depicting reality
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Depicting Reality. Barry Smith http://ontology.buffalo.edu/smith. David Armstrong Universals and Scientific Realism. Armstrong’s Fantology. The spreadsheet ontology. and so on …. 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. Fantology. - PowerPoint PPT PresentationTRANSCRIPT
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Depicting Reality
Barry Smithhttp://ontology.buffalo.edu/smith
David Armstrong
Universals and Scientific Realism
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Armstrong’s Fantology
The spreadsheet ontology
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F G H I J K L M N O P Q R S T U Vabcdefghijk
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F G H I J K L M N O P Q R S T U Va x x x x xbcdefghijk
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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xcdefghijk
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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xdefghijk
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F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xd x xefghijk
and so on …
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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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FantologyThe syntax of first-order predicate logic is a
mirror of reality‘Fa’ (or ‘Rab’) is the key to ontological
structure(Fantology a special case of linguistic
Kantianism: the structure of language is they key to the structure of [knowable] reality)
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For the fantologist “(F(a)”, “R(a,b)” … is the language for ontology
This language reflects the structure of realityThe fantologist sees reality as being made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’
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Fantology infects computer science, too
(Modern forms of this in the world of OWL, where we might talk of “Fology”)
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Formal Ontology vs. Formal Logic (Husserl)
Formal ontology deals with the interconnections of thingswith objects and properties, parts and wholes, relations and collectivesFormal logic deals with the interconnections of truthswith consistency and validity, or and not
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Formal Ontology vs. Formal Logic
Formal ontology deals with formal ontological structuresFormal 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
First principle of fantology
all form is logical form
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pace Russell, Wittgenstein, Armstrong …
where entails is a logical relation,part-whole is an ontological relation
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Standard FOL semantics
‘F’ stands for a property‘a’ 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 in some ways (for example with his Aristotelian doctrine of universals as immanent to particulars)
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... but
He is still a prisoner of fantological syntax
… the forms F(a) and R(a,b) are still the basic key to ontology
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Fantology
Works very well in mathematicsPlatonist theories of properties are here
very attractive
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Second Principle of Fantology
“All generality belongs to the predicateˮ
The ‘a’ in ‘Fa’ is a mere nameContrast this with the way scientists use names:
The electron has a negative charge
DNA-Binding Requirements of the Yeast Protein Rap1p as selected In Silico from Ribosomal Protein Gene Promoter Sequences
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Third Principle of Fantology
“Individuals are mereologically simpleˮ
F G H I J K L M N O P Q R S T U Va x x x x xb x x x x xc x x x x xdefg
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‘a’ leaves no room for ontological complexity
Hence: reality is made of atomsHence: all probability is combinatoricAll 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
Armstrongʼs spreadsheet idea rests on a belief in some future state of ‘total (perfected) scienceʼ (see also Peirce)
when the values of ‘Fʼ and ‘aʼ will be revealed to the elect
(A science as a totality of propositions closed under logical consequence)
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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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Fantology: Some optional elements
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
(Fantology useless e.g. for biomedical ontology)
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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 formAll necessity is logical necessityCf. 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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Fourth Principle of Fantology
“There is no predication in the category of substance”
(Alternatively: the two types of predication are confused)
ArmstrongThere are only property universals
negatively charged (of electrons)phosphorylated (of proteins)
etc.Thus no need for kind universals
electronprotein
etc.
