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Single Idea 8907
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
We can abstract the direction of a line by taking the direction as the equivalence class of that line and all lines parallel to it. There is no subtraction of detail, but a multiplication of it; by swamping it, the specifics of the original line get lost.
Gist of Idea
The abstract direction of a line is the equivalence class of it and all lines parallel to it
Source
David Lewis (On the Plurality of Worlds [1986], 1.7)
Book Ref
Lewis,David: 'On the Plurality of Worlds' [Blackwell 2001], p.85
A Reaction
You can ask how wide a line is, but not how wide a direction is, so a detail IS being subtracted. I don't see how you can define the concept of a banana by just saying it is 'every object which is equivalent to a banana'. 'Parallel' is an abstraction.
The
94 ideas
from 'On the Plurality of Worlds'
10470
|
There are only two kinds: sets, and possibilia (actual and possible particulars)
[Lewis, by Oliver]
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12255
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For Lewis there is no real possibility, since all possibilities are actual
[Oderberg on Lewis]
|
9219
|
Lewis posits possible worlds just as Quine says that physics needs numbers and sets
[Lewis, by Sider]
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15022
|
If possible worlds really exist, then they are part of actuality
[Sider on Lewis]
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16441
|
Lewis rejects actualism because he identifies properties with sets
[Lewis, by Stalnaker]
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7690
|
If sets exist, then defining worlds as proposition sets implies an odd distinction between existing and actual
[Jacquette on Lewis]
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14404
|
The counterpart relation is sortal-relative, so objects need not be a certain way
[Lewis, by Merricks]
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5440
|
A counterpart in a possible world is sufficiently similar, and more similar than anything else
[Lewis, by Mautner]
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5441
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Why should statements about what my 'counterpart' could have done interest me?
[Mautner on Lewis]
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15399
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The property of being F is identical with the set of objects, in all possible worlds, which are F
[Lewis, by Cameron]
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9650
|
Supervenience concerns whether things could differ, so it is a modal notion
[Lewis]
|
16132
|
On mountains or in worlds, reporting contradictions is contradictory, so no such truths can be reported
[Lewis]
|
16133
|
Possible worlds can contain contradictions if such worlds are seen as fictions
[Lewis]
|
9651
|
Verisimilitude might be explained as being close to the possible world where the truth is exact
[Lewis]
|
9652
|
To just expect unexamined emeralds to be grue would be totally unreasonable
[Lewis]
|
9658
|
An explanation tells us how an event was caused
[Lewis]
|
15736
|
A proposition is the property of being a possible world where it holds true
[Lewis]
|
9654
|
A proposition is a set of entire possible worlds which instantiate a particular property
[Lewis]
|
15738
|
Propositions can't have syntactic structure if they are just sets of worlds
[Lewis]
|
14996
|
Natural properties give similarity, joint carving, intrinsicness, specificity, homogeneity...
[Lewis]
|
15743
|
Defining natural properties by means of laws of nature is potentially circular
[Lewis]
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15744
|
We can't define natural properties by resemblance, if they are used to explain resemblance
[Lewis]
|
15751
|
Surely 'slept in by Washington' is a property of some bed?
[Lewis]
|
15735
|
Properties don't have degree; they are determinate, and things have varying relations to them
[Lewis]
|
9656
|
The 'abundant' properties are just any bizarre property you fancy
[Lewis]
|
15741
|
All of the natural properties are included among the intrinsic properties
[Lewis]
|
15737
|
To be a 'property' is to suit a theoretical role
[Lewis]
|
15742
|
A disjunctive property can be unnatural, but intrinsic if its disjuncts are intrinsic
[Lewis]
|
15732
|
Properties don't seem to be sets, because different properties can have the same set
[Lewis]
|
15733
|
Accidentally coextensive properties come apart when we include their possible instances
[Lewis]
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15734
|
If a property is relative, such as being a father or son, then set membership seems relative too
[Lewis]
|
9655
|
Trilateral and triangular seem to be coextensive sets in all possible worlds
[Lewis]
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15739
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There is the property of belonging to a set, so abundant properties are as numerous as the sets
[Lewis]
|
9653
|
It would be easiest to take a property as the set of its instances
[Lewis]
|
10723
|
A property is the set of its actual and possible instances
[Lewis, by Oliver]
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9657
|
You must accept primitive similarity to like tropes, but tropes give a good account of it
[Lewis]
|
15748
|
Trope theory needs a primitive notion for what unites some tropes
[Lewis]
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15749
|
Trope theory (unlike universals) needs a primitive notion of being duplicates
[Lewis]
|
15750
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Tropes need a similarity primitive, so they cannot be used to explain similarity
[Lewis]
|
15745
|
Universals recur, are multiply located, wholly present, make things overlap, and are held in common
[Lewis]
|
15746
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If particles were just made of universals, similar particles would be the same particle
[Lewis]
|
15747
|
Universals aren't parts of things, because that relationship is transitive, and universals need not be
[Lewis]
|
15731
|
Quantification sometimes commits to 'sets', but sometimes just to pluralities (or 'classes')
[Lewis]
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15740
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I don't take 'natural' properties to be fixed by the nature of one possible world
[Lewis]
|
15752
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We might try defining the natural properties by a short list of them
[Lewis]
|
10469
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A world is a maximal mereological sum of spatiotemporally interrelated things
[Lewis]
|
9659
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Causation is when at the closest world without the cause, there is no effect either
[Lewis]
|
8901
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Abstraction is usually explained either by example, or conflation, or abstraction, or negatively
[Lewis]
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8904
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The Way of Abstraction says an incomplete description of a concrete entity is the complete abstraction
[Lewis]
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8938
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The Way of Example compares donkeys and numbers, but what is the difference, and what are numbers?
