1 Against Ontologically Evil Misuse of Predicate Logic Barry Smith

2 Fantology The syntax of first-order predicate logic is a mirror of reality ‘Fa’ (or ‘Rab’ etc.) 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

3 For the fantologist “F(a)”, “R(a,b)” … is the language for ontology This language reflects the structure of reality Reality is made up of atoms plus abstract (1- and n-place) ‘properties’ or ‘attributes’

4 David Armstrong’s spreadsheet ontology

5 FGHIJKLMNOPQRSTUV a b c d e f g h i j k

6 FGHIJKLMNOPQRSTUV axxxxx b c d e f g h i j k

7 FGHIJKLMNOPQRSTUV axxxxx bxxxxx c d e f g h i j k

8 FGHIJKLMNOPQRSTUV axxxxx bxxxxx cxxxxx d e f g h i j k

9 FGHIJKLMNOPQRSTUV axxxxx bxxxxx cxxxxx dxx e f g h i j k and so on …

10 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 (Neokantianism)

11 F(a) All generality belongs to the predicate ‘a’ is a mere name Contrast this with the way scientists use names: Yeast DNA-Binding Requirement Ribosomal Protein Gene Promoter Sequence

12 ‘a’ leaves no room for ontological complexity Hence: reality is made of atoms Fantology cannot do justice to the existence of different levels of granularity on the side of reality Thus conducive to reductionism in philosophy

13 F(a) ‘a’ is a bare name  various doctrines of bare particulars including noumenal views as e.g. in the Tractatus doctrine of simples (more Kantianism)

14 F(a) To understand properties is to understand predication (effectively in terms of functional application à la Frege)

15 Aristotle distinguished 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

16 For Fantology no predication in the category of substance e.g. [Quine] because there are no substances or because the two types of predication are confused or because the bareness of ‘a’ yields an aversion to idea of substances as spatially extended and spatially located

17 Aristotle’s Ontological Square SubstantialAccidental 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 Universal Particular

18 Aristotle’s Ontological Square SubstantialAccidental 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 Universal Particular

19 Aristotle’s Ontological Square SubstantialAccidental 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 Universal Particular

20 Aristotle’s Ontological Square SubstantialAccidental 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 Universal Particular

21 Aristotle’s Ontological Square SubstantialAccidental 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 Universal Particular

22 Standard Predicate Logic – F(a), R(a,b)... SubstantialAccidental Attributes F, G, R Individuals a, b, c this, that Universal Particular

23 Bicategorial Nominalism SubstantialAccidental First substance this man this cat this ox First accident this headache this sun-tan this dread Universal Particular

24 Process Metaphysics, Trope Bundle Theories SubstantialAccidental Events Processes “Everything is flux” Universal Particular

25 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 or Quine’s four- dimensionalism)

26 F(a), R(a,b) … adicity all structures in reality have an adicity -- tendency to deal inadequately not only with time and change but with continuous phenomena in general

27 F(a), R(a,b) … adicity John has a headache What is the adicity of John’s headache (a relation [?] between your consciousness and various processes taking place in an around your brain) ?

28 The extensionalist limitations of fantology lead one into the temptations of possible world metaphysics and other fantasies

29 Fantology leads you to talk nonsense about “family resemblances”

30 Fantology leads to a lazy use of the word ‘property’, just about any old open sentence will serve to designate a property -calculus = property ontology as theft rather than honest toil

31 Fantology leads to a lazy use of the word ‘property’, (in this way, too, fantology is conducive to nominalism)

32 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 F  G stands for a property and so on

33 Strong Booleanism There is a complete lattice of properties: self-identity FvG not-F F G not-G F&G non-self-identity

34 Set theory is Booleanism unremediated Booleanism without any remediating features whatsoever

35 Booleanism responsible, among other things, for Russell’s paradox Russell’s solution Keep Boole avoid the catastrophe by introducing the machinery of ‘types’

36 Booleanism responsible for Russell’s paradox and therefore also responsible for the phobia of quantification over properties and thus in this respect, too, conducive to nominalism

37 Lewis and Armstrong free from Booleanism with their sparse theory of properties

38 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 history analogous to two 5 stone weakling climbing up to breathe the free air at the top of Mount Everest with 1000 ton weights attached to their feet

39 leading them back, on this point, to where Aristotelians were from the very beginning

40 END

41 FOLWUT First-order logic with universal terms

42 Compare the syntax of set theory  (x,y) one (formal) predicate

43 FOLWUT =(x,y) Inst(x,u) Does(x,e) Part(x,y) Inst(x,y) Dep(x,y) Isa(x,y) Exemp(x,d) Loc(x,y)

44 Inst(x,u) no temptation to Booleanism no temptation to Nominalism