Mereology Workshop. Analytic and Phenomenological Perspectives on Parts and Wholes

Mereology (from the Greek word μέρος, for “part” or “portion”) is the discipline that studies part-whole relations and the principles of composition and decomposition governing all objects, whether material or abstract. Mereological questions have been at the centre of philosophical dispute since antiquity, and in contemporary Philosophy we witness a continued interest in them both in the analytic tradition, mainly stemming from the development of classical extensional mereology by Leśniewski and Leonard and Goodman in the early 20th century, and in the phenomenological tradition, stemming from the work of Husserl and his conception of mereology as part of a formal ontology, a general theory of objects as they belong to the category of objects.

In this workshop we aim to bring together these two traditions and discuss questions that are actively being discussed in both of them. In the analytic tradition, the recent publication of Mereology (2021) by A. J. Cotnoir and A. C. Varzi both witnesses the lively state of the debate and illustrates the range of questions that can be explored. These include the following: if the parthood relation is antisymmetric; if whenever an object has a proper part, it must have a further proper part disjoint from it; if two distinct entities can have the same parts; if the operation of composition has priority over the relations of parthood and overlap; if there is a universe (an object having everything as part); if composition ever occurs, always occurs or if it should be restricted in some way, and if so, when it should be restricted; and if a null individual (an object that is part of everything) should be accepted.

 

TIME AND PLACE:
November 2nd–3rd 2023, 10:00–18:30
University of Lisbon
Faculty of Letters, Room B112B

SCHEDULE
November 2nd
10:00–11:30: Kevin Mulligan (Università della Svizzera italiana), ‘Mental
Mereology’
coffee break
12:00–13:30: Francisca Silva (University of St Andrews), ‘Sets as Fusions of
Materially-Equivalent Rigid Embodiments’
lunch
15:00–16:30: Marina Banchetti-Robino (Florida Atlantic University), ‘Classical
Mereology and the Formalization of Quantum Chemical Wholes’
coffee break
17:00–18:30: Aaron Cotnoir (University of St Andrews), ‘Building, Carving, and
Constitution: Another Look at Mutual Parthood’

November 3rd
10:00–11:30: Francesca De Vecchi (San Raffaele University, Milan), ‘Social
Wholes and Parts-Persons. Husserl’s «Unitarian Foundations» Account and its
Relevance for a Phenomenologically Embedded Social Ontology’
coffee break
12:00–13:30: Giorgio Lando (University of L’Aquila), ‘Mereomodal Fractional
Counting’
lunch
15:00–16:30: Roberta De Monticelli (San Raffaele University, Milan),
‘Individuality, Concreteness, and the Gift of Bonds: Phenomenology and
Analytic Metaphysics’
coffee break
17:00–18:30: Peter Simons (Trinity College Dublin), ‘Geometry of the Sphere:
Mereology at Work in Mathematics’
* * *
FUNDING AND REGISTRATION:
The workshop is organised by Pedro Alves, Guillaume Fréchette and Ricardo
Santos and funded by the Centre of Philosophy of the University of Lisbon, the
Portuguese Foundation for Science and Technology (project UIDB/310/2020)
and the Internationale Franz Brentano Gesellschaft.
There are no registration fees, but if you would like to attend please let Moirika
Reker know at c.filosofia@letras.ulisboa.pt. It will also be possible to attend the conference online.

 

ABSTRACTS

Kevin Mulligan (Università della Svizzera italiana)
Mental Mereology
This paper considers two views about mental episodes and their parts. (1) Geach
famously argued that there are mental acts the parts of which must be
simultaneous. I consider the reasons for and against the stronger claim that there
are mental acts the parts of which are simultaneous because these acts are
punctual. (2) Suppose Maria judges that aRb at a time. If it is plausible to say that
her act of judging contains an act of referring to a and an act of referring to b, is
it plausible to say that her act also contains a mental mode of judging?

