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Single Idea 17719
[filed under theme 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
]
Full Idea
The indispensability of arithmetical concepts is evidence that they do in fact accurately represent features of the independent world.
Gist of Idea
Arithmetic concepts are indispensable because they accurately map the world
Source
Carrie Jenkins (Grounding Concepts [2008], Intro)
Book Ref
Jenkins,Carrie: 'Grounding Concepts' [OUP 2008], p.9
A Reaction
This seems to me to be by far the best account of the matter. So why is the world so arithmetical? Dunno, mate; ask someone else.
The
17 ideas
from 'Grounding Concepts'
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17719
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Arithmetic concepts are indispensable because they accurately map the world
[Jenkins]
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17718
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Grounded concepts are trustworthy maps of the world
[Jenkins]
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17717
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Senses produce concepts that map the world, and arithmetic is known through these concepts
[Jenkins]
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17720
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There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence
[Jenkins, by PG]
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17723
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Knowledge is true belief which can be explained just by citing the proposition believed
[Jenkins]
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17725
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'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition...
[Jenkins]
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17724
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It is not easy to show that Hume's Principle is analytic or definitive in the required sense
[Jenkins]
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17727
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We can learn about the world by studying the grounding of our concepts
[Jenkins]
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17726
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Examining accurate, justified or grounded concepts brings understanding of the world
[Jenkins]
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17728
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The concepts we have to use for categorising are ones which map the real world well
[Jenkins]
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17729
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Examining concepts can recover information obtained through the senses
[Jenkins]
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17730
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Combining the concepts of negation and finiteness gives the concept of infinity
[Jenkins]
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17731
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Verificationism is better if it says meaningfulness needs concepts grounded in the senses
[Jenkins]
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17732
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Success semantics explains representation in terms of success in action
[Jenkins]
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17734
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It is not enough that intuition be reliable - we need to know why it is reliable
[Jenkins]
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17739
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The physical effect of world on brain explains the concepts we possess
[Jenkins]
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17740
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Instead of correspondence of proposition to fact, look at correspondence of its parts
[Jenkins]
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