Post on 13-Dec-2015
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VT
The language of set theory is a FOLWUT language
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Against Fantology:The Case of Properties
Barry Smithhttp://ifomis.de
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Armstrong’s
spreadsheet ontology
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F G H I J K L M N O P Q R S T U V
a
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F G H I J K L M N O P Q R S T U V
a x x x x x
b
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F G H I J K L M N O P Q R S T U V
a x x x x x
b x x x x x
c
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F G H I J K L M N O P Q R S T U V
a x x x x x
b x x x x x
c x x x x x
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F G H I J K L M N O P Q R S T U V
a x x x x x
b x x x x x
c x x x x x
d x x
e
f
g
h
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j
k
and so on …
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Fantology
The doctrine, usually tacit, according to which ‘Fa’ (or ‘Rab’) is the key to ontological structure
The syntax of first-order predicate logic is a mirror of reality
(Fantology a special case of linguistic Kantianism: the structure of language is they key to the structure of [knowable] reality)
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Formal Ontology vs. Formal Logic
Formal ontology deals with the interconnections of things
with objects and properties, parts and wholes, relations and collectives
Formal logic deals with the interconnections of truths
with consistency and validity, or and not
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Formal Ontology vs. Formal Logic
Formal ontology deals with formal ontological structures
Formal logic deals with formal logical structures
‘formal’ = obtain in all material spheres of reality
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Formal Ontology and Symbolic Logic
Great advances of Frege, Russell, Wittgenstein, Peano
(in logic, and in philosophy of mathematics)
Leibnizian idea of a universal characteristic
…symbols are a good thing
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But Russell, Wittgenstein, Armstrong …
Entails is a logical relation
Part-whole is an ontological relation
First mistake of fantology:
All form is logical form
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First-order logic
F(a)
R(a,b)
F(a) v R(a,b)
Either a F’s or a stands in R to b
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Standard semantics
F stands for a propertya stands for an individual
properties belong to Platonic realm of forms
orproperties are sets of individuals for which
F(a) is true
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Armstrong
Departs from fantology with his Aristotelian doctrine of universals as immanent to particulars
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Fantology
The forms F(a) and R(a,b) are the basic clue to ontology
(Confusion of logical form and ontological form)
Armstrong recognizes that semantics and epistemology have no implications for ontology
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... but
He is nonetheless a prisoner of fantological syntax
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Fantology infects computer science, too
here I will concentrate on the role of fantology within analytical metaphysics
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Fantology
Works very well in mathematics
Platonist theories of properties here are very attractive
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Fantology
Fa
All generality belongs to the predicate‘a’ is a mere nameContrast this with the way scientists use names:
The electron has a negative chargeDNA-Binding Requirements of the Yeast Protein Rap1p as selected In Silico from Ribosomal Protein Gene Promoter Sequences
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For extreme fantologists ‘a’ leaves no room for ontological complexity
Hence: reality is made of atoms
Hence: all probability is combinatoric
All true ontology is the ontology of ultimate universal furniture – the ontology of a future, perfected physics
Fantology cannot do justice to the existence of different levels of granularity of reality
Thus fantology is conducive to reductionism in philosophy
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Fantology
Tends to make you believe in some future state of ‚total science‘
when the values of ‚F‘ and ‚a‘, all of them,will be revealed to the elect
(A science as a totality of propositions closed under logical consequence)
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Armstrong
The ontology of the basic furniture of reality – must be expressible in F(a), R(a,b) form
Armstrong’s original definition of truthmaking:
the state of affairs that p makes q true :=p & necessarily(p q)
p ranges over truths of basic scienceq ranges over all truths
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For the fantologist
“(F(a)”, “R(a,b)” … is the language for ontology
This language reflects the structure of reality
The fantologist sees reality as being made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’
Truthmaker theory should set us free from this mistake
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Fantology
Fa
The particular corresponds to a bare namenoumenal view of particulars (distinction
between thin and thick particulars)aversion to idea of substances as spatially
extended and spatially located
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Fantology
Fa
noumenal view of particularsCf. Wittgenstein’s Tractatus (doctrine of
simples)
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Fantalogy
FaQuine’s distinction between ontology
and ideologyphysical objects do not instantiate universals; they are just occupied regions of spacetime predicates are just ideology (no singular terms for universals)
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Fantology
All form is logical form
All necessity is logical necessity
Cf. Wittgenstein‘s doctrine of the independence of states of affairs
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Fantology
Fa
To understand properties is to understand predication
(effectively in terms of functional application à la Frege)
