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Single Idea 18954
[filed under theme 5. Theory of Logic / A. Overview of Logic / 2. History of Logic
]
Full Idea
It was essentially the failure to develop a logic of relations that trivialised the logic studied before the end of the nineteenth century.
Gist of Idea
Before the late 19th century logic was trivialised by not dealing with relations
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.3)
Book Ref
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.27
A Reaction
De Morgan, Peirce and Frege were, I believe, the people who put this right.
The
14 ideas
from 'Philosophy of Logic'
18949
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The universal syllogism is now expressed as the transitivity of subclasses
[Putnam]
|
18951
|
For scientific purposes there is a precise concept of 'true-in-L', using set theory
[Putnam]
|
18950
|
Physics is full of non-physical entities, such as space-vectors
[Putnam]
|
18955
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Having a valid form doesn't ensure truth, as it may be meaningless
[Putnam]
|
18953
|
Modern notation frees us from Aristotle's restriction of only using two class-names in premises
[Putnam]
|
18952
|
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)'
[Putnam]
|
18954
|
Before the late 19th century logic was trivialised by not dealing with relations
[Putnam]
|
18956
|
Asserting first-order validity implicitly involves second-order reference to classes
[Putnam]
|
18957
|
Nominalism only makes sense if it is materialist
[Putnam]
|
18958
|
In type theory, 'x ∈ y' is well defined only if x and y are of the appropriate type
[Putnam]
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18959
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Sets larger than the continuum should be studied in an 'if-then' spirit
[Putnam]
|
18960
|
Most predictions are uninteresting, and are only sought in order to confirm a theory
[Putnam]
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18962
|
Unfashionably, I think logic has an empirical foundation
[Putnam]
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18961
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We can identify functions with certain sets - or identify sets with certain functions
[Putnam]
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