valid) because both understood that the argument has a
+suppressed premise, and that Mr. Black in fact meant to make the
+argument (13). Now suppose Mr. Smith questioned the validity of the
+argument because he was not aware that it was a contingent fact that
+``all postmen were fathers''. Yet, once this would be revealed to him,
+Mr. Smith would certainly accept the validity of the argument.
+Therefore, we may accept that a suppressed premise may be contingently
+true, and it becomes clear that only truth, and not logical truth, is
+necessary for the suppressed premise.
+
+A counterexample to this argument has been pointed out to me.\footnote{By
+  Owen Griffiths, in personal communication.} This is that if we take
+the argument:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{13}
+\item
+  I am a philosophy student $\therefore$ \ puppies are cute.
+\end{enumerate}
+
+\noindent This is clearly invalid. But if the conditional ``If I am a philosophy
+student then puppies are cute'' is added as a suppressed premise to
+(14), then we get the new valid argument:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{14}
+\item
+  If I am a philosophy student then puppies are cute, I am a
+philosophy student $\therefore$ \ puppies are cute.
+\end{enumerate}
+
+\noindent It appears there is no problem with adding this conditional if we take
+the view that suppressed premises only need to be contingently true, and
+not analytically true, because considered as a material conditional it
+is true (the antecedent and consequent are true). This seems to be a
+problem for the strategy, as it might allow for many arguments like
+(14), that have true premises and true conclusions yet are not formally
+or materially valid, to be valid by adding these conditionals as
+suppressed premises.
+
+My response to this argument is to say that these conditionals are
+indicative conditionals, not material conditionals, which means they
+involve a different treatment. An indicative conditional is the
+conditional of natural language, and the current discussion is about the
+validity of natural-language arguments, so it makes sense to speak of
+indicative conditionals rather than material conditionals. We may then
+consider views of indicative conditionals which hold that their truth
+values are different to those of material conditionals, and as such we
+can formulate a view that holds that ``If I am a philosophy student then
+puppies are cute'' is false. For instance, we might hold that an
+indicative conditional is true iff it is assertable and is in turn
+assertable iff it passes the Ramsey test. The Ramsey test is a test for
+the assertability of a conditional, it holds that a conditional is
+assertable if someone were to add the antecedent to her set of
+suppositions, she would also have to add the consequent. ``If I am a
+philosophy student then puppies are cute'' would clearly fail the Ramsey
+test. Thus, we can still consider that the suppressed premise may be
+true without the above presenting as a counterexample.
+
+I have only given a rough sketch of a possible response to the objection
+suggested above, and while there are many problems with associating the
+truth conditions of an indicative conditional with those of the material
+conditional, there are still some who adopt this view. However, the
+conditional suggested is one where the antecedent and the consequent are
+both true and yet have nothing to do with each other. This sort of
+conditional is itself a problem case for someone who holds this
+truth-functional view of the indicative conditional, suggesting that
+there is something wrong with equating the indicative conditional with
+the material conditional. However, if the reader insists on the
+indicative conditional and the material conditional having the same
+truth value, even in cases where the antecedent and consequent have no
+relation to each other, then this reader may simply choose to reject
+this section on contingent truth and hold that the suppressed premise
+must be an analytic truth. This does not detract from the fact that the
+suppressed premise is not a logical truth. Of course, the reader may
+still object to the idea of analytic truth. However, this paper defends
+the interpretational account against the counterexample of material
+valid arguments, which themselves rely heavily on the notion of
+analyticity. So, if the reader places no importance on the analytic
+connections between words, then there is no forceful objection to the
+interpretational account and no need for SPS to begin with.
+
+A third objection connects to my answer to the second objection. I have
+stated that the two arguments, the argument prior to the addition of the
+suppressed premise and the argument after this addition, are two
+different arguments. This may lead one to ask, ``what connects the two
+arguments?'' The answer to this is simple: they both have the same aim.
