Against Predicate Logic

1. Against Predicate Logic Barry Smith http://ontologist.com

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

9. 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 Universal Particular

18. Aristotle’s Ontological Square Universal Particular

19. Aristotle’s Ontological Square Universal Particular

20. Aristotle’s Ontological Square Universal Particular

21. Aristotle’s Ontological Square Universal Particular

22. Standard Predicate Logic – F(a), R(a,b) ... Universal Particular

23. Bicategorial Nominalism Universal Particular

24. Process Metaphysics, Trope Bundle Theories 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