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Single Idea 13042
[filed under theme 9. Objects / B. Unity of Objects / 2. Substance / b. Need for substance
]
Full Idea
The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning.
Gist of Idea
If dependence is well-founded, with no infinite backward chains, this implies substances
Source
Michael Potter (Set Theory and Its Philosophy [2004], 03.3)
Book Ref
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.40
A Reaction
Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here.
Related Idea
Idea 13039
Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen]
The
31 ideas
from Michael Potter
22273
|
Traditionally there are twelve categories of judgement, in groups of three
[Potter]
|
22279
|
Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents
[Potter]
|
22281
|
A material conditional cannot capture counterfactual reasoning
[Potter]
|
22283
|
Compositionality should rely on the parsing tree, which may contain more than sentence components
[Potter]
|
22282
|
'Direct compositonality' says the components wholly explain a sentence meaning
[Potter]
|
22284
|
'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers
[Potter]
|
22285
|
Impredicative definitions are circular, but fine for picking out, rather than creating something
[Potter]
|
22291
|
Deductivism can't explain how the world supports unconditional conclusions
[Potter]
|
22287
|
If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete
[Potter]
|
22290
|
The phrase 'the concept "horse"' can't refer to a concept, because it is saturated
[Potter]
|
22295
|
Modern logical truths are true under all interpretations of the non-logical words
[Potter]
|
22296
|
Compositionality is more welcome in logic than in linguistics (which is more contextual)
[Potter]
|
22298
|
Why is fictional arithmetic applicable to the real world?
[Potter]
|
22301
|
The Identity Theory says a proposition is true if it coincides with what makes it true
[Potter]
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22310
|
The formalist defence against Gödel is to reject his metalinguistic concept of truth
[Potter]
|
22324
|
It has been unfortunate that externalism about truth is equated with correspondence
[Potter]
|
22327
|
Knowledge from a drunken schoolteacher is from a reliable and unreliable process
[Potter]
|
10702
|
Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning
[Potter]
|
10703
|
Supposing axioms (rather than accepting them) give truths, but they are conditional
[Potter]
|
10704
|
We can formalize second-order formation rules, but not inference rules
[Potter]
|
10707
|
Mereology elides the distinction between the cards in a pack and the suits
[Potter]
|
13041
|
Collections have fixed members, but fusions can be carved in innumerable ways
[Potter]
|
10708
|
Nowadays we derive our conception of collections from the dependence between them
[Potter]
|
10709
|
Priority is a modality, arising from collections and members
[Potter]
|
13042
|
If dependence is well-founded, with no infinite backward chains, this implies substances
[Potter]
|
10712
|
If set theory didn't found mathematics, it is still needed to count infinite sets
[Potter]
|
10713
|
Usually the only reason given for accepting the empty set is convenience
[Potter]
|
13043
|
A relation is a set consisting entirely of ordered pairs
[Potter]
|
13044
|
Infinity: There is at least one limit level
[Potter]
|
17882
|
It is remarkable that all natural number arithmetic derives from just the Peano Axioms
[Potter]
|
13546
|
The 'limitation of size' principles say whether properties collectivise depends on the number of objects
[Potter]
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