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Single Idea 10697
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
]
Full Idea
Indispensable to cross-reference, lacking distinctive content, and pervading thought and discourse, 'identity' is without question a logical concept. Adding it to predicate calculus significantly increases the number and variety of inferences possible.
Gist of Idea
Identity is clearly a logical concept, and greatly enhances predicate calculus
Source
George Boolos (To be is to be the value of a variable.. [1984], p.54)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.54
A Reaction
It is not at all clear to me that identity is a logical concept. Is 'existence' a logical concept? It seems to fit all of Boolos's criteria? I say that all he really means is that it is basic to thought, but I'm not sure it drives the reasoning process.
The
31 ideas
from George Boolos
10482
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The logic of ZF is classical first-order predicate logic with identity
[Boolos]
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10483
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Mathematics and science do not require very high orders of infinity
[Boolos]
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10484
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The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first
[Boolos]
|
10485
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Naïve sets are inconsistent: there is no set for things that do not belong to themselves
[Boolos]
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10488
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It is lunacy to think we only see ink-marks, and not word-types
[Boolos]
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10487
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I am a fan of abstract objects, and confident of their existence
[Boolos]
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10489
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We deal with abstract objects all the time: software, poems, mistakes, triangles..
[Boolos]
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10491
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Infinite natural numbers is as obvious as infinite sentences in English
[Boolos]
|
10490
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Mathematics isn't surprising, given that we experience many objects as abstract
[Boolos]
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10492
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A few axioms of set theory 'force themselves on us', but most of them don't
[Boolos]
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8693
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An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect
[Boolos]
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13547
|
Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects)
[Boolos, by Potter]
|
18192
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Do the Replacement Axioms exceed the iterative conception of sets?
[Boolos, by Maddy]
|
14249
|
Boolos reinterprets second-order logic as plural logic
[Boolos, by Oliver/Smiley]
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13841
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Why should compactness be definitive of logic?
[Boolos, by Hacking]
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10829
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A sentence can't be a truth of logic if it asserts the existence of certain sets
[Boolos]
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10830
|
Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems
[Boolos]
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10832
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'∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed
[Boolos]
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10833
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Many concepts can only be expressed by second-order logic
[Boolos]
|
10834
|
Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences
[Boolos]
|
7806
|
Boolos invented plural quantification
[Boolos, by Benardete,JA]
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13671
|
Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology
[Boolos, by Shapiro]
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10267
|
We should understand second-order existential quantifiers as plural quantifiers
[Boolos, by Shapiro]
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10225
|
Monadic second-order logic might be understood in terms of plural quantifiers
[Boolos, by Shapiro]
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7785
|
The use of plurals doesn't commit us to sets; there do not exist individuals and collections
[Boolos]
|
10736
|
Boolos showed how plural quantifiers can interpret monadic second-order logic
[Boolos, by Linnebo]
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10780
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Any sentence of monadic second-order logic can be translated into plural first-order logic
[Boolos, by Linnebo]
|
10697
|
Identity is clearly a logical concept, and greatly enhances predicate calculus
[Boolos]
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10698
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Plural forms have no more ontological commitment than to first-order objects
[Boolos]
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10699
|
Does a bowl of Cheerios contain all its sets and subsets?
[Boolos]
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10700
|
First- and second-order quantifiers are two ways of referring to the same things
[Boolos]
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