Francisca Silva (University of St Andrews)
Sets as Fusions of Materially-Equivalent Rigid Embodiments
According to Lewis’s (1991, 1993) influential account, set theory can be reduced
to a primitive notion of singleton and classical extensional mereology (CEM). This
is not surprising. After all, it’s a known result that models for CEM are complete
Boolean algebras with the bottom element removed (what would be the null
element), whereas models for set theory are complete Boolean algebras. This
picture comes with what I take to be two unwelcome consequences: i) that the
sets don’t have their members as parts; and ii) that the empty set is not counted
as a class. I will present reasons for why we should reject these two
consequences, though I also take it they fly in the face of intuitions one might
have about sets. I believe, then, we can do better. Having as a background Fine’s
(1999, 2010) pluralist mereological theory, and in particular his theory of rigid
embodiments, I will try to develop and evaluate the prospects of a theory
according to which the sets are fusions of rigid embodiments having the same
material part. I will conclude by evaluating how much the resulting view departs
from certain axioms of CEM.

Marina Banchetti-Robino (Florida Atlantic University)
Classical Mereology and the Formalization of Quantum Chemical Wholes
This presentation examines the reasons for which classical extensional
mereology is not adequate for formalizing whole–parts relations in quantum
chemical systems and proposes an alternative mereological approach to
formalize such relations. The question of which mereology is appropriate for
formalizing the whole–parts relation in quantum chemical systems is relevant to
contemporary philosophy of chemistry, since this issue is related to the more
general questions of the reducibility of chemical wholes to their parts and of the
reducibility of chemistry to physics, which have been of central importance within
the philosophy of chemistry for several decades. My discussion of atoms and
molecules as they are conceptualized in quantum chemistry will show that
extensional mereology cannot adequately fulfill the task of adequately describing
quantum chemical whole-parts relations, since the properties and behavior of
such wholes are context-dependent and cannot simply be reduced to the
summative properties of their parts. Philosophers of chemistry have long called
for the development of an alternative mereology for quantum chemical systems
and this presentation will propose behavioral mereology as an alternative to the
extensional mereology that philosophers of chemistry find so problematic.
According to behavioral mereology, considerations of what constitutes a part of
a whole are dependent upon the observable behavior displayed by these entities.
Thus, relationality and context-dependence are stipulated from the outset,
making behavioral mereology particularly well-suited for the formalization of
quantum chemical whole-parts relations. In its discussion of which mereology is
most appropriate for formalizing quantum chemical whole-parts relations, this
paper also places contemporary discussions of mereology within the philosophy
of chemistry into a broader historical and philosophical context. In doing so, this
paper bridges the gap between formal mereology, conceived as a branch of
formal ontology, and “applied” mereology, conceived as a branch of philosophy
of science.

Aaron Cotnoir (University of St Andrews)
Building, Carving, and Constitution: Another Look at Mutual Parthood
Of the three major multi-thinger approaches to material constitution, the mutual
parthood view (and the corresponding rejection of antisymmetry) is a rather
minority position in the literature. It is widely thought to be counter-intuitive, and
it faces a number of objections. The goal of this paper is to place the mutual parts
view within the context of a wider background metaphysics of composition and
parthood that helps to alleviate its counter-intuitiveness, and provides the
resources to respond many of the objections to the view. I introduce a formal
framework for the purposes of comparing the three views of constitution. I’ll
suggest that the views (basically) agree on the metaphysics, but merely disagree
on which mereological relations count as parthood. I’ll then suggest that the
dispute between these views won’t be resolved by intuitive or pre-theoretic
judgements, but rather will inevitably involve abductive considerations. I’ll argue
that what are driving the judgements about ‘counterintuitiveness’ are rival
metaphors— the building vs. carving pictures — that push for different
conceptions of parthood and composition. I’ll distinguish between ‘spaces’ and
‘places’ to suggest that there are correspondingly different kinds of failures of
extensionality. Finally, I’ll respond to a number of objections to non-antisymmetric
theories due to Goodman, Fine, and Walters.

