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Single Idea 18883
[filed under theme 18. Thought / E. Abstraction / 7. Abstracta by Equivalence
]
Full Idea
Whenever we have an equivalence relation among things - such as similarity in a certain respect - we can abstract under the equivalence and consider the abstractum.
Gist of Idea
Any equivalence relation among similar things allows the creation of an abstractum
Source
Peter Simons (Modes of Extension: comment on Fine [2008], p.19)
Book Ref
'Being: Developments in Contemporary Metaphysics', ed/tr. Le Poidevin,R [CUP 2008], p.19
A Reaction
This strikes me as dressing up old-fashioned psychological abstractionism in the respectable clothing of Fregean equivalences (such as 'directions'). We can actually do what Simons wants without the precision of partitioned equivalence classes.
Related Idea
Idea 18884
Abstraction is usually seen as producing universals and numbers, but it can do more [Simons]
The
76 ideas
from Peter Simons
8973
|
Einstein's relativity brought events into ontology, as the terms of a simultaneity relationships
[Simons]
|
8979
|
Slow and continuous events (like balding or tree-growth) are called 'processes', not 'events'
[Simons]
|
8981
|
Maybe processes behave like stuff-nouns, and events like count-nouns
[Simons]
|
18883
|
Any equivalence relation among similar things allows the creation of an abstractum
[Simons]
|
18884
|
Abstraction is usually seen as producing universals and numbers, but it can do more
[Simons]
|
18431
|
Internal relations combine some tropes into a nucleus, which bears the non-essential tropes
[Simons, by Edwards]
|
12820
|
Without extensional mereology two objects can occupy the same position
[Simons]
|
12814
|
Classical mereology says there are 'sums', for whose existence there is no other evidence
[Simons]
|
12817
|
'Mereological extensionality' says objects with the same parts are identical
[Simons]
|
12816
|
Classical mereology doesn't handle temporal or modal notions very well
[Simons]
|
12813
|
Two standard formalisations of part-whole theory are the Calculus of Individuals, and Mereology
[Simons]
|
12815
|
Classical mereology doesn't apply well to the objects around us
[Simons]
|
12819
|
A 'part' has different meanings for individuals, classes, and masses
[Simons]
|
12822
|
Proper or improper part: x < y, 'x is (a) part of y'
[Simons]
|
12823
|
Overlap: two parts overlap iff they have a part in common, expressed as 'x o y'
[Simons]
|
12824
|
Disjoint: two individuals are disjoint iff they do not overlap, written 'x | y'
[Simons]
|
12825
|
Product: the product of two individuals is the sum of all of their overlaps, written 'x · y'
[Simons]
|
12826
|
Sum: the sum of individuals is what is overlapped if either of them are, written 'x + y'
[Simons]
|
12827
|
Difference: the difference of individuals is the remainder of an overlap, written 'x - y'
[Simons]
|
12828
|
General sum: the sum of objects satisfying some predicate, written σx(Fx)
[Simons]
|
12829
|
General product: the nucleus of all objects satisfying a predicate, written πx(Fx)
[Simons]
|
12830
|
Universe: the mereological sum of all objects whatever, written 'U'
[Simons]
|
12821
|
The part-relation is transitive and asymmetric (and thus irreflexive)
[Simons]
|
12832
|
Complement: the rest of the Universe apart from some individual, written x-bar
[Simons]
|
12831
|
Atom: an individual with no proper parts, written 'At x'
[Simons]
|
12833
|
If there are c atoms, this gives 2^c - 1 individuals, so there can't be just 2 or 12 individuals
[Simons]
|
12834
|
Criticisms of mereology: parts? transitivity? sums? identity? four-dimensional?
[Simons]
|
12835
|
Does Tibbles remain the same cat when it loses its tail?
