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Single Idea 22298
[filed under theme 6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
]
Full Idea
Fictionalists struggle to explain why arithmetic is applicable to the real world in a way that other stories are not.
Gist of Idea
Why is fictional arithmetic applicable to the real world?
Source
Michael Potter (The Rise of Analytic Philosophy 1879-1930 [2020], 21 'Math')
Book Ref
Potter,Michael: 'The Rise of Anaytic Philosophy 1879-1930' [Routledge 2020], p.143
A Reaction
We know why some novels are realistic and others just the opposite. If a novel aimed to 'model' the real world it would be even closer to it. Fictionalists must explain why some fictions are useful.
The
31 ideas
from Michael Potter
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22273
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Traditionally there are twelve categories of judgement, in groups of three
[Potter]
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22279
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Frege's sign |--- meant judgements, but the modern |- turnstile means inference, with intecedents
[Potter]
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22281
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A material conditional cannot capture counterfactual reasoning
[Potter]
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22283
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Compositionality should rely on the parsing tree, which may contain more than sentence components
[Potter]
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22282
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'Direct compositonality' says the components wholly explain a sentence meaning
[Potter]
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22284
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'Greater than', which is the ancestral of 'successor', strictly orders the natural numbers
[Potter]
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22285
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Impredicative definitions are circular, but fine for picking out, rather than creating something
[Potter]
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22291
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Deductivism can't explain how the world supports unconditional conclusions
[Potter]
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22287
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If 'concrete' is the negative of 'abstract', that means desires and hallucinations are concrete
[Potter]
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22290
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The phrase 'the concept "horse"' can't refer to a concept, because it is saturated
[Potter]
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22295
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Modern logical truths are true under all interpretations of the non-logical words
[Potter]
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22296
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Compositionality is more welcome in logic than in linguistics (which is more contextual)
[Potter]
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22298
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Why is fictional arithmetic applicable to the real world?
[Potter]
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22301
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The Identity Theory says a proposition is true if it coincides with what makes it true
[Potter]
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22310
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The formalist defence against Gödel is to reject his metalinguistic concept of truth
[Potter]
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22324
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It has been unfortunate that externalism about truth is equated with correspondence
[Potter]
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22327
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Knowledge from a drunken schoolteacher is from a reliable and unreliable process
[Potter]
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10702
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Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning
[Potter]
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10703
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Supposing axioms (rather than accepting them) give truths, but they are conditional
[Potter]
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10704
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We can formalize second-order formation rules, but not inference rules
[Potter]
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10707
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Mereology elides the distinction between the cards in a pack and the suits
[Potter]
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13041
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Collections have fixed members, but fusions can be carved in innumerable ways
[Potter]
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10708
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Nowadays we derive our conception of collections from the dependence between them
[Potter]
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10709
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Priority is a modality, arising from collections and members
[Potter]
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13042
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If dependence is well-founded, with no infinite backward chains, this implies substances
[Potter]
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10712
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If set theory didn't found mathematics, it is still needed to count infinite sets
[Potter]
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10713
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Usually the only reason given for accepting the empty set is convenience
[Potter]
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13043
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A relation is a set consisting entirely of ordered pairs
[Potter]
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13044
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Infinity: There is at least one limit level
[Potter]
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17882
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It is remarkable that all natural number arithmetic derives from just the Peano Axioms
[Potter]
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13546
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The 'limitation of size' principles say whether properties collectivise depends on the number of objects
[Potter]
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