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Contrast Aristotle
Predication in the category of substance:
John is a man, Henry is an ox
Predication in the category of accident:
John is hungry, Henry is asleep
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For Fantology
no predication in the category of substance (or the two types of predication are confused)
Armstrong: property universals are all we need
no need for kind universals
(Armstrong’s four-dimensionalism implies that there are no substances)
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There is only one form of states of affairs
Fa
if there was predication in the category of substance, this would mess up Armstrong’s doctrine of states of affairs
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Armstrong’s own view
State of affairs = Substance + universals
Substances are the locus of particularity
Universals explain invariance/similarity
(Both particulars and universals are abstractions from states of affairs)
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Fantology
Fa
yields
the form of the basic ingredients of reality
Thick particulars: a + F + G + H + …
Thin particulars: a (‘irreducible particularity’)
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For Armstrong
tropes are a bad theory for understanding states of affairs
(for understanding how the basic ingredients of reality are joined together)
For Armstrong tropes are congealed states of affairs
(Propositions of the form ‘Fa’ are the key to basic reality)
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Fantology
Fa:
This should be the form of laws of nature (things + universal powers)
(not, for instance, differential equations)
Therefore, again, a noumenal view of science
Armstrong not able to name even one example of a really existing univeral
or of a really existing particular
Compare again Wittgenstein
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Fantology
leads not only to Armstrong’s atoms + properties view of the basic ingredients of reality
but also to trope bundle views(where the a is deleted, and the F, G, H…
are seen as having particularity)Compare: Leibniz’s monadology (each
monad is a bundle of concepts)
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Fantology
Fa
No clear way to deal with time
Armstrong talks not of processes but of particulars gaining or losing properties
But gaining and losing are themselves processes
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Booleanism
if F stands for a property and G stands for a property
then
F&G stands for a property
FvG stands for a property
not-F stands for a property
FG stands for a property
and so on
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Strong Booleanism
There is a complete lattice of properties:
self-identity
FvG
F G
F&G
non-self-identity
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Strong Booleanism
There is a complete lattice of properties:
self-identity
FvG
not-F F G not-G
F&G
non-self-identity
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Booleanism
responsible, among other things, for Russell’s paradox
Armstrong free from Booleanism
With his sparse theory of properties
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That Lewis and Armstrong
arrived at their sparse view of properties against the solid wall of fantological Booleanist orthodoxy
is a miracle of modern intellectual historyanalogous to a 5 stone weakling climbing
up to breathe the free air at the top of Mount Everest with 1000 ton weights attached to his feet
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leading them back, on this point,
to where Aristotelians were from the very beginning
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Fantology
(given its roots in mathematics)
has no satisfactory way of dealing with time
hence leads to banishment of time from the ontology
(as in Armstrong’s four-dimensionalism)
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A better view
In order to do justice to time we need to recognize both properties and processes
better: do not use the word ‘property’ at all, talk rather of
SPQR entities (both universals and instances)
and ofprocess-universals and process-instances
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SPQR
states, powers, qualities, roles,
functions, dispositions, plans, shapes …
Plus
Processes = the expressions, realizations of all of these things in time
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The (Aristotelian) Ontological Sextet
Substances SPQR entities Processes
UniversalsSubstance-universals
SQPR-universals,
Process-types
ParticularsIndividual
Substances
SPQR-instances (Tropes…)
Process-tokens
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Armstrong´s view:
Substances SPQR entities Processes
Universals Properties
Particulars Particulars
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The trope view:
Substances SPQR entities Processes
Universals
ParticularsTropes, bundles
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The set-theoretical view:
Substances SPQR entities Processes
Universals Sets
Particulars Elements
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Armstrong
Property universals are all we needNo need to distinguish kind universals
No need to distinguish predications in the category of
substance from predications in the category of accident
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The (Aristotelian) Ontological Sextet
Substances SPQR entities Processes
UniversalsSubstance-universals
SQPR-universals,
Process-types
ParticularsIndividual
Substances
SPQR-instances (Tropes…)
Process-tokens
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Gene Ontology
Cellular Component Ontology: subcellular structures, locations, and macromolecular complexes;examples: nucleus, telomere Substances
Molecular Function Ontology: tasks performed by individual gene products; transcription factor, DNA helicase SPQR
Biological Process Ontology: broad biological goals accomplished by ordered assemblies of molecular functions; mitosis, purine metabolism Processes
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Fantology implies a poor treatment of relations
R(a,b)
in terms of adicity
What is the adicity of your headache (A relation between your consciousness and various processes taking place in an around your brain) ?
