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Single Idea 18955
[filed under theme 5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
]
Full Idea
I don't think all substitution-instances of a valid schema are 'true'; some are clearly meaningless, such as 'If all boojums are snarks and all snarks are egglehumphs, then all boojums are egglehumphs'.
Gist of Idea
Having a valid form doesn't ensure truth, as it may be meaningless
Source
Hilary Putnam (Philosophy of Logic [1971], Ch.3)
Book Ref
Putnam,Hilary: 'Philosophy of Logic' [Routledge 1972], p.28
A Reaction
This seems like a very good challenge to Quine's claim that it is only form which produces a logical truth. Keep deductive and semantic consequence separate, with two different types of 'logical truth'.
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]
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18950
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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
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Modern notation frees us from Aristotle's restriction of only using two class-names in premises
[Putnam]
|
18952
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'⊃' ('if...then') is used with the definition 'Px ⊃ Qx' is short for '¬(Px & ¬Qx)'
[Putnam]
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18954
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Before the late 19th century logic was trivialised by not dealing with relations
[Putnam]
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18956
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Asserting first-order validity implicitly involves second-order reference to classes
[Putnam]
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18957
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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]
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18960
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Most predictions are uninteresting, and are only sought in order to confirm a theory
[Putnam]
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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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