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Single Idea 6103
[filed under theme 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
]
Full Idea
With the ordinary view of classes you would say that a class that has only one member was the same as that one member; that will land you in terrible difficulties, because in that case that one member is a member of that class, namely, itself.
Clarification
(the problem is classes that turn out to be members of themselves)
Gist of Idea
Normally a class with only one member is a problem, because the class and the member are identical
Source
Bertrand Russell (The Philosophy of Logical Atomism [1918], §VII)
Book Ref
Russell,Bertrand: 'Russell's Logical Atomism', ed/tr. Pears,David [Fontana 1972], p.126
A Reaction
The problem (I think) is that classes (sets) were defined by Frege as being identical with their members (their extension). With hindsight this may have been a mistake. The question is always 'why is that particular a member of that set?'
The
32 ideas
from 'The Philosophy of Logical Atomism'
18348
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Not only atomic truths, but also general and negative truths, have truth-makers
[Russell, by Rami]
|
7744
|
Treat description using quantifiers, and treat proper names as descriptions
[Russell, by McCullogh]
|
21708
|
Russell's new logical atomist was of particulars, universals and facts (not platonic propositions)
[Russell, by Linsky,B]
|
19051
|
Russell's atomic facts are actually compounds, and his true logical atoms are sense data
[Russell, by Quine]
|
18376
|
Russell asserts atomic, existential, negative and general facts
[Russell, by Armstrong]
|
5465
|
Modern trope theory tries, like logical atomism, to reduce things to elementary states
[Russell, by Ellis]
|
6060
|
'Existence' means that a propositional function is sometimes true
[Russell]
|
9022
|
Russell uses 'propositional function' to refer to both predicates and to attributes
[Quine on Russell]
|
21702
|
In 1918 still believes in nonlinguistic analogues of sentences, but he now calls them 'facts'
[Russell, by Quine]
|
6091
|
Propositions don't name facts, because each fact corresponds to a proposition and its negation
[Russell]
|
6089
|
Logical atomism aims at logical atoms as the last residue of analysis
[Russell]
|
6090
|
Facts make propositions true or false, and are expressed by whole sentences
[Russell]
|
6092
|
In a logically perfect language, there will be just one word for every simple object
[Russell]
|
6093
|
The names in a logically perfect language would be private, and could not be shared
[Russell]
|
6094
|
An inventory of the world does not need to include propositions
[Russell]
|
6095
|
The business of metaphysics is to describe the world
[Russell]
|
6096
|
I no longer believe in propositions, especially concerning falsehoods
[Russell]
|
6097
|
The theory of error seems to need the existence of the non-existent
[Russell]
|
6098
|
Perception goes straight to the fact, and not through the proposition
[Russell]
|
6099
|
Modal terms are properties of propositional functions, not of propositions
[Russell]
|
6100
|
Once you have enumerated all the atomic facts, there is a further fact that those are all the facts
[Russell]
|
6101
|
Romulus does not occur in the proposition 'Romulus did not exist'
[Russell]
|
6102
|
You can understand 'author of Waverley', but to understand 'Scott' you must know who it applies to
[Russell]
|
6119
|
You can discuss 'God exists', so 'God' is a description, not a name
[Russell]
|
6103
|
Normally a class with only one member is a problem, because the class and the member are identical
[Russell]
|
6106
|
Reducing entities and premisses makes error less likely
[Russell]
|
6105
|
Logical atoms aims to get down to ultimate simples, with their own unique reality
[Russell]
|
6104
|
Numbers are classes of classes, and hence fictions of fictions
[Russell]
|
10423
|
There are a set of criteria for pinning down a logically proper name
[Russell, by Sainsbury]
|
10426
|
A name has got to name something or it is not a name
[Russell]
|
21712
|
I know longer believe in shadowy things like 'that today is Wednesday' when it is actually Tuesday
[Russell]
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21709
|
You can't name all the facts, so they are not real, but are what propositions assert
[Russell]
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