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Fantology implies a neglect of environments
John kisses Mary
always in some environment
(= roughly, in some spatial region: a room, a car …)
Spatial regions are, like substances, three-dimensional endurants
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Fantology leads you to talk nonsense about family
resemblances
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Fantology
emphasizes the linguistic over the perceptual/physiognomic
(the digitalized over the analogue)
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The limitations of fantology
lead one into the temptations of possible world metaphysics,
and other similar fantasies
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Fantology leads one to talk nonsense about possible worlds
Definition: A possible world W is a pair (L,D) consisting of a set of first-order propositions L and a set of ground-level assertions D. …
Informally, the set L is called the laws of W, and the set D is called the database of W. Other informal terms might be used: L may be called the set of axioms or database constraints for W.
(John Sowa)
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The (Aristotelian) Ontological Sextet
Substances SPQR entities Processes
UniversalsSubstance-universals
SQPR-universals,
Process-types
Particulars
Individual Substances
(including environments)
SPQR-instances (Tropes…)
Process-tokens
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The set-theoretical view:
Substances SPQR entities Processes
Universals Sets
Particulars Elements
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Fantology
is a form of linguistic Kantianism
Semantic Fantology
is a form of set-theoretical Kantianism
The [knowable] world = the [set-theoretic] model of a formal theory
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Arguments against Set Theory
Lesniewski’s Argument: Even set theorists do not understand their own creations; thus they do not know how one important family of sets (the set of real numbers, for example) relates in size to other sets (the set of natural numbers, for example).
Still no generally accepted correct axiomatization of set theory,
Questions re Axiom of Choice, etc.
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Set theory is Booleanism unremediated
Booleanism without any remediating features whatsoever
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There are skew partitions (true) of the same reality
for example reflecting different granularities of analysis. If we identify entities in the world with sets, we cannot do justice to the identity of one and the same object as partitioned on different levels.
Mereology, in contrast, can allow the simultaneous truth of:
An organism is a totality of cells.An organism is a totality of molecules.
France is the totality of its 7 regions.France is the totality of its 116 provinces.
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Dominance of set-theoretic ontology as an account of classes
means that there is no analytic-philosophical treatment of multi-variate statistical classification
in spite of the fact that this is the major approach to classification in all sorts of natural and social sciences
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The application of set theory to a subject-matter
presupposes the isolation of some basic level of Urelemente, which make possible the simulation of the structures appearing on higher levels by means of sets of successively higher types.
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But there is no such basic level of Urelemente in many spheres to which we might wish to direct ontological analysis, and in many spheres there is no unidirectional (upward) growth of complexity generated by simple combination.
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Set theory reduces all complexity to combination or unification
Set theory is a general theory of the structures which arise when objects are conceived as being united together ad libitum on successively higher levels, each object serving as member or element of objects on the next higher level.
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Set theory is of course of considerable mathematical interest
It is however an open question whether there is any theoretical interest attached to the possibility of such ad libitum unification from the perspective of ontology.
For the concrete varieties of complexity which in fact confront us are subject always in their construction to quite subtle sorts of constraints, constraints which vary from context to context.
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Set theory
allows unrestricted (Boolean) combinations
therefore gives as far more objects than we need
{all red things, the number 6}
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Sets are abstract entities
Sets are timeless (they do not change)
Thus a philosopher who countenances them in his ground-floor ontology has already renounced the advantages of a theory which is committed only to changing realia.
He is thereby left with the problem of connecting up the abstracta he countenances with the real entities with which they are in different ways associated.
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Against Set Theory as a Vehicle for Semantics
There are some who would argue that we can understand a theory (for example in logic) only when we have given a set-theoretic semantics for that theory.(This is rather like saying that we can understand French only when we have translated it into English.)And how, on this basis, can we understand the language of set theory itself?
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Truth for empirical sentences
has classically been understood in terms of a correspondence relation (i.e. of some sort of isomorphism) between a judgment or assertion on the one hand and a certain portion of reality on the other. But reality evidently does not come ready-parcelled into judgment-shaped portions Hence practitioners of logical semantics have treated not of truth as such (understood as truth to an autonomous reality), but of truth in a model, where the model is a specially constructed set-theoretic reality-surrogate.
