Gilbert modalities lisbon copia

Can an individuum Be the Same
in Several Possible Worlds?
Gilbert of Poitiers’ Ontology and Theory
of Modalities
Graziana Ciola
Scuola Normale Superiore (Pisa)
graziana.ciola@sns.it
Lisbon, 5/4/2013

Introduction

Gilbert of Poitiers (1076 ca. – 1154)

Certainly authentic works
• Epistola ad Mattheum abbatem Sancti Florentii [PL 118, 1221a-1258b]
• Commentarius in Psalmos
• Commentarius in Epistulas Sancti Pauli
• Commentaria in Boethii opuscula sacra [Häring 1966]
• De Trinitate I
• De Trinitate II
• De hebdomadibus
• Contra Euticen et Nestorium

5/4/13 G. Ciola - Gilbert of Poitiers 2

Introduction

Focus:
a) Gilbert’s conception of modality
b) Gilbert’s ontology in naturalibus
b.1) The particular individual – such as you, me, this table

Thesis:
Given a – b.1,
we have a framework that might let us talk about counterfactual identity


Index

• Ancient and Medieval Conceptions of Modalities
• Gilbert’s Synchronic Modalities
• Gilbert’s Ontology: The Basics
• Individuum: A Modal Definition
• Counterfactual Identity?


Ancient and Medieval Conceptions of Modalities

a) Statistical

b) Diachronic

c) Potentiality


Statistical
Modality as frequency over time:
Reduction of modal terms to quantification over temporal instants i.e. extensional terms

Cfr. J. Hintikka (1973); S. Kunuuttila (1981)

Semantic interpretation:
□ A = always the case that A (i.e. always true that A)
□ ~ A = ~ ◊ A = never the case that A (i.e. always false that A)
◊ A = sometimes the case that A (i.e. sometimes true that A).



a) Statistical

b) Diachronic

c) Potentiality


Diachronic

Account for modality over the linear development of time.
Not reductionist over quantification.
The unrealized possibility is not an authentic possibility.

General structure:
ti > tj
‘A’ is a non-necessary sentence.
If A is possible at the time ti then there is an antecedent possibility of both A and non-A at
the antecedent moment tj.
Therefore, A is possible at ti iff there is a time tj when it is possible for A not to be true at ti.
Yet, if A is at ti, the possibility of non-A at tj, being unrealized, is not an authentic possibility.



a) Statistical

b) Diachronic

c) Potentiality


Possibility as Potentiality

Possibility = Potentiality

Priority of :
- Actuality
- Ontological dimension

‘A’ is possible if the potency of A is going to be actualized.



a), b), and c) are attested in Aristotle, Boethius and are widespread in the subsequent
tradition.

In a), b), c):
- The scope of modalities is exclusively the actual world
- There is a main temporal connotation
- The paradigmatic cases are natural necessities/possibilities

- The authentic possibility seems to imply realization

What is missing?
- A clear definition of possible in a logical sense (i.e. “logical possible”) ≠ “natural possible”
- A synchronic conception of modalities



a), b), and c) are attested in Aristotle, Boethius and are widespread in the subsequent
tradition.

In a), b), c):

- The scope of modalities is exclusively the actual world
- There is a main temporal connotation
- the paradigmatic cases are natural necessities/possibilities

- The authentic possibility seems to imply realization

What is missing?
- A clear definition of possible in a logical sense (i.e. “logical possible”) ≠ “natural possible”
- A synchronic conception of modalities


Synchronic Modalities

Alternative Possibilities
Unrealized, alternative states of things subsist at the same time next to the actual one.
E.g. “Possible worlds” conception of modalities

- Modalities have scope beyond the actual world
- “possible”/”necessary” in a relevant sense is not the natural possibility/necessity, but a
logical one.


Medieval Beginnigns

Theologic Modalities (Knuuttila 2008)

1) Augustine’s doctrine of creation: Ideae and exemplares in mente Dei

2) On God’s omnipotence: relativizing natural necessity
e.g. Petrus Damianus, De Divina omnipotentia


Gilbert of Poitiers – Alternative Histories of the World
Developing 1)
• Basic standard assumptions:
• Only God is necessarily existent
• The creation of this world is an act of God’s free will
• Ideae seminales in mente Dei and providential program

Further step:
The “possible worlds system in a nutshell”:
different providential programs; different unrealized histories of the world, equally possible.