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Armstrong’s own view
State of affairs = Substance + universalsSubstances are the locus of particularityUniversals explain invariance/similarity
(Both particulars and universals are abstractions from states of affairs)
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No tropes
For Armstrong, tropes are congealed states of affairs
(Propositions of the form ‘Fa’ are the key to basic reality)
‘a’ refers always to substances (objects, things)
‘F’ refers always to Platonically conceived universals
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FantologyFa, Gb x(Fx Gx)This should be the form of laws of nature (not,
for instance, differential equations)Therefore, again, a noumenal view of scienceArmstrong not able to name even one example
of a really existing univeral or of a really existing particular
Compare 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
(given its roots in mathematics) has no satisfactory way of dealing with
timehence leads to banishment of time from
the ontology (as in Armstrong’s four-dimensionalism)
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Fifth Principle of Fantology: Booleanism
if F stands for a property and G stands for a property
then F&G stands for a propertyFvG stands for a propertynot-F stands for a propertyFG stands for a propertyand so on
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Strong BooleanismThere is a complete lattice of properties:
self-identity
FvG
F G
F&G
non-self-identity
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Strong BooleanismThere 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 BooleanismWith his sparse theory of properties
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Gene OntologyCellular 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 Dependent Continuants
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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A better view
In order to do justice to time we need to recognize both properties and processes (cf. Davidson’s views on events)
property-universals and property-instances (tropes) (dependent continuants)
process-universals and process-instances (occurrents)
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Dependent Continuants
states, powers, qualities, roles, functions, dispositions, plans, shapes …
PlusProcesses = the expressions,
realizations of all of these things in time (Occurrents)
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The (Aristotelian) Ontological Sextet
Substances Qualities, Roles, Functions, …. Processes
UniversalsSubstance-universals
Dependent Continuant-universals,
Process-universals
ParticularsIndividual
Substances
Dependent Continuant-instances
Process-instances
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Armstrong´s view:
Substances Qualities, Roles, Functions, …. Processes
Universals Properties
Particulars Particulars
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The tropist view:
Substances Qualities, Roles, Functions, …. Processes
Universals
Particulars Tropes, bundles
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The set-theoretical view:
Substances Qualities, Functions, Roles … Processes
Universals Sets
Particulars Elements
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Process Metaphysics
Substances Qualities, Functions, Roles … Processes
UniversalsEverything
is flux
Particulars
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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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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 interestIt 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 sentenceshas 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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Problems with set theory
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
collectionsConsider the collection of trees that is a
certain forest. 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 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 setnor 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 RELATIONSsuch as instantiation, part-whole,
expression (between a function and a process) …
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A better syntax
variables x, y, z … range overuniversals and particulars in all 6 categoriespredicates 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 a man: Inst(John, man)John’s headache depends on John:
Dep(John’s headache, John)
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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 eventsDoes(John,e)
Aristotelian Ontological Sextet
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Fantology
All form is logical formTo 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. PhysiologySNAP vs. SPAN
Synchronic vs. diachronic ontology
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Different ontological perspectives
SNAP vs SPANUniversals vs. ParticularsDifferent 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
processsubstanceThe erosion of the rock necessitates the existence of the rock
qualitysubstance 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 ontologiesintra-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 SignaturesIn 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 dependent continuants and their realizations in processes)
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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)
InitiationPerpetuation
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 anotherProcess 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 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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Substances and processes
t i m
e
process
demand different sorts of inventories
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Substances demand 3-D partonomies
space
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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 headacheThe 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 allProcesses 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
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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+(Qualities, Functions, Roles …), and Processes
Continuants and Occurrents
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 existRather: 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
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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 growththe surgeon and the operation
the virus and its spreadthe temperature and its risethe 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-dimensionalYour life is 4-dimensional
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Three kinds of SNAP entities
1. Substances2. Qualities, functions, roles3. Spatial regions, contexts,
niches, environments
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one-place qualities, functions, roles
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 quality
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 warmergetting 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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Realizable Dependent Continuants (Functions, Dispositions, Roles, …)
and their Realizations
the expression of a functionthe exercise of a rolethe execution of a planthe realization of a disposition
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Realizable entities
promisedebttendencyplandispositiontherapydisease
Dependent Continuants
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Realizable entities and their realizations
expression exercise execution realization applicationcourse
processes
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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 SPANUniversals vs. ParticularsDifferent levels of granularity:
molecular, cellular, organism ...
