Against Ontologically Evil Misuse of Predicate Logic

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Against Ontologically Evil Misuse of Predicate Logic

Barry Smithhttp://ontologist.com

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FantologyThe 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

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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’

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David Armstrong’s

spreadsheet ontology

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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

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a x x x x x

b

c

d

e

f

g

h

i

j

k

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a x x x x x

b x x x x x

c

d

e

f

g

h

i

j

k

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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

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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 …

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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)

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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

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‘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

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F(a)

‘a’ is a bare namevarious doctrines of bare particulars

including noumenal views as e.g. in the

Tractatus doctrine of simples

(more Kantianism)

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F(a)

To understand properties is to understand predication

(effectively in terms of functional application à la Frege)

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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

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For Fantologyno predication in the category of

substancee.g. [Quine] because there are no

substancesor because the two types of predication

are confusedor because the bareness of ‘a’ yields an

aversion to idea of substances as spatially extended and spatially located

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Aristotle’s 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

Uni

vers

alP

artic

ular

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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

Uni

vers

alP

artic

ular

19



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

Uni

vers

alP

artic

ular

20



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

Uni

vers

alP

artic

ular

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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

Uni

vers

alP

artic

ular

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


Attributes

F, G, R

Individuals

a, b, c

this, that

Uni

vers

alP

artic

ular

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Bicategorial NominalismSubstantial Accidental

First substance

this man

this cat

this ox

First accident

this headache

this sun-tan

this dread

Uni

vers

alP

artic

ular

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Process Metaphysics, Trope Bundle Theories


Events

Processes

“Everything is flux”

Uni

vers

alP

artic

ular

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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)

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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

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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) ?

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The extensionalist limitations of fantology

lead one into the temptations of possible world metaphysics

and other fantasies

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Fantology leads you to talk nonsense about “family

resemblances”

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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

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Fantology

leads to a lazy use of the word ‘property’,

(in this way, too, fantology is conducive to nominalism)

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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

FG stands for a property

and so on

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Strong Booleanism

There is a complete lattice of properties:

self-identity

FvG

not-F F G not-G

F&G

non-self-identity

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Set theory is Booleanism unremediated

Booleanism without any remediating features whatsoever

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Booleanism

responsible, among other things, for Russell’s paradox

Russell’s solution

Keep Boole

avoid the catastrophe by introducing the machinery of ‘types’

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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

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Lewis and Armstrong

free from Booleanism

with their sparse theory of properties

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That Lewis and Armstrongarrived at their sparse view of properties

against the solid wall of fantological Booleanist orthodoxy

is a miracle of modern intellectual historyanalogous 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

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leading them back, on this point,

to where Aristotelians were from the very beginning

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END

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FOLWUT

First-order logic with universal terms

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Compare the syntax of set theory

(x,y)

one (formal) predicate

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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)

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Inst(x,u)

no temptation to Booleanism

no temptation to Nominalism

Documents

Against Ontologically Evil Misuse of Predicate Logic