Medieval Beginnigns

Theologic Modalities (Knuuttila 2008)

1) Augustine’s doctrine of creation: Ideae and exemplares in mente Dei

2) On God’s omnipotence: relativizing natural necessity
e.g. Petrus Damianus, De divina omnipotentia


Gilbert of Poitiers – Natural Necessities

Developing 2):
Natural necessity is necessitas consuetudini accomodata

- For God:
Natural necessities are not cogent for God: for him, they are not necessities at all.
• Natural laws are created by God, therefore they are contingent
• Natural laws are in this world, but God might have created it differently

- Also for us:
Natural Necessity is the result of an inference we make from repeated observations of
recurrent phenomena; therefore it is not a necessity properly speaking.

Also from our point of view, natural necessity is neither logical nor metaphysical, but it seems
to be an epistemic construction.

Gilbert of Poitiers – Logical Necessity
Yet, even God seems to be bound by some logical/ontological requirements :

Non-contradiction:
 On the logical plane
 On the ontological plane


Gilbert of Poitiers – A Theoretical Model of Synchronic Modalities
i. Even if it is not systematic, it is articulated;
ii. It distinguishes logical necessity/possibility from natural necessities/possibilities
iii. It is clearly differentiated from temporal-statistical and potency-act modal conceptions
iv. It preserves the possibilities unrealized in the actual world

v. It is coherent with Gilbert’s doctrine of the individual


Gilbert’s Ontology
Revisiting a Boethian distinction

Subsistens /id quod est:
The determinate entity
i.e. a singular thing considered as a self-contained entity

[It is such by means of the inherence of a number of forms in a substratum]

Subsistentia/ id quo est
That by which something is what it is


Subsistentia/id quo est

The formal principle inhering in a substratum
Two main acceptations:
1. Subsistentia formalis = subsistentia/forma simplex/substantialis
Properties and corresponding predicates under the category of substance

2. Subsistentia totalis = tota forma = sua propria forma:
• Subsistentiae formales/substantiales [1]
• + Subsistentiae accidentales = accidents properly speaking = intrinsic accidents:
i.e. properties and corresponding predicates under the category of
• Qualitas
• Quantitas

+ Extrinsecus affixa = status


Extrinsecus affixa = status

Properties and predicates under the other seven “little” categories:
• [Relatio]
• Ubi / Locus
• Quando / Tempus
• Actio
• Passio
• Quies /Motus
• Habere


Modi conuiungendi

• [Generalissima participatio]

• Commixtio
• Compositio -- Subsistentiae
• Appositio


Modi conuiungendi
Compositio

The kind of relation among subsistentiae in the tota forma

Two or more different things:
Stay different
Are connected in a real unity


Modi conuiungendi

• [Generalissima participatio]

• Commixtio
• Compositio
• Appositio


Modi conuiungendi
Appositio

It is the kind of relation among extrinsecus affixa.

Two or more different things stand together:
Without any real unity
Without any ontological or qualitative change

The properties of one appositum cannot be predicated of the other.


Dividual and Individual Subsistences

• Dividual subsistences
Each subsistence in the tota forma, being it substantial or accidental, taken per se.

N.B. Plato’s and Socrates’ humanitates are singular i.e. numerically different, but
“ratione similitudinis fit unione”, therefore not individual

• Individual subsistence
The tota forma of each subsistent
e.g. Plato’s Platonitas = Plato’s humanitas + Plato’s albedo + …[+ something else exclusive of
Plato?]
It is an union of a multiplicity, which gives an unitas
It is individual

 We have a real and conceptual distinction between singular and individual


Dividual and Individual Subsistences
Singular ≠ individual
Real and conceptual distinction
Real – extensional:
• All individuals are singular
Not all singulars are individual

• Singulars: Subsistentiae dividuales
Individuals: Subsistentiae individuales /propriae formae

Conceptual – intensional:
• Similarity --- singulars
• Dissimilarity --- individuals


Individuum
Princupium individuationis

It cannot be:
• The subsistentiae formales
• The accidents properly speaking
• The extrinsecus affixa

They are common


Individuum

It cannot be:

On the onthological level, their appositio doesn’t produce any change among the apposita

On the logical level, they are predicated only extrinsically of the subject


Individuum

It cannot be:

But it appears to be the substistentia totalis i.e. the propria forma
It’s the unity of
common singular formal properties/predicates
and properly accidental properties/predicates
that individuates the individual i.e. the subsistent (extensional) as it is different from every
other

The logical interpretation of the tota forma, in this sense, could appear quite similar to
Leibniz’ complete concept. In a fashion, it is, but, as we will see, there are some main
differences.

Individuum
A Modal Definition
“Illa vero ciuslibet proprietas, que naturali dissimilitudine ab omnibus – que actu vel
potestate fuerunt vel sunt vel futura sunt – differt, non modo ‘singularis’ aut ‘particularis’
sed etiam ‘individua’ vere et vocatur et est. […] Hac igitur ratione Platonis tota forma – nulli
neque actu neque natura conformis – vere est individua.”
CEut., 3, 13, 81 – 15, 90, p. 274

Temporal element:
In the tota forma are included all the properties/predicates that were, are, will be actually
true of the subject.