Francesca De Vecchi (San Raffaele University, Milan)
Social Wholes and Parts-Persons. Husserl’s «Unitarian Foundations» Account and Its Relevance for a Phenomenologically Embedded Social Ontology
I focus on Husserl’s wholes-parts account (Husserl 1901, III Logical Investigation)
and its application on what I call a “qualitative social ontology”, i.e. a
phenomenologically embedded social ontology. I point out that, according to
Husserl, wholes are «unitarian foundations»: unlike mere aggregates or sums,
wholes are characterized by ontological dependence relationships that
qualitatively inter-permeate the being of the wholes and of their parts (1901, III
Logical Investigation, §§ 7, 10, 21). As «unitarian foundations», wholes may have
a double direction of foundation: it is not only the case that wholes are founded
on their parts, but also that in turn they may found their parts, in the sense of
constituting them in defining and individuating their being as the parts of a certain
whole. This is the case of wholes that Husserl calls of «second sort» (Husserl
1901, § 21) and that are typically “emergent wholes” (vs. the wholes that remain
“immanent wholes”). Indeed, emergent wholes are the ones whose parts may
exist independently from one another and even outside the whole of which they
are parts: these kinds of parts, whenever connected together in a certain whole,
constitute a whole that is a new type of things – as, for instance, the persons who
are the parts of a “social whole” and who are individualized by their becoming
parts of that social whole. As also Stein (1922) points out, the structure of a social
whole, and in particular of that kind of social wholes that are communities,
displays a double direction of foundation: there is not only the bottom-up
foundation, from parts-persons to the whole-community, but also a top-down
foundation from the whole-community to the parts-persons, and this top-down
foundation individualizes the being of the parts-persons. I claim that there are
qualitatively different types of social wholes according to the stronger or weaker
individualization activity that the social whole operates on its parts-persons and
according to the intensity of the bonds – more or less deep or superficial, strict or
flexible – that bind the persons as parts of a certain social whole. I show that this
qualitatively ontological perspective allows us to distinguish different modalities
in which parts-persons and social wholes may be ontologically connected, i.e.
different kinds of «unitarian foundations», and to account for the varieties of the
types of social wholes that we experience in our lives.

Giorgio Lando (University of L’Aquila)
Mereomodal Fractional Counting
When we count several kinds of entities (such as chairs or oranges), we often
consider also partial entities: we thus say that there are two and a half oranges
on the table, or three and a half chairs in a furniture factory. In my talk, I shall
contend that these fractional counting claims involve partial entities and that
partial entities are possible parts of entities that are measured with respect to a
possible whole entity. Fractional counting is, therefore, mereomodal. The variety
of modality and the kind of measuring involved are shown to depend on the kind
of involved entities to be counted and on other contextual aspects. This explains
why several answers seem plausible when how-many questions are raised about
some entities and portions of these entities are present. It also explains why some
kinds of entities cannot be fractionally counted, while some others can be
fractionally counted only in far-fetched scenarios. Some difficult cases,
concerning scattered partial entities and very small partial entities, are finally
discussed, and, as a result of this discussion. a limited role in the logical form of
fractional counting claims is attributed to the integrity and structure of partial
entities.

Roberta De Monticelli (San Raffaele University, Milan)
Individuality, Concreteness, and the Gift of Bonds: Phenomenology and Analytic Metaphysics
Post-Quinean Nominalism is widely regarded as a metaphysics of concreteness,
suggesting (in line with scientific naturalism) that ordinary language and common
sense might be in the grip of “ordinary hallucinations” (Varzi 2010), or untutored
belief in abstract entities. Drawing on both medieval and contemporary sources,
this paper argues that, far from encouraging our minds to stick to concreteness
and individuals, an untutored usage of Ockham’s Razor prompts the elision of
concreteness and the everyday world from contemporary metaphysics. A theory
of individuality based on Husserl’s concept of Unitary Foundation is outlined, and
partially traced back to the metaphysicians of essential individuality, or haecceity:
Boethius, Scotus, Leibniz – the champions of the “Unitarian Tradition.”

Peter Simons (Trinity College Dublin)
Geometry of the Sphere: Mereology at Work in Mathematics
Classical mereology was developed by Leśniewski for the foundations of
mathematics, but it has rarely been there applied. A notable exception is Tarski’s
paper “Foundations of the Geometry of Solids”, first published in 1929. Inspired
by Tarski’s approach, but without its main flaw (!), and drawing also on pioneering
work of Mario Pieri, I aim in this work (very much in progress) to capture the
intrinsic geometry of the sphere employing only classical mereology and the
single primitive term ‘disc’. On the basis of a provisional collection of axioms and
definitions, I indicate briefly how the principal geometrical properties of the sphere
may be defined and proved.