Species and Classification in Biology Barry Smith

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3 DNA m

ifomis.org4 DNA Protein Organelle Cell Tissue Organ Organism m m m

ifomis.org5 New golden age of classification* ~ 30 million species 30,000 genes in human 200,000 proteins 100s of cell types 100,000s of disease types 1,000,000s of biochemical pathways (including disease pathways) *… legacy of Human Genome Project

ifomis.org6 DNA Protein Organelle Cell Tissue Organ Organism m m m

ifomis.org7 FUNCTIONAL GENOMICS proteomics, reactomics, metabonomics, phenomics, behaviouromics, toxicopharmacogenomics …

ifomis.org8 The incompatibilities between different scientific cultures and terminologies immunology genetics cell biology

ifomis.org9 have resurrected the problem of the unity of science in a new guise: The logical positivist solution to this problem addressed a world in which sciences are associated with printed texts. What happens when sciences are associated with databases?

ifomis.org10 … when each (chemical, pathological, immunological, toxicological) information system uses its own classifications how can we overcome the incompatibilities which become apparent when data from distinct sources are combined?

ifomis.org11 Answer: “Ontology”

ifomis.org12 = building software artefacts standardized classification systems/ controlled vocabularies so that data from one source should be expressed in a language which makes it compatible with data from every other source

ifomis.org13 Google hits (in millions) ontology 52.4 ontology + philosophy 2.7 ontology + information science 6.0 ontology + database 7.8

ifomis.org14 A Linnaean Species Hierarchy

ifomis.org15 (Small) Disease Hierarchy

ifomis.org16 Combining hierarchies Organisms Diseases

ifomis.org17 via Dependence Relations Organisms Diseases

ifomis.org18 A Window on Reality

ifomis.org19 A Window on Reality Organisms Diseases

ifomis.org20 A Window on Reality

ifomis.org21 How to understand species (aka types, universals, kinds) Species are something like invariants in reality which can be studied by science Species have instances: this mouse, this cell, this cell membrane...

ifomis.org22 Entity =def anything which exists, including things and processes, functions and qualities, beliefs and actions, documents and software

ifomis.org23 Domain =def a portion of reality that forms the subject- matter of a single science or technology or mode of study; proteomics radiology viral infections in mouse

ifomis.org24 Representation =def an image, idea, map, picture, name or description... of some entity or entities.

ifomis.org25 Analogue representations

ifomis.org26 Representational units =def terms, icons, photographs, identifiers... which refer, or are intended to refer, to entities

ifomis.org27 Composite representation =def representation (1) built out of representational units which (2) form a structure that mirrors, or is intended to mirror, the entities in some domain

ifomis.org28 Periodic Table The Periodic Table

ifomis.org29 Ontologies are here

ifomis.org30 Ontologies are representational artifacts

ifomis.org31 What do ontologies represent?

ifomis.org32 A515287DC3300 Dust Collector Fan B521683Gilmer Belt C521682Motor Drive Belt

ifomis.org33 A515287DC3300 Dust Collector Fan B521683Gilmer Belt C521682Motor Drive Belt instances types

ifomis.org34 Two kinds of composite representational artifacts Databases, inventories: represent what is particular in reality = instances Ontologies, terminologies, catalogs: represent what is general in reality = types

ifomis.org35 What do ontologies represent?

ifomis.org36 Ontologies do not represent concepts in people’s heads

ifomis.org37 Ontology is a tool of science Scientists do not describe the concepts in scientists’ heads They describe the types in reality, as a step towards finding ways to reason about (and treat) instances of these types

ifomis.org38 The biologist has a cognitive representation which involves theoretical knowledge derived from textbooks

ifomis.org39 An ontology is like a scientific text; it is a representation of types in reality

ifomis.org40 Two kinds of composite representational artifacts Databases represent instances Ontologies represent types

ifomis.org41 Instances stand in similarity relations Frank and Bill are similar as humans, mammals, animals, etc. Human, mammal and animal are types at different levels of granularity

ifomis.org42 siamese mammal cat organism substance types animal instances frog

ifomis.org43 science needs to find uniform ways of representing types ontology =def a representational artifact whose representational units (which may be drawn from a natural or from some formalized language) are intended to represent 1. types in reality 2. those relations between these types which obtain universally (= for all instances) lung is_a anatomical structure lobe of lung part_of lung