Individuum
A Modal Definition
“Illa vero ciuslibet proprietas, que naturali dissimilitudine ab omnibus – que actu vel
potestate fuerunt vel sunt vel futura sunt – differt, non modo ‘singularis’ aut ‘particularis’
sed etiam ‘individua’ vere et vocatur et est. […] Hac igitur ratione Platonis tota forma – nulli
neque actu neque natura conformis – vere est individua.”
CEut., 3, 13, 81 – 15, 90, p. 274

Modal element:
In the tota forma are included all the possible properties/predicates that might be true of
the subject – also those that are never actualized.
i.e. each subsistent brings in itself each and everyone of his possible predicates
≠ Leibniz’ complete concept


Individuum
In the modal framework

“… actu vel potestate …”
≠ potentiality : some properties may never be actualized
=> authentic possibility

How does it work in Gilbert’s boarder modal framework?
• Infinite pure unrealized possibles
• In the different histories of the world framework  synchronic possible
• Possibile logicum in nuce
• Inter-Worlds i.e. Transworld i.e. Counterfactual Identity?


Individuum
Infinite unrealized possibles

« …qui nondum sunt vel fuerunt: et nunc sunt tam actu quam natura homines infiniti…
Unus vero actu solus est sol preter quem nullus actu vel fuit vel est vel erit quamvis natura
et fuerunt et sunt et futuri sunt infiniti : ideoque infinite sola natura subsistentie »
CEut. 3, 10,63 – 11,74, p. 237


Individuum
Infinite unrealized possibles

« …qui nondum sunt vel fuerunt: et nunc sunt tam actu quam natura homines infiniti…
Unus vero actu solus est sol preter quem nullus actu vel fuit vel est vel erit quamvis natura
et fuerunt et sunt et futuri sunt infiniti : ideoque infinite sola natura subsistentie »
CEut. 3, 10,63 – 11,74, p. 237

Every species has infinite possible never actualized instances
e.g. The sun is actually one and will always be one, but there are infinite possible suns never
realized

How are they possible?
They are not actually possible, they will never be in this world.
But within the broader doctrine of the alternative providential histories, they are
synchronically possible.

Individuum




Individuum
Possibile logicum
• Logical Necessity vs. Natural Necessities

What about the logical possible?
The first clear definition of l.p. is due to Duns Scotus

Yet, Gilbert gives us two strong requirements that go in that direction:
a) An individual is impossible in a certain history of the world if it is in contradiction with the
laws of that world
b) An individual is impossible tout court iff it is in contradiction with
the non-contradiction principle
those logical laws Gilbert assumes to be universally accepted


Individuum




Individuum
Counterfactual identity

We have seen that a common species can have purely possible instances in alternative world
histories

What about actual individuals? Can an individual still be the same in another possible world?


Individuum
Can we think of counterfactual identity in Gilbert’s modal framework?

It would appear so,
by means of the tota forma structure:

• It doesn’t include the extrinsecus affixa

• It includes purely possible, non actualized properties/predicates


Individuum

It would appear so,




Individuum
Extrinsecus affixa
They are not part of the tota forma, but simply apposita; therefore

• The individuation is indifferent to any variation of the status
i.e. by changing its relations, its place, its time, its actions and passions, and what it has, the
individuum stays the same
i.e. what makes the individual that individual doesn’t change

Therefore, the changing of
• the world it relates to
• or any other of his extrinsic properties
theoretically doesn’t affect the individual identity


Individuum

It would appear so,




Individuum
Possible predicates
It’s an open question
1) What kind of possible predicates are included in the tota forma?
• Substantial?
• Qualitative
• Quantitative

2) If any possible internal predicate is actual in another world, how can the individual stay
the same?


Individuum
Possible predicates
It’s an open question
1) What kind of possible predicate are included in the tota forma?
• Substantial? (problematic)
• Qualitative
• Quantitative

2) If any possible internal predicate is actual in another world, how can the individual stay
the same?
- The tota forma would appear to change:
◊pni ≠ pni


Individuum
Possible predicates
About 2)
• ◊pni ≠ pni

• What kind of change on the internal predicates might be identity preserving?
• The one operating on the modal element?
• De re (the cases we have seen)
It is doubtful
• De dicto
Is there, more or less explicitly such a distinction?
• On the temporal one?

This is one among the many open lines of enquiry to be pursued


Gilbert modalities lisbon copia

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