[Lewis]
|
8902
|
If abstractions are non-spatial, then both sets and universals seem to have locations
[Lewis]
|
8903
|
Abstracta can be causal: sets can be causes or effects; there can be universal effects; events may be sets
[Lewis]
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8906
|
If we can abstract the extrinsic relations and features of objects, abstraction isn't universals or tropes
[Lewis]
|
8905
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If universals or tropes are parts of things, then abstraction picks out those parts
[Lewis]
|
8907
|
The abstract direction of a line is the equivalence class of it and all lines parallel to it
[Lewis]
|
8908
|
For most sets, the concept of equivalence is too artificial to explain abstraction
[Lewis]
|
8909
|
Abstractions may well be verbal fictions, in which we ignore some features of an object
[Lewis]
|
9660
|
The impossible can be imagined as long as it is a bit vague
[Lewis]
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16278
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A particular functional role is what gives content to a thought
[Lewis]
|
16279
|
General causal theories of knowledge are refuted by mathematics
[Lewis]
|
9661
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Induction is just reasonable methods of inferring the unobserved from the observed
[Lewis]
|
16280
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Often explanaton seeks fundamental laws, rather than causal histories
[Lewis]
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16274
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If the well-ordering of a pack of cards was by shuffling, the explanation would make it more surprising
[Lewis]
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16281
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Honesty requires philosophical theories we can commit to with our ordinary commonsense
[Lewis]
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11903
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Extreme haecceitists could say I might have been a poached egg, but it is too remote to consider
[Lewis, by Mackie,P]
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13793
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An essential property is one possessed by all counterparts
[Lewis, by Elder]
|
16282
|
Ersatzers say we have one world, and abstract representations of how it might have been
[Lewis]
|
16284
|
Ersatz worlds represent either through language, or by models, or magically
[Lewis]
|
16283
|
For me, all worlds are equal, with each being actual relative to itself
[Lewis]
|
16286
|
Linguistic possible worlds need a complete supply of unique names for each thing
[Lewis]
|
16287
|
Maximal consistency for a world seems a modal distinction, concerning what could be true together
[Lewis]
|
9662
|
Linguistic possible worlds have problems of inconsistencies, no indiscernibles, and vocabulary
[Lewis]
|
16288
|
Analysis reduces primitives and makes understanding explicit (without adding new knowledge)
[Lewis]
|
16289
|
We can't account for an abstraction as 'from' something if the something doesn't exist
[Lewis]
|
16290
|
I believe in properties, which are sets of possible individuals
[Lewis]
|
16291
|
In counterpart theory 'Humphrey' doesn't name one being, but a mereological sum of many beings
[Lewis]
|
15969
|
Two things can never be identical, so there is no problem
[Lewis]
|
15968
|
Identity is simple - absolutely everything is self-identical, and nothing is identical to another thing
[Lewis]
|
9663
|
A thing 'perdures' if it has separate temporal parts, and 'endures' if it is wholly present at different times
[Lewis]
|
9664
|
Endurance is the wrong account, because things change intrinsic properties like shape
[Lewis]
|
9665
|
There are three responses to the problem that intrinsic shapes do not endure
[Lewis]
|
9666
|
It is quite implausible that the future is unreal, as that would terminate everything
[Lewis]
|
9667
|
Mereological composition is unrestricted: any class of things has a mereological sum
[Lewis]
|
9669
|
There are no free-floating possibilia; they have mates in a world, giving them extrinsic properties
[Lewis]
|
15129
|
Haecceitism implies de re differences but qualitative identity
[Lewis]
|
9670
|
Extreme haecceitism says you might possibly be a poached egg
[Lewis]
|
9057
|
Vagueness is semantic indecision: we haven't settled quite what our words are meant to express
[Lewis]
|
9671
|
Whether or not France is hexagonal depends on your standards of precision
[Lewis]
|
19280
|
I can ask questions which create a context in which origin ceases to be essential
[Lewis]
|
14737
|
Properties cannot be relations to times, if there are temporary properties which are intrinsic
[Lewis, by Sider]
|
13268
|
There are no restrictions on composition, because they would be vague, and composition can't be vague
[Lewis, by Sider]
|
16262
|
Sparse properties rest either on universals, or on tropes, or on primitive naturalness
[Lewis, by Maudlin]
|
15398
|
Global intrinsic may make necessarily coextensive properties both intrinsic or both extrinsic
[Cameron on Lewis]
|
15397
|
If a global intrinsic never varies between possible duplicates, all necessary properties are intrinsic
[Cameron on Lewis]
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