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Single Idea 17434
[filed under theme 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / d. Counting via concepts
]
Full Idea
The reason we have a hard time counting the branches and the waves is because our concepts 'branches on the tree' and 'waves on the ocean' do not determine sufficiently precise boundaries: the concepts do not draw a clear invisible line around each thing.
Gist of Idea
We struggle to count branches and waves because our concepts lack clear boundaries
Source
Kathrin Koslicki (Isolation and Non-arbitrary Division [1997], 2.2)
Book Ref
-: 'Synthese' [-], p.413
A Reaction
This is the 'isolation' referred to in Frege.
Related Idea
Idea 17426
A concept creating a unit must isolate and unify what falls under it [Frege]
The
48 ideas
from Kathrin Koslicki
15110
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An essence and what merely follow from it are distinct
[Koslicki]
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15111
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In demonstration, the explanatory order must mirror the causal order of the phenomena
[Koslicki]
|
15112
|
If an object exists, then its essential properties are necessary
[Koslicki]
|
15115
|
In a demonstration the middle term explains, by being part of the definition
[Koslicki]
|
15118
|
A successful Aristotelian 'definition' is what sciences produces after an investigation
[Koslicki]
|
15116
|
Essences cause necessary features, and definitions describe those necessary features
[Koslicki]
|
15113
|
Individuals are perceived, but demonstration and definition require universals
[Koslicki]
|
15114
|
Discovering the Aristotelian essence of thunder will tell us why thunder occurs
[Koslicki]
|
15117
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Greek uses the same word for 'cause' and 'explanation'
[Koslicki]
|
24065
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Structured wholes are united by the teamwork needed for their capacities
[Koslicki]
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24066
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The form explains kind, structure, unity and activity
[Koslicki]
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24067
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Hylomorphic compounds need an individual form for transworld identity
[Koslicki]
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24069
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Much metaphysical debate concerns what is fundamental, rather than what exists
[Koslicki]
|
17439
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There is no deep reason why we count carrots but not asparagus
[Koslicki]
|
17434
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We struggle to count branches and waves because our concepts lack clear boundaries
[Koslicki]
|
17436
|
We talk of snow as what stays the same, when it is a heap or drift or expanse
[Koslicki]
|
17435
|
Objects do not naturally form countable units
[Koslicki]
|
17433
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We can still count squares, even if they overlap
[Koslicki]
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14497
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The clay is just a part of the statue (its matter); the rest consists of its form or structure
[Koslicki]
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14495
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I aim to put the notion of structure or form back into the concepts of part, whole and object
[Koslicki]
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14496
|
Structure or form are right at the centre of modern rigorous modes of enquiry
[Koslicki]
|
13266
|
Wholes in modern mereology are intended to replace sets, so they closely resemble them
[Koslicki]
|
14498
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For three-dimensionalist parthood must be a three-place relation, including times
[Koslicki]
|
14500
|
Wholes are entities distinct from their parts, and have different properties
[Koslicki]
|
14501
|
'Categorical' properties exist in the actual world, and 'hypothetical' properties in other worlds
[Koslicki]
|
13264
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If a whole is just a structure, a dinner party wouldn't need the guests to turn up
[Koslicki]
|
13258
|
The 'aggregative' objections says mereology gets existence and location of objects wrong
[Koslicki]
|
13281
|
Wholes are not just their parts; a whole is an entity distinct from the proper parts
[Koslicki]
|
13283
|
The parts may be the same type as the whole, like a building made of buildings
[Koslicki]
|
13280
|
Statue and clay differ in modal and temporal properties, and in constitution
[Koslicki]
|
13279
|
There are at least six versions of constitution being identity
[Koslicki]
|
13284
|
Should vernacular classifications ever be counted as natural kind terms?
[Koslicki]
|
13285
|
Natural kinds support inductive inferences, from previous samples to the next one
[Koslicki]
|
13287
|
Concepts for species are either intrinsic structure, or relations like breeding or ancestry
[Koslicki]
|
13286
|
There are apparently no scientific laws concerning biological species
[Koslicki]
|
14504
|
The Kripke/Putnam approach to natural kind terms seems to give them excessive stability
[Koslicki]
|
14505
|
Some questions concern mathematical entities, rather than whole structures
[Koslicki]
|
14506
|
'Roses are red; therefore, roses are colored' seems truth-preserving, but not valid in a system
[Koslicki]
|
13288
|
Consequence is truth-preserving, either despite substitutions, or in all interpretations
[Koslicki]
|
13289
|
Structures have positions, constituent types and number, and some invariable parts
[Koslicki]
|
17312
|
It is more explanatory if you show how a number is constructed from basic entities and relations
[Koslicki]
|
17311
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Real definitions don't just single out a thing; they must also explain its essence
[Koslicki]
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17309
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For Fine, essences are propositions true because of identity, so they are just real definitions
[Koslicki]
|
17313
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Modern views want essences just to individuate things across worlds and times
[Koslicki]
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17314
|
The relata of grounding are propositions or facts, but for dependence it is objects and their features
[Koslicki]
|
17315
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We need a less propositional view of essence, and so must distinguish it clearly from real definitions
[Koslicki]
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17316
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We can abstract to a dependent entity by blocking out features of its bearer
[Koslicki]
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17317
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A good explanation captures the real-world dependence among the phenomena
[Koslicki]
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