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Single Idea 8972
[filed under theme 4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
]
Full Idea
Nothing in the world of nominalistically acceptable things could ground or explain the non-identity of the set {A,{A,B}} with the set {B,{A,B}}.
Gist of Idea
What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}?
Source
Peter van Inwagen (Existence,Ontological Commitment and Fictions [2003], p.154)
Book Ref
'The Oxford Handbook of Metaphysics', ed/tr. Loux,M /Zimmerman,D [OUP 2005], p.154
A Reaction
[He cites Goodman for this thought] Van Inwagen is offering this to show that the existence of sets is abstract, whereas Goodman was denying the existence of sets altogether. I'm with Goodman. Nice example.
The
46 ideas
from Peter van Inwagen
6981
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Determinism clashes with free will, as the past determines action, and is beyond our control
[Inwagen, by Jackson]
|
8972
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What in the real world could ground the distinction between the sets {A,{A,B}} and {B,{A,B}}?
[Inwagen]
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17531
|
I assume matter is particulate, made up of 'simples'
[Inwagen]
|
17556
|
Material objects are in space and time, move, have a surface and mass, and are made of some stuff
[Inwagen]
|
17559
|
Is one atom a piece of gold, or is a sizable group of atoms required?
[Inwagen]
|
17558
|
Variables are just like pronouns; syntactic explanations get muddled over dummy letters
[Inwagen]
|
17557
|
Special Composition Question: when is a thing part of something?
[Inwagen]
|
17560
|
If contact causes composition, do two colliding balls briefly make one object?
[Inwagen]
|
17561
|
If bricks compose a house, that is at least one thing, but it might be many things
[Inwagen]
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17562
|
The statue and lump seem to share parts, but the statue is not part of the lump
[Inwagen]
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17564
|
The essence of a star includes the released binding energy which keeps it from collapse
[Inwagen]
|
17563
|
The strong force pulls, but also pushes apart if nucleons get too close together
[Inwagen]
|
17565
|
Nihilism says composition between single things is impossible
[Inwagen]
|
17570
|
The chemical reactions in a human life involve about sixteen elements
[Inwagen]
|
17566
|
I think parthood involves causation, and not just a reasonably stable spatial relationship
[Inwagen]
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17567
|
A flame is like a life, but not nearly so well individuated
[Inwagen]
|
17568
|
A tumour may spread a sort of life, but it is not a life, or an organism
[Inwagen]
|
17569
|
Unlike waves, lives are 'jealous'; it is almost impossible for them to overlap
[Inwagen]
|
17571
|
Every physical thing is either a living organism or a simple
[Inwagen]
|
14228
|
If there are no tables, but tables are things arranged tablewise, the denial of tables is a contradiction
[Liggins on Inwagen]
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14227
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We could refer to tables as 'xs that are arranged tablewise'
[Inwagen]
|
14468
|
Actions by artefacts and natural bodies are disguised cooperations, so we don't need them
[Inwagen]
|
17572
|
Actuality proves possibility, but that doesn't explain how it is possible
[Inwagen]
|
17573
|
There is no reason to think that mere existence is a valuable thing
[Inwagen]
|
17576
|
If God were to 'reassemble' my atoms of ten years ago, the result would certainly not be me
[Inwagen]
|
17575
|
The persistence of artifacts always covertly involves intelligent beings
[Inwagen]
|
17574
|
If you knead clay you make an infinite series of objects, but they are rearrangements, not creations
[Inwagen]
|
17578
|
I reject talk of 'stuff', and treat it in terms of particles
[Inwagen]
|
17577
|
When an electron 'leaps' to another orbit, is the new one the same electron?
[Inwagen]
|
17579
|
Counterparts reduce counterfactual identity to problems about similarity relations
[Inwagen]
|
17580
|
One's mental and other life is centred on the brain, unlike any other part of the body
[Inwagen]
|
17581
|
Being part of an organism's life is a matter of degree, and vague
[Inwagen]
|
17582
|
Singular terms can be vague, because they can contain predicates, which can be vague
[Inwagen]
|
17587
|
The 'Law' of Excluded Middle needs all propositions to be definitely true or definitely false
[Inwagen]
|
17583
|
There are no heaps
[Inwagen]
|
17585
|
Life is vague at both ends, but could it be totally vague?
[Inwagen]
|
17589
|
If you reject transitivity of vague identity, there is no Ship of Theseus problem
[Inwagen]
|
17588
|
We should talk of the transitivity of 'identity', and of 'definite identity'
[Inwagen]
|
17584
|
Some events are only borderline cases of lives
[Inwagen]
|
17586
|
At the lower level, life trails off into mere molecular interaction
[Inwagen]
|
17590
|
A merely possible object clearly isn't there, so that is a defective notion
[Inwagen]
|
17591
|
Merely possible objects must be consistent properties, or haecceities
[Inwagen]
|
14230
|
We can deny whole objects but accept parts, by referring to them as plurals within things
[Inwagen, by Liggins]
|
8264
|
Maybe table-shaped particles exist, but not tables
[Inwagen, by Lowe]
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10662
|
Mereology is 'nihilistic' (just atoms) or 'universal' (no restrictions on what is 'whole')
[Inwagen, by Varzi]
|
7101
|
Virtue theory needs an external standard to judge behaviour and character
[Inwagen, by Statman]
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