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Other problems
If sets don't change, then a set-theoretical ontology cannot do justice the causal-historical continuous orderSince sets divide the world into elements (points) this implies a certain unfaithfulness to boundary phenomena/continuaCan’t do justice to gradations/prototypes
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Mereology can deal more adequately with real-world
collections
Consider the collection of trees that is a certain forst.
What is its cardinality?
Are two trees that share a common root system one or two?
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Mereology can deal more adequately with fields
(e.g. in quantum field theory)
since it does not presuppose the isolation of urelemente/atoms at the bottom of a structural hierarchy
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The standard set-theoretic account of the continuum
initiated by Cantor and Dedekind and contained in all standard textbooks of the theory of sets, will be inadequate for at least the following reasons:
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The experienced continuum
does not sustain the sorts of cardinal number constructions imposed by the Dedekindian approach.
The experienced continuum is not isomorphic to any real-number structure;
standard mathematical oppositions, such as that between a dense and a continuous series, here find no application.
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Set theory can yield at best a model
of the experienced continuum and similar structures, not a theory of these structures themselves (for the latter are after all not sets).
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The experienced continuum
is in every case a concrete, changing phenomenon, a phenomenon existing in time, a whole which can gain and lose parts.
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The application of set theory
to a subject-domain presupposes the isolation of some basic level of Urelemente in such a way as to make possible a simulation of all structures appearing on higher levels by means of sets of successively higher types.
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Theory of the continuum
Set theory: out of unextended building blocks an extended whole can somehow be constructed.
But the experienced continuum is not organized out of particles or atoms,
rather, the wholes, including the medium of space, come before the parts which these wholes might contain and which might be distinguished on various levels within them.
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Set theory leads to paradoxes
In mereology, paradoxes do not arise, since every collection is part of itself, and there cannot be a collection that is not a part of itself
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The alternative to fantology
must take the spatiality and materiality and modular complexity of substances seriously
Mereology plus Granularity plus theory of spatial extension
‘a’ refers to something that is complex
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Mereology
allows a nicer treatment of both plurals and mass nouns than set theory
(but mereology, too, has problems dealing with time,
and with granularity)
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Mereology is much simpler than set theory
Whereas set theory has two distinct operators: element-of and subset-of,
mereology has only one basic operator: part-of
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Mereology makes no distinction between an individual and a
singleton set
nor between different ways of building up collections by level of nesting:
{a,b,c} is identical to {a, {{{b}}, {c}}}.
Nelson Goodman: "No distinction of individuals without distinction of content."
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How are the 6 categories of entity related together?
Via FORMAL RELATIONS
such as instantiation, part-whole, expression (between a function and a
process) …
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A better syntax
variables x, y, z … range over
universals and particulars in all 6 categories
predicates stand only for FORMAL relations such as instantiates, part-of, connected-to, is-a-boundary-of, is-a-niche-for, etc.
FORMAL relations are not extra ingredients of being
(compare jigsaw puzzle pieces and the relations between them)
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This suggests a new syntax:
=(x,y)Part(x,y)Inst(x,y)Dep(x,y)Isa(x,y)
John is wise: Inst(John, wisdom)John is a man: Isa(John, man)
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Compare the syntax of set theory
(x,y)
one (formal) predicate
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Compare the syntax of set theory
Basic Formal Ontology (BFO) has the syntax of set theory but with a PLURALITY of formal relations
Note that logic gives us no clue as to what these are
(they must include: location in space, location at a time …)
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Compare the syntax of description logics
isa(x,y)
one formal predicate
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Compare the syntax of description logics
isameans:
is an instance ofis a sub-class of (is subsumed by)
sometimes also:may be ais a part of
(all symbolized by means of a single relational constant)
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New syntax:
=(x,y)
Part(x,y)
Inst(x,y)
Dep(x,y)
Compare Davidson’s treatment of events
Does(John,e)
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Fantology
All form is logical form
To understand how the world hangs together you need to understand
... and, or, not, all, some ...
No. You need formal-ontological relations like partial identity, spatial location, temporal location, instantiation, ...
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But what ARE the formal relations?
Clue:
Anatomy vs. Physiology
SNAP vs. SPAN
Synchronic vs. diachronic ontology
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Different ontological perspectives
SNAP vs SPAN
Universals vs. Particulars
Different levels of granularity:
molecular, cellular, organism ...
