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Single Idea 23628
[filed under theme 5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
]
Full Idea
The sentence connective 'and' also has an order-sensitive meaning, when it means something like 'and then'.
Gist of Idea
The connective 'and' can have an order-sensitive meaning, as 'and then'
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], 10.4)
Book Ref
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.158
A Reaction
This is support the idea that orders are a feature of reality, just as much as possible concatenation. Relational predicates, he says, refer to series rather than to individuals. Nice point.
The
29 ideas
from Keith Hossack
23621
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Numbers are properties, not sets (because numbers are magnitudes)
[Hossack]
|
23622
|
We can only mentally construct potential infinities, but maths needs actual infinities
[Hossack]
|
23623
|
Predicativism says only predicated sets exist
[Hossack]
|
23624
|
The iterative conception has to appropriate Replacement, to justify the ordinals
[Hossack]
|
23625
|
Limitation of Size justifies Replacement, but then has to appropriate Power Set
[Hossack]
|
23626
|
Transfinite ordinals are needed in proof theory, and for recursive functions and computability
[Hossack]
|
23627
|
'Before' and 'after' are not two relations, but one relation with two orders
[Hossack]
|
23628
|
The connective 'and' can have an order-sensitive meaning, as 'and then'
[Hossack]
|
10666
|
Plural reference will refer to complex facts without postulating complex things
[Hossack]
|
10664
|
Complex particulars are either masses, or composites, or sets
[Hossack]
|
10665
|
Leibniz's Law argues against atomism - water is wet, unlike water molecules
[Hossack]
|
10663
|
A thought can refer to many things, but only predicate a universal and affirm a state of affairs
[Hossack]
|
10668
|
We are committed to a 'group' of children, if they are sitting in a circle
[Hossack]
|
10669
|
Plural reference is just an abbreviation when properties are distributive, but not otherwise
[Hossack]
|
10671
|
Plural definite descriptions pick out the largest class of things that fit the description
[Hossack]
|
10673
|
Plural language can discuss without inconsistency things that are not members of themselves
[Hossack]
|
10675
|
A plural comprehension principle says there are some things one of which meets some condition
[Hossack]
|
10674
|
A plural language gives a single comprehensive induction axiom for arithmetic
[Hossack]
|
10676
|
The Axiom of Choice is a non-logical principle of set-theory
[Hossack]
|
10677
|
Extensional mereology needs two definitions and two axioms
[Hossack]
|
10678
|
The relation of composition is indispensable to the part-whole relation for individuals
[Hossack]
|
10682
|
The fusion of five rectangles can decompose into more than five parts that are rectangles
[Hossack]
|
10681
|
In arithmetic singularists need sets as the instantiator of numeric properties
[Hossack]
|
10680
|
The theory of the transfinite needs the ordinal numbers
[Hossack]
|
10684
|
I take the real numbers to be just lengths
[Hossack]
|
10683
|
We could ignore space, and just talk of the shape of matter
[Hossack]
|
10685
|
Set theory is the science of infinity
[Hossack]
|
10686
|
The Axiom of Choice guarantees a one-one correspondence from sets to ordinals
[Hossack]
|
10687
|
Maybe we reduce sets to ordinals, rather than the other way round
[Hossack]
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