ifomis.org44 is_a A is_a B =def For all x, if x instance_of A then x instance_of B cell division is_a biological process

ifomis.org45 Entities

ifomis.org46 Entities universals (species, types, taxa, …) particulars (individuals, tokens, instances)

ifomis.org47 Canonical instances within the realm of individuals = those individuals which 1. instantiate universals (entering into biological laws) 2. are prototypical  Canonical Anatomy: no Siamese twins, no six-fingered giants, no amputation stumps, …

ifomis.org48 Entities universals instances junk example of junk particulars: desk-mountain

ifomis.org49 Entities human Jane inst

ifomis.org50 Ontologies are More than Just Taxonomies

ifomis.org51 The Gene Ontology 7 million google hits a cross-species controlled vocabulary for annotations of genes and gene products deeper than Darwinianism

ifomis.org52 When a gene is identified three important types of questions need to be addressed: 1. Where is it located in the cell? 2. What functions does it have on the molecular level? 3. To what biological processes do these functions contribute?

ifomis.org53 GO has three ontologies molecular functions cellular components biological processes

ifomis.org54 GO astonishingly influential used by all major species genome projects used by all major pharmacological research groups used by all major bioinformatics research groups

ifomis.org55 GO part of the Open Biological Ontologies consortium Fungal Ontology Plant Ontology Yeast Ontology Disease Ontology Mouse Anatomy Ontology Cell Ontology Sequence Ontology Relations Ontology

ifomis.org56 Each of GO’s ontologies is organized in a graph-theoretical structure involving two sorts of links or edges: is-a (= is a subtype of ) (copulation is-a biological process) part-of (cell wall part-of cell)

ifomis.org57

ifomis.org58 The Gene Ontology a ‘controlled vocabulary’ designed to standardize annotation of genes and gene products used by over 20 genome database and many other groups in academia and industry and methodology much imitated

ifomis.org59 The Methodology of Annotations Scientific curators use experimental observations reported in the biomedical literature to link gene products with GO terms in annotations. The gene annotations taken together yield a slowly growing computer-interpretable map of biological reality, The process of annotating literature also leads to improvements and extensions of the ontology, which institutes a virtuous cycle of improvement in the quality and reach of future annotations and of the ontology itself. The Gene Ontology as Cartoon

ifomis.org60 cellular components molecular functions biological processes 1372 component terms 7271 function terms 8069 process terms

ifomis.org61 The Cellular Component Ontology (counterpart of anatomy) membrane nucleus

ifomis.org62 The Molecular Function Ontology protein stabilization The Molecular Function ontology is (roughly) an ontology of actions on the molecular level of granularity

ifomis.org63 Biological Process Ontology death An ontology of occurrents on the level of granularity of cells, organs and whole organisms

ifomis.org64 GO here an example a.of the sorts of problems confronting life science data integration b.of the degree to which formal methods are relevant to the solution of these problems

ifomis.org65 Each of GO’s ontologies is organized in a graph-theoretical data structure involving two sorts of links or edges: is-a (= is a subtype of ) (copulation is-a biological process) part-of (cell wall part-of cell)

ifomis.org66 Linnaeus

ifomis.org67

ifomis.org68 Entities

ifomis.org69 Entities universals (kinds, types, taxa, …) particulars (individuals, tokens, instances …) Axiom: Nothing is both a universal and a particular

ifomis.org70 Entities universals* *natural, biological, kinds

ifomis.org71 Entities universals instances

ifomis.org72 universals are natural kinds Instances are natural exemplars of natural kinds (problem of non-standard instances) Not all individuals are instances of universals

ifomis.org73 Entities universals instances penumbra of borderline cases

ifomis.org74 Entities universals instances junk example of junk: beachball-desk

ifomis.org75 Primitive relations: inst and part inst(Jane, human being) part(Jane’s heart, Jane’s body) A universal is anything that is instantiated An instance as anything (any individual) that instantiates some universal

ifomis.org76 Entities human Jane inst

ifomis.org77 A is_a B genus(B) species(A) instances

ifomis.org78 is-a D3* e is a f =def universal(e)  universal(f)   x (inst(x, e)  inst(x, f)). genus(A)=def universal(A)   B (B is a A  B  A) species(A)=def universal(A)   B (A is a B  B  A)

ifomis.org79 solve problem of false positives insist that A is_a B holds always as a matter of scientific law