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN dividethey glue SNAP and SPAN entities together
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particularsbecause they traverse the universal-particular dividethey glue universals and particulars together
---- above all instantiation
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by an ontology on any single level of granularitybecause they traverse the granular dividethey glue together entities on different levels of granularity
--- above all parthood
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This generates a first list of formal relations,
e.g. dependence,
but we find some of these relations also within SNAP or within SNAP
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The idea (modified version)
Formal relations are the relations that hold SNAP and SPAN entities/ontologies togetherand analogous relations… they come for free, they do not add anything to being = they are links between categories
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Example:Ontological Dependence
(SPAN, SNAP): process->substance
The erosion of the rock necessitates the existence of the rock
(SNAP, SNAP): SPQR->substance
The token redness of the sand necessitates the existence of the sand
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Generating a typology
Two main types of formal relations:
inter-ontological („transcendental“): obtain between entities of different ontologies
intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra-SPAN)
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Three parameters:
- the arity of the relation
- the types of the relata, expressed as an ordered list, called the signature of the relation
- the formal nature of the relation
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Principal Signatures
In the binary case:
SNAP-SNAP - (SNAPi, SNAPi), i = i
- (SNAPi, SNAPi), i < j, i > j
SPAN-SPAN
SNAP-SPANSPAN-SNAP
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Transtemporal relations
Examples:
Genidentity
(transtemporal generalization of identity/part-whole)
Successive causality
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Genidentity
Also SPAN-SPAN? Is there a form of genidentity among processes?
The such-as-to-have-come-forth-from relation.
Signature: SNAPi-SNAPj
Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting
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Successive Causality
SNAP-SPAN: Agent causationA substance produces causally a process
SPAN-SPAN: Process causationOne process causes another process
SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)
SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)
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Successive Causality
SNAP-SPAN: Agent causation
SPAN-SPAN: Process causation
SPAN-SNAP: Causal repercussion
SNAP-SNAP: Causal origin
do not apply on all levels of granularity
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Our main target: Temporally extended relations
Participation(holds between a substance and a process such as an action or a life or history)
Realization(holds between SPQR… entities and their SPAN expressions)
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Substance->Process
PARTICIPATION(a species of dependence)
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Participation (SNAP-SPAN)
A substance (SNAP) participates in a process (SPAN)
A runner participates in a race
An organ participates in a sickness
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Axes of variation
activity/passivity (agentive)
direct/mediated
benefactor/malefactor (conducive to existence) [MEDICINE]
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SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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Substances
Mesoscopic reality is
divided at its natural joints
into substances:
animals, bones, rocks, potatoes, brains
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The Ontology of Substances
Substances form natural kinds
(universals, species + genera)
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Processes
Processes merge into one another
Process kinds merge into one another
… few clean joints either between instances or between types
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Processes
t i m e
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Nouns and verbs
Substances and processes
Continuants and occurrents
Endurants and perdurants
In preparing an inventory of reality
we keep track of these two different categories of entities in two different ways
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Substances and processes
t i m
e
process
demand different sorts of inventories
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Substances demand 3-D partonomies
space
127
Processes demand 4D-partonomies
t i m e
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Processes
a whistling, a blushing, a speech
a run, the warming of this stone
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Processes may have temporal parts
The first 5 minutes of my headache is a temporal part of my headache
The first game of the match is a temporal part of the whole match
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Substances do not have temporal parts
The first 5-minute phase of my existence is not a temporal part of me
It is a temporal part of that complex process which is my life
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Substances and processes form two distinct orders of being
Substances exist as a whole at every point in time at which they exist at all
Processes unfold through time, and are never present in full at any given instant during which they exist.
When do both exist to be inventoried together?