+The aim of an argument is an imprecise and informal notion; however, I
+want to use it to capture an intuitive idea. The two arguments share the
+same conclusion, and their aim is to use true (and very similar)
+premises to arrive at this conclusion. Suppose that Jones is having a
+discussion of Jill's profession; he would be just as happy receiving the
+argument (11) as he would be receiving the argument (5), possibly even
+happier receiving (11) if he is unaware that a paediatrician is a kind
+of doctor (or if he is a logician who has a strong appreciation for
+formal validity). However, Jones would be disappointed if instead of
+receiving either of these arguments he received (3), for instance, which
+clearly has nothing to do with Jill or her profession. The aim of the
+arguments is informal, and the setting for which Jones might accept or
+reject them, as described, is also informal. The arguments are connected
+by this informality. The matter of validity in logic is strictly a
+formal matter, and thus there is a distinct difference between (5) and
+(11).
+
+\subsection*{The Problem of Modus Ponens}
+
+The final problem I shall explore in relation to SPS is the problem of
+modus ponens. A modus ponens is a deductive argument of the following
+form:
+
+\begin{enumerate}[leftmargin=42] 
+\def\labelenumi{(\arabic{enumi})}
+\setcounter{enumi}{15}
+\item
+  $A, \ A \rightarrow B \ \therefore \ B$
+\end{enumerate}
+
+\noindent Modus ponens is discussed by both Read and Timothy Smiley, in very
+different ways.\footnote{Read, "Formal and Material Consequences,"
+  259-62; Timothy Smiley, "A Tale of Two Tortoises", \emph{Mind} 104,
+  no. 496, (1995): 727.} They both view modus ponens as having a similar
+form to SPS but speak of different consequences related to this
+similarity. Below, I address both in turn.
+
+The problem that Read notes with modus ponens is that the major premise
+of this argument (16) is either false or redundant. While his discussion
+of this problem is limited, he links it with SPS by arguing that in both
+cases the additional premise ``adds psychological perspicuity
+{[}\ldots{]} But at the same time, it is not essential''.\footnote{Read,
+  "Formal and Material Consequences," 262.} To some extent I disagree
+with both points. Considering the second point, the suppressed premise
+and the major premise in the modus ponens argument are vital in making
+the argument valid, and thus are essential to the argument. On the first
+point, there is some sense in which adding the suppressed premise and
+the major modus ponens premise do add psychological perspicuity, but it
+does not necessarily always do this or do this to the extent Read may be
+suggesting. In cases where both parties implicitly know the suppressed
+premise, its addition to the argument may not provide any psychological
+clarity, only logical infallibility. This idea is strengthened when
+considering that most of the arguments we make in everyday life have
+suppressed premises and we do not seem to need to reveal these
+suppressed premises for psychological reasons.\footnote{Smiley, "A Tale
+  of Two Tortoises," 727.} Rather we tend to reveal suppressed premises
+for logical reasons. Given we are holding this discussion in the domain
+of logic, we may accept the resemblance between SPS and modus ponens
+while still rejecting Read's assertion of redundancy.
+
+Smiley's discussion of this matter refers to a paradox that seems to be
+presented by modus ponens and the addition of the suppressed premises.
+The paradox in question originated from Lewis Carroll, who wrote:
+
+\begin{quote}
+If I grant (A) All men are mortal, and (B) Socrates is a man, but not
+(C) The sequence "If all men are mortal, and if Socrates is a man, then
+Socrates is mortal" is valid, then I do not grant (Z) Socrates is
+mortal. Again, if I grant C, but not A and B, I still fail to grant Z.
+Hence, before granting Z, I must grant A and B and C. {[}Now consider{]}
+(D) If A and B and C be true, then Z is true.\footnote{Charles Lutwidge
+  Dodgson, \emph{Lewis Carroll's Symbolic Logic}, W. W. Bartley III,
+  ed., (Clarkson Potter, 1977), 472.}
+\end{quote}
+
+\noindent This becomes paradoxical when we observe an infinite regress occurring
+where we must grant (A), (B), (C), (D), and a further (E) If A and B and
+C and D be true, then Z is true, yet we can think of an infinite number
+of propositions that must be granted before it seems that Z is granted.