ifomis.org80 nearest species nearestspecies(A, B)= def A is_a B &  C ((A is_a C & C is_a B)  (C = A or C = B) B A

ifomis.org81 Definitions highest genus lowest species instances

ifomis.org82 Lowest Species and Highest Genus lowestspecies(A)= def species(A) & not-genus(A) highestgenus(A)= def genus(A) & not-species(A) Theorem: universal(A)  (genus(A) or lowestspecies(A))

ifomis.org83 Axioms Every universal has at least one instance Distinct lowest species never share instances SINGLE INHERITANCE: Every species is the nearest species to exactly one genus

ifomis.org84 Axioms governing inst genus(A) & inst(x, A)   B nearestspecies(B, A) & inst(x, B) EVERY GENUS HAS AN INSTANTIATED SPECIES nearestspecies(A, B)  A’s instances are properly included in B’s instances EACH SPECIES HAS A SMALLER CLASS OF INSTANCES THAN ITS GENUS

ifomis.org85 Axioms nearestspecies(B, A)   C (nearestspecies(C, A) & B  C) EVERY GENUS HAS AT LEAST TWO CHILDREN nearestspecies(B, A) & nearestspecies(C, A) & B  C)  not-  x (inst(x, B) & inst(x, C)) SPECIES OF A COMMON GENUS NEVER SHARE INSTANCES

ifomis.org86 Theorems (genus(A) & inst(x, A))   B (lowestspecies(B) & B is_a A & inst(x, B)) EVERY INSTANCE IS ALSO AN INSTANCE OF SOME LOWEST SPECIES (genus(A) & lowestspecies(B) &  x(inst(x, A) & inst(x, B))  B is_a A) IF AN INSTANCE OF A LOWEST SPECIES IS AN INSTANCE OF A GENUS THEN THE LOWEST SPECIES IS A CHILD OF THE GENUS

ifomis.org87 Theorems universal(A) & universal(B)  (A = B or A is_a B or B is_a A or not-  x(inst(x, A) & inst(x, B))) DISTINCT UNIVERSALS EITHER STAND IN A PARENT-CHILD RELATIONSHIP OR THEY HAVE NO INSTANCES IN COMMON

ifomis.org88 Theorems A is_a B & A is_a C  (B = C or B is_a C or C is_a B) UNIVERSALS WHICH SHARE A CHILD IN COMMON ARE EITHER IDENTICAL OR ONE IS SUBORDINATED TO THE OTHER

ifomis.org89 Theorems (genus(A) & genus(B) &  x(inst(x, A) & inst(x, B)))   C(C is_a A & C is_a B) IF TWO GENERA HAVE A COMMON INSTANCE THEN THEY HAVE A COMMON CHILD

ifomis.org90 Expanding the theory Sexually reproducing organisms Organisms in general To take account of development (child, adult; larva, butterfly) Biological processes Biological functions -- at different levels of granularity

ifomis.org91 How to understand species (aka types, universals, kinds) Species are something like invariants in reality which can be studied by science Species have instances: this mouse, this cell, this cell membrane...

ifomis.org92 Universal, Classes, Sets A class is the extension of universal

ifomis.org93 Class =def a maximal collection of particulars determined by a general term (‘cell’, ‘mouse’, ‘Saarländer’) the class A = the collection of all particulars x for which ‘x is A’ is true

ifomis.org94 Universals and Classes vs. Sums The former are marked by granularity: they divide up the domain into whole units, whose interior parts are traced over. The universal human being is instantiated only by human beings as single, whole units. A mereological sum is not granular in this sense (molecules are parts of the mereological sum of human beings)

ifomis.org95 A bad solution Identify both universals and classes with sets in the mathematical sense Problem of false positives adult  child lion in Leipzig  lion animal owned by the Emporer  mammal mammal weighing less than 200 Kg  animal

ifomis.org96 Sets in the mathematical sense are marked by granularity Granularity = each class or set is laid across reality like a grid consisting (1) of a number of slots or pigeonholes each (2) occupied by some member. Each set is (1) associated with a specific number of slots, each of which (2) must be occupied by some specific member. A class survives the turnover in its instances: both (1) the number of slots and (2) the individuals occupying these slots may vary with time

ifomis.org97 But sets are timeless A set is an abstract structure, existing outside time and space. The set of human beings existing at t is (timelessly) a different entity from the set of human beings existing at t because of births and deaths. Biological classes exist in time Darwin: because the universals of which they are extensions exist in time