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The Four-Dimensionalist Ontology (SPAN)
t i m e
133
The Time-Stamped Ontology (SNAP)
t1
t3t2
here time exists outside the ontology, as an index or time-stamp
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SNAP and SPAN
Substances+SPQR, and processesContinuants, and occurrentsEndurants, and perdurants
In preparing an inventory of realitywe keep track of these two different categories of entities in two different ways
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Fourdimensionalism denies this
– time is just another dimension, analogous to the three spatial dimensions
– only processes exist
– substances are analyzed away as worms/fibers within the four-dimensional process plenum
– there is no change
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There are no substances
Bill Clinton does not exist
Rather: there exists within the four-dimensional plenum a continuous succession of processes which are similar in Billclintonizing way
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Fourdimensionalism
is right in everything it says
But incomplete
138
It needs to be supplemented
Cf. Quantum mechanics: particle vs. wave ontologies
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Two Orthogonal, Complementary Perspectives
SNAP and SPAN
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SNAP and SPAN
the tumor and its growth
the surgeon and the operation
the virus and its spread
the temperature and its rise
the disease and its course
the therapy and its application
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Axiom
Part-relations never traverse the SNAP-SPAN divide
No process is ever part of a substanceand vice versaNo quality is ever part of a process and
vice versaProcess and function belong to two
different orders of being
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SNAP and SPANSNAP entities
- have continuous existence in time
- preserve their identity through change
- exist in toto if they exist at all
SPAN entities
- have temporal parts
- unfold themselves phase by phase
- exist only in their phases/stages
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SNAP vs. SPAN
1. SNAP: a SNAPshot ontology of endurants existing at a time
2. SPAN: a four-dimensionalist ontology of processes
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You are a substance
Your life is a process
You are 3-dimensional
Your life is 4-dimensional
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Three kinds of SNAP entities
1. Substances
2. SPQR… entities
3. Spatial regions, contexts, niches, environments
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one-place SPQR… entities
tropes, individual properties
(‘abstract particulars’)
a blush
my knowledge of French
the whiteness of this cheese
the warmth of this stone
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relational SPQR… entities
John Mary
love
stand in relations of one-sided dependence to a plurality of substances simultaneously
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SNAP entities
provide the principles of individuation/segmentation for SPAN entities
No change without some THING or QUALITY which changes
identity-based change
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Processes, too, are dependent on substances
One-place vs. relational processes
One-place processes:
getting warmer
getting hungrier
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Examples of relational processes
kissings, thumps, conversations,
dances,
Such relational processes
join their carriers together into collectives of greater or lesser duration
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Each is a window on that dimension of reality which is visible through the given ontology
SNAP and SPAN ontologies are partial only
(Realist perspectivalism)
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SNAP: Entities existing in toto at a time
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SNAP
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SPAN: Entities extended in time
SPANEntity extended in time
Portion of Spacetime
Fiat part of process *First phase of a clinical trial
Spacetime worm of 3 + Tdimensions
occupied by life of organism
Temporal interval *projection of organism’s life
onto temporal dimension
Aggregate of processes *Clinical trial
Process[±Relational]
Circulation of blood,secretion of hormones,course of disease, life
Processual Entity[Exists in space and time, unfolds
in time phase by phase]
Temporal boundary ofprocess *
onset of disease, death
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SPAN: Entities extended in time
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SPAN: Entities extended in time
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Relations between SNAP and SPAN
SNAP-entities participate in processes
they have lives, histories
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SPQR… entities and their SPAN realizations
the expression of a function
the exercise of a role
the execution of a plan
the realization of a disposition
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SPQR… entities and their SPAN realizations
function
role
plan
disposition
therapy
disease
SNAP
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SPQR… entities and their SPAN realizations
expression
exercise
execution
realization
application
course
SPAN
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Special role of formal relations
Only they are represented by predicates in the first-order logic representation of our ontology
But what are formal relations?
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Different ontological perspectives
SNAP vs SPAN
Universals vs. Particulars
Different levels of granularity:
molecular, cellular, organism ...
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by either SNAP or SPAN because they traverse the SNAP-SPAN dividethey glue SNAP and SPAN entities together
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by either an inventory of universals or an inventory of particularsbecause they traverse the universal-particular dividethey glue universals and particulars together
---- above all instantiation
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A hypothesis (first rough version)
Formal relations are those relations which are not captured by an ontology on any single level of granularitybecause they traverse the granular dividethey glue together entities on different levels of granularity
--- above all parthood
168
This generates a first list of formal relations,
e.g. dependence,
but we find some of these relations also within SNAP or within SNAP
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The idea (modified version)
Formal relations are the relations that hold SNAP and SPAN entities/ontologies togetherand analogous relations… they come for free, they do not add anything to being = they are links between categories
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Example:Ontological Dependence
(SPAN, SNAP): process->substance
The erosion of the rock necessitates the existence of the rock
(SNAP, SNAP): SPQR->substance
The token redness of the sand necessitates the existence of the sand
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Generating a typology
Two main types of formal relations:
inter-ontological („transcendental“): obtain between entities of different ontologies
intra-ontological: obtain between entities of the same ontology (intra-SNAP, intra-SPAN)
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Three parameters:
- the arity of the relation
- the types of the relata, expressed as an ordered list, called the signature of the relation
- the formal nature of the relation
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Principal Signatures
In the binary case:
SNAP-SNAP - (SNAPi, SNAPi), i = i
- (SNAPi, SNAPi), i < j, i > j
SPAN-SPAN
SNAP-SPANSPAN-SNAP
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Transtemporal relations
Examples:
Genidentity
(transtemporal generalization of identity/part-whole)
Successive causality
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Genidentity
Also SPAN-SPAN? Is there a form of genidentity among processes?