166
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
167
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
168
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
169
This generates a first list of formal relations, e.g. dependence,but we find some of these relations also within SNAP or within SNAP
170
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
171
Example:Ontological Dependence
(occurrent, independent continuant): process substanceThe erosion of the rock necessitates the existence of the rock
(dependent continuant, independent continuant): quality substance The token redness of the ball necessitates the existence of the ball
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Generating a typology
Two main types of formal relations:inter-ontological („transcendental“): obtain
between entities of different ontologiesintra-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 SignaturesIn 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 functions, dispositions, roles … and their occurrent expressions or manifestations)
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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)
InitiationPerpetuation
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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MediationA 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
Spatial Regions
Processuals
Processes
Events
Space-Time Regions
DependentContinuants…
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
DependentContinuants…
Space Regions
Processuals
Processes
Events
Space-Time Regions
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
Space Regions
Processuals
Processes
Events
Space-Time Regions
DependentContinuants…
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
Space Regions
Processuals
Processes
Events
Space-Time Regions
DependentContinuants…
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2nd Family
REALIZATION
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Signatures of meta-relations
SNAP Component SPAN Component
Substances
Spatial Regions
Processuals
Processes
Events
Space-Time Regions
participation
realizationDependentContinuants…
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Realization (function, role ... ->process)
A relation between a dependent continuant 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 functionthe exercise of a rolethe realization of a disposition
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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
ParticipationSubstance Process
RealizationRole Process
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SPAN -> SNAP
Involvement
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SPAN -> SNAP
Involvement
Creation
Sustaining in being
DestructionDemarcation
BlurringDegradation
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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)
InitiationPerpetuation
Termination
Influence
Facilitation
Hindrance
Mediation
Patiency(-agentive)
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SPAN-SNAP
Involvement
Creation
Sustenance
Destruction
ContinuationDegradation
Destruction
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 RelationIntracategorial
Mereological (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 propertiesCf. D.M. ArmstrongUniversals vs. TropesSubstance/attribute vs. bundles
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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)
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Four alternative positions
Substance-Attribute plus Universal Properties
Bundles with Universal Properties
Substance-Attribute plus Tropes
Bundles with Tropes
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Armstrong’s own view
Substance/attribute + universalsSubstances are the locus of particularityUniversals 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 SquareSubstantial 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 SquareSubstantial 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 SquareSubstantial 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 SquareSubstantial 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 SquareSubstantial 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 SquareSubstantial 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 SquareSubstantial Dependent Entities
Exercise of power Exercise of functionMovementAction
SubstancesCollectivesUndetached partsSubstantial boundaries
PowersFunctionsQualitiesShapes
Occ
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Con
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Refining the Ontological Square
Substantial Moments (Dependent)
Exercise of power Exercise of functionMovementAction
SubstancesCollectivesUndetached partsSubstantial boundaries
PowersFunctionsQualitiesShapes
Occ
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nts
Con
tinua
nts
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Refining the Ontological SquareSubstantial Dependent Entities
Exercise of power Exercise of functionMovementAction Processes?
SubstancesCollectivesUndetached partsSubstantial boundaries
PowersFunctionsQualitiesShapes Moments?
Occ
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Con
tinua
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Refining the Ontological SquareSubstantial Dependent Entities
John‘s reddeningJohn‘s blushingJohn‘s bruising
4-DSubstancesCollectivesUndetached partsSubstantial boundaries
John‘s rednessJohn‘s blushJohn‘s bruise
3-D
Occ
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Con
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Refining the Ontological SquareSubstantial Dependent Entities
John‘s reddeningJohn‘s blushingJohn‘s bruising
4-D (perduring)Stuff(Blood, Snow, Tissue)MixturesHoles
John‘s rednessJohn‘s blushJohn‘s bruise
3-D (enduring)
Occ
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Con
tinua
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A Refined Ontological SquareSubstantial Dependent Entities
John‘s reddeningJohn‘s blushingJohn‘s bruising
4-D (perduring)Stuff(Blood, Snow, Tissue)MixturesHoles
John‘s rednessJohn‘s blushJohn‘s bruise
3-D (enduring)
Occ
urre
nts
Con
tinua
nts
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Aristotle’s Ontological SquareSubstantial 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 MetaphysicsSubstantial Accidental
EventsProcesses
“Everything is flux”
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The (Aristotelian) Ontological Sextet
Substances Qualities, Roles, Functions, …. Processes
UniversalsSubstance-universals
Dependent Continuant-universals
Process-universals
ParticularsIndividual
Substances
Dependent Continuant-instances
Process-instances
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The (Aristotelian) Ontological Sextet
SubstancesQualities, Functions, Roles …
Processes
Universals Substance-universals
Dependent Continuant-universals,
Process-types
Particulars
Individual Substances(including
environments)
Dependent Continuant-instances
Process-tokens
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The set-theoretical view:
Substances Qualities, Functions, Roles … Processes
Universals Sets
Particulars Elements
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The OWL view:
Substances Qualities, Functions, Roles … Processes
Universals Classes
Particulars Individuals