[Simons]
|
12838
|
Four-dimensional ontology has no change, since that needs an object, and time to pass
[Simons]
|
12836
|
Fans of process ontology cheat, since river-stages refer to 'rivers'
[Simons]
|
12839
|
Relativity has an ontology of things and events, not on space-time diagrams
[Simons]
|
12837
|
Four dimensional-objects are stranger than most people think
[Simons]
|
12842
|
There are real relational changes, as well as bogus 'Cambridge changes'
[Simons]
|
12840
|
I do not think there is a general identity condition for events
[Simons]
|
12841
|
I don't believe in processes
[Simons]
|
12844
|
Dissective: stuff is dissective if parts of the stuff are always the stuff
[Simons]
|
12843
|
With activities if you are doing it you've done it, with performances you must finish to have done it
[Simons]
|
12845
|
Some natural languages don't distinguish between singular and plural
[Simons]
|
12846
|
A 'group' is a collection with a condition which constitutes their being united
[Simons]
|
18847
|
Each wheel is part of a car, but the four wheels are not a further part
[Simons]
|
12847
|
Mass nouns admit 'much' and 'a little', and resist 'many' and 'few'.
[Simons]
|
12848
|
The same members may form two groups
[Simons]
|
12849
|
Sums are more plausible for pluralities and masses than they are for individuals
[Simons]
|
12850
|
To individuate something we must pick it out, but also know its limits of variation
[Simons]
|
12854
|
An entrepreneur and a museum curator would each be happy with their ship at the end
[Simons]
|
12855
|
The 'best candidate' theories mistakenly assume there is one answer to 'Which is the real ship?'
[Simons]
|
12856
|
Intermittent objects would be respectable if they occurred in nature, as well as in artefacts
[Simons]
|
12857
|
Tibbles isn't Tib-plus-tail, because Tibbles can survive its loss, but the sum can't
[Simons]
|
12859
|
A mixture can have different qualities from its ingredients.
[Simons]
|
12858
|
Mixtures disappear if nearly all of the mixture is one ingredient
[Simons]
|
12860
|
Sortal nouns for continuants tell you their continuance- and cessation-conditions
[Simons]
|
12863
|
Mass terms (unlike plurals) are used with indifference to whether they can exist in units
[Simons]
|
12862
|
Gold is not its atoms, because the atoms must be all gold, but gold contains neutrons
[Simons]
|
12864
|
We say 'b is part of a', 'b is a part of a', 'b are a part of a', or 'b are parts of a'.
[Simons]
|
12861
|
'The wolves' are the matter of 'the pack'; the latter is a group, with different identity conditions
[Simons]
|
12865
|
Analytic philosophers may prefer formal systems because natural language is such mess
[Simons]
|
12866
|
Composition is asymmetric and transitive
[Simons]
|
12867
|
A hand constitutes a fist (when clenched), but a fist is not composed of an augmented hand
[Simons]
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12870
|
We must distinguish the de dicto 'must' of propositions from the de re 'must' of essence
[Simons]
|
12871
|
Objects have their essential properties because of the kind of objects they are
[Simons]
|
12872
|
The zygote is an essential initial part, for a sexually reproduced organism
[Simons]
|
12874
|
An essential part of an essential part is an essential part of the whole
[Simons]
|
12873
|
Original parts are the best candidates for being essential to artefacts
[Simons]
|
12875
|
One false note doesn't make it a performance of a different work
[Simons]
|
12877
|
Sums of things in different categories are found within philosophy.
[Simons]
|
12876
|
Philosophy is stuck on the Fregean view that an individual is anything with a proper name
[Simons]
|
12879
|
Independent objects can exist apart, and maybe even entirely alone
[Simons]
|
12880
|
Moments are things like smiles or skids, which are founded on other things
[Simons]
|
12883
|
Moving disturbances are are moments which continuously change their basis
[Simons]
|
12881
|
A smiling is an event with causes, but the smile is a continuant without causes
[Simons]
|
12882
|
A wave is maintained by a process, but it isn't a process
[Simons]
|
12885
|
Objects like chess games, with gaps in them, are thereby less unified
[Simons]
|
12886
|
A whole requires some unique relation which binds together all of the parts
[Simons]
|
12889
|
The limits of change for an individual depend on the kind of individual
[Simons]
|
12888
|
The wholeness of a melody seems conventional, but of an explosion it seems natural
[Simons]
|
15390
|
Metaphysics attempts to give an account of everything, in terms of categories and principles
[Simons]
|