The such-as-to-have-come-forth-from relation.
Signature: SNAPi-SNAPj
Cut a chunk of matter in two, the sum of the remaining pieces is genidentical to the chunk before cutting
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Successive Causality
SNAP-SPAN: Agent causationA substance produces causally a process
SPAN-SPAN: Process causationOne process causes another process
SPAN-SNAP: Causal repercussionA process results in the modification of a substance (always mediated by process causation)
SNAP-SNAP: Causal originOne substance is the causal origin of another (mediated by other types of causal relations)
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Successive Causality
SNAP-SPAN: Agent causation
SPAN-SPAN: Process causation
SPAN-SNAP: Causal repercussion
SNAP-SNAP: Causal origin
do not apply on all levels of granularity
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Our main target: Temporally extended relations
Participation(holds between a substance and a process such as an action or a life or history)
Realization(holds between SPQR… entities and their SPAN expressions)
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Substance->Process
PARTICIPATION(a species of dependence)
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Participation (SNAP-SPAN)
A substance (SNAP) participates in a process (SPAN)
A runner participates in a race
An organ participates in a sickness
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Axes of variation
activity/passivity (agentive)
direct/mediated
benefactor/malefactor (conducive to existence) [MEDICINE]
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SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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Perpetration
A substance perpetrates an action (direct and agentive participation in a process):
The referee fires the starting-pistol
The captain gives the order
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Initiation
A substance initiates a process:
The referee starts the race
The attorney initiates the process of appeal
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Perpetuation
A substance sustains a process:
The charged filament perpetuates the emission of light
The organism perpetuates the process of metabolism
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Termination
A substance terminates a process:
The operator terminates the projection of the film
The judge terminates the imprisonment of the pardoned convict
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Influence
A substance (or its quality) has an effect on a process
The hilly countryside affects the movement of the troopsThe politicians influence the course of the war
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Facilitation
A substance plays a secondary role in a process (for example by participating in a part or layer of the process)
The catalyst provides the chemical conditions for the reaction
The traffic-police facilitate our rapid progress to the airport
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Hindrance, prevention
A substance has a negative effect on the unfolding of a process (by participating in other processes)
The drug hinders the progression of the disease
The strikers prevent the airplane from departing
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Mediation
A substance plays an indirect role in the unfolding of a process relating other participants:
The Norwegians mediate the discussions between the warring parties
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Patiency
Dual of agentive participation
John kisses [Mary] (John agent)
Mary is kissed [by John] (Mary patient)
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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2nd Family
REALIZATION
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
SPQR…
Spatial Regions
Processuals
Processes
Events
Space-Time Regions
participation
realization
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Realization (SPQR->process)
The most general relation between a dependent (SPQR…) entity and a process
The power to legislate is realized through the passing of a law
The role of antibiotics in treating infections is via the killing of bacteria
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Realization (SNAP-SPAN)
the execution of a plan, algorithm
the expression of a function
the exercise of a role
the realization of a disposition
200
SPQR… entities and their SPAN realizations
plan
function
role
disposition
algorithm
SNAP
201
SPQR… entities and their SPAN realizations
execution
expression
exercise
realization
application
course
SPAN
202
Material examples:
performance of a symphonyprojection of a filmexpression of an emotionutterance of a sentenceapplication of a therapycourse of a diseaseincrease of temperature
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SNAP->SPAN
Participation
Substance -> Process
Realization
SPQR -> Process
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SPAN -> SNAP
Involvement
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SPAN -> SNAP
Involvement
Creation
Sustaining in being
Destruction
DemarcationBlurring
Degradation
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Involvement
process -> substance(sometimes the converse of participation):
Races involve racers
(but not always):
Wars involve civilians
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Creation
A process brings into being a substance:
The declaration of independence creates the new state
The work of the potter creates the vase
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Sustaining in being
A process sustains in being a substance:
The circulation of the blood sustains the body
Levying taxes sustains the army
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Degradation
A process has negative effects upon a substance
Eating sugar contributes to the deterioration of your teeth.
The flow of water erodes the rock
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Destruction
A process puts a substance out of existence
The explosion destroys the car
The falling of the vase on the floor breaks it
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Demarcation
A process creates (fiat or bona fide) boundaries of substances.
