Against%20Ontologically%20Evil%20Misuse%20of%20Predicate%20Logic

1
Against Ontologically Evil Misuse of 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 Armstrongs

• spreadsheet ontology

5
F G H I J K L M N O P Q R S T U V
a
b
c
d
e
f
g
h
i
j
k
6
F G H I J K L M N O P Q R S T U V
a x x x x x
b
c
d
e
f
g
h
i
j
k
7
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
d
e
f
g
h
i
j
k
8
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
e
f
g
h
i
j
k
9
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
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
Aristotles 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
Universal
Particular
18
Aristotles 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
Universal
Particular
19
Aristotles 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
Universal
Particular
20
Aristotles 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
Universal
Particular
21
Aristotles 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
Universal
Particular
22
Standard Predicate Logic F(a), R(a,b) ...
Substantial Accidental
Attributes F, G, R
Individuals a, b, c this, that
Universal
Particular
23
Bicategorial Nominalism
Substantial Accidental

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
Substantial Accidental

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 Armstrongs or Quines 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 Johns 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
• FG 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
• FG
• non-self-identity

34
Set theory is Booleanism unremediated

• Booleanism without any remediating features
  whatsoever

35
Booleanism

• responsible, among other things, for Russells
  paradox
• Russells solution
• Keep Boole
• avoid the catastrophe by introducing the
  machinery of types

36
Booleanism

• responsible for Russells 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