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Single Idea 18952
[filed under theme 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / a. Symbols of PC
]
Full Idea
The symbol '⊃' (read 'if...then') is used with the definition 'Px ⊃ Qx' ('if Px then Qx') is short for '¬(Px & ¬Qx)'.
Gist of Idea
'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)'
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.3)
Book Ref
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.26
A Reaction
So ⊃ and → are just abbreviations, and not really a proper part of the language. Notoriously, though, this is quite a long way from what 'if...then' means in ordinary English, and it leads to paradoxical oddities.
The
14 ideas
from 'Philosophy of Logic'
18949
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The universal syllogism is now expressed as the transitivity of subclasses
[Putnam]
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18951
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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
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Asserting first-order validity implicitly involves second-order reference to classes
[Putnam]
|
18957
|
Nominalism only makes sense if it is materialist
[Putnam]
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18958
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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
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Most predictions are uninteresting, and are only sought in order to confirm a theory
[Putnam]
|
18962
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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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