The tracing of the area by the surgeon defines a boundary, the incision performed by the surgeon yet another one
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Blurring
A process destroys boundaries of substances:
The military stand-off creates the no man's land
The successful transplant obliterates the boundary between original and grafted tissue
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SNAP-SPAN
Participation
Perpetration (+agentive)
Initiation
Perpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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SPAN-SNAP
Involvement
Creation
Sustenance
Destruction
Continuation
DegradationDestruction
Creation
DemarcationBlurring
Qualitative projection
Degradation
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The idea (a closer approximation)
Formal relations are those relations which are not captured by either the SNAP or the SPAN ontologyeither because they traverse the SNAP-SPAN divideor because they traverse the granular divide
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Types of Formal Relation
IntracategorialMereological (part)Topological (connected, temporally precedes)Dependency (e.g. functional ?)
IntercategorialInherence (quality of)Location Participation (agent)Dependency (of process on substance)
TranscendentalsIdentity
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A case study
Disputes about properties
Cf. D.M. Armstrong
Universals vs. Tropes
Substance/attribute vs. bundles
218
Contemporary Bundle views
Bundle views 1: bearers of predication are bundles of universals (particularity is ‘constructed’)
Bundle views 2: nuclear tropes (adding up to thick particulars) + contingent tropes (reflecting contingent predications)
219
Four alternative positions
Substance-Attribute plus Universal Properties
Bundles with Universal Properties
Substance-Attribute plus Tropes
Bundles with Tropes
220
Armstrong’s own view
Substance/attribute + universals
Substances are the locus of particularity
Universals explain invariance/similarity
Plus
States of affairs
(Both particulars and universals are abstractions from states of affairs)
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Not in a SubjectSubstantial
In a SubjectAccidental
Said of a SubjectUniversal, General,Type
Second Substances
man, horse, mammal
Non-substantial Universals
whiteness, knowledge
Not said of a Subject Particular, Individual,Token
First Substances
this individual man, this horse this mind, this body
Individual Accidents
this individual whiteness, knowledge of grammar
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Refining the Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Refining the Ontological Square
Substantial Dependent Entities
Exercise of power Exercise of function
Movement
Action
Substances
Collectives
Undetached parts
Substantial boundaries
Powers
Functions
Qualities
Shapes
Occ
urre
nts
Con
tinua
nts
229
Refining the Ontological Square
Substantial Moments (Dependent)
Exercise of power Exercise of function
Movement
Action
Substances
Collectives
Undetached parts
Substantial boundaries
Powers
Functions
Qualities
Shapes
Occ
urre
nts
Con
tinua
nts
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Refining the Ontological Square
Substantial Dependent Entities
Exercise of power Exercise of function
Movement
Action Processes?
Substances
Collectives
Undetached parts
Substantial boundaries
Powers
Functions
Qualities
Shapes
Moments?
Occ
urre
nts
Con
tinua
nts
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Refining the Ontological Square
Substantial Dependent Entities
John‘s reddening
John‘s blushing
John‘s bruising
4-D
Substances
Collectives
Undetached parts
Substantial boundaries
John‘s redness
John‘s blush
John‘s bruise
3-D
Occ
urre
nts
Con
tinua
nts
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Refining the Ontological Square
Substantial Dependent Entities
John‘s reddening
John‘s blushing
John‘s bruising
4-D (perduring)
Stuff
(Blood, Snow, Tissue)
Mixtures
Holes
John‘s redness
John‘s blush
John‘s bruise
3-D (enduring)
Occ
urre
nts
Con
tinua
nts
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A Refined Ontological Square
Substantial Dependent Entities
John‘s reddening
John‘s blushing
John‘s bruising
4-D (perduring)
Stuff
(Blood, Snow, Tissue)
Mixtures
Holes
John‘s redness
John‘s blush
John‘s bruise
3-D (enduring)
Occ
urre
nts
Con
tinua
nts
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Aristotle’s Ontological Square
Substantial Accidental
Second substance
man
cat
ox
Second accident
headache
sun-tan
dread
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Some philosophers
accept only part of the Aristotelian multi-categorial ontology
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Standard Predicate Logic – F(a), R(a,b) ...
Substantial Accidental
Attributes
F, G, R
Individuals
a, b, c
this, that
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Bicategorial NominalismSubstantial Accidental
First substance
this man
this cat
this ox
First accident
this headache
this sun-tan
this dread
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Process Metaphysics
Substantial Accidental
Events
Processes
“Everything is flux”
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