+We can view (C), (D), etc, as suppressed premises of the argument that
+Carroll reveals in his paradox. This leads Smiley to comment that
+``Lewis Carroll was doomed to detect suppressed hypothetical premises
+even in logically valid arguments, and incidentally to force them all
+into the straitjacket of modus ponens''.\footnote{Smiley, "A Tale of Two
+  Tortoises," 727.} If these are considered to be suppressed premises
+then there is a problem for SPS, for these can be added to any argument,
+and make the argument paradoxical. In addition, this does not seem to be
+what the strategy intends. To solve this, we can examine the
+characteristics of the suppressed premise, which is that its addition
+will make the argument formally valid. Yet the arguments that Lewis
+Carroll imagines are already valid arguments, thus SPS should not be
+employed in these cases. Smiley's examination of the problem also points
+out that the specific wording of the paradox is crucial for its
+paradoxical nature but is itself flawed. Lewis Carroll ``lacked any
+distinct conception of a deduction as opposed to the assertion'', and it
+is this confusion that leads to paradox. \footnote{Smiley, "A Tale of
+  Two Tortoises," 727.} By this Smiley means that (C) is not an
+assertion but a deduction, and so it must be granted, but Carroll seems
+to think that it is merely an assertion that can be accepted or denied.
+Hence, this paradox does not show that even valid arguments might have
+suppressed premises that lead to paradox, thus this objection presents
+no issue to the use of SPS.
+
+The characterisation I have given of SPS prevents contradiction and I
+have shown how it is able to overcome objections about the redundancy of
+the suppressed premise, as well as more generally the nature of the
+suppressed premise and the nature of the arguments to which it pertains.
+Finally, I discussed the problem of Modus Ponens, showing two ways it
+relates to SPS, and that this does not impact the use of the strategy.
+Thus, SPS is a viable addition to the interpretational account and
+explains the relation of material validity to validity, without a need
+to adopt the representational account. Hence by defence of the
+interpretational account succeeds and preferred to the representational
+account.
+
+\newpage  
+\section*{Bibliography}
+
+\refsection
+
+\begin{hangparas}{\hangingindent}{1}
+Adams, Robert Merrihew. ``Theories of Actuality.'' \emph{Noûs} 8, no. 3
+(1974), 211-231.
+
+Beall, Jc, Greg Restall, and Gil Sagi "Logical Consequence",~\emph{The
+Stanford Encyclopedia of Philosophy~}(Summer 2024 Edition), Edward N.
+Zalta \& Uri Nodelman~(eds.),
+\newline
+\url{https://plato.stanford.edu/archives/sum2024/entries/logical-consequence}
+
+Dodgson, Charles Lutwidge \emph{Lewis Carroll's Symbolic Logic}. W. W.
+Bartley III, ed. Clarkson Potter, 1997.
+
+Griffiths, Owen, and Alexander Paseau. 2022. \emph{On True Logic: A
+Monist Manifesto.} Oxford University Press, 2022.
+
+Lewis, David. \emph{On the Plurality of Worlds.} Basil Blackwell, 1986.
+
+Read, Stephen. ``Formal and Material Consequences.'' \emph{Journal of Philosophical Logic} 23,
+no. 3 (1994): 247-265.
+
+Sainsbury, Mark. \emph{Logical Forms: An
+Introduction to Philosophical Logic.} Blackwell, 2001.
+
+Smiley, Timothy. ``A Tale of Two Tortoises.'' \emph{Mind} 104, no. 416 (1995):
+725-736.
+
+Stalnaker, Robert C. "Possible Worlds." \emph{Noûs} 10, no. 1, (1976): 65-75.
+
+Tarski, Alfred. ``What are Logical Notions?''
+\emph{History and Philosophy of Logic} 7, 1986): 143-154.
+\end{hangparas}
\ No newline at end of file